12a
0054
(K12a
0054
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 4 12 11 6 9 1 8
Solving Sequence
5,10 3,6
2 1 4 7 9 11 8 12
c
5
c
2
c
1
c
4
c
6
c
9
c
10
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.70479 × 10
114
u
95
− 2.20755 × 10
114
u
94
+ ··· + 2.05537 × 10
115
b − 3.80401 × 10
115
,
8.56716 × 10
113
u
95
− 4.40413 × 10
114
u
94
+ ··· + 4.11073 × 10
115
a + 1.80283 × 10
116
, u
96
− 2u
95
+ ··· − 12u − 8i
I
u
2
= hb + 1, −u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 3u
2
+ a + 2u − 1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v −1i
* 3 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
= h1.70 × 10
114
u
95
− 2.21 × 10
114
u
94
+ · · · + 2.06 × 10
115
b − 3.80 ×
10
115
, 8.57 × 10
113
u
95
− 4.40 × 10
114
u
94
+ · · · + 4.11 × 10
115
a + 1.80 ×
10
116
, u
96
− 2u
95
+ · · · − 12u − 8i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−0.0208409u
95
+ 0.107137u
94
+ ··· − 7.91306u − 4.38566
−0.0829433u
95
+ 0.107404u
94
+ ··· + 3.53916u + 1.85077
a
6
=
1
−u
2
a
2
=
−0.103784u
95
+ 0.214541u
94
+ ··· − 4.37390u − 2.53489
−0.0829433u
95
+ 0.107404u
94
+ ··· + 3.53916u + 1.85077
a
1
=
0.0473624u
95
− 0.0186442u
94
+ ··· − 5.36990u − 2.42402
−0.137727u
95
+ 0.287200u
94
+ ··· + 2.40951u − 0.488149
a
4
=
−0.213197u
95
+ 0.429416u
94
+ ··· − 1.62144u − 0.459408
0.0719032u
95
− 0.0553870u
94
+ ··· − 0.297884u − 2.76461
a
7
=
−0.0903647u
95
+ 0.268555u
94
+ ··· − 2.96038u − 2.91217
0.199681u
95
− 0.470810u
94
+ ··· − 2.74051u − 0.214459
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
12
=
−0.0255767u
95
+ 0.0598845u
94
+ ··· − 5.58218u − 3.51029
0.00949794u
95
+ 0.0415095u
94
+ ··· + 2.45224u + 0.0562999
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.236170u
95
+ 0.601131u
94
+ ··· + 0.772462u − 8.63749
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
96
+ 41u
95
+ ··· + 401u + 1
c
2
, c
4
u
96
− 11u
95
+ ··· + 7u + 1
c
3
, c
6
u
96
− 2u
95
+ ··· + 1536u − 512
c
5
, c
9
u
96
− 2u
95
+ ··· − 12u − 8
c
7
, c
12
u
96
+ 5u
95
+ ··· − 8u + 1
c
8
, c
10
u
96
+ 24u
95
+ ··· + 48u + 64
c
11
u
96
− 55u
95
+ ··· − 218u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
96
+ 39y
95
+ ··· − 140705y + 1
c
2
, c
4
y
96
− 41y
95
+ ··· − 401y + 1
c
3
, c
6
y
96
+ 60y
95
+ ··· + 1835008y + 262144
c
5
, c
9
y
96
+ 24y
95
+ ··· + 48y + 64
c
7
, c
12
y
96
− 55y
95
+ ··· − 218y + 1
c
8
, c
10
y
96
+ 92y
95
+ ··· − 879872y + 4096
c
11
y
96
− 23y
95
+ ··· − 43342y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.331849 + 0.953547I
a = −0.991852 + 0.187481I
b = −1.226360 + 0.183799I
−2.99925 − 3.60208I 0
u = −0.331849 − 0.953547I
a = −0.991852 − 0.187481I
b = −1.226360 − 0.183799I
−2.99925 + 3.60208I 0
u = 0.420726 + 0.894455I
a = 0.0748654 + 0.0783523I
b = 0.326390 + 0.493463I
−0.09751 + 2.03694I 0
u = 0.420726 − 0.894455I
a = 0.0748654 − 0.0783523I
b = 0.326390 − 0.493463I
−0.09751 − 2.03694I 0
u = −0.763608 + 0.666822I
a = 0.370790 − 0.523796I
b = 0.479897 + 0.066967I
3.69919 + 1.25518I 0
u = −0.763608 − 0.666822I
a = 0.370790 + 0.523796I
b = 0.479897 − 0.066967I
3.69919 − 1.25518I 0
u = −0.917832 + 0.330602I
a = −0.422961 + 0.922598I
b = 1.011070 − 0.616866I
2.58601 + 6.51221I 0
u = −0.917832 − 0.330602I
a = −0.422961 − 0.922598I
b = 1.011070 + 0.616866I
2.58601 − 6.51221I 0
u = −0.846687 + 0.463347I
a = 0.080098 − 1.096030I
b = 0.571760 + 0.611302I
3.84701 + 1.59882I 0
u = −0.846687 − 0.463347I
a = 0.080098 + 1.096030I
b = 0.571760 − 0.611302I
3.84701 − 1.59882I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.214407 + 0.917724I
a = −1.21899 + 1.73083I
b = −1.043700 − 0.362721I
−3.72115 − 1.69356I −8.89200 + 0.I
u = −0.214407 − 0.917724I
a = −1.21899 − 1.73083I
b = −1.043700 + 0.362721I
−3.72115 + 1.69356I −8.89200 + 0.I
u = 0.399586 + 0.985773I
a = −0.64535 − 1.97533I
b = −1.015690 + 0.459888I
−2.29930 + 5.98929I 0
u = 0.399586 − 0.985773I
a = −0.64535 + 1.97533I
b = −1.015690 − 0.459888I
−2.29930 − 5.98929I 0
u = 0.105934 + 0.913879I
a = −1.49280 + 0.48603I
b = −1.144490 − 0.244528I
−4.04166 − 0.52516I −8.55610 + 0.I
u = 0.105934 − 0.913879I
a = −1.49280 − 0.48603I
b = −1.144490 + 0.244528I
−4.04166 + 0.52516I −8.55610 + 0.I
u = 0.543375 + 0.935475I
a = 0.306378 + 0.400786I
b = 0.588526 + 0.269748I
−0.07900 + 2.11206I 0
u = 0.543375 − 0.935475I
a = 0.306378 − 0.400786I
b = 0.588526 − 0.269748I
−0.07900 − 2.11206I 0
u = 0.287889 + 0.845646I
a = 0.949105 + 0.732014I
b = −0.483494 − 0.489887I
−0.67980 + 2.01844I −2.00000 − 3.46901I
u = 0.287889 − 0.845646I
a = 0.949105 − 0.732014I
b = −0.483494 + 0.489887I
−0.67980 − 2.01844I −2.00000 + 3.46901I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.002493 + 1.116370I
a = 1.228320 + 0.018327I
b = 0.949803 − 0.482210I
−3.12502 + 4.24954I 0
u = 0.002493 − 1.116370I
a = 1.228320 − 0.018327I
b = 0.949803 + 0.482210I
−3.12502 − 4.24954I 0
u = −0.508460 + 0.999100I
a = −0.361486 + 0.232503I
b = 0.336484 − 0.738021I
1.95677 − 6.48071I 0
u = −0.508460 − 0.999100I
a = −0.361486 − 0.232503I
b = 0.336484 + 0.738021I
1.95677 + 6.48071I 0
u = −0.416500 + 0.770558I
a = −0.483230 − 1.295950I
b = 0.671787 − 0.640819I
4.46916 + 0.68945I 3.28117 + 0.85960I
u = −0.416500 − 0.770558I
a = −0.483230 + 1.295950I
b = 0.671787 + 0.640819I
4.46916 − 0.68945I 3.28117 − 0.85960I
u = 0.332265 + 1.076590I
a = 1.42109 + 1.04142I
b = 1.046100 − 0.573034I
−1.83045 + 6.55518I 0
u = 0.332265 − 1.076590I
a = 1.42109 − 1.04142I
b = 1.046100 + 0.573034I
−1.83045 − 6.55518I 0
u = 0.177267 + 1.115030I
a = 0.907127 + 0.317756I
b = 0.879589 + 0.432826I
−2.75506 + 0.64484I 0
u = 0.177267 − 1.115030I
a = 0.907127 − 0.317756I
b = 0.879589 − 0.432826I
−2.75506 − 0.64484I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.247496 + 0.816258I
a = 2.79839 − 0.99348I
b = 0.969526 + 0.629311I
3.58367 − 4.30558I −0.11915 + 6.48044I
u = −0.247496 − 0.816258I
a = 2.79839 + 0.99348I
b = 0.969526 − 0.629311I
3.58367 + 4.30558I −0.11915 − 6.48044I
u = 0.840798 + 0.068830I
a = −0.306920 − 0.930091I
b = 0.918979 + 0.594287I
1.56693 − 2.64898I −0.12373 + 1.94416I
u = 0.840798 − 0.068830I
a = −0.306920 + 0.930091I
b = 0.918979 − 0.594287I
1.56693 + 2.64898I −0.12373 − 1.94416I
u = 0.039988 + 0.842192I
a = 0.669881 − 0.384390I
b = −0.173785 + 0.414358I
−1.31139 + 1.53275I −3.91456 − 5.18456I
u = 0.039988 − 0.842192I
a = 0.669881 + 0.384390I
b = −0.173785 − 0.414358I
−1.31139 − 1.53275I −3.91456 + 5.18456I
u = 0.799059 + 0.846331I
a = 1.07319 + 1.14008I
b = −0.806160 − 0.624229I
2.43670 + 0.52493I 0
u = 0.799059 − 0.846331I
a = 1.07319 − 1.14008I
b = −0.806160 + 0.624229I
2.43670 − 0.52493I 0
u = −0.767472 + 0.888370I
a = −0.084906 + 0.851187I
b = −1.332930 + 0.034727I
0.72602 − 2.90143I 0
u = −0.767472 − 0.888370I
a = −0.084906 − 0.851187I
b = −1.332930 − 0.034727I
0.72602 + 2.90143I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.885713 + 0.776635I
a = −0.572131 + 1.015580I
b = 1.108900 − 0.724154I
6.26538 + 5.58089I 0
u = −0.885713 − 0.776635I
a = −0.572131 − 1.015580I
b = 1.108900 + 0.724154I
6.26538 − 5.58089I 0
u = 0.857556 + 0.825746I
a = 0.080065 − 0.973811I
b = −1.340690 + 0.009120I
4.57395 − 1.45279I 0
u = 0.857556 − 0.825746I
a = 0.080065 + 0.973811I
b = −1.340690 − 0.009120I
4.57395 + 1.45279I 0
u = 0.830770 + 0.862931I
a = −0.586564 − 1.051620I
b = 1.112920 + 0.756547I
10.10790 − 1.19035I 0
u = 0.830770 − 0.862931I
a = −0.586564 + 1.051620I
b = 1.112920 − 0.756547I
10.10790 + 1.19035I 0
u = 0.760213 + 0.255609I
a = −0.148446 + 1.002920I
b = 0.776189 − 0.607942I
2.00761 + 2.10017I 0.83891 − 4.53868I
u = 0.760213 − 0.255609I
a = −0.148446 − 1.002920I
b = 0.776189 + 0.607942I
2.00761 − 2.10017I 0.83891 + 4.53868I
u = −0.838980 + 0.859841I
a = 0.17172 + 2.31211I
b = −0.839704 − 0.634470I
6.20074 − 1.00773I 0
u = −0.838980 − 0.859841I
a = 0.17172 − 2.31211I
b = −0.839704 + 0.634470I
6.20074 + 1.00773I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.474625 + 1.104840I
a = 1.12838 − 1.39898I
b = 1.091600 + 0.599495I
−0.12483 − 11.51150I 0
u = −0.474625 − 1.104840I
a = 1.12838 + 1.39898I
b = 1.091600 − 0.599495I
−0.12483 + 11.51150I 0
u = −0.870715 + 0.833568I
a = −0.05442 − 1.45713I
b = 0.556085 + 0.944376I
7.96094 − 0.52062I 0
u = −0.870715 − 0.833568I
a = −0.05442 + 1.45713I
b = 0.556085 − 0.944376I
7.96094 + 0.52062I 0
u = −0.894404 + 0.820640I
a = 1.08831 − 1.18593I
b = −0.861586 + 0.633055I
6.13236 + 3.94857I 0
u = −0.894404 − 0.820640I
a = 1.08831 + 1.18593I
b = −0.861586 − 0.633055I
6.13236 − 3.94857I 0
u = 0.781161 + 0.930558I
a = 0.06641 − 2.24202I
b = −0.888865 + 0.621738I
2.17830 + 5.41664I 0
u = 0.781161 − 0.930558I
a = 0.06641 + 2.24202I
b = −0.888865 − 0.621738I
2.17830 − 5.41664I 0
u = 0.806984 + 0.930820I
a = 0.56083 + 2.34249I
b = 1.126410 − 0.722210I
9.89480 + 7.30761I 0
u = 0.806984 − 0.930820I
a = 0.56083 − 2.34249I
b = 1.126410 + 0.722210I
9.89480 − 7.30761I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.703854 + 1.011630I
a = 0.305278 − 0.370471I
b = 0.679665 − 0.142081I
2.66867 − 6.83395I 0
u = −0.703854 − 1.011630I
a = 0.305278 + 0.370471I
b = 0.679665 + 0.142081I
2.66867 + 6.83395I 0
u = 0.703787 + 0.300436I
a = 1.45363 + 1.29987I
b = −0.925873 − 0.325878I
−0.02370 − 2.00842I −1.62743 + 4.29984I
u = 0.703787 − 0.300436I
a = 1.45363 − 1.29987I
b = −0.925873 + 0.325878I
−0.02370 + 2.00842I −1.62743 − 4.29984I
u = 0.846783 + 0.902988I
a = −0.09596 + 1.47858I
b = 0.583726 − 0.977505I
11.73460 + 5.11833I 0
u = 0.846783 − 0.902988I
a = −0.09596 − 1.47858I
b = 0.583726 + 0.977505I
11.73460 − 5.11833I 0
u = −0.812021 + 0.937351I
a = 1.02775 − 1.15508I
b = −0.792949 + 0.675723I
5.95824 − 5.15041I 0
u = −0.812021 − 0.937351I
a = 1.02775 + 1.15508I
b = −0.792949 − 0.675723I
5.95824 + 5.15041I 0
u = 0.844920 + 0.911321I
a = −1.228240 − 0.696496I
b = 0.535424 + 0.960203I
11.70970 + 1.16815I 0
u = 0.844920 − 0.911321I
a = −1.228240 + 0.696496I
b = 0.535424 − 0.960203I
11.70970 − 1.16815I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.938146 + 0.839572I
a = −0.02587 + 1.49281I
b = 0.518746 − 0.964023I
11.59380 − 4.19583I 0
u = 0.938146 − 0.839572I
a = −0.02587 − 1.49281I
b = 0.518746 + 0.964023I
11.59380 + 4.19583I 0
u = 0.964249 + 0.810539I
a = −0.600574 − 0.998151I
b = 1.135580 + 0.716044I
9.6993 − 10.3238I 0
u = 0.964249 − 0.810539I
a = −0.600574 + 0.998151I
b = 1.135580 − 0.716044I
9.6993 + 10.3238I 0
u = 0.807188 + 0.967313I
a = 0.010286 − 0.719507I
b = −1.367010 − 0.045646I
4.13276 + 7.64866I 0
u = 0.807188 − 0.967313I
a = 0.010286 + 0.719507I
b = −1.367010 + 0.045646I
4.13276 − 7.64866I 0
u = −0.818771 + 0.967967I
a = −1.077720 + 0.692980I
b = 0.495683 − 0.960350I
7.53995 − 5.75065I 0
u = −0.818771 − 0.967967I
a = −1.077720 − 0.692980I
b = 0.495683 + 0.960350I
7.53995 + 5.75065I 0
u = −0.374478 + 0.621105I
a = −0.250485 − 1.236750I
b = 0.790669 + 0.824031I
4.94910 − 3.81882I 2.10350 + 10.02722I
u = −0.374478 − 0.621105I
a = −0.250485 + 1.236750I
b = 0.790669 − 0.824031I
4.94910 + 3.81882I 2.10350 − 10.02722I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.798420 + 1.005590I
a = 0.54011 − 2.13936I
b = 1.143510 + 0.704102I
5.55281 − 11.82450I 0
u = −0.798420 − 1.005590I
a = 0.54011 + 2.13936I
b = 1.143510 − 0.704102I
5.55281 + 11.82450I 0
u = −0.822932 + 0.988050I
a = 0.10986 + 2.15970I
b = −0.907528 − 0.655336I
5.60270 − 10.30350I 0
u = −0.822932 − 0.988050I
a = 0.10986 − 2.15970I
b = −0.907528 + 0.655336I
5.60270 + 10.30350I 0
u = 0.852797 + 1.004360I
a = −1.040640 − 0.796571I
b = 0.485399 + 0.990678I
11.0580 + 10.7846I 0
u = 0.852797 − 1.004360I
a = −1.040640 + 0.796571I
b = 0.485399 − 0.990678I
11.0580 − 10.7846I 0
u = 0.846509 + 1.032650I
a = 0.40884 + 2.10501I
b = 1.160850 − 0.710725I
8.9763 + 16.9659I 0
u = 0.846509 − 1.032650I
a = 0.40884 − 2.10501I
b = 1.160850 + 0.710725I
8.9763 − 16.9659I 0
u = −0.593118 + 0.166075I
a = 1.21211 + 2.60731I
b = −1.065150 − 0.117254I
−0.593809 + 0.331522I 1.43748 − 9.72886I
u = −0.593118 − 0.166075I
a = 1.21211 − 2.60731I
b = −1.065150 + 0.117254I
−0.593809 − 0.331522I 1.43748 + 9.72886I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.254616 + 0.556672I
a = −0.397794 + 1.141700I
b = 0.937472 − 0.785999I
4.51649 + 2.17388I −1.65157 + 5.92574I
u = −0.254616 − 0.556672I
a = −0.397794 − 1.141700I
b = 0.937472 + 0.785999I
4.51649 − 2.17388I −1.65157 − 5.92574I
u = 0.265888 + 0.464329I
a = −2.42948 − 5.30179I
b = −0.833958 + 0.214787I
0.614687 + 0.409343I −5.88588 − 9.56935I
u = 0.265888 − 0.464329I
a = −2.42948 + 5.30179I
b = −0.833958 − 0.214787I
0.614687 − 0.409343I −5.88588 + 9.56935I
u = 0.463872
a = 1.34884
b = −0.0516319
1.25812 8.69990
u = −0.262621
a = 2.59919
b = −0.826000
−1.19847 −8.67400
14
II.
I
u
2
= hb +1, −u
8
+2u
7
+· · · +a−1, u
9
−u
8
+2u
7
−u
6
+3u
5
−u
4
+2u
3
+u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
−1
a
6
=
1
−u
2
a
2
=
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u
−1
a
1
=
−1
0
a
4
=
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
−1
a
7
=
1
−u
2
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
12
=
u
5
+ u
u
5
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
8
− 8u
7
+ 12u
6
− 11u
5
+ 18u
4
− 17u
3
+ 15u
2
− 6u + 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
7
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
9
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
10
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
11
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
12
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
, c
9
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
7
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
8
, c
10
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
11
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = −1.004430 + 0.297869I
b = −1.00000
−3.42837 − 2.09337I −6.83106 + 4.06115I
u = −0.140343 − 0.966856I
a = −1.004430 − 0.297869I
b = −1.00000
−3.42837 + 2.09337I −6.83106 − 4.06115I
u = −0.628449 + 0.875112I
a = −0.275254 + 0.816341I
b = −1.00000
−1.02799 − 2.45442I −7.33502 + 3.27944I
u = −0.628449 − 0.875112I
a = −0.275254 − 0.816341I
b = −1.00000
−1.02799 + 2.45442I −7.33502 − 3.27944I
u = 0.796005 + 0.733148I
a = 0.070080 − 0.850995I
b = −1.00000
2.72642 − 1.33617I −2.78826 + 0.80685I
u = 0.796005 − 0.733148I
a = 0.070080 + 0.850995I
b = −1.00000
2.72642 + 1.33617I −2.78826 − 0.80685I
u = 0.728966 + 0.986295I
a = −0.195086 − 0.635552I
b = −1.00000
1.95319 + 7.08493I −4.66194 − 6.93476I
u = 0.728966 − 0.986295I
a = −0.195086 + 0.635552I
b = −1.00000
1.95319 − 7.08493I −4.66194 + 6.93476I
u = −0.512358
a = 3.80937
b = −1.00000
−0.446489 15.2330
18
III. I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
3
=
0
v
2
− 3v − 1
a
6
=
1
0
a
2
=
v
2
− 3v − 1
v
2
− 3v − 1
a
1
=
v
2
− 3v − 1
−v
2
+ 2v + 3
a
4
=
−2v
2
+ 5v + 4
−2v
2
+ 5v + 3
a
7
=
−v
2
+ 3v + 1
v
2
− 2v − 3
a
9
=
v
0
a
11
=
v
0
a
8
=
v
0
a
12
=
v
2
− 2v − 1
−v
2
+ 2v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6v
2
− 19v − 9
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
8
, c
9
c
10
u
3
c
6
u
3
+ u
2
+ 2u + 1
c
7
, c
11
(u + 1)
3
c
12
(u − 1)
3
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
y
3
− y
2
+ 2y − 1
c
5
, c
8
, c
9
c
10
y
3
c
7
, c
11
, c
12
(y − 1)
3
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.539798 + 0.182582I
a = 0
b = 0.877439 − 0.744862I
4.66906 + 2.82812I 2.80443 − 4.65175I
v = −0.539798 − 0.182582I
a = 0
b = 0.877439 + 0.744862I
4.66906 − 2.82812I 2.80443 + 4.65175I
v = 3.07960
a = 0
b = −0.754878
0.531480 −10.6090
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
3
− u
2
+ 2u − 1)(u
96
+ 41u
95
+ ··· + 401u + 1)
c
2
((u − 1)
9
)(u
3
+ u
2
− 1)(u
96
− 11u
95
+ ··· + 7u + 1)
c
3
u
9
(u
3
− u
2
+ 2u − 1)(u
96
− 2u
95
+ ··· + 1536u − 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)(u
96
− 11u
95
+ ··· + 7u + 1)
c
5
u
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
96
− 2u
95
+ ··· − 12u − 8)
c
6
u
9
(u
3
+ u
2
+ 2u + 1)(u
96
− 2u
95
+ ··· + 1536u − 512)
c
7
(u + 1)
3
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
96
+ 5u
95
+ ··· − 8u + 1)
c
8
u
3
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
96
+ 24u
95
+ ··· + 48u + 64)
c
9
u
3
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
96
− 2u
95
+ ··· − 12u − 8)
c
10
u
3
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
96
+ 24u
95
+ ··· + 48u + 64)
c
11
(u + 1)
3
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
96
− 55u
95
+ ··· − 218u + 1)
c
12
(u − 1)
3
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
96
+ 5u
95
+ ··· − 8u + 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
3
+ 3y
2
+ 2y − 1)(y
96
+ 39y
95
+ ··· − 140705y + 1)
c
2
, c
4
((y − 1)
9
)(y
3
− y
2
+ 2y − 1)(y
96
− 41y
95
+ ··· − 401y + 1)
c
3
, c
6
y
9
(y
3
+ 3y
2
+ 2y − 1)(y
96
+ 60y
95
+ ··· + 1835008y + 262144)
c
5
, c
9
y
3
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
96
+ 24y
95
+ ··· + 48y + 64)
c
7
, c
12
(y − 1)
3
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
96
− 55y
95
+ ··· − 218y + 1)
c
8
, c
10
y
3
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
96
+ 92y
95
+ ··· − 879872y + 4096)
c
11
(y − 1)
3
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
96
− 23y
95
+ ··· − 43342y + 1)
24
