12a
0015
(K12a
0015
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 12 11 4 7 1 9 10
Solving Sequence
4,8
5
9,11
12 7 10 1 6 3 2
c
4
c
8
c
11
c
7
c
9
c
12
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.07638 × 10
604
u
137
− 8.77338 × 10
604
u
136
+ ··· + 8.40968 × 10
606
b − 6.86516 × 10
608
,
1.65090 × 10
604
u
137
− 8.14368 × 10
604
u
136
+ ··· + 1.68194 × 10
607
a − 7.75391 × 10
608
,
u
138
− u
137
+ ··· + 20480u + 4096i
I
v
1
= ha, 963772v
11
+ 658631v
10
+ ··· + 707733b + 3141326,
v
12
+ v
11
− 4v
10
+ 5v
9
+ 19v
8
− 9v
7
− 31v
6
− 29v
5
+ 31v
4
+ 18v
3
+ 3v
2
+ 3v + 1i
* 2 irreducible components of dim
C
= 0, with total 150 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
= h2.08 × 10
604
u
137
− 8.77 × 10
604
u
136
+ · · · + 8.41 × 10
606
b − 6.87 ×
10
608
, 1.65 × 10
604
u
137
− 8.14 × 10
604
u
136
+ · · · + 1.68 × 10
607
a − 7.75 ×
10
608
, u
138
− u
137
+ · · · + 20480u + 4096i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
u
a
11
=
−0.000981550u
137
+ 0.00484185u
136
+ ··· + 217.405u + 46.1011
−0.00246903u
137
+ 0.0104325u
136
+ ··· + 395.215u + 81.6340
a
12
=
−0.000781310u
137
+ 0.00309620u
136
+ ··· + 139.466u + 29.2946
−0.00226879u
137
+ 0.00868684u
136
+ ··· + 317.275u + 64.8275
a
7
=
0.00204430u
137
+ 0.00306538u
136
+ ··· + 227.091u + 38.9117
0.00663207u
137
− 0.00116817u
136
+ ··· + 254.146u + 32.6295
a
10
=
0.00130809u
137
− 0.00169966u
136
+ ··· − 15.4882u − 3.73180
0.000676355u
137
+ 0.00282735u
136
+ ··· + 176.518u + 33.2890
a
1
=
0.00439295u
137
− 0.00147919u
136
+ ··· + 168.616u + 28.0993
0.00376122u
137
+ 0.00304781u
136
+ ··· + 360.623u + 65.1201
a
6
=
−0.00223744u
137
+ 0.00437981u
136
+ ··· + 114.339u + 25.0860
0.00215551u
137
+ 0.00290062u
136
+ ··· + 282.955u + 53.1853
a
3
=
0.00294739u
137
+ 0.000658646u
136
+ ··· + 125.123u + 20.7746
0.00255322u
137
+ 0.00251675u
136
+ ··· + 220.759u + 39.9007
a
2
=
0.00113636u
137
− 0.000399544u
136
+ ··· − 9.71148u − 4.35571
0.00149437u
137
+ 0.00230841u
136
+ ··· + 154.579u + 28.1483
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0290540u
137
+ 0.0285193u
136
+ ··· − 46.2850u + 54.5174
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
138
+ 67u
137
+ ··· + 33u + 1
c
2
, c
5
u
138
+ 7u
137
+ ··· + 9u + 1
c
3
u
138
− 7u
137
+ ··· − 98472303u + 13657673
c
4
, c
8
u
138
− u
137
+ ··· + 20480u + 4096
c
6
u
138
− 9u
137
+ ··· + 30021u − 1831
c
7
u
138
− 3u
137
+ ··· + 206471u + 14069
c
9
u
138
+ 9u
137
+ ··· + 3u + 1
c
10
, c
12
u
138
− 3u
137
+ ··· − 23u + 1
c
11
u
138
+ 23u
137
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
138
+ 15y
137
+ ··· − 35y + 1
c
2
, c
5
y
138
+ 67y
137
+ ··· + 33y + 1
c
3
y
138
− 37y
137
+ ··· + 2159732187820305y + 186532031774929
c
4
, c
8
y
138
+ 65y
137
+ ··· + 503316480y + 16777216
c
6
y
138
− 137y
137
+ ··· − 472810103y + 3352561
c
7
y
138
− 109y
137
+ ··· + 23684604833y + 197936761
c
9
y
138
+ 23y
137
+ ··· + 9y + 1
c
10
, c
12
y
138
− 89y
137
+ ··· − 23y + 1
c
11
y
138
− 9y
137
+ ··· − 23y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.225717 + 0.984869I
a = −0.294640 + 0.216111I
b = −1.54630 + 0.69058I
−2.26109 + 1.21839I 0
u = −0.225717 − 0.984869I
a = −0.294640 − 0.216111I
b = −1.54630 − 0.69058I
−2.26109 − 1.21839I 0
u = 0.968613 + 0.291315I
a = 0.147565 − 0.690953I
b = 1.43298 + 0.17677I
−3.85751 − 5.17156I 0
u = 0.968613 − 0.291315I
a = 0.147565 + 0.690953I
b = 1.43298 − 0.17677I
−3.85751 + 5.17156I 0
u = −0.844113 + 0.492611I
a = −0.358384 − 1.057380I
b = 0.165311 + 0.318348I
2.70862 + 2.80444I 0
u = −0.844113 − 0.492611I
a = −0.358384 + 1.057380I
b = 0.165311 − 0.318348I
2.70862 − 2.80444I 0
u = −0.495236 + 0.898497I
a = 1.017350 + 0.325698I
b = 2.36836 + 0.83423I
2.48949 − 5.71532I 0
u = −0.495236 − 0.898497I
a = 1.017350 − 0.325698I
b = 2.36836 − 0.83423I
2.48949 + 5.71532I 0
u = 0.407051 + 0.951666I
a = −1.18240 + 1.26696I
b = −1.79540 + 1.09338I
−1.49189 + 2.01388I 0
u = 0.407051 − 0.951666I
a = −1.18240 − 1.26696I
b = −1.79540 − 1.09338I
−1.49189 − 2.01388I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.691921 + 0.666142I
a = −0.667786 + 0.443380I
b = 0.193633 − 0.004783I
1.63530 + 4.17072I 0
u = 0.691921 − 0.666142I
a = −0.667786 − 0.443380I
b = 0.193633 + 0.004783I
1.63530 − 4.17072I 0
u = 0.647033 + 0.696244I
a = 0.415181 + 0.391117I
b = 0.727346 + 0.112079I
1.41425 + 1.45110I 0
u = 0.647033 − 0.696244I
a = 0.415181 − 0.391117I
b = 0.727346 − 0.112079I
1.41425 − 1.45110I 0
u = 0.362183 + 0.876985I
a = −0.05970 − 1.44009I
b = −0.197138 + 0.136703I
1.44585 + 2.70079I 0
u = 0.362183 − 0.876985I
a = −0.05970 + 1.44009I
b = −0.197138 − 0.136703I
1.44585 − 2.70079I 0
u = 0.924692 + 0.109605I
a = 0.345184 + 0.971895I
b = 1.52213 − 0.03534I
−4.26855 − 1.64031I 0
u = 0.924692 − 0.109605I
a = 0.345184 − 0.971895I
b = 1.52213 + 0.03534I
−4.26855 + 1.64031I 0
u = −0.790483 + 0.476530I
a = −0.442068 + 0.500118I
b = −0.611556 + 0.121924I
−0.04648 + 3.17550I 0
u = −0.790483 − 0.476530I
a = −0.442068 − 0.500118I
b = −0.611556 − 0.121924I
−0.04648 − 3.17550I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.883665 + 0.175408I
a = 0.527861 − 0.719630I
b = −0.049223 + 0.483166I
−0.821300 − 0.506241I 0
u = 0.883665 − 0.175408I
a = 0.527861 + 0.719630I
b = −0.049223 − 0.483166I
−0.821300 + 0.506241I 0
u = −0.466251 + 0.764985I
a = 0.742615 + 0.929151I
b = −0.156769 + 0.062810I
0.18427 − 8.79554I 0
u = −0.466251 − 0.764985I
a = 0.742615 − 0.929151I
b = −0.156769 − 0.062810I
0.18427 + 8.79554I 0
u = 1.000430 + 0.471347I
a = 0.281303 − 0.942139I
b = −0.212406 + 0.367643I
0.61052 − 7.36350I 0
u = 1.000430 − 0.471347I
a = 0.281303 + 0.942139I
b = −0.212406 − 0.367643I
0.61052 + 7.36350I 0
u = 0.390996 + 0.800553I
a = −1.025010 + 0.479217I
b = −2.38378 + 1.07374I
1.65391 + 0.55987I 0
u = 0.390996 − 0.800553I
a = −1.025010 − 0.479217I
b = −2.38378 − 1.07374I
1.65391 − 0.55987I 0
u = 0.354325 + 1.078600I
a = 1.182780 − 0.495498I
b = 2.23291 − 1.06563I
−2.10779 + 5.70362I 0
u = 0.354325 − 1.078600I
a = 1.182780 + 0.495498I
b = 2.23291 + 1.06563I
−2.10779 − 5.70362I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13904
a = 0.622593
b = 0.160363
1.10281 0
u = −0.166480 + 1.130730I
a = 0.991148 + 0.913261I
b = 1.60834 + 0.78839I
−5.25889 + 0.99512I 0
u = −0.166480 − 1.130730I
a = 0.991148 − 0.913261I
b = 1.60834 − 0.78839I
−5.25889 − 0.99512I 0
u = −1.055350 + 0.441739I
a = 0.456966 + 1.245590I
b = −0.067158 + 0.137579I
−1.00538 + 8.27121I 0
u = −1.055350 − 0.441739I
a = 0.456966 − 1.245590I
b = −0.067158 − 0.137579I
−1.00538 − 8.27121I 0
u = −0.805473 + 0.284873I
a = 3.54683 + 1.54981I
b = 3.92832 + 1.44251I
−2.05908 + 3.02563I 0
u = −0.805473 − 0.284873I
a = 3.54683 − 1.54981I
b = 3.92832 − 1.44251I
−2.05908 − 3.02563I 0
u = −0.523047 + 0.667669I
a = −0.21618 − 1.43239I
b = 0.160767 + 0.189881I
3.16409 + 1.56319I 0
u = −0.523047 − 0.667669I
a = −0.21618 + 1.43239I
b = 0.160767 − 0.189881I
3.16409 − 1.56319I 0
u = 0.494515 + 1.057540I
a = 0.96886 − 2.59242I
b = 1.06381 − 2.11928I
−2.24796 + 3.24421I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.494515 − 1.057540I
a = 0.96886 + 2.59242I
b = 1.06381 + 2.11928I
−2.24796 − 3.24421I 0
u = −0.147750 + 0.819139I
a = −0.58094 − 1.46237I
b = −0.178726 + 0.046191I
0.93710 − 3.59535I 0
u = −0.147750 − 0.819139I
a = −0.58094 + 1.46237I
b = −0.178726 − 0.046191I
0.93710 + 3.59535I 0
u = −0.309016 + 0.768051I
a = 0.703220 − 0.056139I
b = 1.58701 − 1.45199I
−2.00907 − 3.90626I 0
u = −0.309016 − 0.768051I
a = 0.703220 + 0.056139I
b = 1.58701 + 1.45199I
−2.00907 + 3.90626I 0
u = −0.419130 + 1.104740I
a = −0.741253 + 0.461461I
b = −1.271310 + 0.295904I
−4.22588 − 1.00117I 0
u = −0.419130 − 1.104740I
a = −0.741253 − 0.461461I
b = −1.271310 − 0.295904I
−4.22588 + 1.00117I 0
u = −0.403023 + 1.112730I
a = −0.855650 + 0.551969I
b = −1.82414 − 0.52868I
−5.07002 − 1.85762I 0
u = −0.403023 − 1.112730I
a = −0.855650 − 0.551969I
b = −1.82414 + 0.52868I
−5.07002 + 1.85762I 0
u = −0.482224 + 1.095960I
a = −1.240380 − 0.414603I
b = −2.33757 − 0.89688I
−1.36324 − 11.29470I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482224 − 1.095960I
a = −1.240380 + 0.414603I
b = −2.33757 + 0.89688I
−1.36324 + 11.29470I 0
u = 0.617415 + 1.032780I
a = 0.678337 + 0.307189I
b = 1.188460 + 0.067653I
0.34659 + 3.64206I 0
u = 0.617415 − 1.032780I
a = 0.678337 − 0.307189I
b = 1.188460 − 0.067653I
0.34659 − 3.64206I 0
u = −0.299210 + 1.174910I
a = −0.57189 − 2.80569I
b = −0.62514 − 2.34158I
−6.50973 − 0.24697I 0
u = −0.299210 − 1.174910I
a = −0.57189 + 2.80569I
b = −0.62514 + 2.34158I
−6.50973 + 0.24697I 0
u = 0.594539 + 0.516126I
a = −2.04149 + 2.38783I
b = −2.48085 + 2.13800I
−0.564734 + 1.063680I −9.1645 − 19.4771I
u = 0.594539 − 0.516126I
a = −2.04149 − 2.38783I
b = −2.48085 − 2.13800I
−0.564734 − 1.063680I −9.1645 + 19.4771I
u = −0.471282 + 1.118030I
a = 1.30102 + 1.05181I
b = 1.89906 + 0.90378I
−3.90439 − 6.62338I 0
u = −0.471282 − 1.118030I
a = 1.30102 − 1.05181I
b = 1.89906 − 0.90378I
−3.90439 + 6.62338I 0
u = 0.468994 + 0.629619I
a = 2.43302 − 2.37091I
b = 2.65913 − 1.95873I
−0.61751 + 1.70960I −9.8208 + 17.9498I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.468994 − 0.629619I
a = 2.43302 + 2.37091I
b = 2.65913 + 1.95873I
−0.61751 − 1.70960I −9.8208 − 17.9498I
u = 0.382806 + 1.155410I
a = 0.359131 + 0.027006I
b = 1.60372 + 0.55083I
−4.91525 + 3.17082I 0
u = 0.382806 − 1.155410I
a = 0.359131 − 0.027006I
b = 1.60372 − 0.55083I
−4.91525 − 3.17082I 0
u = 0.080035 + 1.216100I
a = 0.526288 + 0.157565I
b = 1.74683 + 0.65547I
−5.86217 − 4.68661I 0
u = 0.080035 − 1.216100I
a = 0.526288 − 0.157565I
b = 1.74683 − 0.65547I
−5.86217 + 4.68661I 0
u = 1.204080 + 0.239536I
a = −0.459385 + 1.051260I
b = 0.090805 + 0.133302I
−5.12215 − 5.13211I 0
u = 1.204080 − 0.239536I
a = −0.459385 − 1.051260I
b = 0.090805 − 0.133302I
−5.12215 + 5.13211I 0
u = −0.514859 + 1.134730I
a = 0.541995 + 0.245560I
b = 1.32232 − 0.99331I
−4.22507 − 5.81215I 0
u = −0.514859 − 1.134730I
a = 0.541995 − 0.245560I
b = 1.32232 + 0.99331I
−4.22507 + 5.81215I 0
u = −0.752443 + 0.039638I
a = −0.852096 + 0.385900I
b = −0.613279 − 0.275254I
−1.00356 − 2.77254I 0.77684 + 5.56890I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.752443 − 0.039638I
a = −0.852096 − 0.385900I
b = −0.613279 + 0.275254I
−1.00356 + 2.77254I 0.77684 − 5.56890I
u = −0.536143 + 0.485236I
a = 0.51276 + 1.88327I
b = −0.0175137 + 0.1051560I
0.61191 + 7.14983I 3.75978 − 1.57652I
u = −0.536143 − 0.485236I
a = 0.51276 − 1.88327I
b = −0.0175137 − 0.1051560I
0.61191 − 7.14983I 3.75978 + 1.57652I
u = 0.722812
a = 1.01964
b = 0.245406
1.24576 9.34870
u = −0.633518 + 0.347110I
a = 0.253544 − 0.635653I
b = −1.255390 + 0.218624I
−1.79923 + 1.22022I −1.34511 − 3.56182I
u = −0.633518 − 0.347110I
a = 0.253544 + 0.635653I
b = −1.255390 − 0.218624I
−1.79923 − 1.22022I −1.34511 + 3.56182I
u = 0.229996 + 1.259400I
a = −0.198398 + 0.489472I
b = −0.374227 + 0.829231I
0.42778 + 2.94009I 0
u = 0.229996 − 1.259400I
a = −0.198398 − 0.489472I
b = −0.374227 − 0.829231I
0.42778 − 2.94009I 0
u = 0.237164 + 1.259150I
a = 0.793025 + 0.477523I
b = 1.72121 − 0.62807I
−9.23975 − 1.47869I 0
u = 0.237164 − 1.259150I
a = 0.793025 − 0.477523I
b = 1.72121 + 0.62807I
−9.23975 + 1.47869I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.625704 + 1.124680I
a = 0.957652 + 0.155716I
b = 2.25228 + 0.59171I
0.72901 − 8.31835I 0
u = −0.625704 − 1.124680I
a = 0.957652 − 0.155716I
b = 2.25228 − 0.59171I
0.72901 + 8.31835I 0
u = 1.179740 + 0.520421I
a = −0.361647 + 1.213850I
b = 0.071610 + 0.151034I
−3.53057 − 13.07050I 0
u = 1.179740 − 0.520421I
a = −0.361647 − 1.213850I
b = 0.071610 − 0.151034I
−3.53057 + 13.07050I 0
u = 0.185406 + 0.682883I
a = 0.27266 + 1.97980I
b = −0.0381996 + 0.1034590I
−0.44372 − 3.17076I −5.30905 − 2.16030I
u = 0.185406 − 0.682883I
a = 0.27266 − 1.97980I
b = −0.0381996 − 0.1034590I
−0.44372 + 3.17076I −5.30905 + 2.16030I
u = −0.557227 + 1.166990I
a = −0.81226 − 2.43716I
b = −0.89747 − 1.94437I
−4.70709 − 8.12492I 0
u = −0.557227 − 1.166990I
a = −0.81226 + 2.43716I
b = −0.89747 + 1.94437I
−4.70709 + 8.12492I 0
u = 0.484539 + 1.201990I
a = −0.873032 + 0.170491I
b = −2.13899 + 0.63134I
−4.09738 + 5.40863I 0
u = 0.484539 − 1.201990I
a = −0.873032 − 0.170491I
b = −2.13899 − 0.63134I
−4.09738 − 5.40863I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.652158 + 1.121780I
a = −0.753877 + 0.285874I
b = −1.301380 + 0.047036I
−1.92373 − 8.69899I 0
u = −0.652158 − 1.121780I
a = −0.753877 − 0.285874I
b = −1.301380 − 0.047036I
−1.92373 + 8.69899I 0
u = 0.354774 + 1.248840I
a = −0.616679 + 0.303202I
b = −1.43627 − 0.89821I
−8.72518 + 2.65013I 0
u = 0.354774 − 1.248840I
a = −0.616679 − 0.303202I
b = −1.43627 + 0.89821I
−8.72518 − 2.65013I 0
u = 0.456208 + 0.530857I
a = 1.13919 − 1.09802I
b = 0.157090 − 0.007597I
2.30178 − 0.05398I 5.52630 − 2.50446I
u = 0.456208 − 0.530857I
a = 1.13919 + 1.09802I
b = 0.157090 + 0.007597I
2.30178 + 0.05398I 5.52630 + 2.50446I
u = 0.969289 + 0.894952I
a = −0.1042660 − 0.0526307I
b = 0.190558 − 0.272536I
1.00721 + 1.59954I 0
u = 0.969289 − 0.894952I
a = −0.1042660 + 0.0526307I
b = 0.190558 + 0.272536I
1.00721 − 1.59954I 0
u = 0.499313 + 1.221980I
a = 0.800563 + 0.576581I
b = 1.75153 − 0.48262I
−7.72780 + 6.66125I 0
u = 0.499313 − 1.221980I
a = 0.800563 − 0.576581I
b = 1.75153 + 0.48262I
−7.72780 − 6.66125I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.027575 + 0.669982I
a = −0.131081 + 0.975115I
b = −0.33991 + 1.63785I
0.77901 + 2.40486I 0.57490 − 3.33955I
u = −0.027575 − 0.669982I
a = −0.131081 − 0.975115I
b = −0.33991 − 1.63785I
0.77901 − 2.40486I 0.57490 + 3.33955I
u = −1.239130 + 0.488019I
a = 0.294086 − 0.385560I
b = −0.134296 − 0.114140I
−4.27455 − 4.31705I 0
u = −1.239130 − 0.488019I
a = 0.294086 + 0.385560I
b = −0.134296 + 0.114140I
−4.27455 + 4.31705I 0
u = −0.760986 + 1.097480I
a = 0.114324 − 0.213713I
b = 0.064421 − 0.580905I
−0.61746 + 4.04978I 0
u = −0.760986 − 1.097480I
a = 0.114324 + 0.213713I
b = 0.064421 + 0.580905I
−0.61746 − 4.04978I 0
u = −0.533533 + 0.393622I
a = −0.97725 + 1.40364I
b = −1.94209 + 0.34526I
−2.78368 − 1.46397I −3.71074 + 3.08918I
u = −0.533533 − 0.393622I
a = −0.97725 − 1.40364I
b = −1.94209 − 0.34526I
−2.78368 + 1.46397I −3.71074 − 3.08918I
u = 0.047521 + 0.644878I
a = −1.179240 − 0.068407I
b = −2.32332 − 1.43336I
−2.35739 − 0.94653I −10.41057 − 1.05373I
u = 0.047521 − 0.644878I
a = −1.179240 + 0.068407I
b = −2.32332 + 1.43336I
−2.35739 + 0.94653I −10.41057 + 1.05373I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.589342 + 1.220770I
a = −0.514128 + 0.291135I
b = −1.27522 − 0.92426I
−6.77899 + 10.82090I 0
u = 0.589342 − 1.220770I
a = −0.514128 − 0.291135I
b = −1.27522 + 0.92426I
−6.77899 − 10.82090I 0
u = 0.678071 + 1.188740I
a = −0.952054 + 0.115631I
b = −2.23325 + 0.53630I
−1.67408 + 13.49120I 0
u = 0.678071 − 1.188740I
a = −0.952054 − 0.115631I
b = −2.23325 − 0.53630I
−1.67408 − 13.49120I 0
u = −0.699582 + 1.215180I
a = −1.250860 − 0.275217I
b = −2.33543 − 0.61493I
−3.4406 − 14.6175I 0
u = −0.699582 − 1.215180I
a = −1.250860 + 0.275217I
b = −2.33543 + 0.61493I
−3.4406 + 14.6175I 0
u = −0.06214 + 1.41839I
a = 0.821700 − 0.319634I
b = 1.51310 − 0.76091I
−7.96952 + 4.57151I 0
u = −0.06214 − 1.41839I
a = 0.821700 + 0.319634I
b = 1.51310 + 0.76091I
−7.96952 − 4.57151I 0
u = −0.447357 + 0.348451I
a = −3.00586 − 0.37306I
b = −3.58489 + 0.07302I
−1.48464 + 2.67615I −11.3832 + 12.0268I
u = −0.447357 − 0.348451I
a = −3.00586 + 0.37306I
b = −3.58489 − 0.07302I
−1.48464 − 2.67615I −11.3832 − 12.0268I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36012 + 0.45602I
a = −0.330074 − 0.370600I
b = −0.146651 − 0.049871I
−2.10145 + 4.63629I 0
u = −1.36012 − 0.45602I
a = −0.330074 + 0.370600I
b = −0.146651 + 0.049871I
−2.10145 − 4.63629I 0
u = 0.60934 + 1.31602I
a = 1.191370 − 0.282012I
b = 2.21784 − 0.64053I
−8.6772 + 11.5041I 0
u = 0.60934 − 1.31602I
a = 1.191370 + 0.282012I
b = 2.21784 + 0.64053I
−8.6772 − 11.5041I 0
u = 0.69110 + 1.28047I
a = −0.618692 + 0.364479I
b = −1.177280 + 0.552949I
−2.30827 + 6.50477I 0
u = 0.69110 − 1.28047I
a = −0.618692 − 0.364479I
b = −1.177280 − 0.552949I
−2.30827 − 6.50477I 0
u = 0.76319 + 1.24643I
a = 1.251390 − 0.245316I
b = 2.33016 − 0.55434I
−5.8957 + 20.0114I 0
u = 0.76319 − 1.24643I
a = 1.251390 + 0.245316I
b = 2.33016 + 0.55434I
−5.8957 − 20.0114I 0
u = −0.76896 + 1.29555I
a = 0.676542 + 0.349738I
b = 1.289450 + 0.515918I
−4.86223 − 11.95560I 0
u = −0.76896 − 1.29555I
a = 0.676542 − 0.349738I
b = 1.289450 − 0.515918I
−4.86223 + 11.95560I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07354 + 1.51167I
a = −0.916297 − 0.278761I
b = −1.68989 − 0.67622I
−11.8703 − 9.0599I 0
u = −0.07354 − 1.51167I
a = −0.916297 + 0.278761I
b = −1.68989 + 0.67622I
−11.8703 + 9.0599I 0
u = −0.269804 + 0.381004I
a = 1.069040 + 0.014526I
b = −0.926287 + 0.440409I
−1.85090 + 1.10618I −2.51777 − 1.83567I
u = −0.269804 − 0.381004I
a = 1.069040 − 0.014526I
b = −0.926287 − 0.440409I
−1.85090 − 1.10618I −2.51777 + 1.83567I
u = 0.17686 + 1.52587I
a = −0.777083 − 0.221638I
b = −1.42378 − 0.57653I
−11.67560 + 0.10597I 0
u = 0.17686 − 1.52587I
a = −0.777083 + 0.221638I
b = −1.42378 + 0.57653I
−11.67560 − 0.10597I 0
u = −0.63750 + 1.40717I
a = 0.576430 + 0.245891I
b = 1.079120 + 0.326947I
−7.63817 − 3.16727I 0
u = −0.63750 − 1.40717I
a = 0.576430 − 0.245891I
b = 1.079120 − 0.326947I
−7.63817 + 3.16727I 0
18
II. I
v
1
= ha, 9.64 × 10
5
v
11
+ 6.59 × 10
5
v
10
+ · · · + 7.08 × 10
5
b + 3.14 ×
10
6
, v
12
+ v
11
+ · · · + 3v + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
v
0
a
5
=
1
0
a
9
=
v
0
a
11
=
0
−1.36177v
11
− 0.930621v
10
+ ··· − 5.08294v − 4.43857
a
12
=
−0.222666v
11
− 0.152658v
10
+ ··· + 0.0683153v − 0.431153
−1.36177v
11
− 0.930621v
10
+ ··· − 5.08294v − 4.43857
a
7
=
v
−0.546453v
11
− 0.201388v
10
+ ··· − 2.43405v − 1.91940
a
10
=
0.181358v
11
+ 0.113940v
10
+ ··· + 1.48874v + 0.345065
−0.678951v
11
− 0.501804v
10
+ ··· − 2.40704v − 2.15346
a
1
=
−0.306346v
11
− 0.227326v
10
+ ··· − 1.34123v − 0.522212
−0.678951v
11
− 0.501804v
10
+ ··· − 2.40704v − 2.15346
a
6
=
0.306346v
11
+ 0.227326v
10
+ ··· + 1.34123v + 0.522212
0.678951v
11
+ 0.501804v
10
+ ··· + 2.40704v + 2.15346
a
3
=
0.0350655v
11
− 0.0129173v
10
+ ··· − 0.00328231v + 1.62035
−0.678951v
11
− 0.501804v
10
+ ··· − 2.40704v − 1.15346
a
2
=
0.714016v
11
+ 0.488886v
10
+ ··· + 2.40376v + 2.77380
−0.678951v
11
− 0.501804v
10
+ ··· − 2.40704v − 1.15346
(ii) Obstruction class = 1
(iii) Cusp Shapes =
821
10257
v
11
+
8666
235911
v
10
+ ··· +
189289
10257
v +
16124
235911
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
8
u
12
c
6
, c
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
7
, c
12
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
10
, c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
8
y
12
c
6
, c
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
7
, c
10
, c
11
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.695888 + 0.967642I
a = 0
b = 0.289622 + 0.827421I
1.89061 + 2.95419I 6.39280 − 3.57892I
v = −0.695888 − 0.967642I
a = 0
b = 0.289622 − 0.827421I
1.89061 − 2.95419I 6.39280 + 3.57892I
v = 1.185950 + 0.118836I
a = 0
b = −0.861379 − 0.162890I
1.89061 − 1.10558I 3.63443 + 2.52768I
v = 1.185950 − 0.118836I
a = 0
b = −0.861379 + 0.162890I
1.89061 + 1.10558I 3.63443 − 2.52768I
v = −0.383184 + 0.075842I
a = 0
b = −0.74515 − 1.88172I
−1.89061 − 2.95419I −7.91752 + 1.81989I
v = −0.383184 − 0.075842I
a = 0
b = −0.74515 + 1.88172I
−1.89061 + 2.95419I −7.91752 − 1.81989I
v = 0.125911 + 0.369768I
a = 0
b = −1.25704 − 1.58618I
−1.89061 − 1.10558I 3.59610 + 6.57635I
v = 0.125911 − 0.369768I
a = 0
b = −1.25704 + 1.58618I
−1.89061 + 1.10558I 3.59610 − 6.57635I
v = 1.38214 + 1.64413I
a = 0
b = 0.520868 − 0.215334I
3.66314I 2.83009 − 6.37777I
v = 1.38214 − 1.64413I
a = 0
b = 0.520868 + 0.215334I
− 3.66314I 2.83009 + 6.37777I
22
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −2.11493 + 0.37491I
a = 0
b = −0.446919 − 0.343418I
7.72290I −2.53591 − 7.46338I
v = −2.11493 − 0.37491I
a = 0
b = −0.446919 + 0.343418I
− 7.72290I −2.53591 + 7.46338I
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
138
+ 67u
137
+ ··· + 33u + 1)
c
2
((u
2
+ u + 1)
6
)(u
138
+ 7u
137
+ ··· + 9u + 1)
c
3
((u
2
− u + 1)
6
)(u
138
− 7u
137
+ ··· − 9.84723 × 10
7
u + 1.36577 × 10
7
)
c
4
, c
8
u
12
(u
138
− u
137
+ ··· + 20480u + 4096)
c
5
((u
2
− u + 1)
6
)(u
138
+ 7u
137
+ ··· + 9u + 1)
c
6
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
138
− 9u
137
+ ··· + 30021u − 1831)
c
7
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
138
− 3u
137
+ ··· + 206471u + 14069)
c
9
((u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
)(u
138
+ 9u
137
+ ··· + 3u + 1)
c
10
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
138
− 3u
137
+ ··· − 23u + 1)
c
11
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
138
+ 23u
137
+ ··· + 3u + 1)
c
12
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
138
− 3u
137
+ ··· − 23u + 1)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
138
+ 15y
137
+ ··· − 35y + 1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
138
+ 67y
137
+ ··· + 33y + 1)
c
3
(y
2
+ y + 1)
6
· (y
138
− 37y
137
+ ··· + 2159732187820305y + 186532031774929)
c
4
, c
8
y
12
(y
138
+ 65y
137
+ ··· + 5.03316 × 10
8
y + 1.67772 × 10
7
)
c
6
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
138
− 137y
137
+ ··· − 472810103y + 3352561)
c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
138
− 109y
137
+ ··· + 23684604833y + 197936761)
c
9
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
138
+ 23y
137
+ ··· + 9y + 1)
c
10
, c
12
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
138
− 89y
137
+ ··· − 23y + 1)
c
11
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
138
− 9y
137
+ ··· − 23y + 1)
25
