12n
0099
(K12n
0099
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 10 3 11 1 12 8 6
Solving Sequence
8,11
9
3,12
7 10 6 1 2 5 4
c
8
c
11
c
7
c
10
c
6
c
12
c
1
c
5
c
4
c
2
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.67717 × 10
122
u
80
+ 2.40640 × 10
123
u
79
+ ··· + 1.36344 × 10
123
b − 1.28567 × 10
122
,
− 1.49380 × 10
122
u
80
+ 9.63422 × 10
122
u
79
+ ··· + 6.81720 × 10
122
a − 3.22718 × 10
124
,
u
81
− 4u
80
+ ··· + 83u + 1i
I
u
2
= hb, −u
3
+ a − 2, u
4
+ u
2
+ u + 1i
I
u
3
= hb, −u
3
+ u
2
+ a − 2u + 1, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
u
4
= h−au + b + 2u, a
2
+ au − 3a − 3u + 2, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 95 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−5.68 × 10
122
u
80
+ 2.41 × 10
123
u
79
+ · · · + 1.36 × 10
123
b − 1.29 ×
10
122
, −1.49 × 10
122
u
80
+ 9.63 × 10
122
u
79
+ · · · + 6.82 × 10
122
a − 3.23 ×
10
124
, u
81
− 4u
80
+ · · · + 83u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
3
=
0.219123u
80
− 1.41322u
79
+ ··· + 157.415u + 47.3388
0.416386u
80
− 1.76495u
79
+ ··· − 43.2149u + 0.0942957
a
12
=
u
u
a
7
=
−0.327866u
80
+ 1.87240u
79
+ ··· − 62.8797u − 27.5857
−0.435511u
80
+ 1.87462u
79
+ ··· + 47.9628u + 0.199503
a
10
=
u
3
u
3
+ u
a
6
=
−0.236666u
80
+ 1.65002u
79
+ ··· − 61.3415u − 27.5686
−0.457531u
80
+ 2.08795u
79
+ ··· + 57.2670u + 0.314050
a
1
=
0.253925u
80
− 0.469551u
79
+ ··· + 57.0053u + 9.60025
−0.376132u
80
+ 1.67454u
79
+ ··· + 43.3245u + 0.630057
a
2
=
0.0290630u
80
− 0.406433u
79
+ ··· + 115.361u + 29.5970
0.334532u
80
− 1.24445u
79
+ ··· − 23.7001u + 0.0863807
a
5
=
−0.567784u
80
+ 2.57406u
79
+ ··· − 60.4666u − 27.1793
−0.334532u
80
+ 1.24445u
79
+ ··· + 23.7001u − 0.0863807
a
4
=
0.197263u
80
− 0.351727u
79
+ ··· − 200.629u − 47.2445
−0.416386u
80
+ 1.76495u
79
+ ··· + 43.2149u − 0.0942957
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.523679u
80
− 1.64827u
79
+ ··· + 61.1096u − 9.44591
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
81
+ 33u
80
+ ··· + 130u + 1
c
2
, c
4
u
81
− 13u
80
+ ··· − 12u + 1
c
3
, c
7
u
81
− 3u
80
+ ··· + 1024u + 1024
c
5
u
81
+ u
80
+ ··· + 8905262u + 2124511
c
6
u
81
+ 5u
80
+ ··· − 47488u + 22208
c
8
, c
11
u
81
+ 4u
80
+ ··· + 83u − 1
c
9
u
81
+ 8u
80
+ ··· + 256u + 16
c
10
u
81
+ 30u
80
+ ··· + 6303u − 1
c
12
u
81
− 4u
80
+ ··· − 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
81
+ 43y
80
+ ··· + 5274y −1
c
2
, c
4
y
81
− 33y
80
+ ··· + 130y −1
c
3
, c
7
y
81
+ 57y
80
+ ··· − 27787264y −1048576
c
5
y
81
+ 47y
80
+ ··· + 59668081079090y −4513546989121
c
6
y
81
+ 103y
80
+ ··· − 19451522048y −493195264
c
8
, c
11
y
81
+ 30y
80
+ ··· + 6303y −1
c
9
y
81
− 20y
80
+ ··· − 1152y −256
c
10
y
81
+ 46y
80
+ ··· + 39786411y −1
c
12
y
81
− 6y
80
+ ··· + 11y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.505398 + 0.861438I
a = −4.37384 − 2.52183I
b = 0.603292 − 0.010555I
−1.02453 − 2.05291I −171.972 + 28.532I
u = −0.505398 − 0.861438I
a = −4.37384 + 2.52183I
b = 0.603292 + 0.010555I
−1.02453 + 2.05291I −171.972 − 28.532I
u = −0.009112 + 1.005390I
a = −0.308654 + 0.203514I
b = −0.336499 − 0.810387I
−4.60609 − 1.52975I 0
u = −0.009112 − 1.005390I
a = −0.308654 − 0.203514I
b = −0.336499 + 0.810387I
−4.60609 + 1.52975I 0
u = 0.742803 + 0.679982I
a = −0.167793 + 0.282223I
b = 0.67879 + 1.59644I
6.21314 − 4.26930I 0
u = 0.742803 − 0.679982I
a = −0.167793 − 0.282223I
b = 0.67879 − 1.59644I
6.21314 + 4.26930I 0
u = 0.724035 + 0.675293I
a = 1.163810 + 0.739644I
b = 0.239752 − 1.287670I
0.58736 − 1.68614I 0
u = 0.724035 − 0.675293I
a = 1.163810 − 0.739644I
b = 0.239752 + 1.287670I
0.58736 + 1.68614I 0
u = −0.264835 + 0.948397I
a = −0.02548 − 2.76624I
b = 0.086690 − 1.153850I
1.73887 + 0.56914I 0
u = −0.264835 − 0.948397I
a = −0.02548 + 2.76624I
b = 0.086690 + 1.153850I
1.73887 − 0.56914I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.479721 + 0.852602I
a = −1.22325 − 1.39529I
b = −1.59287 + 0.05128I
−8.92096 + 1.95711I −29.9268 + 41.7453I
u = 0.479721 − 0.852602I
a = −1.22325 + 1.39529I
b = −1.59287 − 0.05128I
−8.92096 − 1.95711I −29.9268 − 41.7453I
u = −0.615664 + 0.829871I
a = −1.37738 + 1.51974I
b = 0.154661 − 1.382630I
3.68961 + 0.58365I 0
u = −0.615664 − 0.829871I
a = −1.37738 − 1.51974I
b = 0.154661 + 1.382630I
3.68961 − 0.58365I 0
u = 0.825094 + 0.624144I
a = −0.916453 − 0.626602I
b = −1.357180 + 0.050552I
2.74432 − 4.49163I 0
u = 0.825094 − 0.624144I
a = −0.916453 + 0.626602I
b = −1.357180 − 0.050552I
2.74432 + 4.49163I 0
u = −0.524882 + 0.802233I
a = 4.37321 + 0.45617I
b = 0.458462 + 0.233945I
−1.11518 − 1.63608I −22.5154 + 16.4209I
u = −0.524882 − 0.802233I
a = 4.37321 − 0.45617I
b = 0.458462 − 0.233945I
−1.11518 + 1.63608I −22.5154 − 16.4209I
u = 0.703049 + 0.783366I
a = 0.83771 + 1.13988I
b = 1.42270 + 0.44570I
1.96531 + 1.49483I 0
u = 0.703049 − 0.783366I
a = 0.83771 − 1.13988I
b = 1.42270 − 0.44570I
1.96531 − 1.49483I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.026493 + 0.936757I
a = 0.59780 + 2.29454I
b = 0.439042 + 1.154740I
0.95414 − 4.42889I −4.00000 + 4.19606I
u = −0.026493 − 0.936757I
a = 0.59780 − 2.29454I
b = 0.439042 − 1.154740I
0.95414 + 4.42889I −4.00000 − 4.19606I
u = −0.671407 + 0.627762I
a = −0.913409 − 0.028748I
b = −0.412488 + 0.213180I
1.15026 − 1.50439I 2.46877 + 2.61626I
u = −0.671407 − 0.627762I
a = −0.913409 + 0.028748I
b = −0.412488 − 0.213180I
1.15026 + 1.50439I 2.46877 − 2.61626I
u = −0.599484 + 0.904512I
a = 2.63171 − 1.35351I
b = 0.277078 + 1.371800I
3.45045 − 5.35632I 0
u = −0.599484 − 0.904512I
a = 2.63171 + 1.35351I
b = 0.277078 − 1.371800I
3.45045 + 5.35632I 0
u = −0.561505 + 0.944951I
a = 1.70785 + 3.15850I
b = 0.110600 − 0.423339I
−1.63060 − 2.73282I 0
u = −0.561505 − 0.944951I
a = 1.70785 − 3.15850I
b = 0.110600 + 0.423339I
−1.63060 + 2.73282I 0
u = −0.455620 + 1.013820I
a = −0.238189 + 0.544842I
b = 0.029747 + 0.351694I
−0.39491 − 2.82152I 0
u = −0.455620 − 1.013820I
a = −0.238189 − 0.544842I
b = 0.029747 − 0.351694I
−0.39491 + 2.82152I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.761415 + 0.820530I
a = 0.531324 − 0.454947I
b = −0.42765 − 1.74880I
8.06491 + 2.92024I 0
u = 0.761415 − 0.820530I
a = 0.531324 + 0.454947I
b = −0.42765 + 1.74880I
8.06491 − 2.92024I 0
u = −0.108997 + 1.122070I
a = −2.39634 − 0.23797I
b = −0.890661 + 0.321140I
−3.72961 − 3.73093I 0
u = −0.108997 − 1.122070I
a = −2.39634 + 0.23797I
b = −0.890661 − 0.321140I
−3.72961 + 3.73093I 0
u = 0.997287 + 0.541891I
a = −0.369368 − 0.079618I
b = −0.66734 − 1.50573I
7.29123 − 11.70270I 0
u = 0.997287 − 0.541891I
a = −0.369368 + 0.079618I
b = −0.66734 + 1.50573I
7.29123 + 11.70270I 0
u = 0.959008 + 0.624962I
a = −0.148070 + 0.092204I
b = 0.36850 + 1.64315I
9.10043 − 4.86820I 0
u = 0.959008 − 0.624962I
a = −0.148070 − 0.092204I
b = 0.36850 − 1.64315I
9.10043 + 4.86820I 0
u = 0.682699 + 0.926132I
a = 1.43843 + 0.92415I
b = 1.54169 − 0.19466I
1.52644 + 3.83350I 0
u = 0.682699 − 0.926132I
a = 1.43843 − 0.92415I
b = 1.54169 + 0.19466I
1.52644 − 3.83350I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.745953 + 0.906662I
a = −1.80870 − 0.05187I
b = −0.63390 + 1.61836I
7.80552 + 2.77364I 0
u = 0.745953 − 0.906662I
a = −1.80870 + 0.05187I
b = −0.63390 − 1.61836I
7.80552 − 2.77364I 0
u = −0.714581 + 0.401247I
a = −1.165920 − 0.348917I
b = −0.616988 − 0.161976I
1.29375 − 1.45245I 3.62930 + 4.86424I
u = −0.714581 − 0.401247I
a = −1.165920 + 0.348917I
b = −0.616988 + 0.161976I
1.29375 + 1.45245I 3.62930 − 4.86424I
u = 0.062348 + 0.798476I
a = 1.53880 + 1.10941I
b = 0.880183 − 0.328930I
−2.15630 + 0.07606I −8.00350 + 0.07144I
u = 0.062348 − 0.798476I
a = 1.53880 − 1.10941I
b = 0.880183 + 0.328930I
−2.15630 − 0.07606I −8.00350 − 0.07144I
u = 0.675941 + 0.993873I
a = −0.976588 − 0.077747I
b = 0.00539 + 1.42943I
−0.36837 + 7.06216I 0
u = 0.675941 − 0.993873I
a = −0.976588 + 0.077747I
b = 0.00539 − 1.42943I
−0.36837 − 7.06216I 0
u = 0.680506 + 0.995566I
a = 2.16987 + 0.15146I
b = 0.83647 − 1.48482I
5.25967 + 9.70670I 0
u = 0.680506 − 0.995566I
a = 2.16987 − 0.15146I
b = 0.83647 + 1.48482I
5.25967 − 9.70670I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.753433 + 0.220803I
a = −0.235608 + 0.164102I
b = 0.020461 + 0.617454I
−1.20619 − 3.00339I 2.21341 + 3.98452I
u = 0.753433 − 0.220803I
a = −0.235608 − 0.164102I
b = 0.020461 − 0.617454I
−1.20619 + 3.00339I 2.21341 − 3.98452I
u = 0.292757 + 1.184200I
a = −0.573258 + 0.779271I
b = −0.077263 + 0.631820I
−5.47007 + 0.37522I 0
u = 0.292757 − 1.184200I
a = −0.573258 − 0.779271I
b = −0.077263 − 0.631820I
−5.47007 − 0.37522I 0
u = −1.152240 + 0.412570I
a = −0.130976 + 0.209918I
b = −0.16545 + 1.48707I
7.13557 + 1.25582I 0
u = −1.152240 − 0.412570I
a = −0.130976 − 0.209918I
b = −0.16545 − 1.48707I
7.13557 − 1.25582I 0
u = −0.684988 + 1.023750I
a = −1.51416 + 0.44312I
b = −0.757611 + 0.003546I
−0.12016 − 3.83503I 0
u = −0.684988 − 1.023750I
a = −1.51416 − 0.44312I
b = −0.757611 − 0.003546I
−0.12016 + 3.83503I 0
u = 0.703453 + 1.042720I
a = −1.25123 − 1.15161I
b = −1.45915 − 0.22710I
1.48186 + 10.21890I 0
u = 0.703453 − 1.042720I
a = −1.25123 + 1.15161I
b = −1.45915 + 0.22710I
1.48186 − 10.21890I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.532163 + 1.140700I
a = 0.456393 − 0.597727I
b = 0.060321 − 0.542689I
−3.86039 + 7.78753I 0
u = 0.532163 − 1.140700I
a = 0.456393 + 0.597727I
b = 0.060321 + 0.542689I
−3.86039 − 7.78753I 0
u = −1.138710 + 0.566751I
a = −0.479445 − 0.126460I
b = −0.25605 − 1.48232I
6.96738 − 5.09561I 0
u = −1.138710 − 0.566751I
a = −0.479445 + 0.126460I
b = −0.25605 + 1.48232I
6.96738 + 5.09561I 0
u = 0.752599 + 1.093140I
a = 1.79634 − 0.18613I
b = 0.51625 − 1.63587I
7.63873 + 11.12540I 0
u = 0.752599 − 1.093140I
a = 1.79634 + 0.18613I
b = 0.51625 + 1.63587I
7.63873 − 11.12540I 0
u = −0.240383 + 1.329020I
a = 0.39785 + 1.40917I
b = 0.123794 + 1.279290I
0.90648 − 3.26112I 0
u = −0.240383 − 1.329020I
a = 0.39785 − 1.40917I
b = 0.123794 − 1.279290I
0.90648 + 3.26112I 0
u = 0.729533 + 1.141910I
a = −2.16101 + 0.00371I
b = −0.75699 + 1.47497I
5.4200 + 17.9748I 0
u = 0.729533 − 1.141910I
a = −2.16101 − 0.00371I
b = −0.75699 − 1.47497I
5.4200 − 17.9748I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.100629 + 1.380790I
a = −1.09077 − 1.42258I
b = −0.50450 − 1.33076I
−0.35544 − 9.04141I 0
u = −0.100629 − 1.380790I
a = −1.09077 + 1.42258I
b = −0.50450 + 1.33076I
−0.35544 + 9.04141I 0
u = −0.87285 + 1.14057I
a = 0.715969 + 0.518957I
b = −0.05609 + 1.43328I
5.23560 − 2.02485I 0
u = −0.87285 − 1.14057I
a = 0.715969 − 0.518957I
b = −0.05609 − 1.43328I
5.23560 + 2.02485I 0
u = −0.80039 + 1.23078I
a = −1.41250 − 0.47345I
b = −0.35709 − 1.43000I
4.66300 − 8.19652I 0
u = −0.80039 − 1.23078I
a = −1.41250 + 0.47345I
b = −0.35709 + 1.43000I
4.66300 + 8.19652I 0
u = −0.455946 + 0.115914I
a = −0.197228 + 1.245260I
b = 0.21037 + 1.44375I
4.09035 − 3.09672I −6.42475 + 2.99947I
u = −0.455946 − 0.115914I
a = −0.197228 − 1.245260I
b = 0.21037 − 1.44375I
4.09035 + 3.09672I −6.42475 − 2.99947I
u = −0.293387 + 0.220524I
a = 4.39202 + 0.48966I
b = 0.455347 − 0.441128I
−1.004280 − 0.810007I −4.84130 − 2.46574I
u = −0.293387 − 0.220524I
a = 4.39202 − 0.48966I
b = 0.455347 + 0.441128I
−1.004280 + 0.810007I −4.84130 + 2.46574I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0125912
a = 45.4131
b = 0.612334
−1.00318 −10.1710
13
II. I
u
2
= hb, −u
3
+ a − 2, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
3
=
u
3
+ 2
0
a
12
=
u
u
a
7
=
1
0
a
10
=
u
3
u
3
+ u
a
6
=
u
3
+ u
2
+ 1
u
3
+ u
2
+ u + 1
a
1
=
−u
3
− u
2
− u − 1
−u
2
− u − 1
a
2
=
−u
2
− u + 1
−u
2
− u − 1
a
5
=
u
3
+ u
2
+ u + 1
u
2
+ u + 1
a
4
=
u
3
+ 2
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9u
3
− 2u
2
+ 2u − 1
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
8
, c
9
u
4
+ u
2
+ u + 1
c
6
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
10
u
4
− 2u
3
+ 3u
2
− u + 1
c
11
u
4
+ u
2
− u + 1
c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
8
, c
9
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
y
4
− y
3
+ 2y
2
+ 7y + 4
c
10
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = 2.39923 + 0.32564I
b = 0
−0.66484 − 1.39709I 1.58487 + 5.38446I
u = −0.547424 − 0.585652I
a = 2.39923 − 0.32564I
b = 0
−0.66484 + 1.39709I 1.58487 − 5.38446I
u = 0.547424 + 1.120870I
a = 0.100768 − 0.400532I
b = 0
−4.26996 + 7.64338I −15.0849 − 3.8174I
u = 0.547424 − 1.120870I
a = 0.100768 + 0.400532I
b = 0
−4.26996 − 7.64338I −15.0849 + 3.8174I
17
III. I
u
3
= hb, −u
3
+ u
2
+ a − 2u + 1, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
3
=
u
3
− u
2
+ 2u − 1
0
a
12
=
u
u
a
7
=
1
0
a
10
=
u
3
u
3
+ u
a
6
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
−u
5
− 2u
3
+ u
2
− 2u + 1
a
1
=
−u
4
− u
2
+ u − 1
2u
5
− u
4
+ 3u
3
− 2u
2
+ 3u − 2
a
2
=
−u
4
+ u
3
− 2u
2
+ 3u − 2
2u
5
− u
4
+ 3u
3
− 2u
2
+ 3u − 2
a
5
=
u
4
+ u
2
− u + 1
−2u
5
+ u
4
− 3u
3
+ 2u
2
− 3u + 2
a
4
=
u
3
− u
2
+ 2u − 1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
5
+ u
4
+ 2u
2
+ 3u − 12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
8
, c
9
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
6
(u
3
− u
2
+ 1)
2
c
10
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
8
, c
9
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
(y
3
− y
2
+ 2y −1)
2
c
10
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = 0.13238 + 2.74513I
b = 0
−1.91067 − 2.82812I −14.1402 + 3.6935I
u = −0.498832 − 1.001300I
a = 0.13238 − 2.74513I
b = 0
−1.91067 + 2.82812I −14.1402 − 3.6935I
u = 0.284920 + 1.115140I
a = −0.307599 + 0.479689I
b = 0
−6.04826 −14.4399 + 2.5036I
u = 0.284920 − 1.115140I
a = −0.307599 − 0.479689I
b = 0
−6.04826 −14.4399 − 2.5036I
u = 0.713912 + 0.305839I
a = 0.175218 + 0.614017I
b = 0
−1.91067 − 2.82812I −8.91986 + 1.90022I
u = 0.713912 − 0.305839I
a = 0.175218 − 0.614017I
b = 0
−1.91067 + 2.82812I −8.91986 − 1.90022I
21
IV. I
u
4
= h−au + b + 2u, a
2
+ au − 3a − 3u + 2, u
2
+ u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u + 1
a
3
=
a
au − 2u
a
12
=
u
u
a
7
=
−2au − a + 5u + 4
−au + 2u − 1
a
10
=
1
u + 1
a
6
=
−2au − 2a + 3u + 4
−2au − a + 2u + 1
a
1
=
−3au − 3a + 8u + 6
−3au + 6u − 2
a
2
=
−au − a + 3u + 3
−au + 2u − 1
a
5
=
−2au − a + 5u + 4
−au + 2u − 1
a
4
=
−au + a + 2u
au − 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −21au − 42a + 25u + 91
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
2
− 3u + 1)
2
c
2
, c
3
(u
2
+ u − 1)
2
c
4
, c
7
(u
2
− u − 1)
2
c
5
, c
6
u
4
− 3u
3
+ 8u
2
− 3u + 1
c
8
(u
2
+ u + 1)
2
c
9
u
4
c
10
, c
11
(u
2
− u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
(y
2
− 7y + 1)
2
c
2
, c
3
, c
4
c
7
(y
2
− 3y + 1)
2
c
5
, c
6
y
4
+ 7y
3
+ 48y
2
+ 7y + 1
c
8
, c
10
, c
11
(y
2
+ y + 1)
2
c
9
y
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.19098 − 1.40126I
b = 1.61803
−8.88264 − 2.02988I 15.5000 + 44.1304I
u = −0.500000 + 0.866025I
a = 2.30902 + 0.53523I
b = −0.618034
−0.98696 − 2.02988I 15.5000 − 37.2022I
u = −0.500000 − 0.866025I
a = 1.19098 + 1.40126I
b = 1.61803
−8.88264 + 2.02988I 15.5000 − 44.1304I
u = −0.500000 − 0.866025I
a = 2.30902 − 0.53523I
b = −0.618034
−0.98696 + 2.02988I 15.5000 + 37.2022I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
2
− 3u + 1)
2
(u
81
+ 33u
80
+ ··· + 130u + 1)
c
2
((u − 1)
10
)(u
2
+ u − 1)
2
(u
81
− 13u
80
+ ··· − 12u + 1)
c
3
u
10
(u
2
+ u − 1)
2
(u
81
− 3u
80
+ ··· + 1024u + 1024)
c
4
((u + 1)
10
)(u
2
− u − 1)
2
(u
81
− 13u
80
+ ··· − 12u + 1)
c
5
(u
4
+ u
2
+ u + 1)(u
4
− 3u
3
+ 8u
2
− 3u + 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
81
+ u
80
+ ··· + 8905262u + 2124511)
c
6
(u
3
− u
2
+ 1)
2
(u
4
− 3u
3
+ 8u
2
− 3u + 1)(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
81
+ 5u
80
+ ··· − 47488u + 22208)
c
7
u
10
(u
2
− u − 1)
2
(u
81
− 3u
80
+ ··· + 1024u + 1024)
c
8
(u
2
+ u + 1)
2
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
81
+ 4u
80
+ ··· + 83u − 1)
c
9
u
4
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
81
+ 8u
80
+ ··· + 256u + 16)
c
10
(u
2
− u + 1)
2
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
81
+ 30u
80
+ ··· + 6303u − 1)
c
11
(u
2
− u + 1)
2
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
81
+ 4u
80
+ ··· + 83u − 1)
c
12
(u
2
− 3u + 1)
2
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
81
− 4u
80
+ ··· − 5u + 1)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
2
− 7y + 1)
2
(y
81
+ 43y
80
+ ··· + 5274y −1)
c
2
, c
4
((y −1)
10
)(y
2
− 3y + 1)
2
(y
81
− 33y
80
+ ··· + 130y −1)
c
3
, c
7
y
10
(y
2
− 3y + 1)
2
(y
81
+ 57y
80
+ ··· − 2.77873 × 10
7
y −1048576)
c
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
4
+ 7y
3
+ 48y
2
+ 7y + 1)
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
81
+ 47y
80
+ ··· + 59668081079090y −4513546989121)
c
6
((y
3
− y
2
+ 2y −1)
2
)(y
4
− y
3
+ 2y
2
+ 7y + 4)(y
4
+ 7y
3
+ ··· + 7y + 1)
· (y
81
+ 103y
80
+ ··· − 19451522048y −493195264)
c
8
, c
11
(y
2
+ y + 1)
2
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
81
+ 30y
80
+ ··· + 6303y −1)
c
9
y
4
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
81
− 20y
80
+ ··· − 1152y −256)
c
10
((y
2
+ y + 1)
2
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
81
+ 46y
80
+ ··· + 39786411y −1)
c
12
((y
2
− 7y + 1)
2
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
81
− 6y
80
+ ··· + 11y −1)
27
