12a
1200
(K12a
1200
)
A knot diagram
1
Linearized knot diagam
4 10 12 9 2 11 3 1 5 7 6 8
Solving Sequence
1,4 2,9
5 6 10 8 12 3 7 11
c
1
c
4
c
5
c
9
c
8
c
12
c
3
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.47770 × 10
71
u
37
− 6.71387 × 10
72
u
36
+ ··· + 8.89209 × 10
71
b + 3.00786 × 10
74
,
− 3.75982 × 10
73
u
37
− 1.01509 × 10
75
u
36
+ ··· + 1.35160 × 10
74
a + 6.53327 × 10
76
,
u
38
+ 28u
37
+ ··· − 20672u − 1216i
I
u
2
= h1.23963 × 10
66
u
44
− 1.60230 × 10
67
u
43
+ ··· + 2.01296 × 10
66
b − 2.34540 × 10
67
,
2.22813 × 10
69
au
44
+ 2.15790 × 10
69
u
44
+ ··· + 2.36150 × 10
72
a − 1.72905 × 10
72
,
u
45
− 14u
44
+ ··· + 647u − 95i
I
u
3
= h25355163523791u
16
− 260299596465976u
15
+ ··· + 37179633494568b + 433910338329094,
433910338329094u
16
− 4443396595810751u
15
+ ··· + 483335235429384a + 6883326552789727,
u
17
− 11u
16
+ ··· + 61u − 13i
I
u
4
= hu
6
+ u
3
+ au + 2u
2
+ b, u
5
a − 2u
6
+ 2u
5
− u
4
+ u
2
a − 4u
3
+ a
2
+ 2au + 2u − 4, u
7
+ 2u
4
+ 2u
3
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 159 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−2.48 × 10
71
u
37
− 6.71 × 10
72
u
36
+ · · · + 8.89 × 10
71
b + 3.01 ×
10
74
, −3.76 × 10
73
u
37
− 1.02 × 10
75
u
36
+ · · · + 1.35 × 10
74
a + 6.53 ×
10
76
, u
38
+ 28u
37
+ · · · − 20672u − 1216i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
0.278176u
37
+ 7.51030u
36
+ ··· − 7216.69u − 483.374
0.278641u
37
+ 7.55038u
36
+ ··· − 5267.09u − 338.262
a
5
=
0.424357u
37
+ 11.7318u
36
+ ··· − 10457.3u − 615.084
0.150150u
37
+ 4.27796u
36
+ ··· − 8156.22u − 516.018
a
6
=
0.200449u
37
+ 5.56029u
36
+ ··· − 4888.93u − 281.649
0.156639u
37
+ 4.39770u
36
+ ··· − 6405.46u − 397.016
a
10
=
1.33444u
37
+ 36.6406u
36
+ ··· − 35526.8u − 2221.43
0.472053u
37
+ 13.1388u
36
+ ··· − 19942.2u − 1283.85
a
8
=
−0.000464714u
37
− 0.0400856u
36
+ ··· − 1949.60u − 145.111
0.278641u
37
+ 7.55038u
36
+ ··· − 5267.09u − 338.262
a
12
=
−0.274206u
37
− 7.45387u
36
+ ··· + 2300.05u + 100.066
−0.150150u
37
− 4.27796u
36
+ ··· + 8157.22u + 516.018
a
3
=
0.623672u
37
+ 17.0040u
36
+ ··· − 7186.67u − 372.024
0.332004u
37
+ 9.32506u
36
+ ··· − 14197.7u − 889.830
a
7
=
0.936820u
37
+ 25.3070u
36
+ ··· − 10048.7u − 559.487
0.968072u
37
+ 26.7304u
36
+ ··· − 27389.6u − 1696.11
a
11
=
−0.0194774u
37
− 0.714546u
36
+ ··· + 2524.43u + 121.508
0.496891u
37
+ 13.3900u
36
+ ··· − 1264.32u − 16.4375
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0832928u
37
+ 1.12467u
36
+ ··· + 28762.4u + 1917.32
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
− 28u
37
+ ··· + 20672u − 1216
c
2
, c
7
u
38
+ u
37
+ ··· + 3u − 1
c
3
, c
5
u
38
− 3u
37
+ ··· + 54u − 7
c
4
, c
8
, c
9
c
12
u
38
− 19u
36
+ ··· − u + 1
c
6
, c
10
, c
11
u
38
+ 8u
37
+ ··· − 50u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
− 4y
37
+ ··· + 24750464y + 1478656
c
2
, c
7
y
38
− 37y
37
+ ··· − 51y + 1
c
3
, c
5
y
38
+ 7y
37
+ ··· + 948y + 49
c
4
, c
8
, c
9
c
12
y
38
− 38y
37
+ ··· − 35y + 1
c
6
, c
10
, c
11
y
38
+ 36y
37
+ ··· − 316y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682195 + 0.762723I
a = −0.498556 − 1.296080I
b = −1.32867 − 0.50392I
5.16261 + 6.22750I 0
u = −0.682195 − 0.762723I
a = −0.498556 + 1.296080I
b = −1.32867 + 0.50392I
5.16261 − 6.22750I 0
u = −0.948277 + 0.506166I
a = 0.357357 − 0.741251I
b = −0.036323 − 0.883794I
4.64617 + 7.95698I 0
u = −0.948277 − 0.506166I
a = 0.357357 + 0.741251I
b = −0.036323 + 0.883794I
4.64617 − 7.95698I 0
u = −0.294503 + 0.866980I
a = −0.585565 + 0.337901I
b = 0.120503 + 0.607186I
6.70670 − 3.19363I 0
u = −0.294503 − 0.866980I
a = −0.585565 − 0.337901I
b = 0.120503 − 0.607186I
6.70670 + 3.19363I 0
u = −0.809538 + 0.384223I
a = −0.450170 + 0.858186I
b = −0.034695 + 0.867701I
−1.50443 + 3.87717I 0. − 6.90669I
u = −0.809538 − 0.384223I
a = −0.450170 − 0.858186I
b = −0.034695 − 0.867701I
−1.50443 − 3.87717I 0. + 6.90669I
u = −0.078087 + 1.138990I
a = 0.084984 − 0.995053I
b = −1.126720 − 0.174497I
7.14423 − 1.93403I 0
u = −0.078087 − 1.138990I
a = 0.084984 + 0.995053I
b = −1.126720 + 0.174497I
7.14423 + 1.93403I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19263
a = −1.16981
b = −1.39515
8.14584 0
u = 1.19671
a = 0.140227
b = −0.167811
−2.28978 0
u = −0.409471 + 0.689495I
a = 0.28064 + 1.47948I
b = 1.135010 + 0.412302I
2.51458 + 1.40446I 0. + 1.66220I
u = −0.409471 − 0.689495I
a = 0.28064 − 1.47948I
b = 1.135010 − 0.412302I
2.51458 − 1.40446I 0. − 1.66220I
u = −0.486590 + 0.508142I
a = 1.33553 + 1.63331I
b = 1.47981 + 0.11611I
13.69540 + 0.47437I 10.57797 + 0.I
u = −0.486590 − 0.508142I
a = 1.33553 − 1.63331I
b = 1.47981 − 0.11611I
13.69540 − 0.47437I 10.57797 + 0.I
u = 1.254080 + 0.517048I
a = −0.211408 − 0.032930I
b = 0.248096 + 0.150605I
1.85469 − 1.68737I 0
u = 1.254080 − 0.517048I
a = −0.211408 + 0.032930I
b = 0.248096 − 0.150605I
1.85469 + 1.68737I 0
u = −0.534423 + 0.232538I
a = 0.849709 − 1.051240I
b = 0.209652 − 0.759395I
−0.216786 − 1.102140I 6.06046 − 0.98798I
u = −0.534423 − 0.232538I
a = 0.849709 + 1.051240I
b = 0.209652 + 0.759395I
−0.216786 + 1.102140I 6.06046 + 0.98798I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.79600 + 1.25404I
a = 0.280283 + 1.010800I
b = 1.49069 + 0.45311I
16.6042 + 5.5812I 0
u = −0.79600 − 1.25404I
a = 0.280283 − 1.010800I
b = 1.49069 − 0.45311I
16.6042 − 5.5812I 0
u = −1.26064 + 1.00414I
a = −0.616800 − 0.532433I
b = −1.312200 − 0.051852I
7.87194 − 0.16156I 0
u = −1.26064 − 1.00414I
a = −0.616800 + 0.532433I
b = −1.312200 + 0.051852I
7.87194 + 0.16156I 0
u = −1.02376 + 1.27175I
a = −0.347514 − 0.890216I
b = −1.48790 − 0.46941I
8.78158 + 8.86700I 0
u = −1.02376 − 1.27175I
a = −0.347514 + 0.890216I
b = −1.48790 + 0.46941I
8.78158 − 8.86700I 0
u = −0.026194 + 0.314902I
a = 1.304250 + 0.123198I
b = 0.072959 − 0.407482I
0.104937 − 1.022030I 1.88495 + 5.89504I
u = −0.026194 − 0.314902I
a = 1.304250 − 0.123198I
b = 0.072959 + 0.407482I
0.104937 + 1.022030I 1.88495 − 5.89504I
u = −1.11118 + 1.40570I
a = 0.306522 + 0.814258I
b = 1.48520 + 0.47391I
8.0623 + 14.2088I 0
u = −1.11118 − 1.40570I
a = 0.306522 − 0.814258I
b = 1.48520 − 0.47391I
8.0623 − 14.2088I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.11056 + 1.52382I
a = −0.256748 − 0.786495I
b = −1.48361 − 0.48221I
14.4591 + 18.3981I 0
u = −1.11056 − 1.52382I
a = −0.256748 + 0.786495I
b = −1.48361 + 0.48221I
14.4591 − 18.3981I 0
u = −2.18875 + 0.58924I
a = 0.574000 + 0.132729I
b = 1.334550 − 0.047713I
13.29000 + 2.22094I 0
u = −2.18875 − 0.58924I
a = 0.574000 − 0.132729I
b = 1.334550 + 0.047713I
13.29000 − 2.22094I 0
u = −1.53894 + 1.77068I
a = 0.341740 + 0.404686I
b = 1.242490 + 0.017674I
7.26991 − 3.65388I 0
u = −1.53894 − 1.77068I
a = 0.341740 − 0.404686I
b = 1.242490 − 0.017674I
7.26991 + 3.65388I 0
u = −1.95702 + 2.08898I
a = −0.295957 − 0.310278I
b = −1.227360 + 0.011029I
13.0421 − 6.7762I 0
u = −1.95702 − 2.08898I
a = −0.295957 + 0.310278I
b = −1.227360 − 0.011029I
13.0421 + 6.7762I 0
8
II. I
u
2
=
h1.24×10
66
u
44
−1.60×10
67
u
43
+· · ·+ 2.01 ×10
66
b−2.35×10
67
, 2.23×10
69
au
44
+
2.16 × 10
69
u
44
+ · · · + 2.36 × 10
72
a − 1.73 × 10
72
, u
45
− 14u
44
+ · · · + 647u − 95i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
a
−0.615824u
44
+ 7.95994u
43
+ ··· + 50.6359u + 11.6515
a
5
=
0.615824au
44
− 0.491264u
44
+ ··· − 11.6515a − 11.2843
−0.336732u
44
+ 4.56789u
43
+ ··· + 307.564u − 46.6701
a
6
=
0.929888au
44
− 0.300893u
44
+ ··· + 51.1995a + 3.39628
−0.382414au
44
− 0.271052u
44
+ ··· − 10.1434a − 38.4007
a
10
=
0.459564au
44
+ 0.593910u
44
+ ··· + 55.6239a + 93.8232
0.146361au
44
− 0.615824u
44
+ ··· + 31.9895a + 11.6515
a
8
=
0.615824u
44
− 7.95994u
43
+ ··· + a − 11.6515
−0.615824u
44
+ 7.95994u
43
+ ··· + 50.6359u + 11.6515
a
12
=
0.661589au
44
− 0.0317001u
44
+ ··· + 58.5032a + 44.3396
−0.661589au
44
− 0.459564u
44
+ ··· − 58.5032a − 54.6239
a
3
=
−0.0360838au
44
+ 0.167204u
44
+ ··· + 4.77789a + 46.2078
0.103674au
44
− 0.311210u
44
+ ··· + 31.7125a − 4.01151
a
7
=
0.550513au
44
− 0.0645878u
44
+ ··· + 35.7555a + 70.1492
−0.0874292au
44
− 0.798455u
44
+ ··· + 39.9458a − 99.3659
a
11
=
0.680827au
44
− 0.423692u
44
+ ··· + 153.624a − 54.8531
−0.749233au
44
+ 0.213638u
44
+ ··· − 77.8171a − 54.6297
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.08751u
44
+ 43.6285u
43
+ ··· + 3503.19u − 546.068
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
45
+ 14u
44
+ ··· + 647u + 95)
2
c
2
, c
7
u
90
+ 2u
89
+ ··· + 36484534u + 8946419
c
3
, c
5
u
90
+ 3u
89
+ ··· − 321472u + 57793
c
4
, c
8
, c
9
c
12
u
90
+ u
89
+ ··· − 4u
2
+ 1
c
6
, c
10
, c
11
(u
45
− 3u
44
+ ··· + 15u
2
− 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
45
+ 26y
44
+ ··· − 136951y −9025)
2
c
2
, c
7
y
90
− 20y
89
+ ··· − 2040881454030634y + 80038412923561
c
3
, c
5
y
90
+ 9y
89
+ ··· + 26479752282y + 3340030849
c
4
, c
8
, c
9
c
12
y
90
− 69y
89
+ ··· − 8y + 1
c
6
, c
10
, c
11
(y
45
+ 45y
44
+ ··· + 30y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.611610 + 0.781700I
a = 0.729264 − 1.039030I
b = −1.262600 − 0.392766I
2.32033 + 8.38253I 0. − 9.64974I
u = −0.611610 + 0.781700I
a = −0.472221 − 1.245730I
b = −0.366184 − 1.205550I
2.32033 + 8.38253I 0. − 9.64974I
u = −0.611610 − 0.781700I
a = 0.729264 + 1.039030I
b = −1.262600 + 0.392766I
2.32033 − 8.38253I 0. + 9.64974I
u = −0.611610 − 0.781700I
a = −0.472221 + 1.245730I
b = −0.366184 + 1.205550I
2.32033 − 8.38253I 0. + 9.64974I
u = 0.539451 + 0.881956I
a = −0.829441 − 0.107208I
b = 1.250180 − 0.180411I
1.59150 − 2.15051I 0
u = 0.539451 + 0.881956I
a = −0.482101 + 1.122630I
b = 0.352890 + 0.789364I
1.59150 − 2.15051I 0
u = 0.539451 − 0.881956I
a = −0.829441 + 0.107208I
b = 1.250180 + 0.180411I
1.59150 + 2.15051I 0
u = 0.539451 − 0.881956I
a = −0.482101 − 1.122630I
b = 0.352890 − 0.789364I
1.59150 + 2.15051I 0
u = −0.149036 + 0.922013I
a = −0.001131 − 1.359660I
b = −0.247151 − 1.342480I
10.83630 − 0.43960I 11.40794 + 0.I
u = −0.149036 + 0.922013I
a = 1.37673 − 0.49059I
b = −1.253790 − 0.201595I
10.83630 − 0.43960I 11.40794 + 0.I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.149036 − 0.922013I
a = −0.001131 + 1.359660I
b = −0.247151 + 1.342480I
10.83630 + 0.43960I 11.40794 + 0.I
u = −0.149036 − 0.922013I
a = 1.37673 + 0.49059I
b = −1.253790 + 0.201595I
10.83630 + 0.43960I 11.40794 + 0.I
u = 0.666316 + 0.841914I
a = 0.428169 − 0.840537I
b = 0.113870 − 0.741259I
−0.32693 − 2.59057I 0
u = 0.666316 + 0.841914I
a = 0.475542 + 0.511609I
b = −0.992955 + 0.199582I
−0.32693 − 2.59057I 0
u = 0.666316 − 0.841914I
a = 0.428169 + 0.840537I
b = 0.113870 + 0.741259I
−0.32693 + 2.59057I 0
u = 0.666316 − 0.841914I
a = 0.475542 − 0.511609I
b = −0.992955 − 0.199582I
−0.32693 + 2.59057I 0
u = 0.638115 + 0.635046I
a = 0.912716 + 0.034496I
b = −1.228450 + 0.253822I
5.51564 − 1.64544I 5.84263 − 1.31809I
u = 0.638115 + 0.635046I
a = 0.768321 − 1.162400I
b = −0.560511 − 0.601629I
5.51564 − 1.64544I 5.84263 − 1.31809I
u = 0.638115 − 0.635046I
a = 0.912716 − 0.034496I
b = −1.228450 − 0.253822I
5.51564 + 1.64544I 5.84263 + 1.31809I
u = 0.638115 − 0.635046I
a = 0.768321 + 1.162400I
b = −0.560511 + 0.601629I
5.51564 + 1.64544I 5.84263 + 1.31809I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.11036
a = 0.144304 + 0.256392I
b = −0.160229 + 0.284686I
−2.27006 0
u = 1.11036
a = 0.144304 − 0.256392I
b = −0.160229 − 0.284686I
−2.27006 0
u = −0.775611 + 0.416273I
a = −1.56216 − 0.30077I
b = −0.121214 + 0.254236I
8.62121 + 3.17668I 4.82175 − 5.04350I
u = −0.775611 + 0.416273I
a = −0.257914 + 0.189364I
b = −1.336830 + 0.417007I
8.62121 + 3.17668I 4.82175 − 5.04350I
u = −0.775611 − 0.416273I
a = −1.56216 + 0.30077I
b = −0.121214 − 0.254236I
8.62121 − 3.17668I 4.82175 + 5.04350I
u = −0.775611 − 0.416273I
a = −0.257914 − 0.189364I
b = −1.336830 − 0.417007I
8.62121 − 3.17668I 4.82175 + 5.04350I
u = −0.681944 + 0.897038I
a = −0.690712 + 0.859416I
b = 1.309170 + 0.393232I
8.8609 + 12.5151I 0
u = −0.681944 + 0.897038I
a = 0.425318 + 1.136100I
b = 0.299902 + 1.205670I
8.8609 + 12.5151I 0
u = −0.681944 − 0.897038I
a = −0.690712 − 0.859416I
b = 1.309170 − 0.393232I
8.8609 − 12.5151I 0
u = −0.681944 − 0.897038I
a = 0.425318 − 1.136100I
b = 0.299902 − 1.205670I
8.8609 − 12.5151I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.211924 + 1.112060I
a = −0.479293 − 1.016480I
b = 0.066519 − 0.176869I
3.71495 − 4.17242I 0
u = −0.211924 + 1.112060I
a = 0.164472 + 0.028472I
b = −1.231970 + 0.317586I
3.71495 − 4.17242I 0
u = −0.211924 − 1.112060I
a = −0.479293 + 1.016480I
b = 0.066519 + 0.176869I
3.71495 + 4.17242I 0
u = −0.211924 − 1.112060I
a = 0.164472 − 0.028472I
b = −1.231970 − 0.317586I
3.71495 + 4.17242I 0
u = 0.653910 + 0.547063I
a = −1.086380 + 0.896906I
b = −1.91786 + 0.58852I
5.97311 − 0.46804I 7.56258 + 9.30382I
u = 0.653910 + 0.547063I
a = 1.28241 − 1.97286I
b = 1.201060 + 0.007824I
5.97311 − 0.46804I 7.56258 + 9.30382I
u = 0.653910 − 0.547063I
a = −1.086380 − 0.896906I
b = −1.91786 − 0.58852I
5.97311 + 0.46804I 7.56258 − 9.30382I
u = 0.653910 − 0.547063I
a = 1.28241 + 1.97286I
b = 1.201060 − 0.007824I
5.97311 + 0.46804I 7.56258 − 9.30382I
u = 0.576783 + 1.030760I
a = 0.873639 + 0.089311I
b = −1.318070 + 0.145393I
6.72958 − 3.09750I 0
u = 0.576783 + 1.030760I
a = 0.437503 − 1.033930I
b = −0.411842 − 0.952021I
6.72958 − 3.09750I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.576783 − 1.030760I
a = 0.873639 − 0.089311I
b = −1.318070 − 0.145393I
6.72958 + 3.09750I 0
u = 0.576783 − 1.030760I
a = 0.437503 + 1.033930I
b = −0.411842 + 0.952021I
6.72958 + 3.09750I 0
u = −0.418461 + 0.682095I
a = 0.41304 + 1.48489I
b = 0.452920 + 1.334230I
2.86075 + 2.90624I 6.70323 − 8.96973I
u = −0.418461 + 0.682095I
a = −1.12521 + 1.35432I
b = 1.185680 + 0.339637I
2.86075 + 2.90624I 6.70323 − 8.96973I
u = −0.418461 − 0.682095I
a = 0.41304 − 1.48489I
b = 0.452920 − 1.334230I
2.86075 − 2.90624I 6.70323 + 8.96973I
u = −0.418461 − 0.682095I
a = −1.12521 − 1.35432I
b = 1.185680 − 0.339637I
2.86075 − 2.90624I 6.70323 + 8.96973I
u = 1.178110 + 0.303143I
a = −0.326728 + 0.359344I
b = 0.011662 + 0.553716I
1.78035 − 1.52529I 0
u = 1.178110 + 0.303143I
a = −0.122713 − 0.438429I
b = 0.493854 − 0.324300I
1.78035 − 1.52529I 0
u = 1.178110 − 0.303143I
a = −0.326728 − 0.359344I
b = 0.011662 − 0.553716I
1.78035 + 1.52529I 0
u = 1.178110 − 0.303143I
a = −0.122713 + 0.438429I
b = 0.493854 + 0.324300I
1.78035 + 1.52529I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.354893 + 0.613023I
a = −0.80218 + 1.22978I
b = −0.253625 + 1.040460I
1.59061 + 0.21798I 2.72267 + 0.45000I
u = 0.354893 + 0.613023I
a = −1.09182 − 1.04581I
b = 1.038570 + 0.055317I
1.59061 + 0.21798I 2.72267 + 0.45000I
u = 0.354893 − 0.613023I
a = −0.80218 − 1.22978I
b = −0.253625 − 1.040460I
1.59061 − 0.21798I 2.72267 − 0.45000I
u = 0.354893 − 0.613023I
a = −1.09182 + 1.04581I
b = 1.038570 − 0.055317I
1.59061 − 0.21798I 2.72267 − 0.45000I
u = 0.712444 + 1.138040I
a = −0.212487 + 0.798192I
b = −0.154669 + 0.667898I
4.38368 − 4.83757I 0
u = 0.712444 + 1.138040I
a = −0.360514 − 0.361601I
b = 1.059760 − 0.326849I
4.38368 − 4.83757I 0
u = 0.712444 − 1.138040I
a = −0.212487 − 0.798192I
b = −0.154669 − 0.667898I
4.38368 + 4.83757I 0
u = 0.712444 − 1.138040I
a = −0.360514 + 0.361601I
b = 1.059760 + 0.326849I
4.38368 + 4.83757I 0
u = 0.793086 + 1.112180I
a = 0.482589 − 0.784671I
b = 1.56067 − 0.52472I
7.73394 − 5.25113I 0
u = 0.793086 + 1.112180I
a = −0.350583 + 1.153260I
b = −1.255430 + 0.085588I
7.73394 − 5.25113I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.793086 − 1.112180I
a = 0.482589 + 0.784671I
b = 1.56067 + 0.52472I
7.73394 + 5.25113I 0
u = 0.793086 − 1.112180I
a = −0.350583 − 1.153260I
b = −1.255430 − 0.085588I
7.73394 + 5.25113I 0
u = 0.253150 + 0.576313I
a = 0.93483 − 1.72737I
b = 1.69263 − 0.97809I
12.01940 + 4.51852I 17.3811 − 5.6393I
u = 0.253150 + 0.576313I
a = 0.34122 + 3.08688I
b = −1.232160 − 0.101472I
12.01940 + 4.51852I 17.3811 − 5.6393I
u = 0.253150 − 0.576313I
a = 0.93483 + 1.72737I
b = 1.69263 + 0.97809I
12.01940 − 4.51852I 17.3811 + 5.6393I
u = 0.253150 − 0.576313I
a = 0.34122 − 3.08688I
b = −1.232160 + 0.101472I
12.01940 − 4.51852I 17.3811 + 5.6393I
u = 0.486761 + 1.290350I
a = −0.288375 + 0.934430I
b = −1.48316 + 0.65192I
15.0045 − 7.7049I 0
u = 0.486761 + 1.290350I
a = −0.062701 − 1.173080I
b = 1.346110 − 0.082739I
15.0045 − 7.7049I 0
u = 0.486761 − 1.290350I
a = −0.288375 − 0.934430I
b = −1.48316 − 0.65192I
15.0045 + 7.7049I 0
u = 0.486761 − 1.290350I
a = −0.062701 + 1.173080I
b = 1.346110 + 0.082739I
15.0045 + 7.7049I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.298408 + 0.518145I
a = 0.160912 + 0.325351I
b = 1.331610 − 0.284286I
3.05397 − 0.51778I 4.68541 − 4.29429I
u = −0.298408 + 0.518145I
a = 1.52344 + 1.69258I
b = 0.216596 + 0.013712I
3.05397 − 0.51778I 4.68541 − 4.29429I
u = −0.298408 − 0.518145I
a = 0.160912 − 0.325351I
b = 1.331610 + 0.284286I
3.05397 + 0.51778I 4.68541 + 4.29429I
u = −0.298408 − 0.518145I
a = 1.52344 − 1.69258I
b = 0.216596 − 0.013712I
3.05397 + 0.51778I 4.68541 + 4.29429I
u = −0.48885 + 1.42397I
a = 0.480075 + 0.691881I
b = −0.228923 + 0.089425I
9.94023 − 6.86720I 0
u = −0.48885 + 1.42397I
a = −0.105551 − 0.124529I
b = 1.219900 − 0.345387I
9.94023 − 6.86720I 0
u = −0.48885 − 1.42397I
a = 0.480075 − 0.691881I
b = −0.228923 − 0.089425I
9.94023 + 6.86720I 0
u = −0.48885 − 1.42397I
a = −0.105551 + 0.124529I
b = 1.219900 + 0.345387I
9.94023 + 6.86720I 0
u = 1.30403 + 1.57384I
a = −0.317525 + 0.634119I
b = −1.138430 + 0.205272I
7.21426 − 4.49667I 0
u = 1.30403 + 1.57384I
a = 0.278035 − 0.492975I
b = 1.41206 − 0.32718I
7.21426 − 4.49667I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.30403 − 1.57384I
a = −0.317525 − 0.634119I
b = −1.138430 − 0.205272I
7.21426 + 4.49667I 0
u = 1.30403 − 1.57384I
a = 0.278035 + 0.492975I
b = 1.41206 + 0.32718I
7.21426 + 4.49667I 0
u = 1.03866 + 1.81167I
a = 0.185228 − 0.628944I
b = 1.165440 − 0.361396I
4.20549 − 6.43436I 0
u = 1.03866 + 1.81167I
a = −0.127441 + 0.570229I
b = −1.331830 + 0.317689I
4.20549 − 6.43436I 0
u = 1.03866 − 1.81167I
a = 0.185228 + 0.628944I
b = 1.165440 + 0.361396I
4.20549 + 6.43436I 0
u = 1.03866 − 1.81167I
a = −0.127441 − 0.570229I
b = −1.331830 − 0.317689I
4.20549 + 6.43436I 0
u = 0.88495 + 1.89707I
a = −0.144548 + 0.642165I
b = −1.139300 + 0.488014I
9.10603 − 8.38435I 0
u = 0.88495 + 1.89707I
a = 0.018811 − 0.591785I
b = 1.346150 − 0.294066I
9.10603 − 8.38435I 0
u = 0.88495 − 1.89707I
a = −0.144548 − 0.642165I
b = −1.139300 − 0.488014I
9.10603 + 8.38435I 0
u = 0.88495 − 1.89707I
a = 0.018811 + 0.591785I
b = 1.346150 + 0.294066I
9.10603 + 8.38435I 0
20
III. I
u
3
=
h2.54×10
13
u
16
−2.60×10
14
u
15
+· · ·+3.72×10
13
b+4.34×10
14
, 4.34×10
14
u
16
−
4.44 × 10
15
u
15
+ · · · + 4.83 × 10
14
a + 6.88 × 10
15
, u
17
− 11u
16
+ · · · + 61u − 13i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
−0.897742u
16
+ 9.19320u
15
+ ··· + 51.7535u − 14.2413
−0.681964u
16
+ 7.00113u
15
+ ··· + 40.5210u − 11.6706
a
5
=
−0.580585u
16
+ 5.92362u
15
+ ··· + 27.9777u − 9.09389
−0.462812u
16
+ 4.80350u
15
+ ··· + 27.3218u − 7.54760
a
6
=
−0.405201u
16
+ 4.13662u
15
+ ··· + 21.3399u − 7.56285
−0.375250u
16
+ 3.87515u
15
+ ··· + 20.9267u − 5.69881
a
10
=
−1.05032u
16
+ 10.7472u
15
+ ··· + 64.2093u − 17.6504
−0.305860u
16
+ 3.10669u
15
+ ··· + 16.4902u − 4.78869
a
8
=
−0.215778u
16
+ 2.19206u
15
+ ··· + 11.2325u − 2.57066
−0.681964u
16
+ 7.00113u
15
+ ··· + 40.5210u − 11.6706
a
12
=
−0.117773u
16
+ 1.12012u
15
+ ··· + 1.65596u − 0.546296
−0.462812u
16
+ 4.80350u
15
+ ··· + 26.3218u − 7.54760
a
3
=
−0.194696u
16
+ 1.96627u
15
+ ··· + 15.1175u − 4.23860
−0.175383u
16
+ 1.78700u
15
+ ··· + 7.63785u − 2.53105
a
7
=
−0.0383098u
16
+ 0.354981u
15
+ ··· − 3.47878u + 1.37647
−0.566894u
16
+ 5.77956u
15
+ ··· + 33.6425u − 9.36356
a
11
=
−1.28094u
16
+ 13.1157u
15
+ ··· + 65.7878u − 20.0167
−0.489126u
16
+ 5.04876u
15
+ ··· + 30.3915u − 8.70823
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
14747391055457
3098302791214
u
16
−
590594498534627
12393211164856
u
15
+ ··· −
1018255900118941
4647454186821
u +
2397735479791261
37179633494568
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 11u
16
+ ··· + 61u − 13
c
2
, c
7
u
17
− u
16
+ ··· + 5u
2
+ 1
c
3
, c
5
u
17
+ 3u
16
+ ··· + 3u + 1
c
4
, c
8
u
17
− 7u
15
+ ··· − 7u
2
+ 1
c
6
u
17
+ 3u
16
+ ··· − 2u − 1
c
9
, c
12
u
17
− 7u
15
+ ··· + 7u
2
− 1
c
10
, c
11
u
17
− 3u
16
+ ··· − 2u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 13y
16
+ ··· − 829y −169
c
2
, c
7
y
17
+ 3y
16
+ ··· − 10y −1
c
3
, c
5
y
17
+ 3y
16
+ ··· − 5y −1
c
4
, c
8
, c
9
c
12
y
17
− 14y
16
+ ··· + 14y −1
c
6
, c
10
, c
11
y
17
+ 17y
16
+ ··· + 18y
2
− 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672523 + 0.994302I
a = −0.231992 + 1.105750I
b = −1.255470 + 0.512970I
4.86856 − 6.83059I 4.20585 + 10.23104I
u = 0.672523 − 0.994302I
a = −0.231992 − 1.105750I
b = −1.255470 − 0.512970I
4.86856 + 6.83059I 4.20585 − 10.23104I
u = 0.739575 + 0.064407I
a = 0.475693 + 0.886639I
b = 0.294705 + 0.686375I
−0.84670 + 1.37045I −5.30898 − 4.32463I
u = 0.739575 − 0.064407I
a = 0.475693 − 0.886639I
b = 0.294705 − 0.686375I
−0.84670 − 1.37045I −5.30898 + 4.32463I
u = 1.29126
a = 0.338230
b = 0.436742
−2.05037 18.8440
u = 0.227690 + 0.618552I
a = −0.24105 − 1.81338I
b = 1.066790 − 0.561990I
3.26404 − 1.84385I 9.66761 + 2.94728I
u = 0.227690 − 0.618552I
a = −0.24105 + 1.81338I
b = 1.066790 + 0.561990I
3.26404 + 1.84385I 9.66761 − 2.94728I
u = 1.39451 + 0.50448I
a = −0.386813 + 0.041871I
b = −0.560538 − 0.136750I
2.28339 − 1.51196I 11.74266 − 3.04379I
u = 1.39451 − 0.50448I
a = −0.386813 − 0.041871I
b = −0.560538 + 0.136750I
2.28339 + 1.51196I 11.74266 + 3.04379I
u = −0.221722 + 0.326447I
a = 2.34722 + 1.33971I
b = −0.957777 + 0.469199I
9.57721 + 2.19585I 10.18532 − 0.67460I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.221722 − 0.326447I
a = 2.34722 − 1.33971I
b = −0.957777 − 0.469199I
9.57721 − 2.19585I 10.18532 + 0.67460I
u = 0.70704 + 1.73293I
a = −0.071556 + 0.682925I
b = −1.234060 + 0.358853I
5.17054 − 6.41143I 8.12565 + 7.83272I
u = 0.70704 − 1.73293I
a = −0.071556 − 0.682925I
b = −1.234060 − 0.358853I
5.17054 + 6.41143I 8.12565 − 7.83272I
u = −0.06721 + 1.99987I
a = −0.186400 − 0.566671I
b = 1.145800 − 0.334688I
11.28100 − 8.47803I 10.04502 + 7.78423I
u = −0.06721 − 1.99987I
a = −0.186400 + 0.566671I
b = 1.145800 + 0.334688I
11.28100 + 8.47803I 10.04502 − 7.78423I
u = 1.40196 + 2.02720I
a = 0.202703 − 0.492303I
b = 1.282180 − 0.279271I
8.19546 − 5.71646I 8.91465 + 6.33996I
u = 1.40196 − 2.02720I
a = 0.202703 + 0.492303I
b = 1.282180 + 0.279271I
8.19546 + 5.71646I 8.91465 − 6.33996I
25
IV.
I
u
4
= hu
6
+ u
3
+ au + 2u
2
+ b, u
5
a − 2u
6
+ · · · + a
2
− 4, u
7
+ 2u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
a
−u
6
− u
3
− au − 2u
2
a
5
=
−u
6
a − 2u
6
+ u
5
− u
3
a − 2u
2
a − 4u
3
− 2u
2
+ 2u − 2
−u
6
− 2u
3
− 2u
2
+ u − 2
a
6
=
−u
6
a + u
5
a − u
6
+ u
5
− u
3
a − u
2
a − 2u
3
+ au + 2u − 1
−u
6
− u
4
a − u
3
a − 2u
3
− au − 2u
2
− a − 2
a
10
=
−u
6
a + u
5
a + u
5
− 2u
3
a − u
4
+ 2au + u
2
− a + u − 2
−u
6
− u
2
a − u
3
− 2u
2
− a
a
8
=
u
6
+ u
3
+ au + 2u
2
+ a
−u
6
− u
3
− au − 2u
2
a
12
=
u
6
+ u
4
a + 2u
3
+ au + 2u
2
+ a + 1
u
6
− u
4
a − u
5
+ 2u
3
− au − a − 2u + 2
a
3
=
−u
6
a − 2u
6
− u
4
a + u
5
− u
3
a − 2u
2
a − 4u
3
− au − 2u
2
− a + 2u − 1
u
5
a + u
2
a + au + u − 2
a
7
=
−u
6
a − u
6
+ u
5
− 2u
3
a − u
4
− u
2
a − u
3
+ au − u
2
− a + u − 1
−u
6
+ u
5
+ u
3
a − u
4
− u
2
a − u
3
− u
2
− 1
a
11
=
u
4
a + u
5
+ u
3
a − u
4
+ 2au + 2u
2
+ a − 1
u
5
a − u
6
− u
4
a − 2u
3
− au − u
2
− a − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
6
− 3u
5
+ 2u
4
+ 9u
3
+ 3u
2
− 2u + 12
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 2u
4
+ 2u
3
+ u + 1)
2
c
2
, c
7
u
14
+ u
13
+ ··· + 10u − 7
c
3
, c
5
u
14
− 8u
13
+ ··· − 2u + 1
c
4
, c
8
u
14
− 8u
12
+ ··· − 10u − 7
c
6
(u
7
− u
6
+ 4u
5
− 3u
4
+ 4u
3
− 3u
2
− 1)
2
c
9
, c
12
u
14
− 8u
12
+ ··· + 10u − 7
c
10
, c
11
(u
7
+ u
6
+ 4u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 4y
5
− 2y
4
+ 4y
3
+ y −1)
2
c
2
, c
7
y
14
− 7y
13
+ ··· − 30y + 49
c
3
, c
5
y
14
− 10y
13
+ ··· − 14y + 1
c
4
, c
8
, c
9
c
12
y
14
− 16y
13
+ ··· − 100y + 49
c
6
, c
10
, c
11
(y
7
+ 7y
6
+ 18y
5
+ 17y
4
− 4y
3
− 15y
2
− 6y −1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.900716 + 0.538193I
a = 1.050160 + 0.494892I
b = 1.44605 + 0.54572I
11.31250 − 4.40574I 5.74423 + 3.20281I
u = −0.900716 + 0.538193I
a = −0.91628 − 1.15337I
b = −1.212240 + 0.119430I
11.31250 − 4.40574I 5.74423 + 3.20281I
u = −0.900716 − 0.538193I
a = 1.050160 − 0.494892I
b = 1.44605 − 0.54572I
11.31250 + 4.40574I 5.74423 − 3.20281I
u = −0.900716 − 0.538193I
a = −0.91628 + 1.15337I
b = −1.212240 − 0.119430I
11.31250 + 4.40574I 5.74423 − 3.20281I
u = 0.386298 + 0.728050I
a = −1.098970 − 0.313372I
b = 1.208430 − 0.210612I
1.98837 − 1.74054I 5.22031 − 0.02742I
u = 0.386298 + 0.728050I
a = 0.46148 − 1.41496I
b = −0.196378 − 0.921156I
1.98837 − 1.74054I 5.22031 − 0.02742I
u = 0.386298 − 0.728050I
a = −1.098970 + 0.313372I
b = 1.208430 + 0.210612I
1.98837 + 1.74054I 5.22031 + 0.02742I
u = 0.386298 − 0.728050I
a = 0.46148 + 1.41496I
b = −0.196378 + 0.921156I
1.98837 + 1.74054I 5.22031 + 0.02742I
u = −0.705834
a = −1.72443
b = −1.98557
6.21285 13.2580
u = −0.705834
a = 2.81309
b = 1.21716
6.21285 13.2580
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.867335 + 1.068730I
a = −0.494795 + 0.762932I
b = 0.382866 + 0.494187I
4.97682 − 2.64701I 1.40643 + 3.44312I
u = 0.867335 + 1.068730I
a = 0.454076 + 0.010265I
b = −1.244520 + 0.132917I
4.97682 − 2.64701I 1.40643 + 3.44312I
u = 0.867335 − 1.068730I
a = −0.494795 − 0.762932I
b = 0.382866 − 0.494187I
4.97682 + 2.64701I 1.40643 − 3.44312I
u = 0.867335 − 1.068730I
a = 0.454076 − 0.010265I
b = −1.244520 − 0.132917I
4.97682 + 2.64701I 1.40643 − 3.44312I
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
7
+ 2u
4
+ 2u
3
+ u + 1)
2
)(u
17
− 11u
16
+ ··· + 61u − 13)
· (u
38
− 28u
37
+ ··· + 20672u − 1216)
· (u
45
+ 14u
44
+ ··· + 647u + 95)
2
c
2
, c
7
(u
14
+ u
13
+ ··· + 10u − 7)(u
17
− u
16
+ ··· + 5u
2
+ 1)
· (u
38
+ u
37
+ ··· + 3u − 1)(u
90
+ 2u
89
+ ··· + 3.64845 × 10
7
u + 8946419)
c
3
, c
5
(u
14
− 8u
13
+ ··· − 2u + 1)(u
17
+ 3u
16
+ ··· + 3u + 1)
· (u
38
− 3u
37
+ ··· + 54u − 7)(u
90
+ 3u
89
+ ··· − 321472u + 57793)
c
4
, c
8
(u
14
− 8u
12
+ ··· − 10u − 7)(u
17
− 7u
15
+ ··· − 7u
2
+ 1)
· (u
38
− 19u
36
+ ··· − u + 1)(u
90
+ u
89
+ ··· − 4u
2
+ 1)
c
6
((u
7
− u
6
+ ··· − 3u
2
− 1)
2
)(u
17
+ 3u
16
+ ··· − 2u − 1)
· (u
38
+ 8u
37
+ ··· − 50u − 4)(u
45
− 3u
44
+ ··· + 15u
2
− 1)
2
c
9
, c
12
(u
14
− 8u
12
+ ··· + 10u − 7)(u
17
− 7u
15
+ ··· + 7u
2
− 1)
· (u
38
− 19u
36
+ ··· − u + 1)(u
90
+ u
89
+ ··· − 4u
2
+ 1)
c
10
, c
11
((u
7
+ u
6
+ ··· + 3u
2
+ 1)
2
)(u
17
− 3u
16
+ ··· − 2u + 1)
· (u
38
+ 8u
37
+ ··· − 50u − 4)(u
45
− 3u
44
+ ··· + 15u
2
− 1)
2
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
7
+ 4y
5
− 2y
4
+ 4y
3
+ y −1)
2
)(y
17
+ 13y
16
+ ··· − 829y −169)
· (y
38
− 4y
37
+ ··· + 24750464y + 1478656)
· (y
45
+ 26y
44
+ ··· − 136951y −9025)
2
c
2
, c
7
(y
14
− 7y
13
+ ··· − 30y + 49)(y
17
+ 3y
16
+ ··· − 10y −1)
· (y
38
− 37y
37
+ ··· − 51y + 1)
· (y
90
− 20y
89
+ ··· − 2040881454030634y + 80038412923561)
c
3
, c
5
(y
14
− 10y
13
+ ··· − 14y + 1)(y
17
+ 3y
16
+ ··· − 5y −1)
· (y
38
+ 7y
37
+ ··· + 948y + 49)
· (y
90
+ 9y
89
+ ··· + 26479752282y + 3340030849)
c
4
, c
8
, c
9
c
12
(y
14
− 16y
13
+ ··· − 100y + 49)(y
17
− 14y
16
+ ··· + 14y −1)
· (y
38
− 38y
37
+ ··· − 35y + 1)(y
90
− 69y
89
+ ··· − 8y + 1)
c
6
, c
10
, c
11
(y
7
+ 7y
6
+ 18y
5
+ 17y
4
− 4y
3
− 15y
2
− 6y −1)
2
· (y
17
+ 17y
16
+ ··· + 18y
2
− 1)(y
38
+ 36y
37
+ ··· − 316y + 16)
· (y
45
+ 45y
44
+ ··· + 30y −1)
2
32
