12a
0880
(K12a
0880
)
A knot diagram
1
Linearized knot diagam
4 6 7 10 3 2 11 12 5 1 9 8
Solving Sequence
8,12
9
1,4
2 11 7 3 6 10 5
c
8
c
12
c
1
c
11
c
7
c
3
c
6
c
10
c
4
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
15
+ u
14
+ 7u
13
+ 6u
12
+ 17u
11
+ 12u
10
+ 14u
9
+ 6u
8
− 3u
7
− 6u
6
− 5u
5
− 3u
4
+ 2u
3
+ 2u
2
+ b + u − 1,
− u
15
− u
14
− 7u
13
− 6u
12
− 17u
11
− 12u
10
− 14u
9
− 6u
8
+ 3u
7
+ 6u
6
+ 5u
5
+ 3u
4
− u
3
− 2u
2
+ a + u + 1,
u
17
+ u
16
+ ··· + 2u − 1i
I
u
2
= h6u
71
+ 3u
70
+ ··· + 2b + 6, 13u
71
+ 37u
70
+ ··· + 2a + 22, u
72
+ 3u
71
+ ··· + 4u + 1i
I
u
3
= hu
2
+ b, a + 1, u
3
− u
2
+ 2u − 1i
I
u
4
= h−u
2
a + b, −u
2
a + a
2
+ u
2
− 2a + 2, u
3
− u
2
+ 2u − 1i
* 4 irreducible components of dim
C
= 0, with total 98 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
= hu
15
+ u
14
+ · · · + b − 1, −u
15
− u
14
+ · · · + a + 1, u
17
+ u
16
+ · · · + 2u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
u
15
+ u
14
+ ··· − u − 1
−u
15
− u
14
+ ··· − u + 1
a
2
=
−u
15
− u
14
+ ··· − u
2
− u
u
15
+ u
14
+ ··· + u
2
+ u
a
11
=
u
u
3
+ u
a
7
=
−u
4
− u
2
+ 1
−u
6
− 2u
4
− u
2
a
3
=
u
15
+ u
14
+ ··· + 2u
2
− 1
−u
15
− u
14
+ ··· − u + 1
a
6
=
u
16
+ u
15
+ ··· + u
3
+ 1
−u
16
− u
15
+ ··· − u
3
− 2u
2
a
10
=
u
5
+ 2u
3
+ u
−u
5
− u
3
+ u
a
5
=
−u
12
− u
11
− 6u
10
− 5u
9
− 13u
8
− 8u
7
− 11u
6
− 3u
5
− 2u
4
+ u
3
− u − 1
u
12
+ u
11
+ 5u
10
+ 5u
9
+ 8u
8
+ 8u
7
+ 3u
6
+ 3u
5
− u
4
− u
3
+ u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
16
− 4u
15
− 32u
14
− 30u
13
− 98u
12
− 86u
11
− 136u
10
−
108u
9
− 70u
8
− 40u
7
+ 10u
6
+ 18u
5
+ 12u
4
− 2u
3
− 4u
2
− 8u − 12
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
17
− 3u
16
+ ··· − 13u
2
+ 1
c
2
, c
5
, c
6
c
8
, c
11
, c
12
u
17
− u
16
+ ··· + 2u + 1
c
3
, c
7
u
17
+ u
16
+ ··· − 2u + 1
c
4
, c
9
u
17
− 7u
16
+ ··· − 24u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
17
+ 13y
16
+ ··· + 26y −1
c
2
, c
5
, c
6
c
8
, c
11
, c
12
y
17
+ 17y
16
+ ··· + 10y −1
c
3
, c
7
y
17
+ 5y
16
+ ··· + 10y −1
c
4
, c
9
y
17
+ 7y
16
+ ··· + 256y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.091941 + 1.094580I
a = 0.581769 − 0.777593I
b = −0.435961 − 0.127897I
3.05673 − 2.28115I −9.55605 + 3.69550I
u = 0.091941 − 1.094580I
a = 0.581769 + 0.777593I
b = −0.435961 + 0.127897I
3.05673 + 2.28115I −9.55605 − 3.69550I
u = −0.721066 + 0.328898I
a = 0.222416 − 1.215200I
b = 1.360620 + 0.079969I
1.60562 + 8.48162I −11.6917 − 8.7222I
u = −0.721066 − 0.328898I
a = 0.222416 + 1.215200I
b = 1.360620 − 0.079969I
1.60562 − 8.48162I −11.6917 + 8.7222I
u = −0.474834 + 0.556801I
a = 0.363619 − 1.313000I
b = 0.251475 − 0.004597I
3.62349 − 0.43208I −6.82365 − 2.95346I
u = −0.474834 − 0.556801I
a = 0.363619 + 1.313000I
b = 0.251475 + 0.004597I
3.62349 + 0.43208I −6.82365 + 2.95346I
u = 0.602130 + 0.282651I
a = −0.29346 − 1.46942I
b = −0.984788 + 0.619269I
−1.19117 − 2.88336I −13.9594 + 7.1058I
u = 0.602130 − 0.282651I
a = −0.29346 + 1.46942I
b = −0.984788 − 0.619269I
−1.19117 + 2.88336I −13.9594 − 7.1058I
u = 0.065351 + 1.353320I
a = −0.09164 + 1.99081I
b = 0.31972 − 2.23621I
8.04992 − 2.40798I −3.08239 + 2.80961I
u = 0.065351 − 1.353320I
a = −0.09164 − 1.99081I
b = 0.31972 + 2.23621I
8.04992 + 2.40798I −3.08239 − 2.80961I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24047 + 1.42815I
a = −3.28620 − 0.25955I
b = 4.26275 + 0.06839I
9.86744 − 9.13272I −4.35551 + 6.02598I
u = 0.24047 − 1.42815I
a = −3.28620 + 0.25955I
b = 4.26275 − 0.06839I
9.86744 + 9.13272I −4.35551 − 6.02598I
u = −0.28648 + 1.44189I
a = 2.80799 − 1.15056I
b = −3.99833 + 0.90955I
12.9584 + 15.8554I −3.84401 − 8.82100I
u = −0.28648 − 1.44189I
a = 2.80799 + 1.15056I
b = −3.99833 − 0.90955I
12.9584 − 15.8554I −3.84401 + 8.82100I
u = −0.16848 + 1.47926I
a = 1.76249 + 0.47839I
b = −2.52677 − 0.32597I
16.6406 + 4.3048I −0.33728 − 2.80753I
u = −0.16848 − 1.47926I
a = 1.76249 − 0.47839I
b = −2.52677 + 0.32597I
16.6406 − 4.3048I −0.33728 + 2.80753I
u = 0.301943
a = −1.13397
b = 0.502560
−0.656393 −14.7000
6
II. I
u
2
=
h6u
71
+3u
70
+· · ·+2b+6, 13u
71
+37u
70
+· · ·+2a+22, u
72
+3u
71
+· · ·+4u+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
−
13
2
u
71
−
37
2
u
70
+ ··· −
73
2
u − 11
−3u
71
−
3
2
u
70
+ ··· −
11
2
u − 3
a
2
=
u
71
+
5
2
u
70
+ ··· +
11
2
u +
1
2
1
2
u
69
+ u
68
+ ··· + 3u +
1
2
a
11
=
u
u
3
+ u
a
7
=
−u
4
− u
2
+ 1
−u
6
− 2u
4
− u
2
a
3
=
−14u
71
− 41u
70
+ ··· − 62u −
37
2
7
2
u
71
+ 21u
70
+ ··· + 14u +
7
2
a
6
=
6u
71
+ 18u
70
+ ··· + 32u + 15
3
2
u
71
−
1
2
u
70
+ ··· +
3
2
u + 3
a
10
=
u
5
+ 2u
3
+ u
−u
5
− u
3
+ u
a
5
=
−
23
2
u
71
−
67
2
u
70
+ ··· −
107
2
u − 15
u
71
+
27
2
u
70
+ ··· +
15
2
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes =
33
2
u
71
+ 36u
70
+ ··· + 50u +
29
2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
72
− 15u
71
+ ··· − 73808u + 6497
c
2
, c
5
, c
6
c
8
, c
11
, c
12
u
72
− 3u
71
+ ··· − 4u + 1
c
3
, c
7
u
72
+ 3u
71
+ ··· − 604u + 137
c
4
, c
9
(u
36
+ 3u
35
+ ··· + 12u + 8)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
72
+ 25y
71
+ ··· + 288840316y + 42211009
c
2
, c
5
, c
6
c
8
, c
11
, c
12
y
72
+ 65y
71
+ ··· − 4y + 1
c
3
, c
7
y
72
+ 5y
71
+ ··· + 440196y + 18769
c
4
, c
9
(y
36
+ 21y
35
+ ··· + 752y + 64)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.028099 + 1.172780I
a = −0.871667 + 1.020780I
b = 1.43262 − 0.20599I
0.543677 + 0.795055I 0
u = −0.028099 − 1.172780I
a = −0.871667 − 1.020780I
b = 1.43262 + 0.20599I
0.543677 − 0.795055I 0
u = −0.486820 + 0.662033I
a = 0.20277 − 1.54250I
b = 0.859587 − 0.132580I
8.43073 − 7.86342I −5.29136 + 3.41606I
u = −0.486820 − 0.662033I
a = 0.20277 + 1.54250I
b = 0.859587 + 0.132580I
8.43073 + 7.86342I −5.29136 − 3.41606I
u = 0.263106 + 1.148630I
a = −0.175976 + 0.566859I
b = −0.690420 − 0.221203I
1.54122 − 4.89012I 0
u = 0.263106 − 1.148630I
a = −0.175976 − 0.566859I
b = −0.690420 + 0.221203I
1.54122 + 4.89012I 0
u = −0.739526 + 0.334846I
a = −0.06745 + 1.51141I
b = −1.48882 − 0.07395I
7.26375 + 12.12330I −7.67566 − 8.67883I
u = −0.739526 − 0.334846I
a = −0.06745 − 1.51141I
b = −1.48882 + 0.07395I
7.26375 − 12.12330I −7.67566 + 8.67883I
u = 0.309257 + 1.151650I
a = 0.004957 − 0.470407I
b = 1.155150 + 0.255668I
6.92907 − 8.07419I 0
u = 0.309257 − 1.151650I
a = 0.004957 + 0.470407I
b = 1.155150 − 0.255668I
6.92907 + 8.07419I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.693334 + 0.387106I
a = −0.512995 − 0.563906I
b = 1.189500 − 0.307569I
9.40092 + 2.42015I −5.02486 − 3.32106I
u = −0.693334 − 0.387106I
a = −0.512995 + 0.563906I
b = 1.189500 + 0.307569I
9.40092 − 2.42015I −5.02486 + 3.32106I
u = −0.074263 + 1.210030I
a = 1.12364 − 1.15238I
b = −2.07024 + 0.42184I
5.33274 + 4.20528I 0
u = −0.074263 − 1.210030I
a = 1.12364 + 1.15238I
b = −2.07024 − 0.42184I
5.33274 − 4.20528I 0
u = −0.550109 + 0.561117I
a = −0.61451 + 1.33701I
b = −0.264237 − 0.424531I
10.05060 + 1.78164I −3.59526 − 2.92936I
u = −0.550109 − 0.561117I
a = −0.61451 − 1.33701I
b = −0.264237 + 0.424531I
10.05060 − 1.78164I −3.59526 + 2.92936I
u = −0.458914 + 0.629950I
a = −0.25151 + 1.42096I
b = −0.592588 + 0.193257I
2.73562 − 4.37909I −9.14116 + 3.46632I
u = −0.458914 − 0.629950I
a = −0.25151 − 1.42096I
b = −0.592588 − 0.193257I
2.73562 + 4.37909I −9.14116 − 3.46632I
u = 0.134798 + 1.220550I
a = 0.259072 − 0.959718I
b = −0.145300 + 0.658090I
2.81331 − 1.98395I 0
u = 0.134798 − 1.220550I
a = 0.259072 + 0.959718I
b = −0.145300 − 0.658090I
2.81331 + 1.98395I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.689123 + 0.339547I
a = −0.143228 + 0.704284I
b = −1.182920 + 0.007819I
2.73562 + 4.37909I −9.14116 − 3.46632I
u = −0.689123 − 0.339547I
a = −0.143228 − 0.704284I
b = −1.182920 − 0.007819I
2.73562 − 4.37909I −9.14116 + 3.46632I
u = 0.760429 + 0.051408I
a = 0.619326 − 0.928464I
b = −0.017927 − 0.618723I
3.56538 + 4.16794I −8.26901 − 3.74387I
u = 0.760429 − 0.051408I
a = 0.619326 + 0.928464I
b = −0.017927 + 0.618723I
3.56538 − 4.16794I −8.26901 + 3.74387I
u = 0.713507 + 0.060631I
a = −0.512274 + 0.427549I
b = −0.066731 + 0.606152I
−1.75773 + 1.27972I −13.2127 − 5.1177I
u = 0.713507 − 0.060631I
a = −0.512274 − 0.427549I
b = −0.066731 − 0.606152I
−1.75773 − 1.27972I −13.2127 + 5.1177I
u = 0.622211 + 0.330313I
a = 0.29143 + 1.89834I
b = 1.24066 − 0.71866I
4.23221 − 5.96236I −8.77056 + 6.49736I
u = 0.622211 − 0.330313I
a = 0.29143 − 1.89834I
b = 1.24066 + 0.71866I
4.23221 + 5.96236I −8.77056 − 6.49736I
u = 0.309852 + 1.260530I
a = −0.075247 + 1.082060I
b = −0.60498 − 1.61917I
7.62672 + 0.29835I 0
u = 0.309852 − 1.260530I
a = −0.075247 − 1.082060I
b = −0.60498 + 1.61917I
7.62672 − 0.29835I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.670396 + 0.166557I
a = 0.828226 + 0.508262I
b = 0.402874 − 0.740462I
0.543677 − 0.795055I −12.98650 + 0.87860I
u = 0.670396 − 0.166557I
a = 0.828226 − 0.508262I
b = 0.402874 + 0.740462I
0.543677 + 0.795055I −12.98650 − 0.87860I
u = 0.263561 + 1.285520I
a = 0.397587 − 0.820456I
b = −0.113302 + 1.168640I
2.40132 − 2.25171I 0
u = 0.263561 − 1.285520I
a = 0.397587 + 0.820456I
b = −0.113302 − 1.168640I
2.40132 + 2.25171I 0
u = −0.627964 + 0.272720I
a = −1.005100 − 0.078332I
b = −0.916212 − 0.274601I
1.54122 + 4.89012I −10.17132 − 8.17154I
u = −0.627964 − 0.272720I
a = −1.005100 + 0.078332I
b = −0.916212 + 0.274601I
1.54122 − 4.89012I −10.17132 + 8.17154I
u = 0.472092 + 0.409617I
a = 0.75723 − 1.63308I
b = −1.293070 − 0.105552I
4.76567 + 2.49919I −7.13527 + 0.48445I
u = 0.472092 − 0.409617I
a = 0.75723 + 1.63308I
b = −1.293070 + 0.105552I
4.76567 − 2.49919I −7.13527 − 0.48445I
u = 0.267646 + 1.351260I
a = −1.38835 + 0.81532I
b = 1.62169 − 1.37738I
5.33274 − 4.20528I 0
u = 0.267646 − 1.351260I
a = −1.38835 − 0.81532I
b = 1.62169 + 1.37738I
5.33274 + 4.20528I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.557533 + 0.252581I
a = 0.982249 + 0.864931I
b = 0.715436 + 0.371416I
−1.75773 + 1.27972I −13.2127 − 5.1177I
u = −0.557533 − 0.252581I
a = 0.982249 − 0.864931I
b = 0.715436 − 0.371416I
−1.75773 − 1.27972I −13.2127 + 5.1177I
u = −0.199074 + 1.399440I
a = 0.306691 + 0.999684I
b = 0.09647 − 2.03402I
7.62672 + 0.29835I 0
u = −0.199074 − 1.399440I
a = 0.306691 − 0.999684I
b = 0.09647 + 2.03402I
7.62672 − 0.29835I 0
u = 0.20042 + 1.40204I
a = −2.12639 − 1.01851I
b = 2.70046 + 1.07463I
4.76567 − 2.49919I 0
u = 0.20042 − 1.40204I
a = −2.12639 + 1.01851I
b = 2.70046 − 1.07463I
4.76567 + 2.49919I 0
u = −0.22137 + 1.40379I
a = −0.922863 − 0.664443I
b = 0.91344 + 1.71767I
3.56538 + 4.16794I 0
u = −0.22137 − 1.40379I
a = −0.922863 + 0.664443I
b = 0.91344 − 1.71767I
3.56538 − 4.16794I 0
u = −0.24258 + 1.40964I
a = 1.51890 + 0.27038I
b = −1.91772 − 1.23335I
6.92907 + 8.07419I 0
u = −0.24258 − 1.40964I
a = 1.51890 − 0.27038I
b = −1.91772 + 1.23335I
6.92907 − 8.07419I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23483 + 1.41097I
a = 2.72376 + 0.25541I
b = −3.50164 − 0.05571I
4.23221 − 5.96236I 0
u = 0.23483 − 1.41097I
a = 2.72376 − 0.25541I
b = −3.50164 + 0.05571I
4.23221 + 5.96236I 0
u = 0.18986 + 1.43138I
a = 2.63821 + 1.69759I
b = −3.36954 − 1.98298I
10.6075 0
u = 0.18986 − 1.43138I
a = 2.63821 − 1.69759I
b = −3.36954 + 1.98298I
10.6075 0
u = −0.26545 + 1.43725I
a = 2.04182 − 0.85451I
b = −2.83123 + 0.45931I
8.43073 + 7.86342I 0
u = −0.26545 − 1.43725I
a = 2.04182 + 0.85451I
b = −2.83123 − 0.45931I
8.43073 − 7.86342I 0
u = −0.27920 + 1.43702I
a = −2.55048 + 0.93395I
b = 3.60942 − 0.57373I
7.26375 + 12.12330I 0
u = −0.27920 − 1.43702I
a = −2.55048 − 0.93395I
b = 3.60942 + 0.57373I
7.26375 − 12.12330I 0
u = −0.15360 + 1.46034I
a = −1.60146 + 0.26365I
b = 2.39859 − 0.62513I
10.05060 + 1.78164I 0
u = −0.15360 − 1.46034I
a = −1.60146 − 0.26365I
b = 2.39859 + 0.62513I
10.05060 − 1.78164I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13067 + 1.46551I
a = 2.05831 − 0.71219I
b = −2.99639 + 1.12544I
9.40092 − 2.42015I 0
u = −0.13067 − 1.46551I
a = 2.05831 + 0.71219I
b = −2.99639 − 1.12544I
9.40092 + 2.42015I 0
u = −0.25867 + 1.45576I
a = −1.61176 + 1.49131I
b = 2.21138 − 1.42343I
15.3281 + 5.8880I 0
u = −0.25867 − 1.45576I
a = −1.61176 − 1.49131I
b = 2.21138 + 1.42343I
15.3281 − 5.8880I 0
u = −0.477473 + 0.201626I
a = −0.86751 − 1.69455I
b = −0.528630 − 0.550025I
2.40132 − 2.25171I −5.72106 − 2.85348I
u = −0.477473 − 0.201626I
a = −0.86751 + 1.69455I
b = −0.528630 + 0.550025I
2.40132 + 2.25171I −5.72106 + 2.85348I
u = −0.12268 + 1.48064I
a = −2.53271 + 0.75877I
b = 3.57037 − 1.15531I
15.3281 − 5.8880I 0
u = −0.12268 − 1.48064I
a = −2.53271 − 0.75877I
b = 3.57037 + 1.15531I
15.3281 + 5.8880I 0
u = 0.411433 + 0.249923I
a = −0.620932 + 1.023680I
b = 0.787442 − 0.018352I
−0.556807 −12.02614 + 0.I
u = 0.411433 − 0.249923I
a = −0.620932 − 1.023680I
b = 0.787442 + 0.018352I
−0.556807 −12.02614 + 0.I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.066940 + 0.465647I
a = 0.69822 − 1.36466I
b = −0.313196 − 0.593198I
2.81331 − 1.98395I −6.78982 + 3.37609I
u = −0.066940 − 0.465647I
a = 0.69822 + 1.36466I
b = −0.313196 + 0.593198I
2.81331 + 1.98395I −6.78982 − 3.37609I
17
III. I
u
3
= hu
2
+ b, a + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
−1
−u
2
a
2
=
−u
2
− 1
u
2
a
11
=
u
u
2
− u + 1
a
7
=
u
−u
a
3
=
u − 2
−u
2
− u + 1
a
6
=
−u
2
+ 2u − 1
u
2
− 3u + 1
a
10
=
1
u
2
a
5
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 8u − 20
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
10
u
3
+ u
2
− 1
c
2
, c
8
u
3
− u
2
+ 2u − 1
c
4
, c
9
u
3
c
5
, c
6
, c
11
c
12
u
3
+ u
2
+ 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
10
y
3
− y
2
+ 2y − 1
c
2
, c
5
, c
6
c
8
, c
11
, c
12
y
3
+ 3y
2
+ 2y − 1
c
4
, c
9
y
3
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.00000
b = 1.66236 − 0.56228I
6.04826 − 5.65624I −4.98049 + 5.95889I
u = 0.215080 − 1.307140I
a = −1.00000
b = 1.66236 + 0.56228I
6.04826 + 5.65624I −4.98049 − 5.95889I
u = 0.569840
a = −1.00000
b = −0.324718
−2.22691 −18.0390
21
IV. I
u
4
= h−u
2
a + b, −u
2
a + a
2
+ u
2
− 2a + 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
a
u
2
a
a
2
=
−u
2
a + au + u
2
− 2a − 2u + 2
−au + 2u
a
11
=
u
u
2
− u + 1
a
7
=
u
−u
a
3
=
−au + 2a
u
2
a + au − a
a
6
=
−2u
2
a + 2au + 3u
2
− 2a − u + 4
2u
2
a − 2au − u
2
+ a
a
10
=
1
u
2
a
5
=
a
u
2
a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
2
a − 3au − 5u
2
+ 5a + 5u − 20
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
10
(u
3
+ u
2
− 1)
2
c
2
, c
8
(u
3
− u
2
+ 2u − 1)
2
c
4
, c
9
u
6
c
5
, c
6
, c
11
c
12
(u
3
+ u
2
+ 2u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
10
(y
3
− y
2
+ 2y − 1)
2
c
2
, c
5
, c
6
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y − 1)
2
c
4
, c
9
y
6
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.162359 + 0.986732I
b = −0.28492 − 1.73159I
6.04826 −8.87505 + 0.I
u = 0.215080 + 1.307140I
a = 0.500000 − 0.424452I
b = −0.592519 + 0.986732I
1.91067 − 2.82812I −13.06248 + 4.84887I
u = 0.215080 − 1.307140I
a = −0.162359 − 0.986732I
b = −0.28492 + 1.73159I
6.04826 −8.87505 + 0.I
u = 0.215080 − 1.307140I
a = 0.500000 + 0.424452I
b = −0.592519 − 0.986732I
1.91067 + 2.82812I −13.06248 − 4.84887I
u = 0.569840
a = 1.16236 + 0.98673I
b = 0.377439 + 0.320410I
1.91067 − 2.82812I −13.06248 + 4.84887I
u = 0.569840
a = 1.16236 − 0.98673I
b = 0.377439 − 0.320410I
1.91067 + 2.82812I −13.06248 − 4.84887I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
((u
3
+ u
2
− 1)
3
)(u
17
− 3u
16
+ ··· − 13u
2
+ 1)
· (u
72
− 15u
71
+ ··· − 73808u + 6497)
c
2
, c
8
((u
3
− u
2
+ 2u − 1)
3
)(u
17
− u
16
+ ··· + 2u + 1)(u
72
− 3u
71
+ ··· − 4u + 1)
c
3
, c
7
((u
3
+ u
2
− 1)
3
)(u
17
+ u
16
+ ··· − 2u + 1)(u
72
+ 3u
71
+ ··· − 604u + 137)
c
4
, c
9
u
9
(u
17
− 7u
16
+ ··· − 24u + 8)(u
36
+ 3u
35
+ ··· + 12u + 8)
2
c
5
, c
6
, c
11
c
12
((u
3
+ u
2
+ 2u + 1)
3
)(u
17
− u
16
+ ··· + 2u + 1)(u
72
− 3u
71
+ ··· − 4u + 1)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
((y
3
− y
2
+ 2y − 1)
3
)(y
17
+ 13y
16
+ ··· + 26y − 1)
· (y
72
+ 25y
71
+ ··· + 288840316y + 42211009)
c
2
, c
5
, c
6
c
8
, c
11
, c
12
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
17
+ 17y
16
+ ··· + 10y − 1)
· (y
72
+ 65y
71
+ ··· − 4y + 1)
c
3
, c
7
((y
3
− y
2
+ 2y − 1)
3
)(y
17
+ 5y
16
+ ··· + 10y − 1)
· (y
72
+ 5y
71
+ ··· + 440196y + 18769)
c
4
, c
9
y
9
(y
17
+ 7y
16
+ ··· + 256y − 64)(y
36
+ 21y
35
+ ··· + 752y + 64)
2
27
