12a
0973
(K12a
0973
)
A knot diagram
1
Linearized knot diagam
4 6 11 7 3 10 12 1 5 2 9 8
Solving Sequence
7,12
8 1
5,9
10 4 2 6 11 3
c
7
c
12
c
8
c
9
c
4
c
1
c
6
c
11
c
3
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.35250 × 10
19
u
68
+ 1.52019 × 10
20
u
67
+ ··· + 7.20665 × 10
16
b 1.45619 × 10
20
,
1.63550 × 10
20
u
68
1.16390 × 10
21
u
67
+ ··· + 7.20665 × 10
17
a + 1.58514 × 10
21
, u
69
8u
68
+ ··· 10u 10i
I
u
2
= h−418u
41
a + 4923u
41
+ ··· + 678a + 3495, 9u
41
a + 5u
41
+ ··· 7a 7, u
42
+ 3u
41
+ ··· + 5u
2
+ 1i
I
u
3
= h−49u
27
179u
26
+ ··· + b + 73, 49u
27
157u
26
+ ··· + 2a + 45, u
28
+ 5u
27
+ ··· + 5u 2i
I
u
4
= hb + a + 1, a
2
+ 2a + 2, u 1i
I
u
5
= hb
2
+ 1, a 1, u 1i
* 5 irreducible components of dim
C
= 0, with total 185 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−2.35 × 10
19
u
68
+ 1.52 × 10
20
u
67
+ · · · + 7.21 × 10
16
b 1.46 ×
10
20
, 1.64 × 10
20
u
68
1.16 × 10
21
u
67
+ · · · + 7.21 × 10
17
a + 1.59 ×
10
21
, u
69
8u
68
+ · · · 10u 10i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
u
u
3
+ u
a
5
=
226.943u
68
+ 1615.04u
67
+ ··· 4182.43u 2199.55
326.435u
68
2109.42u
67
+ ··· + 3194.47u + 2020.62
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
82.8459u
68
+ 525.174u
67
+ ··· 606.720u 434.740
47.5032u
68
+ 340.802u
67
+ ··· 867.752u 464.686
a
4
=
99.4919u
68
494.382u
67
+ ··· 987.960u 178.938
326.435u
68
2109.42u
67
+ ··· + 3194.47u + 2020.62
a
2
=
2.48706u
68
116.531u
67
+ ··· + 1591.68u + 652.740
237.970u
68
+ 1506.76u
67
+ ··· 2016.02u 1339.41
a
6
=
140.563u
68
+ 954.919u
67
+ ··· 1924.02u 1096.13
92.3884u
68
582.486u
67
+ ··· + 701.122u + 490.867
a
11
=
u
5
2u
3
+ u
u
7
3u
5
+ 2u
3
+ u
a
3
=
132.795u
68
+ 982.255u
67
+ ··· 2956.37u 1491.42
189.880u
68
1202.66u
67
+ ··· + 1575.95u + 1056.73
(ii) Obstruction class = 1
(iii) Cusp Shapes =
66317713337372322259
72066517868837587
u
68
395960086414396085656
72066517868837587
u
67
+ ··· +
214616945799686719930
72066517868837587
u +
234050075169388786136
72066517868837587
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
69
2u
68
+ ··· + 15u + 2
c
2
, c
5
u
69
17u
68
+ ··· 2616u + 178
c
3
, c
9
u
69
u
68
+ ··· + 65u + 7
c
6
, c
10
u
69
+ u
68
+ ··· + 4u + 1
c
7
, c
8
, c
12
u
69
+ 8u
68
+ ··· 10u + 10
c
11
u
69
24u
68
+ ··· 55370u + 3680
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
69
+ 34y
68
+ ··· 423y 4
c
2
, c
5
y
69
+ 37y
68
+ ··· + 290564y 31684
c
3
, c
9
y
69
y
68
+ ··· + 487y 49
c
6
, c
10
y
69
+ 41y
68
+ ··· 114y 1
c
7
, c
8
, c
12
y
69
64y
68
+ ··· 480y 100
c
11
y
69
24y
67
+ ··· 28395420y 13542400
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.868440 + 0.483662I
a = 0.912537 0.457992I
b = 0.78037 + 1.18617I
3.92123 10.99340I 0
u = 0.868440 0.483662I
a = 0.912537 + 0.457992I
b = 0.78037 1.18617I
3.92123 + 10.99340I 0
u = 1.004670 + 0.238764I
a = 0.594983 0.585884I
b = 0.69863 + 1.27589I
5.06148 0.24659I 0
u = 1.004670 0.238764I
a = 0.594983 + 0.585884I
b = 0.69863 1.27589I
5.06148 + 0.24659I 0
u = 1.012040 + 0.304922I
a = 0.039969 0.686585I
b = 0.302198 + 1.079960I
0.82632 + 4.88400I 0
u = 1.012040 0.304922I
a = 0.039969 + 0.686585I
b = 0.302198 1.079960I
0.82632 4.88400I 0
u = 0.796032 + 0.401340I
a = 0.849185 + 0.332533I
b = 0.747119 1.175180I
0.24939 5.31755I 0
u = 0.796032 0.401340I
a = 0.849185 0.332533I
b = 0.747119 + 1.175180I
0.24939 + 5.31755I 0
u = 0.159321 + 0.873285I
a = 0.645247 1.002530I
b = 0.075891 + 0.782690I
7.17042 4.82412I 0
u = 0.159321 0.873285I
a = 0.645247 + 1.002530I
b = 0.075891 0.782690I
7.17042 + 4.82412I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.016060 + 0.469890I
a = 0.023007 + 0.712554I
b = 0.343919 0.941847I
4.51207 + 9.58162I 0
u = 1.016060 0.469890I
a = 0.023007 0.712554I
b = 0.343919 + 0.941847I
4.51207 9.58162I 0
u = 0.266486 + 0.813768I
a = 0.12465 + 2.28012I
b = 0.93383 1.32092I
5.8290 + 15.5826I 0
u = 0.266486 0.813768I
a = 0.12465 2.28012I
b = 0.93383 + 1.32092I
5.8290 15.5826I 0
u = 0.264240 + 0.767756I
a = 0.02698 2.34538I
b = 0.94752 + 1.33761I
2.02592 + 9.53444I 12.0000 8.2979I
u = 0.264240 0.767756I
a = 0.02698 + 2.34538I
b = 0.94752 1.33761I
2.02592 9.53444I 12.0000 + 8.2979I
u = 0.735812 + 0.309797I
a = 0.358081 0.648381I
b = 0.027915 + 0.183287I
0.229732 0.511314I 12.00000 + 3.02569I
u = 0.735812 0.309797I
a = 0.358081 + 0.648381I
b = 0.027915 0.183287I
0.229732 + 0.511314I 12.00000 3.02569I
u = 0.327216 + 0.726908I
a = 1.08381 1.03727I
b = 0.163298 + 1.101030I
5.83717 + 3.57229I 3.24235 4.34300I
u = 0.327216 0.726908I
a = 1.08381 + 1.03727I
b = 0.163298 1.101030I
5.83717 3.57229I 3.24235 + 4.34300I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.182202 + 0.731968I
a = 0.12259 + 2.51031I
b = 0.97825 1.25630I
7.52448 + 3.97074I 2.97605 4.37299I
u = 0.182202 0.731968I
a = 0.12259 2.51031I
b = 0.97825 + 1.25630I
7.52448 3.97074I 2.97605 + 4.37299I
u = 0.141810 + 0.727491I
a = 0.73975 + 1.29757I
b = 0.071157 0.902395I
3.49350 1.03541I 6.28419 + 1.98961I
u = 0.141810 0.727491I
a = 0.73975 1.29757I
b = 0.071157 + 0.902395I
3.49350 + 1.03541I 6.28419 1.98961I
u = 1.258590 + 0.214133I
a = 1.82559 + 0.64253I
b = 0.614542 0.851057I
1.09011 2.55626I 0
u = 1.258590 0.214133I
a = 1.82559 0.64253I
b = 0.614542 + 0.851057I
1.09011 + 2.55626I 0
u = 0.619514 + 0.334758I
a = 0.442106 + 0.621239I
b = 0.453459 1.081140I
4.61730 + 0.35259I 6.07447 2.03240I
u = 0.619514 0.334758I
a = 0.442106 0.621239I
b = 0.453459 + 1.081140I
4.61730 0.35259I 6.07447 + 2.03240I
u = 1.308440 + 0.052584I
a = 0.813935 0.965678I
b = 0.741809 0.425202I
0.676833 + 0.903361I 0
u = 1.308440 0.052584I
a = 0.813935 + 0.965678I
b = 0.741809 + 0.425202I
0.676833 0.903361I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.213372 + 0.647007I
a = 0.187195 + 1.175120I
b = 0.239512 0.446632I
1.48768 2.82752I 10.61297 + 4.54088I
u = 0.213372 0.647007I
a = 0.187195 1.175120I
b = 0.239512 + 0.446632I
1.48768 + 2.82752I 10.61297 4.54088I
u = 1.313940 + 0.185825I
a = 0.263962 0.957942I
b = 0.23798 + 1.42678I
0.28087 + 2.43912I 0
u = 1.313940 0.185825I
a = 0.263962 + 0.957942I
b = 0.23798 1.42678I
0.28087 2.43912I 0
u = 1.331810 + 0.141866I
a = 0.525861 + 0.460107I
b = 0.711505 0.727008I
5.25079 + 0.90513I 0
u = 1.331810 0.141866I
a = 0.525861 0.460107I
b = 0.711505 + 0.727008I
5.25079 0.90513I 0
u = 1.322150 + 0.239265I
a = 0.416981 + 0.944061I
b = 0.42035 1.41450I
0.42998 + 3.50686I 0
u = 1.322150 0.239265I
a = 0.416981 0.944061I
b = 0.42035 + 1.41450I
0.42998 3.50686I 0
u = 1.329770 + 0.262879I
a = 1.009020 0.474295I
b = 0.425069 + 0.714282I
1.11700 2.51905I 0
u = 1.329770 0.262879I
a = 1.009020 + 0.474295I
b = 0.425069 0.714282I
1.11700 + 2.51905I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.357270 + 0.206241I
a = 0.96898 + 1.56134I
b = 1.53669 0.35028I
6.20600 3.52848I 0
u = 1.357270 0.206241I
a = 0.96898 1.56134I
b = 1.53669 + 0.35028I
6.20600 + 3.52848I 0
u = 0.057222 + 0.613921I
a = 0.45083 2.67794I
b = 0.445910 + 1.147090I
4.79032 0.41441I 3.11636 0.63359I
u = 0.057222 0.613921I
a = 0.45083 + 2.67794I
b = 0.445910 1.147090I
4.79032 + 0.41441I 3.11636 + 0.63359I
u = 1.372270 + 0.256005I
a = 0.258911 0.504237I
b = 0.273541 + 0.740903I
3.52844 + 6.11839I 0
u = 1.372270 0.256005I
a = 0.258911 + 0.504237I
b = 0.273541 0.740903I
3.52844 6.11839I 0
u = 1.337860 + 0.400221I
a = 0.675739 + 0.414936I
b = 0.119834 0.582435I
2.48250 + 0.25666I 0
u = 1.337860 0.400221I
a = 0.675739 0.414936I
b = 0.119834 + 0.582435I
2.48250 0.25666I 0
u = 1.368320 + 0.296862I
a = 1.36824 1.41998I
b = 1.15446 + 1.21553I
2.61702 7.69609I 0
u = 1.368320 0.296862I
a = 1.36824 + 1.41998I
b = 1.15446 1.21553I
2.61702 + 7.69609I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.395000 + 0.217224I
a = 1.024710 0.262655I
b = 0.511787 + 0.937399I
0.96256 2.32589I 0
u = 1.395000 0.217224I
a = 1.024710 + 0.262655I
b = 0.511787 0.937399I
0.96256 + 2.32589I 0
u = 1.41152 + 0.30993I
a = 1.25640 + 1.29535I
b = 1.10256 1.36810I
3.30905 13.44170I 0
u = 1.41152 0.30993I
a = 1.25640 1.29535I
b = 1.10256 + 1.36810I
3.30905 + 13.44170I 0
u = 1.41855 + 0.33131I
a = 1.15404 1.34303I
b = 1.06498 + 1.35771I
0.4669 19.7231I 0
u = 1.41855 0.33131I
a = 1.15404 + 1.34303I
b = 1.06498 1.35771I
0.4669 + 19.7231I 0
u = 1.47390 + 0.05110I
a = 0.222152 + 0.497540I
b = 0.921224 + 0.764166I
6.98532 + 4.23874I 0
u = 1.47390 0.05110I
a = 0.222152 0.497540I
b = 0.921224 0.764166I
6.98532 4.23874I 0
u = 1.44914 + 0.29118I
a = 0.886541 + 0.130386I
b = 0.038437 1.008160I
0.12573 7.29892I 0
u = 1.44914 0.29118I
a = 0.886541 0.130386I
b = 0.038437 + 1.008160I
0.12573 + 7.29892I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.149396 + 0.483213I
a = 0.92897 2.24105I
b = 1.205130 + 0.293627I
1.40154 + 0.91152I 19.9758 6.5138I
u = 0.149396 0.483213I
a = 0.92897 + 2.24105I
b = 1.205130 0.293627I
1.40154 0.91152I 19.9758 + 6.5138I
u = 1.51556 + 0.01247I
a = 0.216306 0.255235I
b = 0.892429 0.782962I
4.11378 + 9.97459I 0
u = 1.51556 0.01247I
a = 0.216306 + 0.255235I
b = 0.892429 + 0.782962I
4.11378 9.97459I 0
u = 0.022386 + 0.455647I
a = 1.54684 + 2.36603I
b = 0.268232 1.098250I
3.88008 0.05245I 3.33474 0.17274I
u = 0.022386 0.455647I
a = 1.54684 2.36603I
b = 0.268232 + 1.098250I
3.88008 + 0.05245I 3.33474 + 0.17274I
u = 1.63858 + 0.03272I
a = 0.0553486 + 0.1159980I
b = 0.070510 0.151550I
8.56507 + 1.52283I 0
u = 1.63858 0.03272I
a = 0.0553486 0.1159980I
b = 0.070510 + 0.151550I
8.56507 1.52283I 0
u = 0.356524
a = 1.04146
b = 0.194341
0.630482 15.9080
11
II. I
u
2
= h−418u
41
a + 4923u
41
+ · · · + 678a + 3495, 9u
41
a + 5u
41
+ · · ·
7a 7, u
42
+ 3u
41
+ · · · + 5u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
u
u
3
+ u
a
5
=
a
0.537275au
41
6.32776u
41
+ ··· 0.871465a 4.49229
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
0.320051au
41
+ 1.71080u
41
+ ··· 0.327763a + 1.33033
2.78792au
41
+ 0.537275u
41
+ ··· + 2.97558a + 0.128535
a
4
=
0.537275au
41
6.32776u
41
+ ··· + 0.128535a 4.49229
0.537275au
41
6.32776u
41
+ ··· 0.871465a 4.49229
a
2
=
6.32776au
41
+ 4.83033u
41
+ ··· 4.49229a + 5.38046
1
a
6
=
0.564267au
41
+ 4.49614u
41
+ ··· + 0.795630a + 4.91774
1.07841au
41
0.965296u
41
+ ··· 0.160668a + 1.24036
a
11
=
u
5
2u
3
+ u
u
7
3u
5
+ 2u
3
+ u
a
3
=
0.465296au
41
5.21208u
41
+ ··· + 0.259640a 4.02442
0.262211au
41
4.06427u
41
+ ··· 0.406170a 3.70437
(ii) Obstruction class = 1
(iii) Cusp Shapes = 23u
41
44u
40
+ ··· + 15u 35
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
84
13u
83
+ ··· 1468u + 136
c
2
, c
5
(u
42
+ 13u
41
+ ··· + 12u + 1)
2
c
3
, c
9
u
84
u
83
+ ··· + 192u + 46
c
6
, c
10
u
84
+ 7u
83
+ ··· + 8u + 2
c
7
, c
8
, c
12
(u
42
3u
41
+ ··· + 5u
2
+ 1)
2
c
11
(u
42
+ 15u
41
+ ··· + 152u + 16)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
84
21y
83
+ ··· + 334320y + 18496
c
2
, c
5
(y
42
+ 27y
41
+ ··· + 6y + 1)
2
c
3
, c
9
y
84
+ 13y
83
+ ··· 57840y + 2116
c
6
, c
10
y
84
11y
83
+ ··· 56y + 4
c
7
, c
8
, c
12
(y
42
37y
41
+ ··· + 10y + 1)
2
c
11
(y
42
+ 9y
41
+ ··· 448y + 256)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.960240 + 0.479028I
a = 0.418127 + 0.776729I
b = 0.348636 0.818060I
0.52500 + 1.63086I 13.9232 7.9008I
u = 0.960240 + 0.479028I
a = 0.647743 + 0.156432I
b = 0.645086 + 0.597788I
0.52500 + 1.63086I 13.9232 7.9008I
u = 0.960240 0.479028I
a = 0.418127 0.776729I
b = 0.348636 + 0.818060I
0.52500 1.63086I 13.9232 + 7.9008I
u = 0.960240 0.479028I
a = 0.647743 0.156432I
b = 0.645086 0.597788I
0.52500 1.63086I 13.9232 + 7.9008I
u = 0.782440 + 0.467392I
a = 0.681568 0.667303I
b = 0.302811 + 0.722288I
0.177946 0.302389I 17.5842 + 3.6764I
u = 0.782440 + 0.467392I
a = 0.100018 0.271626I
b = 0.249493 0.359059I
0.177946 0.302389I 17.5842 + 3.6764I
u = 0.782440 0.467392I
a = 0.681568 + 0.667303I
b = 0.302811 0.722288I
0.177946 + 0.302389I 17.5842 3.6764I
u = 0.782440 0.467392I
a = 0.100018 + 0.271626I
b = 0.249493 + 0.359059I
0.177946 + 0.302389I 17.5842 3.6764I
u = 0.239459 + 0.836071I
a = 0.61659 + 1.30013I
b = 0.928490 0.762052I
2.74325 6.31693I 8.89354 + 10.94201I
u = 0.239459 + 0.836071I
a = 0.11258 1.88230I
b = 0.499186 + 0.965297I
2.74325 6.31693I 8.89354 + 10.94201I
15
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.239459 0.836071I
a = 0.61659 1.30013I
b = 0.928490 + 0.762052I
2.74325 + 6.31693I 8.89354 10.94201I
u = 0.239459 0.836071I
a = 0.11258 + 1.88230I
b = 0.499186 0.965297I
2.74325 + 6.31693I 8.89354 10.94201I
u = 0.262054 + 0.762195I
a = 0.024696 1.026100I
b = 0.641434 + 0.625699I
1.49261 3.94030I 12.21696 + 2.22964I
u = 0.262054 + 0.762195I
a = 0.06445 + 1.97334I
b = 0.577595 1.070350I
1.49261 3.94030I 12.21696 + 2.22964I
u = 0.262054 0.762195I
a = 0.024696 + 1.026100I
b = 0.641434 0.625699I
1.49261 + 3.94030I 12.21696 2.22964I
u = 0.262054 0.762195I
a = 0.06445 1.97334I
b = 0.577595 + 1.070350I
1.49261 + 3.94030I 12.21696 2.22964I
u = 1.158050 + 0.323812I
a = 1.175940 0.016766I
b = 0.83974 1.30924I
3.59230 + 1.50157I 0
u = 1.158050 + 0.323812I
a = 0.185663 1.293630I
b = 0.153647 + 0.885810I
3.59230 + 1.50157I 0
u = 1.158050 0.323812I
a = 1.175940 + 0.016766I
b = 0.83974 + 1.30924I
3.59230 1.50157I 0
u = 1.158050 0.323812I
a = 0.185663 + 1.293630I
b = 0.153647 0.885810I
3.59230 1.50157I 0
16
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.768285 + 0.169398I
a = 0.977633 0.369659I
b = 0.219726 + 0.857795I
0.149243 + 0.024529I 14.2018 + 0.3715I
u = 0.768285 + 0.169398I
a = 0.573528 + 0.091019I
b = 0.035955 0.712483I
0.149243 + 0.024529I 14.2018 + 0.3715I
u = 0.768285 0.169398I
a = 0.977633 + 0.369659I
b = 0.219726 0.857795I
0.149243 0.024529I 14.2018 0.3715I
u = 0.768285 0.169398I
a = 0.573528 0.091019I
b = 0.035955 + 0.712483I
0.149243 0.024529I 14.2018 0.3715I
u = 0.095814 + 0.752969I
a = 1.01912 + 1.91294I
b = 0.224862 0.729633I
6.81946 5.41964I 0.76314 + 6.46458I
u = 0.095814 + 0.752969I
a = 1.18382 2.37183I
b = 1.16460 + 1.37599I
6.81946 5.41964I 0.76314 + 6.46458I
u = 0.095814 0.752969I
a = 1.01912 1.91294I
b = 0.224862 + 0.729633I
6.81946 + 5.41964I 0.76314 6.46458I
u = 0.095814 0.752969I
a = 1.18382 + 2.37183I
b = 1.16460 1.37599I
6.81946 + 5.41964I 0.76314 6.46458I
u = 1.257660 + 0.148327I
a = 0.342248 + 1.357940I
b = 2.04472 + 0.19287I
0.08089 4.23886I 0
u = 1.257660 + 0.148327I
a = 1.84195 1.50760I
b = 0.195600 + 0.251632I
0.08089 4.23886I 0
17
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.257660 0.148327I
a = 0.342248 1.357940I
b = 2.04472 0.19287I
0.08089 + 4.23886I 0
u = 1.257660 0.148327I
a = 1.84195 + 1.50760I
b = 0.195600 0.251632I
0.08089 + 4.23886I 0
u = 0.300937 + 0.614729I
a = 0.451308 0.124828I
b = 0.470554 + 0.414789I
1.25837 3.52745I 12.3965 + 7.5906I
u = 0.300937 + 0.614729I
a = 0.49117 + 2.22423I
b = 0.256252 1.219250I
1.25837 3.52745I 12.3965 + 7.5906I
u = 0.300937 0.614729I
a = 0.451308 + 0.124828I
b = 0.470554 0.414789I
1.25837 + 3.52745I 12.3965 7.5906I
u = 0.300937 0.614729I
a = 0.49117 2.22423I
b = 0.256252 + 1.219250I
1.25837 + 3.52745I 12.3965 7.5906I
u = 1.343140 + 0.147248I
a = 0.676553 + 1.020740I
b = 0.245033 0.359099I
5.35856 + 0.88423I 0
u = 1.343140 + 0.147248I
a = 0.409698 0.285106I
b = 1.23802 0.82397I
5.35856 + 0.88423I 0
u = 1.343140 0.147248I
a = 0.676553 1.020740I
b = 0.245033 + 0.359099I
5.35856 0.88423I 0
u = 1.343140 0.147248I
a = 0.409698 + 0.285106I
b = 1.23802 + 0.82397I
5.35856 0.88423I 0
18
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.350600 + 0.156105I
a = 1.111500 0.042964I
b = 0.966724 0.612624I
2.69089 + 2.86448I 0
u = 1.350600 + 0.156105I
a = 1.09270 1.48631I
b = 1.16188 + 1.45455I
2.69089 + 2.86448I 0
u = 1.350600 0.156105I
a = 1.111500 + 0.042964I
b = 0.966724 + 0.612624I
2.69089 2.86448I 0
u = 1.350600 0.156105I
a = 1.09270 + 1.48631I
b = 1.16188 1.45455I
2.69089 2.86448I 0
u = 1.325060 + 0.305145I
a = 1.65141 0.92720I
b = 0.308670 + 0.576187I
2.35941 + 9.23081I 0
u = 1.325060 + 0.305145I
a = 0.93668 + 1.64637I
b = 1.45134 1.41737I
2.35941 + 9.23081I 0
u = 1.325060 0.305145I
a = 1.65141 + 0.92720I
b = 0.308670 0.576187I
2.35941 9.23081I 0
u = 1.325060 0.305145I
a = 0.93668 1.64637I
b = 1.45134 + 1.41737I
2.35941 9.23081I 0
u = 1.354450 + 0.204945I
a = 0.653795 + 1.227520I
b = 1.64085 + 0.08495I
6.18100 3.49130I 0
u = 1.354450 + 0.204945I
a = 1.03958 + 1.68431I
b = 1.162330 0.617434I
6.18100 3.49130I 0
19
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.354450 0.204945I
a = 0.653795 1.227520I
b = 1.64085 0.08495I
6.18100 + 3.49130I 0
u = 1.354450 0.204945I
a = 1.03958 1.68431I
b = 1.162330 + 0.617434I
6.18100 + 3.49130I 0
u = 1.353640 + 0.241636I
a = 0.420027 1.135670I
b = 2.15100 0.88032I
1.56074 9.78519I 0
u = 1.353640 + 0.241636I
a = 0.82513 2.14053I
b = 0.577643 + 0.735027I
1.56074 9.78519I 0
u = 1.353640 0.241636I
a = 0.420027 + 1.135670I
b = 2.15100 + 0.88032I
1.56074 + 9.78519I 0
u = 1.353640 0.241636I
a = 0.82513 + 2.14053I
b = 0.577643 0.735027I
1.56074 + 9.78519I 0
u = 0.144544 + 0.590446I
a = 2.59218 0.33124I
b = 1.94312 + 0.50922I
3.19731 + 6.71563I 7.9709 11.9381I
u = 0.144544 + 0.590446I
a = 0.59156 + 3.42387I
b = 0.526695 0.528784I
3.19731 + 6.71563I 7.9709 11.9381I
u = 0.144544 0.590446I
a = 2.59218 + 0.33124I
b = 1.94312 0.50922I
3.19731 6.71563I 7.9709 + 11.9381I
u = 0.144544 0.590446I
a = 0.59156 3.42387I
b = 0.526695 + 0.528784I
3.19731 6.71563I 7.9709 + 11.9381I
20
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.385400 + 0.231075I
a = 0.842146 0.149667I
b = 0.652354 0.129474I
4.04574 + 6.56231I 0
u = 1.385400 + 0.231075I
a = 1.13820 0.87061I
b = 0.39448 + 1.58816I
4.04574 + 6.56231I 0
u = 1.385400 0.231075I
a = 0.842146 + 0.149667I
b = 0.652354 + 0.129474I
4.04574 6.56231I 0
u = 1.385400 0.231075I
a = 1.13820 + 0.87061I
b = 0.39448 1.58816I
4.04574 6.56231I 0
u = 1.40816 + 0.31027I
a = 0.750785 + 0.777943I
b = 0.881123 0.618446I
3.81728 + 7.83428I 0
u = 1.40816 + 0.31027I
a = 0.87212 1.16243I
b = 0.786301 + 1.156800I
3.81728 + 7.83428I 0
u = 1.40816 0.31027I
a = 0.750785 0.777943I
b = 0.881123 + 0.618446I
3.81728 7.83428I 0
u = 1.40816 0.31027I
a = 0.87212 + 1.16243I
b = 0.786301 1.156800I
3.81728 7.83428I 0
u = 1.40979 + 0.34355I
a = 0.534093 1.069130I
b = 1.138840 + 0.792011I
2.49752 + 10.57050I 0
u = 1.40979 + 0.34355I
a = 0.94022 + 1.18948I
b = 0.621719 1.029070I
2.49752 + 10.57050I 0
21
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.40979 0.34355I
a = 0.534093 + 1.069130I
b = 1.138840 0.792011I
2.49752 10.57050I 0
u = 1.40979 0.34355I
a = 0.94022 1.18948I
b = 0.621719 + 1.029070I
2.49752 10.57050I 0
u = 1.48272 + 0.02635I
a = 0.431060 + 0.243095I
b = 0.732925 0.295301I
7.72912 + 1.38578I 0
u = 1.48272 + 0.02635I
a = 0.248658 + 0.110722I
b = 0.978134 0.192963I
7.72912 + 1.38578I 0
u = 1.48272 0.02635I
a = 0.431060 0.243095I
b = 0.732925 + 0.295301I
7.72912 1.38578I 0
u = 1.48272 0.02635I
a = 0.248658 0.110722I
b = 0.978134 + 0.192963I
7.72912 1.38578I 0
u = 0.144890 + 0.477535I
a = 1.27863 1.51403I
b = 1.339940 + 0.096804I
1.40479 + 0.89511I 16.7235 7.1356I
u = 0.144890 + 0.477535I
a = 0.67161 2.68352I
b = 0.951172 + 0.346493I
1.40479 + 0.89511I 16.7235 7.1356I
u = 0.144890 0.477535I
a = 1.27863 + 1.51403I
b = 1.339940 0.096804I
1.40479 0.89511I 16.7235 + 7.1356I
u = 0.144890 0.477535I
a = 0.67161 + 2.68352I
b = 0.951172 0.346493I
1.40479 0.89511I 16.7235 + 7.1356I
22
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.224607 + 0.302512I
a = 1.118150 0.435820I
b = 0.962841 + 0.477795I
2.19147 4.73089I 12.96994 + 0.46313I
u = 0.224607 + 0.302512I
a = 0.91977 + 4.19208I
b = 0.944884 0.764273I
2.19147 4.73089I 12.96994 + 0.46313I
u = 0.224607 0.302512I
a = 1.118150 + 0.435820I
b = 0.962841 0.477795I
2.19147 + 4.73089I 12.96994 0.46313I
u = 0.224607 0.302512I
a = 0.91977 4.19208I
b = 0.944884 + 0.764273I
2.19147 + 4.73089I 12.96994 0.46313I
23
III. I
u
3
= h−49u
27
179u
26
+ · · · + b + 73, 49u
27
157u
26
+ · · · + 2a +
45, u
28
+ 5u
27
+ · · · + 5u 2i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
u
u
3
+ u
a
5
=
24.5000u
27
+ 78.5000u
26
+ ··· + 62.5000u 22.5000
49u
27
+ 179u
26
+ ··· + 234u 73
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
17
2
u
27
+
67
2
u
26
+ ··· +
95
2
u
29
2
u
27
+ 4u
26
+ ··· + 5u 1
a
4
=
73.5000u
27
+ 257.500u
26
+ ··· + 296.500u 95.5000
49u
27
+ 179u
26
+ ··· + 234u 73
a
2
=
17.5000u
27
+ 62.5000u
26
+ ··· + 88.5000u 27.5000
9u
27
+ 34u
26
+ ··· + 46u 15
a
6
=
28.5000u
27
+ 107.500u
26
+ ··· + 150.500u 44.5000
7u
27
+ 27u
26
+ ··· + 44u 13
a
11
=
u
5
2u
3
+ u
u
7
3u
5
+ 2u
3
+ u
a
3
=
28.5000u
27
+ 93.5000u
26
+ ··· + 84.5000u 29.5000
32u
27
+ 116u
26
+ ··· + 150u 47
(ii) Obstruction class = 1
(iii) Cusp Shapes = 129u
27
478u
26
+ 881u
25
+ 4666u
24
2235u
23
20091u
22
+
3205u
21
+ 49483u
20
8921u
19
73524u
18
+ 33538u
17
+ 56824u
16
71086u
15
+
6166u
14
+ 75329u
13
60825u
12
23342u
11
+ 50941u
10
27703u
9
3414u
8
+ 25038u
7
14215u
6
634u
5
+ 2218u
4
4157u
3
+ 1496u
2
652u + 188
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
28
2u
27
+ ··· 2u + 1
c
2
u
28
14u
27
+ ··· 61u + 4
c
3
, c
9
u
28
+ u
27
+ ··· 3u
2
1
c
5
u
28
+ 14u
27
+ ··· + 61u + 4
c
6
, c
10
u
28
+ u
27
+ ··· + u 1
c
7
, c
8
u
28
+ 5u
27
+ ··· + 5u 2
c
11
u
28
+ 15u
27
+ ··· + 429u + 50
c
12
u
28
5u
27
+ ··· 5u 2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
18y
27
+ ··· + 10y + 1
c
2
, c
5
y
28
+ 12y
27
+ ··· 601y + 16
c
3
, c
9
y
28
+ 11y
27
+ ··· + 6y + 1
c
6
, c
10
y
28
11y
27
+ ··· + 11y + 1
c
7
, c
8
, c
12
y
28
29y
27
+ ··· + 19y + 4
c
11
y
28
9y
27
+ ··· + 2459y + 2500
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.877488 + 0.532355I
a = 0.469607 0.360347I
b = 0.313041 + 0.719408I
0.376250 + 0.203371I 6.98213 3.63755I
u = 0.877488 0.532355I
a = 0.469607 + 0.360347I
b = 0.313041 0.719408I
0.376250 0.203371I 6.98213 + 3.63755I
u = 0.267177 + 0.824004I
a = 0.01691 + 1.46353I
b = 0.555226 0.879438I
2.28640 4.92867I 7.87391 + 6.42165I
u = 0.267177 0.824004I
a = 0.01691 1.46353I
b = 0.555226 + 0.879438I
2.28640 + 4.92867I 7.87391 6.42165I
u = 1.143300 + 0.390612I
a = 0.424056 + 0.355571I
b = 0.452229 0.657406I
1.89570 + 1.31467I 8.82064 3.97086I
u = 1.143300 0.390612I
a = 0.424056 0.355571I
b = 0.452229 + 0.657406I
1.89570 1.31467I 8.82064 + 3.97086I
u = 0.083365 + 0.754526I
a = 0.70347 1.65365I
b = 0.843669 + 0.619007I
5.17011 5.43287I 6.79731 + 6.43533I
u = 0.083365 0.754526I
a = 0.70347 + 1.65365I
b = 0.843669 0.619007I
5.17011 + 5.43287I 6.79731 6.43533I
u = 1.299390 + 0.128660I
a = 0.710161 0.349638I
b = 1.012100 + 0.597930I
4.74917 1.24347I 8.84968 + 7.10640I
u = 1.299390 0.128660I
a = 0.710161 + 0.349638I
b = 1.012100 0.597930I
4.74917 + 1.24347I 8.84968 7.10640I
27
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 1.309960 + 0.153721I
a = 1.22846 + 1.53140I
b = 1.342480 0.088387I
1.10542 3.46605I 14.1620 + 2.9245I
u = 1.309960 0.153721I
a = 1.22846 1.53140I
b = 1.342480 + 0.088387I
1.10542 + 3.46605I 14.1620 2.9245I
u = 1.326270 + 0.293409I
a = 0.81815 + 1.57284I
b = 1.141380 0.619740I
0.74358 + 9.17814I 12.0776 8.4771I
u = 1.326270 0.293409I
a = 0.81815 1.57284I
b = 1.141380 + 0.619740I
0.74358 9.17814I 12.0776 + 8.4771I
u = 1.354790 + 0.209495I
a = 1.00567 1.76892I
b = 1.68788 + 0.34102I
5.88008 + 3.48216I 1.41167 0.94003I
u = 1.354790 0.209495I
a = 1.00567 + 1.76892I
b = 1.68788 0.34102I
5.88008 3.48216I 1.41167 + 0.94003I
u = 1.383060 + 0.180942I
a = 0.598183 + 0.238833I
b = 0.811390 0.408562I
1.94211 7.75510I 13.1188 + 7.1328I
u = 1.383060 0.180942I
a = 0.598183 0.238833I
b = 0.811390 + 0.408562I
1.94211 + 7.75510I 13.1188 7.1328I
u = 1.45160
a = 0.461569
b = 0.878416
8.14287 21.0860
u = 1.41716 + 0.33447I
a = 0.777192 0.947146I
b = 0.745151 + 0.921906I
3.06763 + 9.10984I 12.8570 6.9062I
28
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 1.41716 0.33447I
a = 0.777192 + 0.947146I
b = 0.745151 0.921906I
3.06763 9.10984I 12.8570 + 6.9062I
u = 0.131202 + 0.507634I
a = 1.24475 + 2.50073I
b = 1.37990 0.32442I
1.129910 0.800287I 5.73261 3.91984I
u = 0.131202 0.507634I
a = 1.24475 2.50073I
b = 1.37990 + 0.32442I
1.129910 + 0.800287I 5.73261 + 3.91984I
u = 0.077747 + 0.422589I
a = 2.09913 2.33438I
b = 1.039480 + 0.164835I
2.89795 + 5.51987I 6.44293 5.45114I
u = 0.077747 0.422589I
a = 2.09913 + 2.33438I
b = 1.039480 0.164835I
2.89795 5.51987I 6.44293 + 5.45114I
u = 0.353314
a = 0.860948
b = 0.788838
2.02232 20.3740
u = 1.64990 + 0.04012I
a = 0.0309221 + 0.0130317I
b = 0.103705 0.292446I
8.50737 + 1.47561I 0. + 32.8247I
u = 1.64990 0.04012I
a = 0.0309221 0.0130317I
b = 0.103705 + 0.292446I
8.50737 1.47561I 0. 32.8247I
29
IV. I
u
4
= hb + a + 1, a
2
+ 2a + 2, u 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
1
a
8
=
1
1
a
1
=
1
0
a
5
=
a
a 1
a
9
=
0
1
a
10
=
2a + 2
a 1
a
4
=
1
a 1
a
2
=
a 2
1
a
6
=
1
1
a
11
=
0
1
a
3
=
1
a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
u
2
+ 1
c
3
, c
12
(u + 1)
2
c
7
, c
8
(u 1)
2
c
9
, c
10
u
2
2u + 2
c
11
u
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
(y + 1)
2
c
3
, c
7
, c
8
c
12
(y 1)
2
c
9
, c
10
y
2
+ 4
c
11
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.00000 + 1.00000I
b = 1.000000I
1.64493 8.00000
u = 1.00000
a = 1.00000 1.00000I
b = 1.000000I
1.64493 8.00000
33
V. I
u
5
= hb
2
+ 1, a 1, u 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
1
a
8
=
1
1
a
1
=
1
0
a
5
=
1
b
a
9
=
0
1
a
10
=
1
b + 1
a
4
=
b + 1
b
a
2
=
b
1
a
6
=
b + 2
2b
a
11
=
0
1
a
3
=
b + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
10
u
2
+ 1
c
3
, c
6
u
2
2u + 2
c
7
, c
8
(u 1)
2
c
9
, c
12
(u + 1)
2
c
11
u
2
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
10
(y + 1)
2
c
3
, c
6
y
2
+ 4
c
7
, c
8
, c
9
c
12
(y 1)
2
c
11
y
2
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 1.000000I
1.64493 8.00000
u = 1.00000
a = 1.00000
b = 1.000000I
1.64493 8.00000
37
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
+ 1)
2
)(u
28
2u
27
+ ··· 2u + 1)(u
69
2u
68
+ ··· + 15u + 2)
· (u
84
13u
83
+ ··· 1468u + 136)
c
2
((u
2
+ 1)
2
)(u
28
14u
27
+ ··· 61u + 4)(u
42
+ 13u
41
+ ··· + 12u + 1)
2
· (u
69
17u
68
+ ··· 2616u + 178)
c
3
, c
9
((u + 1)
2
)(u
2
2u + 2)(u
28
+ u
27
+ ··· 3u
2
1)
· (u
69
u
68
+ ··· + 65u + 7)(u
84
u
83
+ ··· + 192u + 46)
c
5
((u
2
+ 1)
2
)(u
28
+ 14u
27
+ ··· + 61u + 4)(u
42
+ 13u
41
+ ··· + 12u + 1)
2
· (u
69
17u
68
+ ··· 2616u + 178)
c
6
, c
10
(u
2
+ 1)(u
2
2u + 2)(u
28
+ u
27
+ ··· + u 1)(u
69
+ u
68
+ ··· + 4u + 1)
· (u
84
+ 7u
83
+ ··· + 8u + 2)
c
7
, c
8
((u 1)
4
)(u
28
+ 5u
27
+ ··· + 5u 2)(u
42
3u
41
+ ··· + 5u
2
+ 1)
2
· (u
69
+ 8u
68
+ ··· 10u + 10)
c
11
u
4
(u
28
+ 15u
27
+ ··· + 429u + 50)(u
42
+ 15u
41
+ ··· + 152u + 16)
2
· (u
69
24u
68
+ ··· 55370u + 3680)
c
12
((u + 1)
4
)(u
28
5u
27
+ ··· 5u 2)(u
42
3u
41
+ ··· + 5u
2
+ 1)
2
· (u
69
+ 8u
68
+ ··· 10u + 10)
38
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y + 1)
4
)(y
28
18y
27
+ ··· + 10y + 1)(y
69
+ 34y
68
+ ··· 423y 4)
· (y
84
21y
83
+ ··· + 334320y + 18496)
c
2
, c
5
((y + 1)
4
)(y
28
+ 12y
27
+ ··· 601y + 16)
· ((y
42
+ 27y
41
+ ··· + 6y + 1)
2
)(y
69
+ 37y
68
+ ··· + 290564y 31684)
c
3
, c
9
((y 1)
2
)(y
2
+ 4)(y
28
+ 11y
27
+ ··· + 6y + 1)
· (y
69
y
68
+ ··· + 487y 49)(y
84
+ 13y
83
+ ··· 57840y + 2116)
c
6
, c
10
((y + 1)
2
)(y
2
+ 4)(y
28
11y
27
+ ··· + 11y + 1)
· (y
69
+ 41y
68
+ ··· 114y 1)(y
84
11y
83
+ ··· 56y + 4)
c
7
, c
8
, c
12
((y 1)
4
)(y
28
29y
27
+ ··· + 19y + 4)(y
42
37y
41
+ ··· + 10y + 1)
2
· (y
69
64y
68
+ ··· 480y 100)
c
11
y
4
(y
28
9y
27
+ ··· + 2459y + 2500)
· (y
42
+ 9y
41
+ ··· 448y + 256)
2
· (y
69
24y
67
+ ··· 28395420y 13542400)
39