12n
0876
(K12n
0876
)
A knot diagram
1
Linearized knot diagam
4 8 10 1 10 12 11 3 6 2 7 6
Solving Sequence
7,11 2,8
3 12 6 10 4 1 5 9
c
7
c
2
c
11
c
6
c
10
c
3
c
1
c
4
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
19
− 38u
18
+ ··· + 4b − 40, −4u
19
+ 33u
18
+ ··· + 4a + 38, u
20
− 8u
19
+ ··· − 84u + 8i
I
u
2
= h6a
5
u
3
+ 8a
4
u
3
+ ··· + 2a − 2, −2a
4
u
3
+ a
3
u
3
+ ··· + 15a + 9, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
3
= h−u
12
− u
11
− 8u
10
− 8u
9
− 23u
8
− 23u
7
− 28u
6
− 27u
5
− 11u
4
− 10u
3
+ 2u
2
+ b,
− u
10
− 8u
8
− 23u
6
− 28u
4
+ u
3
− 12u
2
+ a + 2u,
u
14
+ 10u
12
+ 39u
10
+ 74u
8
− 2u
7
+ 68u
6
− 9u
5
+ 24u
4
− 11u
3
− 2u + 1i
I
u
4
= hu
2
+ b + 2u + 2, −u
3
− u
2
+ a − 3u − 2, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
5
= h−u
3
− u
2
+ b − 2u − 1, 2u
3
+ 2u
2
+ a + 5u + 3, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
6
= hb + u − 1, 2a − u + 1, u
2
− u + 2i
* 6 irreducible components of dim
C
= 0, with total 68 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
= h5u
19
− 38u
18
+ · · · + 4b − 40, −4u
19
+ 33u
18
+ · · · + 4a + 38, u
20
−
8u
19
+ · · · − 84u + 8i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
2
=
u
19
−
33
4
u
18
+ ··· +
401
4
u −
19
2
−
5
4
u
19
+
19
2
u
18
+ ··· −
207
2
u + 10
a
8
=
1
u
2
a
3
=
5
4
u
19
−
35
4
u
18
+ ··· +
103
4
u −
3
2
3
4
u
19
−
9
2
u
18
+ ··· +
41
2
u − 2
a
12
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
10
=
−u
19
+
13
2
u
18
+ ··· − 10u +
1
2
1
2
u
18
− 3u
17
+ ··· −
67
2
u + 4
a
4
=
7
4
u
19
−
51
4
u
18
+ ··· +
633
4
u − 17
−
3
4
u
19
+ 6u
18
+ ··· − 161u + 18
a
1
=
−u
3
− 2u
u
3
+ u
a
5
=
−
9
4
u
19
+
69
4
u
18
+ ··· −
1071
4
u + 27
5
4
u
19
− 9u
18
+ ··· + 86u − 8
a
9
=
−
1
2
u
19
+ 4u
18
+ ··· −
147
2
u +
17
2
−u
19
+
15
2
u
18
+ ··· −
159
2
u + 8
(ii) Obstruction class = −1
(iii) Cusp Shapes
= u
19
−8u
18
+42u
17
−163u
16
+506u
15
−1312u
14
+2893u
13
−5517u
12
+9157u
11
−13296u
10
+
16896u
9
−18758u
8
+18092u
7
−15031u
6
+10601u
5
−6223u
4
+2945u
3
−1076u
2
+282u −46
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
20
− 11u
19
+ ··· − 44u + 8
c
2
, c
8
, c
10
u
20
− 3u
19
+ ··· − 3u + 1
c
3
u
20
+ u
19
+ ··· + 9u
2
+ 1
c
5
, c
9
u
20
+ 3u
19
+ ··· + 4u + 1
c
6
, c
7
, c
11
c
12
u
20
+ 8u
19
+ ··· + 84u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
20
+ 9y
19
+ ··· + 48y + 64
c
2
, c
8
, c
10
y
20
− 15y
19
+ ··· − y + 1
c
3
y
20
+ 9y
19
+ ··· + 18y + 1
c
5
, c
9
y
20
− 19y
19
+ ··· + 6y + 1
c
6
, c
7
, c
11
c
12
y
20
+ 22y
19
+ ··· + 240y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615618 + 0.809804I
a = 0.149188 − 1.170140I
b = 0.085977 + 1.072180I
−0.57301 − 3.95011I −2.11978 + 4.63331I
u = 0.615618 − 0.809804I
a = 0.149188 + 1.170140I
b = 0.085977 − 1.072180I
−0.57301 + 3.95011I −2.11978 − 4.63331I
u = 0.931383 + 0.280268I
a = 1.201130 − 0.003287I
b = −0.170316 + 0.290909I
−0.03598 + 5.05200I −0.41236 − 3.99248I
u = 0.931383 − 0.280268I
a = 1.201130 + 0.003287I
b = −0.170316 − 0.290909I
−0.03598 − 5.05200I −0.41236 + 3.99248I
u = 0.746449 + 0.775861I
a = −0.471110 + 1.236680I
b = −0.100180 − 1.158660I
1.47378 − 10.55160I 0.34887 + 7.91165I
u = 0.746449 − 0.775861I
a = −0.471110 − 1.236680I
b = −0.100180 + 1.158660I
1.47378 + 10.55160I 0.34887 − 7.91165I
u = 0.733781 + 0.211411I
a = −1.008810 − 0.357032I
b = 0.277449 − 0.014017I
−2.40729 − 0.59322I −4.18556 − 0.45547I
u = 0.733781 − 0.211411I
a = −1.008810 + 0.357032I
b = 0.277449 + 0.014017I
−2.40729 + 0.59322I −4.18556 + 0.45547I
u = −0.024618 + 1.249360I
a = 0.348669 + 0.434224I
b = 0.033771 − 1.123880I
4.75638 − 1.46611I 2.62808 + 4.96498I
u = −0.024618 − 1.249360I
a = 0.348669 − 0.434224I
b = 0.033771 + 1.123880I
4.75638 + 1.46611I 2.62808 − 4.96498I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.259646 + 1.352180I
a = 0.352486 − 0.235426I
b = −0.865270 + 0.246592I
2.47957 − 4.10039I 3.08727 − 0.58697I
u = 0.259646 − 1.352180I
a = 0.352486 + 0.235426I
b = −0.865270 − 0.246592I
2.47957 + 4.10039I 3.08727 + 0.58697I
u = 0.240761 + 0.325217I
a = −0.616636 − 1.071860I
b = −0.002796 + 0.413272I
−0.172616 − 0.899774I −3.76752 + 7.66615I
u = 0.240761 − 0.325217I
a = −0.616636 + 1.071860I
b = −0.002796 − 0.413272I
−0.172616 + 0.899774I −3.76752 − 7.66615I
u = 0.23882 + 1.63854I
a = −0.282035 − 0.978235I
b = −0.02878 + 3.04561I
9.5379 − 14.3084I 2.45273 + 7.13980I
u = 0.23882 − 1.63854I
a = −0.282035 + 0.978235I
b = −0.02878 − 3.04561I
9.5379 + 14.3084I 2.45273 − 7.13980I
u = 0.19941 + 1.65855I
a = 0.329642 + 0.850090I
b = −0.11179 − 2.80281I
7.82775 − 7.13457I 0.46687 + 4.13636I
u = 0.19941 − 1.65855I
a = 0.329642 − 0.850090I
b = −0.11179 + 2.80281I
7.82775 + 7.13457I 0.46687 − 4.13636I
u = 0.05874 + 1.80462I
a = −0.252521 − 0.599270I
b = −0.11806 + 2.38692I
16.5920 − 2.0882I −4.99860 + 4.75350I
u = 0.05874 − 1.80462I
a = −0.252521 + 0.599270I
b = −0.11806 − 2.38692I
16.5920 + 2.0882I −4.99860 − 4.75350I
6
II. I
u
2
=
h6a
5
u
3
+8a
4
u
3
+· · ·+2a−2, −2a
4
u
3
+a
3
u
3
+· · ·+15a+9, u
4
+u
3
+3u
2
+2u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
2
=
a
−3a
5
u
3
− 4a
4
u
3
+ ··· − a + 1
a
8
=
1
u
2
a
3
=
−3a
5
u
3
− 4a
4
u
3
+ ··· −
5
2
a
2
+ 1
5a
5
u
3
+ 7a
4
u
3
+ ··· − a − 2
a
12
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
10
=
−a
2
u
4a
5
u
3
+
11
2
a
4
u
3
+ ··· −
1
2
a −
1
2
a
4
=
2a
5
u
3
+
3
2
a
4
u
3
+ ··· +
5
2
a −
1
2
−3a
5
u
3
+
3
2
a
4
u
3
+ ··· −
17
2
a −
1
2
a
1
=
−u
3
− 2u
u
3
+ u
a
5
=
2a
5
u
3
+ a
4
u
3
+ ··· + 4a − 1
−a
5
u
3
+
11
2
a
4
u
3
+ ··· − 12a −
5
2
a
9
=
17
2
a
5
u
3
+
27
2
a
4
u
3
+ ··· − 4a − 4
−
21
2
a
5
u
3
− 17a
4
u
3
+ ··· + 5a +
15
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4a
5
u
3
+ 6a
5
u
2
− 8a
4
u
3
+ 6a
5
u + 8a
4
u
2
− 6a
3
u
3
+ 4a
5
+ 8a
4
u + 24a
3
u
2
− 4u
3
a
2
+
6a
4
+ 20a
3
u + 30a
2
u
2
+ 12a
3
+ 26a
2
u + 20u
2
a + 2u
3
+ 14a
2
+ 14au + 12u
2
+ 6a + 2u
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
4
+ u
3
+ u
2
+ 1)
6
c
2
, c
8
, c
10
u
24
− u
23
+ ··· − 1188u + 328
c
3
u
24
+ 3u
23
+ ··· − 3996u + 648
c
5
, c
9
u
24
+ 5u
23
+ ··· + 168u + 8
c
6
, c
7
, c
11
c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
6
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
c
2
, c
8
, c
10
y
24
− 15y
23
+ ··· − 453584y + 107584
c
3
y
24
− 3y
23
+ ··· − 5750352y + 419904
c
5
, c
9
y
24
− 7y
23
+ ··· − 7776y + 64
c
6
, c
7
, c
11
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
6
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 0.103728 − 1.096500I
b = −1.09009 + 1.02540I
−2.06694 − 1.74886I −1.65348 − 2.34394I
u = −0.395123 + 0.506844I
a = 0.16699 + 1.52687I
b = 0.83629 − 1.36113I
−2.06694 + 4.57907I −1.65348 − 7.47354I
u = −0.395123 + 0.506844I
a = −1.78646 + 0.12907I
b = −0.283051 + 0.216704I
−2.06694 − 1.74886I −1.65348 − 2.34394I
u = −0.395123 + 0.506844I
a = 1.63057 − 0.79455I
b = 0.357314 − 0.054366I
−2.06694 + 4.57907I −1.65348 − 7.47354I
u = −0.395123 + 0.506844I
a = −0.39246 − 1.95028I
b = 0.628050 + 0.462471I
4.93480 + 2.83021I 2.00000 − 9.81749I
u = −0.395123 + 0.506844I
a = 1.17687 + 1.78486I
b = −0.547258 − 1.222920I
4.93480 + 2.83021I 2.00000 − 9.81749I
u = −0.395123 − 0.506844I
a = 0.103728 + 1.096500I
b = −1.09009 − 1.02540I
−2.06694 + 1.74886I −1.65348 + 2.34394I
u = −0.395123 − 0.506844I
a = 0.16699 − 1.52687I
b = 0.83629 + 1.36113I
−2.06694 − 4.57907I −1.65348 + 7.47354I
u = −0.395123 − 0.506844I
a = −1.78646 − 0.12907I
b = −0.283051 − 0.216704I
−2.06694 + 1.74886I −1.65348 + 2.34394I
u = −0.395123 − 0.506844I
a = 1.63057 + 0.79455I
b = 0.357314 + 0.054366I
−2.06694 − 4.57907I −1.65348 + 7.47354I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 − 0.506844I
a = −0.39246 + 1.95028I
b = 0.628050 − 0.462471I
4.93480 − 2.83021I 2.00000 + 9.81749I
u = −0.395123 − 0.506844I
a = 1.17687 − 1.78486I
b = −0.547258 + 1.222920I
4.93480 − 2.83021I 2.00000 + 9.81749I
u = −0.10488 + 1.55249I
a = 0.104373 − 0.975826I
b = 0.81052 + 3.36343I
11.93650 + 4.57907I 5.65348 − 7.47354I
u = −0.10488 + 1.55249I
a = −1.045950 − 0.024912I
b = 1.324300 + 0.197152I
4.93480 + 6.32793I 2.00000 − 5.12960I
u = −0.10488 + 1.55249I
a = −0.617508 + 0.929773I
b = 0.28030 − 2.29404I
11.93650 + 4.57907I 5.65348 − 7.47354I
u = −0.10488 + 1.55249I
a = −0.145302 + 1.200950I
b = −0.31108 − 3.25723I
11.93650 + 1.74886I 5.65348 + 2.34394I
u = −0.10488 + 1.55249I
a = 0.079320 − 0.763538I
b = −0.58732 + 3.42729I
4.93480 + 6.32793I 2.00000 − 5.12960I
u = −0.10488 + 1.55249I
a = 0.225836 − 0.692087I
b = 1.08202 + 1.93847I
11.93650 + 1.74886I 5.65348 + 2.34394I
u = −0.10488 − 1.55249I
a = 0.104373 + 0.975826I
b = 0.81052 − 3.36343I
11.93650 − 4.57907I 5.65348 + 7.47354I
u = −0.10488 − 1.55249I
a = −1.045950 + 0.024912I
b = 1.324300 − 0.197152I
4.93480 − 6.32793I 2.00000 + 5.12960I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 − 1.55249I
a = −0.617508 − 0.929773I
b = 0.28030 + 2.29404I
11.93650 − 4.57907I 5.65348 + 7.47354I
u = −0.10488 − 1.55249I
a = −0.145302 − 1.200950I
b = −0.31108 + 3.25723I
11.93650 − 1.74886I 5.65348 − 2.34394I
u = −0.10488 − 1.55249I
a = 0.079320 + 0.763538I
b = −0.58732 − 3.42729I
4.93480 − 6.32793I 2.00000 + 5.12960I
u = −0.10488 − 1.55249I
a = 0.225836 + 0.692087I
b = 1.08202 − 1.93847I
11.93650 − 1.74886I 5.65348 − 2.34394I
12
III. I
u
3
=
h−u
12
−u
11
+· · ·+2u
2
+b, −u
10
−8u
8
+· · ·+a+2u, u
14
+10u
12
+· · ·−2u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
2
=
u
10
+ 8u
8
+ 23u
6
+ 28u
4
− u
3
+ 12u
2
− 2u
u
12
+ u
11
+ ··· + 10u
3
− 2u
2
a
8
=
1
u
2
a
3
=
u
11
+ u
10
+ ··· + 10u
2
− 2u
u
13
+ u
12
+ ··· + 10u
3
− 2u
2
a
12
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
10
=
−u
12
− 9u
10
− 31u
8
− 51u
6
+ 2u
5
− 40u
4
+ 7u
3
− 12u
2
+ 6u
−u
13
+ u
12
+ ··· − u + 1
a
4
=
u
11
+ 9u
9
+ 30u
7
+ 45u
5
− u
4
+ 29u
3
− 4u
2
+ 6u − 3
u
10
+ 7u
8
+ 17u
6
+ 16u
4
− 2u
3
+ 4u
2
− 3u
a
1
=
−u
3
− 2u
u
3
+ u
a
5
=
u
9
+ 7u
7
+ 17u
5
+ 17u
3
− u
2
+ 6u − 2
u
12
+ u
11
+ ··· + 2u
2
− 4u
a
9
=
−u
13
− u
12
+ ··· + 6u + 1
u
12
− u
11
+ ··· − u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
13
+2u
12
−8u
11
+17u
10
−24u
9
+51u
8
−37u
7
+60u
6
−43u
5
+12u
4
−41u
3
−15u
2
−11u+6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 3u
13
+ ··· + 7u
2
+ 1
c
2
, c
10
u
14
− u
13
+ ··· − u + 1
c
3
u
14
− u
12
+ ··· + 22u + 29
c
4
u
14
+ 3u
13
+ ··· + 7u
2
+ 1
c
5
u
14
+ u
13
+ ··· + 4u
2
+ 1
c
6
, c
7
u
14
+ 10u
12
+ ··· − 2u + 1
c
8
u
14
+ u
13
+ ··· + u + 1
c
9
u
14
− u
13
+ ··· + 4u
2
+ 1
c
11
, c
12
u
14
+ 10u
12
+ ··· + 2u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
14
+ 11y
13
+ ··· + 14y + 1
c
2
, c
8
, c
10
y
14
− 11y
13
+ ··· + 5y + 1
c
3
y
14
− 2y
13
+ ··· + 1082y + 841
c
5
, c
9
y
14
− 3y
13
+ ··· + 8y + 1
c
6
, c
7
, c
11
c
12
y
14
+ 20y
13
+ ··· − 4y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.311609 + 0.942763I
a = 0.291653 + 1.169250I
b = −0.737119 − 1.186440I
7.09672 + 0.19743I 7.21171 − 0.40759I
u = −0.311609 − 0.942763I
a = 0.291653 − 1.169250I
b = −0.737119 + 1.186440I
7.09672 − 0.19743I 7.21171 + 0.40759I
u = 0.161029 + 1.344040I
a = 0.433516 + 0.120817I
b = −0.916757 + 0.574654I
2.08475 − 4.90341I −1.06931 + 6.62394I
u = 0.161029 − 1.344040I
a = 0.433516 − 0.120817I
b = −0.916757 − 0.574654I
2.08475 + 4.90341I −1.06931 − 6.62394I
u = 0.23888 + 1.43943I
a = −0.435879 + 0.255328I
b = 0.231007 − 1.380650I
3.18169 + 0.60898I −3.58539 − 1.80775I
u = 0.23888 − 1.43943I
a = −0.435879 − 0.255328I
b = 0.231007 + 1.380650I
3.18169 − 0.60898I −3.58539 + 1.80775I
u = −0.293216 + 0.377036I
a = −1.27142 − 2.57328I
b = 0.845482 + 0.700844I
5.21647 + 1.94152I 5.99803 − 0.90958I
u = −0.293216 − 0.377036I
a = −1.27142 + 2.57328I
b = 0.845482 − 0.700844I
5.21647 − 1.94152I 5.99803 + 0.90958I
u = −0.09214 + 1.54037I
a = −0.305542 + 0.999070I
b = −0.50480 − 2.83803I
11.88620 + 3.33387I 5.15657 − 1.10675I
u = −0.09214 − 1.54037I
a = −0.305542 − 0.999070I
b = −0.50480 + 2.83803I
11.88620 − 3.33387I 5.15657 + 1.10675I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376292 + 0.105089I
a = 1.06759 + 1.35883I
b = 0.290833 + 0.885340I
−2.11738 + 2.98340I −1.73215 − 4.07562I
u = 0.376292 − 0.105089I
a = 1.06759 − 1.35883I
b = 0.290833 − 0.885340I
−2.11738 − 2.98340I −1.73215 + 4.07562I
u = −0.07924 + 1.76897I
a = 0.220085 − 0.669149I
b = 0.29136 + 2.47039I
17.0648 + 1.9156I 10.52053 + 0.88434I
u = −0.07924 − 1.76897I
a = 0.220085 + 0.669149I
b = 0.29136 − 2.47039I
17.0648 − 1.9156I 10.52053 − 0.88434I
17
IV. I
u
4
= hu
2
+ b + 2u + 2, −u
3
− u
2
+ a − 3u − 2, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
2
=
u
3
+ u
2
+ 3u + 2
−u
2
− 2u − 2
a
8
=
1
u
2
a
3
=
u
3
+ 2u
−1
a
12
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
10
=
u
3
+ u
2
+ 3u + 2
−u
2
− u − 2
a
4
=
−u
3
− 2u
2
− 3u − 4
u
2
+ 2
a
1
=
−u
3
− 2u
u
3
+ u
a
5
=
−u
3
− 2u
2
− 3u − 3
2u
2
+ u + 2
a
9
=
u
3
+ 3u + 1
−u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
+ u
3
+ u
2
+ 1
c
2
, c
8
u
4
− 2u
3
+ u
2
− 3u + 4
c
3
u
4
− 3u
3
+ u
2
+ 2u + 1
c
5
, c
9
(u − 1)
4
c
6
, c
7
, c
11
c
12
u
4
− u
3
+ 3u
2
− 2u + 1
c
10
(u + 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
2
, c
8
y
4
− 2y
3
− 3y
2
− y + 16
c
3
y
4
− 7y
3
+ 15y
2
− 2y + 1
c
5
, c
9
, c
10
(y −1)
4
c
6
, c
7
, c
11
c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 0.95668 + 1.22719I
b = −1.108990 − 0.613156I
4.93480 2.00000
u = −0.395123 − 0.506844I
a = 0.95668 − 1.22719I
b = −1.108990 + 0.613156I
4.93480 2.00000
u = −0.10488 + 1.55249I
a = 0.043315 + 0.641200I
b = 0.60898 − 2.77934I
4.93480 2.00000
u = −0.10488 − 1.55249I
a = 0.043315 − 0.641200I
b = 0.60898 + 2.77934I
4.93480 2.00000
21
V.
I
u
5
= h−u
3
− u
2
+ b − 2u − 1, 2u
3
+ 2u
2
+ a + 5u + 3, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
2
=
−2u
3
− 2u
2
− 5u − 3
u
3
+ u
2
+ 2u + 1
a
8
=
1
u
2
a
3
=
−2u
3
− 2u
2
− 5u − 2
u
3
+ 2u
2
+ 2u + 1
a
12
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
10
=
3u
3
+ 2u
2
+ 7u + 4
−u
3
− u − 1
a
4
=
−u
3
− 3u + 1
u
a
1
=
−u
3
− 2u
u
3
+ u
a
5
=
−u
3
− 3u + 2
u
2
+ 2u
a
9
=
2u
3
+ 2u
2
+ 5u + 3
−u
3
− u
2
− 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
+ u
3
+ u
2
+ 1
c
2
, c
8
(u + 1)
4
c
3
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
5
, c
9
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
c
6
, c
7
, c
11
c
12
u
4
− u
3
+ 3u
2
− 2u + 1
c
10
u
4
− 2u
3
+ u
2
− 3u + 4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
2
, c
8
(y −1)
4
c
3
, c
6
, c
7
c
11
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
5
, c
9
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
10
y
4
− 2y
3
− 3y
2
− y + 16
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −1.30849 − 1.94753I
b = 0.351808 + 0.720342I
4.93480 2.00000
u = −0.395123 − 0.506844I
a = −1.30849 + 1.94753I
b = 0.351808 − 0.720342I
4.93480 2.00000
u = −0.10488 + 1.55249I
a = 0.808493 + 0.270093I
b = −0.851808 − 0.911292I
4.93480 2.00000
u = −0.10488 − 1.55249I
a = 0.808493 − 0.270093I
b = −0.851808 + 0.911292I
4.93480 2.00000
25
VI. I
u
6
= hb + u − 1, 2a − u + 1, u
2
− u + 2i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
2
=
1
2
u −
1
2
−u + 1
a
8
=
1
u − 2
a
3
=
1
2
u +
1
2
−1
a
12
=
−u
u
a
6
=
u − 1
−u + 2
a
10
=
1
2
u −
1
2
1
a
4
=
1
2
u +
3
2
−u − 1
a
1
=
−u + 2
−2
a
5
=
−
3
2
u +
3
2
u − 3
a
9
=
−
1
2
u +
1
2
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
2
− u + 2
c
2
, c
8
, c
10
(u + 1)
2
c
5
, c
9
(u − 1)
2
c
6
, c
7
, c
11
c
12
u
2
+ u + 2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
11
c
12
y
2
+ 3y + 4
c
2
, c
5
, c
8
c
9
, c
10
(y −1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.32288I
a = −0.250000 + 0.661438I
b = 0.50000 − 1.32288I
4.93480 2.00000
u = 0.50000 − 1.32288I
a = −0.250000 − 0.661438I
b = 0.50000 + 1.32288I
4.93480 2.00000
29
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 2)(u
4
+ u
3
+ u
2
+ 1)
8
(u
14
− 3u
13
+ ··· + 7u
2
+ 1)
· (u
20
− 11u
19
+ ··· − 44u + 8)
c
2
, c
10
((u + 1)
6
)(u
4
− 2u
3
+ u
2
− 3u + 4)(u
14
− u
13
+ ··· − u + 1)
· (u
20
− 3u
19
+ ··· − 3u + 1)(u
24
− u
23
+ ··· − 1188u + 328)
c
3
(u
2
− u + 2)(u
4
− 3u
3
+ u
2
+ 2u + 1)(u
4
+ u
3
+ 3u
2
+ 2u + 1)
· (u
14
− u
12
+ ··· + 22u + 29)(u
20
+ u
19
+ ··· + 9u
2
+ 1)
· (u
24
+ 3u
23
+ ··· − 3996u + 648)
c
4
(u
2
− u + 2)(u
4
+ u
3
+ u
2
+ 1)
8
(u
14
+ 3u
13
+ ··· + 7u
2
+ 1)
· (u
20
− 11u
19
+ ··· − 44u + 8)
c
5
((u − 1)
6
)(u
4
+ 2u
3
+ ··· + 3u + 2)(u
14
+ u
13
+ ··· + 4u
2
+ 1)
· (u
20
+ 3u
19
+ ··· + 4u + 1)(u
24
+ 5u
23
+ ··· + 168u + 8)
c
6
, c
7
(u
2
+ u + 2)(u
4
− u
3
+ 3u
2
− 2u + 1)
8
(u
14
+ 10u
12
+ ··· − 2u + 1)
· (u
20
+ 8u
19
+ ··· + 84u + 8)
c
8
((u + 1)
6
)(u
4
− 2u
3
+ u
2
− 3u + 4)(u
14
+ u
13
+ ··· + u + 1)
· (u
20
− 3u
19
+ ··· − 3u + 1)(u
24
− u
23
+ ··· − 1188u + 328)
c
9
((u − 1)
6
)(u
4
+ 2u
3
+ ··· + 3u + 2)(u
14
− u
13
+ ··· + 4u
2
+ 1)
· (u
20
+ 3u
19
+ ··· + 4u + 1)(u
24
+ 5u
23
+ ··· + 168u + 8)
c
11
, c
12
(u
2
+ u + 2)(u
4
− u
3
+ 3u
2
− 2u + 1)
8
(u
14
+ 10u
12
+ ··· + 2u + 1)
· (u
20
+ 8u
19
+ ··· + 84u + 8)
30
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ 3y + 4)(y
4
+ y
3
+ 3y
2
+ 2y + 1)
8
(y
14
+ 11y
13
+ ··· + 14y + 1)
· (y
20
+ 9y
19
+ ··· + 48y + 64)
c
2
, c
8
, c
10
((y −1)
6
)(y
4
− 2y
3
+ ··· − y + 16)(y
14
− 11y
13
+ ··· + 5y + 1)
· (y
20
− 15y
19
+ ··· − y + 1)(y
24
− 15y
23
+ ··· − 453584y + 107584)
c
3
(y
2
+ 3y + 4)(y
4
− 7y
3
+ 15y
2
− 2y + 1)(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
14
− 2y
13
+ ··· + 1082y + 841)(y
20
+ 9y
19
+ ··· + 18y + 1)
· (y
24
− 3y
23
+ ··· − 5750352y + 419904)
c
5
, c
9
((y −1)
6
)(y
4
+ 2y
3
+ y
2
+ 3y + 4)(y
14
− 3y
13
+ ··· + 8y + 1)
· (y
20
− 19y
19
+ ··· + 6y + 1)(y
24
− 7y
23
+ ··· − 7776y + 64)
c
6
, c
7
, c
11
c
12
(y
2
+ 3y + 4)(y
4
+ 5y
3
+ ··· + 2y + 1)
8
(y
14
+ 20y
13
+ ··· − 4y + 1)
· (y
20
+ 22y
19
+ ··· + 240y + 64)
31
