12a
0232
(K12a
0232
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 12 2 10 4 8 1 5 11
Solving Sequence
2,6
3 7
4,10
8 1 11 9 12 5
c
2
c
6
c
3
c
7
c
1
c
10
c
9
c
12
c
5
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
23
− 7u
22
+ ··· + 4b − 22, u
23
+ 15u
22
+ ··· + 8a − 66, u
24
+ 5u
23
+ ··· − 12u − 4i
I
u
2
= h−u
37
+ 2u
36
+ ··· + 2b − 1, −u
37
a + 3u
37
+ ··· + a − 6, u
38
− 2u
37
+ ··· − 2u + 1i
I
u
3
= h−au + b − a, a
2
+ a + 1, u
2
+ 1i
I
u
4
= hau + b − a + u, a
2
+ a + 1, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 108 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
=
h−3u
23
−7u
22
+· · ·+4b−22, u
23
+15u
22
+· · ·+8a−66, u
24
+5u
23
+· · ·−12u−4i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
−0.125000u
23
− 1.87500u
22
+ ··· + 13.1250u + 8.25000
3
4
u
23
+
7
4
u
22
+ ··· +
35
4
u +
11
2
a
8
=
−
1
8
u
23
−
3
8
u
22
+ ··· +
13
8
u +
3
4
1
4
u
23
+
5
4
u
22
+ ··· −
3
4
u −
1
2
a
1
=
u
2
+ 1
−u
4
a
11
=
−
3
8
u
23
−
13
8
u
22
+ ··· +
67
8
u +
19
4
7
4
u
23
+
29
4
u
22
+ ··· −
21
4
u −
1
2
a
9
=
−
3
8
u
23
−
9
8
u
22
+ ··· +
35
8
u +
13
4
3
4
u
23
+
15
4
u
22
+ ··· −
11
4
u −
1
2
a
12
=
−
1
8
u
23
−
3
8
u
22
+ ··· +
13
8
u +
7
4
3
4
u
23
+
13
4
u
22
+ ··· −
17
4
u −
3
2
a
5
=
7
8
u
23
+
29
8
u
22
+ ··· −
35
8
u −
11
4
3
4
u
23
+
7
4
u
22
+ ··· +
35
4
u +
11
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11u
23
+ 55u
22
+ 202u
21
+ 511u
20
+ 1091u
19
+ 1935u
18
+
3107u
17
+ 4507u
16
+ 6140u
15
+ 7797u
14
+ 9280u
13
+ 10305u
12
+ 10665u
11
+ 10334u
10
+
9374u
9
+ 7922u
8
+ 6201u
7
+ 4343u
6
+ 2630u
5
+ 1231u
4
+ 311u
3
− 76u
2
− 124u − 58
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 13u
23
+ ··· − 56u + 16
c
2
, c
6
u
24
− 5u
23
+ ··· + 12u − 4
c
3
u
24
+ 5u
23
+ ··· − 256u − 64
c
4
, c
5
, c
8
c
11
u
24
− 4u
22
+ ··· − 2u − 1
c
7
, c
9
, c
10
c
12
u
24
+ 8u
23
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 3y
23
+ ··· − 11552y + 256
c
2
, c
6
y
24
+ 13y
23
+ ··· − 56y + 16
c
3
y
24
− 7y
23
+ ··· − 40960y + 4096
c
4
, c
5
, c
8
c
11
y
24
− 8y
23
+ ··· − 4y + 1
c
7
, c
9
, c
10
c
12
y
24
+ 20y
23
+ ··· + 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.257222 + 1.017220I
a = 0.401654 − 0.008767I
b = 0.272209 − 0.624992I
−3.50051 + 2.57930I −16.8117 − 4.7598I
u = 0.257222 − 1.017220I
a = 0.401654 + 0.008767I
b = 0.272209 + 0.624992I
−3.50051 − 2.57930I −16.8117 + 4.7598I
u = −0.908792 + 0.262544I
a = 1.44352 − 1.19871I
b = 0.476457 + 0.127868I
3.72106 + 11.69860I −5.36042 − 8.05318I
u = −0.908792 − 0.262544I
a = 1.44352 + 1.19871I
b = 0.476457 − 0.127868I
3.72106 − 11.69860I −5.36042 + 8.05318I
u = 0.769198 + 0.739991I
a = −0.486482 + 0.038089I
b = 0.467190 + 0.882825I
7.88027 − 3.10260I −2.08649 + 2.69746I
u = 0.769198 − 0.739991I
a = −0.486482 − 0.038089I
b = 0.467190 − 0.882825I
7.88027 + 3.10260I −2.08649 − 2.69746I
u = −0.848943 + 0.362352I
a = −1.20123 + 1.01267I
b = −0.567849 − 0.040943I
5.70577 + 0.22260I −1.77984 + 2.03296I
u = −0.848943 − 0.362352I
a = −1.20123 − 1.01267I
b = −0.567849 + 0.040943I
5.70577 − 0.22260I −1.77984 − 2.03296I
u = −0.292804 + 0.863918I
a = −0.320360 + 0.625045I
b = −0.081672 + 0.710622I
−0.53022 − 1.37947I −5.11379 + 4.42535I
u = −0.292804 − 0.863918I
a = −0.320360 − 0.625045I
b = −0.081672 − 0.710622I
−0.53022 + 1.37947I −5.11379 − 4.42535I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.736879 + 0.861025I
a = 0.481995 − 0.036451I
b = −0.337196 − 1.007010I
7.52630 + 8.69544I −3.16830 − 8.31175I
u = 0.736879 − 0.861025I
a = 0.481995 + 0.036451I
b = −0.337196 + 1.007010I
7.52630 − 8.69544I −3.16830 + 8.31175I
u = −0.741563
a = 1.82111
b = 0.349010
−5.65295 −15.3580
u = −0.441869 + 1.180010I
a = −0.07853 − 1.44892I
b = −0.32749 − 2.36407I
−9.05396 − 4.24780I −18.5113 + 3.9565I
u = −0.441869 − 1.180010I
a = −0.07853 + 1.44892I
b = −0.32749 + 2.36407I
−9.05396 + 4.24780I −18.5113 − 3.9565I
u = −0.139106 + 1.265020I
a = 0.512595 + 0.449475I
b = 1.292080 + 0.305072I
0.20869 − 2.74167I −5.66024 + 3.24559I
u = −0.139106 − 1.265020I
a = 0.512595 − 0.449475I
b = 1.292080 − 0.305072I
0.20869 + 2.74167I −5.66024 − 3.24559I
u = −0.601530 + 1.137570I
a = −0.60703 + 1.34772I
b = −1.24236 + 1.92686I
3.38318 − 5.58195I −4.62085 + 2.23324I
u = −0.601530 − 1.137570I
a = −0.60703 − 1.34772I
b = −1.24236 − 1.92686I
3.38318 + 5.58195I −4.62085 − 2.23324I
u = −0.267870 + 1.300090I
a = −0.722509 − 0.703157I
b = −1.78732 − 0.89031I
−1.42153 + 7.81679I −9.52899 − 7.40459I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.267870 − 1.300090I
a = −0.722509 + 0.703157I
b = −1.78732 + 0.89031I
−1.42153 − 7.81679I −9.52899 + 7.40459I
u = −0.589102 + 1.197530I
a = 0.70080 − 1.54523I
b = 1.50441 − 2.44048I
0.8984 − 17.1574I −8.6015 + 11.3063I
u = −0.589102 − 1.197530I
a = 0.70080 + 1.54523I
b = 1.50441 + 2.44048I
0.8984 + 17.1574I −8.6015 − 11.3063I
u = 0.395000
a = −0.569953
b = 0.314058
−0.952863 −10.1550
7
II. I
u
2
=
h−u
37
+2u
36
+· · ·+2b −1, −u
37
a+3u
37
+· · ·+a −6, u
38
−2u
37
+· · ·−2u +1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
a
1
2
u
37
− u
36
+ ··· −
1
2
u +
1
2
a
8
=
1
2
u
37
a −
1
2
u
37
+ ··· +
1
2
a −
1
2
1
2
u
37
a + u
37
+ ··· −
1
2
a −
3
2
a
1
=
u
2
+ 1
−u
4
a
11
=
1
2
u
36
−
1
2
u
35
+ ··· + a − 1
1
2
u
37
−
1
2
u
36
+ ··· + au +
1
2
a
9
=
−u
36
a +
1
2
u
36
+ ··· +
1
2
a − 1
−
1
2
u
37
a +
3
2
u
37
+ ··· + 5u −
5
2
a
12
=
−u
37
+ 2u
36
+ ··· +
1
2
a + 1
−
3
2
u
37
+ 4u
36
+ ··· +
1
2
a +
3
2
a
5
=
−
1
2
u
37
+
3
2
u
36
+ ··· + a − 2u
−
1
2
u
35
+
1
2
u
34
+ ··· +
3
2
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −2u
35
−16u
33
−64u
31
+ 4u
30
−160u
29
+ 28u
28
−270u
27
+ 96u
26
−312u
25
+ 192u
24
−
244u
23
+ 228u
22
−132u
21
+ 120u
20
−66u
19
−56u
18
−36u
17
−128u
16
+ 12u
15
−48u
14
+
44u
13
+ 32u
12
+ 16u
11
+ 32u
10
− 28u
9
+ 4u
8
− 20u
7
+ 4u
6
+ 4u
4
+ 6u
3
− 4u
2
− 8
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
38
+ 20u
37
+ ··· + 4u + 1)
2
c
2
, c
6
(u
38
+ 2u
37
+ ··· + 2u + 1)
2
c
3
(u
38
− 2u
37
+ ··· − 48u + 4)
2
c
4
, c
5
, c
8
c
11
u
76
− u
75
+ ··· − 10u + 1
c
7
, c
9
, c
10
c
12
u
76
+ 27u
75
+ ··· + 50u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
38
+ 32y
36
+ ··· + 16y + 1)
2
c
2
, c
6
(y
38
+ 20y
37
+ ··· + 4y + 1)
2
c
3
(y
38
− 14y
37
+ ··· − 744y + 16)
2
c
4
, c
5
, c
8
c
11
y
76
− 27y
75
+ ··· − 50y + 1
c
7
, c
9
, c
10
c
12
y
76
+ 45y
75
+ ··· − 850y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.092692 + 1.025860I
a = 0.318432 + 1.014780I
b = 0.334512 + 0.975336I
−1.74996 − 2.04750I −12.12731 + 2.88539I
u = 0.092692 + 1.025860I
a = 0.039232 − 0.182499I
b = 1.017750 − 0.618683I
−1.74996 − 2.04750I −12.12731 + 2.88539I
u = 0.092692 − 1.025860I
a = 0.318432 − 1.014780I
b = 0.334512 − 0.975336I
−1.74996 + 2.04750I −12.12731 − 2.88539I
u = 0.092692 − 1.025860I
a = 0.039232 + 0.182499I
b = 1.017750 + 0.618683I
−1.74996 + 2.04750I −12.12731 − 2.88539I
u = 0.879654 + 0.307202I
a = 1.23008 + 1.04497I
b = 0.628001 + 0.013623I
4.78266 − 5.95391I −3.44271 + 3.17174I
u = 0.879654 + 0.307202I
a = −1.40216 − 1.08867I
b = −0.396763 + 0.200388I
4.78266 − 5.95391I −3.44271 + 3.17174I
u = 0.879654 − 0.307202I
a = 1.23008 − 1.04497I
b = 0.628001 − 0.013623I
4.78266 + 5.95391I −3.44271 − 3.17174I
u = 0.879654 − 0.307202I
a = −1.40216 + 1.08867I
b = −0.396763 − 0.200388I
4.78266 + 5.95391I −3.44271 − 3.17174I
u = 0.417100 + 0.987049I
a = −0.244327 − 0.928480I
b = 0.99403 − 1.23227I
−0.72961 − 1.85914I −8.12259 + 1.13673I
u = 0.417100 + 0.987049I
a = −0.11634 + 1.93055I
b = 0.68195 + 2.26923I
−0.72961 − 1.85914I −8.12259 + 1.13673I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.417100 − 0.987049I
a = −0.244327 + 0.928480I
b = 0.99403 + 1.23227I
−0.72961 + 1.85914I −8.12259 − 1.13673I
u = 0.417100 − 0.987049I
a = −0.11634 − 1.93055I
b = 0.68195 − 2.26923I
−0.72961 + 1.85914I −8.12259 − 1.13673I
u = −0.751160 + 0.801850I
a = −0.632410 + 0.158393I
b = 0.180392 − 0.828562I
7.77825 − 2.79187I −2.37424 + 2.87718I
u = −0.751160 + 0.801850I
a = 0.314560 + 0.230340I
b = −0.600746 + 1.023140I
7.77825 − 2.79187I −2.37424 + 2.87718I
u = −0.751160 − 0.801850I
a = −0.632410 − 0.158393I
b = 0.180392 + 0.828562I
7.77825 + 2.79187I −2.37424 − 2.87718I
u = −0.751160 − 0.801850I
a = 0.314560 − 0.230340I
b = −0.600746 − 1.023140I
7.77825 + 2.79187I −2.37424 − 2.87718I
u = −0.526392 + 1.014900I
a = −0.419575 + 0.987304I
b = 0.069923 + 1.154680I
1.44131 − 2.65190I −4.42318 + 2.95185I
u = −0.526392 + 1.014900I
a = −0.08723 + 1.46483I
b = −0.84966 + 1.95526I
1.44131 − 2.65190I −4.42318 + 2.95185I
u = −0.526392 − 1.014900I
a = −0.419575 − 0.987304I
b = 0.069923 − 1.154680I
1.44131 + 2.65190I −4.42318 − 2.95185I
u = −0.526392 − 1.014900I
a = −0.08723 − 1.46483I
b = −0.84966 − 1.95526I
1.44131 + 2.65190I −4.42318 − 2.95185I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.463054 + 1.059920I
a = 0.096981 − 1.116530I
b = −1.12569 − 1.36983I
−1.64453 − 3.37129I −10.06940 + 3.97155I
u = −0.463054 + 1.059920I
a = −0.44289 − 1.98577I
b = 0.40811 − 2.85964I
−1.64453 − 3.37129I −10.06940 + 3.97155I
u = −0.463054 − 1.059920I
a = 0.096981 + 1.116530I
b = −1.12569 + 1.36983I
−1.64453 + 3.37129I −10.06940 − 3.97155I
u = −0.463054 − 1.059920I
a = −0.44289 + 1.98577I
b = 0.40811 + 2.85964I
−1.64453 + 3.37129I −10.06940 − 3.97155I
u = 0.369116 + 1.125930I
a = 0.394531 − 1.005700I
b = 0.57224 − 1.83555I
−4.11479 + 2.70212I −12.89170 − 3.76810I
u = 0.369116 + 1.125930I
a = 0.043624 + 0.868515I
b = −0.506712 + 0.873442I
−4.11479 + 2.70212I −12.89170 − 3.76810I
u = 0.369116 − 1.125930I
a = 0.394531 + 1.005700I
b = 0.57224 + 1.83555I
−4.11479 − 2.70212I −12.89170 + 3.76810I
u = 0.369116 − 1.125930I
a = 0.043624 − 0.868515I
b = −0.506712 − 0.873442I
−4.11479 − 2.70212I −12.89170 + 3.76810I
u = 0.536688 + 1.074140I
a = 0.351361 + 1.092920I
b = −0.182927 + 1.250470I
0.50867 + 8.15703I −6.43185 − 7.89440I
u = 0.536688 + 1.074140I
a = 0.12188 − 1.56571I
b = −0.71430 − 2.45999I
0.50867 + 8.15703I −6.43185 − 7.89440I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.536688 − 1.074140I
a = 0.351361 − 1.092920I
b = −0.182927 − 1.250470I
0.50867 − 8.15703I −6.43185 + 7.89440I
u = 0.536688 − 1.074140I
a = 0.12188 + 1.56571I
b = −0.71430 + 2.45999I
0.50867 − 8.15703I −6.43185 + 7.89440I
u = 0.424797 + 0.672856I
a = −0.573283 + 0.461174I
b = −0.799729 − 1.006180I
0.24459 + 5.40327I −7.14076 − 8.73282I
u = 0.424797 + 0.672856I
a = 2.15958 + 0.01504I
b = 1.15044 − 1.04061I
0.24459 + 5.40327I −7.14076 − 8.73282I
u = 0.424797 − 0.672856I
a = −0.573283 − 0.461174I
b = −0.799729 + 1.006180I
0.24459 − 5.40327I −7.14076 + 8.73282I
u = 0.424797 − 0.672856I
a = 2.15958 − 0.01504I
b = 1.15044 + 1.04061I
0.24459 − 5.40327I −7.14076 + 8.73282I
u = −0.606947 + 0.511177I
a = −0.829981 + 0.188456I
b = −0.573546 + 0.654578I
2.90982 − 1.84462I −1.62797 + 3.07541I
u = −0.606947 + 0.511177I
a = −1.49164 + 0.70399I
b = −0.684526 − 0.462319I
2.90982 − 1.84462I −1.62797 + 3.07541I
u = −0.606947 − 0.511177I
a = −0.829981 − 0.188456I
b = −0.573546 − 0.654578I
2.90982 + 1.84462I −1.62797 − 3.07541I
u = −0.606947 − 0.511177I
a = −1.49164 − 0.70399I
b = −0.684526 + 0.462319I
2.90982 + 1.84462I −1.62797 − 3.07541I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.504117 + 1.123560I
a = −0.318845 − 1.236270I
b = −0.11066 − 2.22477I
−3.18042 + 5.01836I −11.22503 − 3.99262I
u = 0.504117 + 1.123560I
a = 0.45678 + 1.63903I
b = 1.08898 + 2.11659I
−3.18042 + 5.01836I −11.22503 − 3.99262I
u = 0.504117 − 1.123560I
a = −0.318845 + 1.236270I
b = −0.11066 + 2.22477I
−3.18042 − 5.01836I −11.22503 + 3.99262I
u = 0.504117 − 1.123560I
a = 0.45678 − 1.63903I
b = 1.08898 − 2.11659I
−3.18042 − 5.01836I −11.22503 + 3.99262I
u = −0.350867 + 1.182120I
a = −0.332778 − 0.899175I
b = −1.46268 − 1.13492I
−5.61147 + 2.22079I −15.5130 − 1.9644I
u = −0.350867 + 1.182120I
a = −0.63487 − 1.32116I
b = −0.89277 − 2.13230I
−5.61147 + 2.22079I −15.5130 − 1.9644I
u = −0.350867 − 1.182120I
a = −0.332778 + 0.899175I
b = −1.46268 + 1.13492I
−5.61147 − 2.22079I −15.5130 + 1.9644I
u = −0.350867 − 1.182120I
a = −0.63487 + 1.32116I
b = −0.89277 + 2.13230I
−5.61147 − 2.22079I −15.5130 + 1.9644I
u = 0.649945 + 0.400847I
a = 0.907087 − 0.030828I
b = 0.669846 + 0.531686I
2.46586 − 3.52445I −2.75723 + 3.36629I
u = 0.649945 + 0.400847I
a = −1.71404 − 0.47572I
b = −0.401143 + 0.674066I
2.46586 − 3.52445I −2.75723 + 3.36629I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.649945 − 0.400847I
a = 0.907087 + 0.030828I
b = 0.669846 − 0.531686I
2.46586 + 3.52445I −2.75723 − 3.36629I
u = 0.649945 − 0.400847I
a = −1.71404 + 0.47572I
b = −0.401143 − 0.674066I
2.46586 + 3.52445I −2.75723 − 3.36629I
u = −0.736881 + 0.188549I
a = 1.80671 − 0.41605I
b = 0.309194 − 0.424971I
−1.63069 + 5.81244I −10.15602 − 5.45281I
u = −0.736881 + 0.188549I
a = 1.78520 − 1.08774I
b = 0.649257 + 0.400799I
−1.63069 + 5.81244I −10.15602 − 5.45281I
u = −0.736881 − 0.188549I
a = 1.80671 + 0.41605I
b = 0.309194 + 0.424971I
−1.63069 − 5.81244I −10.15602 + 5.45281I
u = −0.736881 − 0.188549I
a = 1.78520 + 1.08774I
b = 0.649257 − 0.400799I
−1.63069 − 5.81244I −10.15602 + 5.45281I
u = −0.521806 + 1.155510I
a = 0.36985 − 1.41416I
b = 0.12817 − 2.40791I
−4.40741 − 10.53470I −13.1011 + 8.4995I
u = −0.521806 + 1.155510I
a = 0.33140 − 1.85479I
b = 1.14785 − 2.73713I
−4.40741 − 10.53470I −13.1011 + 8.4995I
u = −0.521806 − 1.155510I
a = 0.36985 + 1.41416I
b = 0.12817 + 2.40791I
−4.40741 + 10.53470I −13.1011 − 8.4995I
u = −0.521806 − 1.155510I
a = 0.33140 + 1.85479I
b = 1.14785 + 2.73713I
−4.40741 + 10.53470I −13.1011 − 8.4995I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.213295 + 1.276410I
a = 0.662381 − 0.531928I
b = 1.69785 − 0.73713I
−0.48674 − 2.48291I −7.53122 + 2.48903I
u = 0.213295 + 1.276410I
a = −0.474667 + 0.655902I
b = −1.214850 + 0.565221I
−0.48674 − 2.48291I −7.53122 + 2.48903I
u = 0.213295 − 1.276410I
a = 0.662381 + 0.531928I
b = 1.69785 + 0.73713I
−0.48674 + 2.48291I −7.53122 − 2.48903I
u = 0.213295 − 1.276410I
a = −0.474667 − 0.655902I
b = −1.214850 − 0.565221I
−0.48674 + 2.48291I −7.53122 − 2.48903I
u = 0.595105 + 1.170590I
a = −0.56398 − 1.46203I
b = −1.37249 − 2.35989I
2.18721 + 11.36400I −6.56181 − 6.84677I
u = 0.595105 + 1.170590I
a = 0.69980 + 1.41296I
b = 1.30389 + 1.99102I
2.18721 + 11.36400I −6.56181 − 6.84677I
u = 0.595105 − 1.170590I
a = −0.56398 + 1.46203I
b = −1.37249 + 2.35989I
2.18721 − 11.36400I −6.56181 + 6.84677I
u = 0.595105 − 1.170590I
a = 0.69980 − 1.41296I
b = 1.30389 − 1.99102I
2.18721 − 11.36400I −6.56181 + 6.84677I
u = 0.626124 + 0.193865I
a = −1.60011 − 0.43169I
b = −0.072389 − 0.405022I
−0.611163 − 0.610877I −8.09323 + 0.39189I
u = 0.626124 + 0.193865I
a = 1.20644 + 1.13811I
b = 0.766850 − 0.115790I
−0.611163 − 0.610877I −8.09323 + 0.39189I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626124 − 0.193865I
a = −1.60011 + 0.43169I
b = −0.072389 + 0.405022I
−0.611163 + 0.610877I −8.09323 − 0.39189I
u = 0.626124 − 0.193865I
a = 1.20644 − 1.13811I
b = 0.766850 + 0.115790I
−0.611163 + 0.610877I −8.09323 − 0.39189I
u = −0.351526 + 0.483850I
a = 0.452401 + 1.125970I
b = 0.847436 − 0.808834I
0.203455 − 0.349653I −6.40967 + 1.75614I
u = −0.351526 + 0.483850I
a = 2.63083 + 0.52836I
b = 0.814911 + 1.130250I
0.203455 − 0.349653I −6.40967 + 1.75614I
u = −0.351526 − 0.483850I
a = 0.452401 − 1.125970I
b = 0.847436 + 0.808834I
0.203455 + 0.349653I −6.40967 − 1.75614I
u = −0.351526 − 0.483850I
a = 2.63083 − 0.52836I
b = 0.814911 − 1.130250I
0.203455 + 0.349653I −6.40967 − 1.75614I
18
III. I
u
3
= h−au + b − a, a
2
+ a + 1, u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
1
a
7
=
u
u
a
4
=
1
1
a
10
=
a
au + a
a
8
=
a + u + 1
au + a + 2u + 1
a
1
=
0
−1
a
11
=
a
au + 2a
a
9
=
−au + a + 1
a + u + 1
a
12
=
a + 1
au + 2a + u + 1
a
5
=
au
au − a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8a − 16
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
6
(u
2
+ 1)
2
c
3
u
4
c
4
, c
5
, c
8
c
11
u
4
− u
2
+ 1
c
7
, c
10
(u
2
− u + 1)
2
c
9
, c
12
(u
2
+ u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
4
c
2
, c
6
(y + 1)
4
c
3
y
4
c
4
, c
5
, c
8
c
11
(y
2
− y + 1)
2
c
7
, c
9
, c
10
c
12
(y
2
+ y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.500000 + 0.866025I
b = −1.36603 + 0.36603I
−1.64493 + 4.05977I −12.00000 − 6.92820I
u = 1.000000I
a = −0.500000 − 0.866025I
b = 0.36603 − 1.36603I
−1.64493 − 4.05977I −12.00000 + 6.92820I
u = − 1.000000I
a = −0.500000 + 0.866025I
b = 0.36603 + 1.36603I
−1.64493 + 4.05977I −12.00000 − 6.92820I
u = − 1.000000I
a = −0.500000 − 0.866025I
b = −1.36603 − 0.36603I
−1.64493 − 4.05977I −12.00000 + 6.92820I
22
IV. I
u
4
= hau + b − a + u, a
2
+ a + 1, u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
1
a
7
=
u
u
a
4
=
1
1
a
10
=
a
−au + a − u
a
8
=
u − 1
−au + u − 1
a
1
=
0
−1
a
11
=
a
−au + 2a − u
a
9
=
au + u − 1
u − 1
a
12
=
a + 1
2a − u + 1
a
5
=
au
au + a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
6
(u
2
+ 1)
2
c
3
u
4
c
4
, c
5
, c
8
c
11
u
4
− u
2
+ 1
c
7
, c
10
(u
2
− u + 1)
2
c
9
, c
12
(u
2
+ u + 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
4
c
2
, c
6
(y + 1)
4
c
3
y
4
c
4
, c
5
, c
8
c
11
(y
2
− y + 1)
2
c
7
, c
9
, c
10
c
12
(y
2
+ y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.500000 + 0.866025I
b = 0.366025 + 0.366025I
−1.64493 −12.0000
u = 1.000000I
a = −0.500000 − 0.866025I
b = −1.36603 − 1.36603I
−1.64493 −12.0000
u = − 1.000000I
a = −0.500000 + 0.866025I
b = −1.36603 + 1.36603I
−1.64493 −12.0000
u = − 1.000000I
a = −0.500000 − 0.866025I
b = 0.366025 − 0.366025I
−1.64493 −12.0000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
24
+ 13u
23
+ ··· − 56u + 16)(u
38
+ 20u
37
+ ··· + 4u + 1)
2
c
2
, c
6
((u
2
+ 1)
4
)(u
24
− 5u
23
+ ··· + 12u − 4)(u
38
+ 2u
37
+ ··· + 2u + 1)
2
c
3
u
8
(u
24
+ 5u
23
+ ··· − 256u − 64)(u
38
− 2u
37
+ ··· − 48u + 4)
2
c
4
, c
5
, c
8
c
11
((u
4
− u
2
+ 1)
2
)(u
24
− 4u
22
+ ··· − 2u − 1)(u
76
− u
75
+ ··· − 10u + 1)
c
7
, c
10
((u
2
− u + 1)
4
)(u
24
+ 8u
23
+ ··· + 4u + 1)(u
76
+ 27u
75
+ ··· + 50u + 1)
c
9
, c
12
((u
2
+ u + 1)
4
)(u
24
+ 8u
23
+ ··· + 4u + 1)(u
76
+ 27u
75
+ ··· + 50u + 1)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
8
)(y
24
− 3y
23
+ ··· − 11552y + 256)
· (y
38
+ 32y
36
+ ··· + 16y + 1)
2
c
2
, c
6
((y + 1)
8
)(y
24
+ 13y
23
+ ··· − 56y + 16)(y
38
+ 20y
37
+ ··· + 4y + 1)
2
c
3
y
8
(y
24
− 7y
23
+ ··· − 40960y + 4096)
· (y
38
− 14y
37
+ ··· − 744y + 16)
2
c
4
, c
5
, c
8
c
11
((y
2
− y + 1)
4
)(y
24
− 8y
23
+ ··· − 4y + 1)(y
76
− 27y
75
+ ··· − 50y + 1)
c
7
, c
9
, c
10
c
12
((y
2
+ y + 1)
4
)(y
24
+ 20y
23
+ ··· + 4y + 1)
· (y
76
+ 45y
75
+ ··· − 850y + 1)
28
