12a
0587
(K12a
0587
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 12 2 11 6 4 1 8 5
Solving Sequence
3,9
4 10
5,7
2 1 11 6 8 12
c
3
c
9
c
4
c
2
c
1
c
10
c
6
c
8
c
12
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.83230 × 10
210
u
94
+ 2.87938 × 10
210
u
93
+ ··· + 6.01126 × 10
209
b + 1.51610 × 10
211
,
− 6.22396 × 10
212
u
94
− 5.32040 × 10
212
u
93
+ ··· + 1.38259 × 10
211
a − 3.59834 × 10
213
,
u
95
+ u
94
+ ··· + 14u + 1i
I
u
2
= hb + u, −5u
3
+ u
2
+ 3a + u + 1, u
4
− u
2
+ 1i
I
u
3
= hu
3
+ b − u, −2u
3
− 2u
2
+ 3a + u + 1, u
4
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 103 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
= h3.83 × 10
210
u
94
+ 2.88 × 10
210
u
93
+ · · · + 6.01 × 10
209
b + 1.52 ×
10
211
, −6.22 × 10
212
u
94
− 5.32 × 10
212
u
93
+ · · · + 1.38 × 10
211
a − 3.60 ×
10
213
, u
95
+ u
94
+ · · · + 14u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
45.0167u
94
+ 38.4814u
93
+ ··· + 2267.19u + 260.261
−6.37520u
94
− 4.78997u
93
+ ··· − 257.604u − 25.2210
a
2
=
1.59454u
94
+ 0.308707u
93
+ ··· − 66.9417u − 32.4693
7.62210u
94
+ 6.21989u
93
+ ··· + 361.151u + 39.4626
a
1
=
9.21664u
94
+ 6.52860u
93
+ ··· + 294.209u + 6.99328
7.62210u
94
+ 6.21989u
93
+ ··· + 361.151u + 39.4626
a
11
=
−11.7276u
94
+ 0.556507u
93
+ ··· + 490.732u + 114.762
−13.6943u
94
− 10.5472u
93
+ ··· − 561.915u − 56.4554
a
6
=
28.2378u
94
+ 25.1088u
93
+ ··· + 1538.65u + 179.735
0.930224u
94
+ 1.04484u
93
+ ··· + 81.7759u + 13.0061
a
8
=
19.8661u
94
+ 26.6636u
93
+ ··· + 1975.80u + 268.892
−12.5392u
94
− 9.28515u
93
+ ··· − 487.948u − 46.1105
a
12
=
3.02163u
94
+ 1.62086u
93
+ ··· + 14.8334u − 24.3382
7.07489u
94
+ 5.79666u
93
+ ··· + 336.703u + 36.8118
(ii) Obstruction class = −1
(iii) Cusp Shapes = −43.6001u
94
− 30.2490u
93
+ ··· − 1486.07u − 149.913
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
95
+ 45u
94
+ ··· + 5812u + 169
c
2
, c
6
u
95
− 3u
94
+ ··· − 64u − 13
c
3
, c
4
, c
9
u
95
− u
94
+ ··· + 14u − 1
c
5
, c
12
u
95
− 3u
94
+ ··· − 544u − 52
c
7
, c
11
u
95
+ 5u
94
+ ··· − 22u − 1
c
8
529(529u
95
− 345u
94
+ ··· − 1.01241 × 10
8
u + 1.22522 × 10
7
)
c
10
529(529u
95
+ 1035u
94
+ ··· + 6.65199 × 10
7
u + 1.26008 × 10
7
)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
95
+ 15y
94
+ ··· + 2924000y −28561
c
2
, c
6
y
95
− 45y
94
+ ··· + 5812y −169
c
3
, c
4
, c
9
y
95
− 93y
94
+ ··· + 88y −1
c
5
, c
12
y
95
+ 83y
94
+ ··· − 1192y −2704
c
7
, c
11
y
95
− 57y
94
+ ··· + 304y −1
c
8
279841(279841y
95
− 2.19233 × 10
7
y
94
+ ··· + 8.54386 × 10
15
y −1.50117 × 10
14
)
c
10
279841(279841y
95
− 1.00515 × 10
7
y
94
+ ··· + 2.52702 × 10
16
y −1.58780 × 10
14
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.324076 + 0.932614I
a = −0.57215 − 1.46473I
b = 1.106370 + 0.298292I
−8.62975 − 0.07531I 0
u = 0.324076 − 0.932614I
a = −0.57215 + 1.46473I
b = 1.106370 − 0.298292I
−8.62975 + 0.07531I 0
u = 0.740982 + 0.622306I
a = 0.271489 + 0.025604I
b = −1.207240 + 0.119440I
−10.13730 − 5.06463I 0
u = 0.740982 − 0.622306I
a = 0.271489 − 0.025604I
b = −1.207240 − 0.119440I
−10.13730 + 5.06463I 0
u = 0.893227 + 0.368349I
a = −0.219033 + 0.457967I
b = 0.831308 − 0.551679I
−0.1180870 + 0.0250280I 0
u = 0.893227 − 0.368349I
a = −0.219033 − 0.457967I
b = 0.831308 + 0.551679I
−0.1180870 − 0.0250280I 0
u = 0.569885 + 0.872471I
a = −0.19005 − 1.86439I
b = 1.143560 + 0.616829I
−6.8689 − 13.3214I 0
u = 0.569885 − 0.872471I
a = −0.19005 + 1.86439I
b = 1.143560 − 0.616829I
−6.8689 + 13.3214I 0
u = −0.530173 + 0.768074I
a = −0.75856 − 1.22838I
b = 0.385983 + 0.866786I
−4.58095 + 7.84168I 0
u = −0.530173 − 0.768074I
a = −0.75856 + 1.22838I
b = 0.385983 − 0.866786I
−4.58095 − 7.84168I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.563129 + 0.738059I
a = −0.28918 − 1.51880I
b = −0.284444 + 0.674957I
−4.69329 − 2.77756I 0
u = −0.563129 − 0.738059I
a = −0.28918 + 1.51880I
b = −0.284444 − 0.674957I
−4.69329 + 2.77756I 0
u = 0.461536 + 0.798582I
a = −0.528916 + 1.097220I
b = 0.413376 − 0.527923I
−0.62347 − 2.22932I 0
u = 0.461536 − 0.798582I
a = −0.528916 − 1.097220I
b = 0.413376 + 0.527923I
−0.62347 + 2.22932I 0
u = −1.028620 + 0.372700I
a = 0.336932 + 1.297890I
b = 0.792047 − 0.591034I
0.00681 + 4.54787I 0
u = −1.028620 − 0.372700I
a = 0.336932 − 1.297890I
b = 0.792047 + 0.591034I
0.00681 − 4.54787I 0
u = 0.657206 + 0.901845I
a = 0.644915 − 0.664953I
b = −1.111150 + 0.535210I
−7.03870 + 7.43919I 0
u = 0.657206 − 0.901845I
a = 0.644915 + 0.664953I
b = −1.111150 − 0.535210I
−7.03870 − 7.43919I 0
u = −0.555423 + 1.010360I
a = −0.23176 + 1.60411I
b = 1.060760 − 0.514305I
−2.49114 + 6.53115I 0
u = −0.555423 − 1.010360I
a = −0.23176 − 1.60411I
b = 1.060760 + 0.514305I
−2.49114 − 6.53115I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.445712 + 0.635397I
a = 0.11193 − 1.81470I
b = −1.139330 + 0.600773I
−1.72270 + 8.42111I 0
u = −0.445712 − 0.635397I
a = 0.11193 + 1.81470I
b = −1.139330 − 0.600773I
−1.72270 − 8.42111I 0
u = 1.066390 + 0.614208I
a = −0.16248 + 1.40511I
b = −0.778605 − 0.254375I
−2.29481 − 2.77237I 0
u = 1.066390 − 0.614208I
a = −0.16248 − 1.40511I
b = −0.778605 + 0.254375I
−2.29481 + 2.77237I 0
u = −0.890509 + 0.889227I
a = 0.352038 + 0.577350I
b = −1.021720 − 0.391174I
−3.42941 − 0.01024I 0
u = −0.890509 − 0.889227I
a = 0.352038 − 0.577350I
b = −1.021720 + 0.391174I
−3.42941 + 0.01024I 0
u = 0.337463 + 0.657456I
a = 0.20569 + 2.01133I
b = −0.979429 − 0.576485I
1.42526 − 3.92148I 0
u = 0.337463 − 0.657456I
a = 0.20569 − 2.01133I
b = −0.979429 + 0.576485I
1.42526 + 3.92148I 0
u = −0.519994 + 0.514146I
a = −0.573261 + 0.194172I
b = 1.027730 + 0.525528I
−2.04737 − 4.42997I 0
u = −0.519994 − 0.514146I
a = −0.573261 − 0.194172I
b = 1.027730 − 0.525528I
−2.04737 + 4.42997I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688347 + 0.015904I
a = −1.00082 − 1.58321I
b = −0.745151 − 0.178389I
−3.31796 − 2.34016I −17.3652 + 3.7071I
u = −0.688347 − 0.015904I
a = −1.00082 + 1.58321I
b = −0.745151 + 0.178389I
−3.31796 + 2.34016I −17.3652 − 3.7071I
u = 0.634046 + 0.217215I
a = 0.789475 − 0.701622I
b = 0.546456 + 0.509073I
−0.559909 + 0.111371I −8.00000 + 1.58099I
u = 0.634046 − 0.217215I
a = 0.789475 + 0.701622I
b = 0.546456 − 0.509073I
−0.559909 − 0.111371I −8.00000 − 1.58099I
u = −0.167463 + 0.634472I
a = 0.94089 + 1.19979I
b = −0.616501 − 0.643520I
2.51116 − 0.85388I −1.53097 + 2.15494I
u = −0.167463 − 0.634472I
a = 0.94089 − 1.19979I
b = −0.616501 + 0.643520I
2.51116 + 0.85388I −1.53097 − 2.15494I
u = −1.349460 + 0.003354I
a = −1.023390 − 0.016086I
b = 0.363060 + 0.020561I
−6.49407 + 0.00002I 0
u = −1.349460 − 0.003354I
a = −1.023390 + 0.016086I
b = 0.363060 − 0.020561I
−6.49407 − 0.00002I 0
u = 1.370850 + 0.152453I
a = −0.394075 + 0.330422I
b = 0.391587 − 0.786955I
−2.29932 − 1.84849I 0
u = 1.370850 − 0.152453I
a = −0.394075 − 0.330422I
b = 0.391587 + 0.786955I
−2.29932 + 1.84849I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.285873 + 0.537667I
a = 0.640866 − 1.135400I
b = −0.334758 + 0.847402I
0.65285 − 3.08282I −5.72735 + 6.58681I
u = 0.285873 − 0.537667I
a = 0.640866 + 1.135400I
b = −0.334758 − 0.847402I
0.65285 + 3.08282I −5.72735 − 6.58681I
u = −1.41992 + 0.06769I
a = 0.423092 − 0.516069I
b = −0.578569 + 0.777127I
−5.89719 + 3.01762I 0
u = −1.41992 − 0.06769I
a = 0.423092 + 0.516069I
b = −0.578569 − 0.777127I
−5.89719 − 3.01762I 0
u = −1.42403 + 0.14320I
a = −0.293544 − 0.361005I
b = 0.199462 + 1.104120I
−4.83461 + 5.45013I 0
u = −1.42403 − 0.14320I
a = −0.293544 + 0.361005I
b = 0.199462 − 1.104120I
−4.83461 − 5.45013I 0
u = 1.42892 + 0.08720I
a = −0.92447 + 1.27995I
b = −0.961852 + 0.399126I
−8.27189 + 2.49117I 0
u = 1.42892 − 0.08720I
a = −0.92447 − 1.27995I
b = −0.961852 − 0.399126I
−8.27189 − 2.49117I 0
u = 1.43420 + 0.13326I
a = 1.52406 − 1.83104I
b = 1.017390 + 0.428965I
−8.23402 − 3.27950I 0
u = 1.43420 − 0.13326I
a = 1.52406 + 1.83104I
b = 1.017390 − 0.428965I
−8.23402 + 3.27950I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45321 + 0.01462I
a = −1.08757 + 1.42578I
b = −1.042040 − 0.600114I
−7.36301 − 2.23164I 0
u = 1.45321 − 0.01462I
a = −1.08757 − 1.42578I
b = −1.042040 + 0.600114I
−7.36301 + 2.23164I 0
u = 1.45978 + 0.07323I
a = −0.090635 + 0.736569I
b = −0.77265 − 1.19938I
−8.95103 − 5.08029I 0
u = 1.45978 − 0.07323I
a = −0.090635 − 0.736569I
b = −0.77265 + 1.19938I
−8.95103 + 5.08029I 0
u = −1.45946 + 0.20650I
a = 0.89169 + 1.37027I
b = 1.106580 − 0.585561I
−4.42188 + 6.98601I 0
u = −1.45946 − 0.20650I
a = 0.89169 − 1.37027I
b = 1.106580 + 0.585561I
−4.42188 − 6.98601I 0
u = −1.48216 + 0.02984I
a = −0.467979 − 0.695967I
b = −1.42038 + 0.80271I
−11.08730 + 2.97745I 0
u = −1.48216 − 0.02984I
a = −0.467979 + 0.695967I
b = −1.42038 − 0.80271I
−11.08730 − 2.97745I 0
u = −1.48776 + 0.00307I
a = −1.174830 + 0.041396I
b = −0.948018 − 0.139900I
−7.28570 − 0.05797I 0
u = −1.48776 − 0.00307I
a = −1.174830 − 0.041396I
b = −0.948018 + 0.139900I
−7.28570 + 0.05797I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.512086
a = −0.351550
b = 1.26425
−5.16409 −21.4310
u = 1.49274
a = −0.625686
b = −1.62427
−11.6983 0
u = 0.234531 + 0.448531I
a = −0.597145 + 0.065732I
b = 0.369329 + 0.395606I
−0.71598 − 1.49940I −6.15907 + 3.34895I
u = 0.234531 − 0.448531I
a = −0.597145 − 0.065732I
b = 0.369329 − 0.395606I
−0.71598 + 1.49940I −6.15907 − 3.34895I
u = 1.49156 + 0.20895I
a = 0.83745 − 1.19974I
b = 1.250940 + 0.625768I
−8.04831 − 11.47770I 0
u = 1.49156 − 0.20895I
a = 0.83745 + 1.19974I
b = 1.250940 − 0.625768I
−8.04831 + 11.47770I 0
u = −0.337519 + 0.313167I
a = −0.81445 + 1.60127I
b = 0.643763 − 0.919367I
−3.06247 + 3.79289I −12.8027 − 12.4163I
u = −0.337519 − 0.313167I
a = −0.81445 − 1.60127I
b = 0.643763 + 0.919367I
−3.06247 − 3.79289I −12.8027 + 12.4163I
u = 0.457671
a = 0.744423
b = 0.436249
−0.800628 −11.8890
u = 1.52280 + 0.25579I
a = 0.446441 − 0.808912I
b = −0.057837 + 0.708672I
−11.46720 − 0.79382I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52280 − 0.25579I
a = 0.446441 + 0.808912I
b = −0.057837 − 0.708672I
−11.46720 + 0.79382I 0
u = −1.53199 + 0.27313I
a = 0.435468 + 0.585455I
b = −0.366714 − 0.819444I
−7.20531 + 6.12991I 0
u = −1.53199 − 0.27313I
a = 0.435468 − 0.585455I
b = −0.366714 + 0.819444I
−7.20531 − 6.12991I 0
u = −0.089043 + 0.433089I
a = 2.65903 − 3.82631I
b = −0.952211 + 0.388329I
−3.11696 + 1.47900I −4.54348 − 4.47757I
u = −0.089043 − 0.433089I
a = 2.65903 + 3.82631I
b = −0.952211 − 0.388329I
−3.11696 − 1.47900I −4.54348 + 4.47757I
u = 1.53594 + 0.26544I
a = 0.568714 − 0.525422I
b = −0.387652 + 0.998965I
−11.3324 − 11.6288I 0
u = 1.53594 − 0.26544I
a = 0.568714 + 0.525422I
b = −0.387652 − 0.998965I
−11.3324 + 11.6288I 0
u = 0.422131 + 0.107983I
a = −0.45738 − 1.67606I
b = 1.171970 + 0.672778I
−4.81368 − 2.48540I −22.8854 + 6.6337I
u = 0.422131 − 0.107983I
a = −0.45738 + 1.67606I
b = 1.171970 − 0.672778I
−4.81368 + 2.48540I −22.8854 − 6.6337I
u = −1.53098 + 0.39379I
a = −0.40652 − 1.44972I
b = −1.151730 + 0.452179I
−14.5947 + 5.0254I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53098 − 0.39379I
a = −0.40652 + 1.44972I
b = −1.151730 − 0.452179I
−14.5947 − 5.0254I 0
u = −1.57837 + 0.18063I
a = 0.587660 + 0.219510I
b = 1.386840 + 0.091526I
−17.8165 + 7.9839I 0
u = −1.57837 − 0.18063I
a = 0.587660 − 0.219510I
b = 1.386840 − 0.091526I
−17.8165 − 7.9839I 0
u = −1.56353 + 0.30289I
a = −0.67347 − 1.52002I
b = −1.192820 + 0.662030I
−13.8217 + 17.6321I 0
u = −1.56353 − 0.30289I
a = −0.67347 + 1.52002I
b = −1.192820 − 0.662030I
−13.8217 − 17.6321I 0
u = 1.58570 + 0.33378I
a = −0.58741 + 1.42117I
b = −1.134900 − 0.594549I
−9.5017 − 11.4013I 0
u = 1.58570 − 0.33378I
a = −0.58741 − 1.42117I
b = −1.134900 + 0.594549I
−9.5017 + 11.4013I 0
u = 1.62550 + 0.15463I
a = 0.672705 + 0.179863I
b = 1.158440 − 0.175281I
−12.26950 − 3.43058I 0
u = 1.62550 − 0.15463I
a = 0.672705 − 0.179863I
b = 1.158440 + 0.175281I
−12.26950 + 3.43058I 0
u = −1.66015 + 0.23571I
a = 0.309280 − 0.288553I
b = 1.152050 + 0.402083I
−14.9337 − 3.0765I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.66015 − 0.23571I
a = 0.309280 + 0.288553I
b = 1.152050 − 0.402083I
−14.9337 + 3.0765I 0
u = −0.254207 + 0.093976I
a = −0.02448 − 12.67700I
b = −0.775297 − 0.496292I
−3.15119 − 2.08241I −30.9227 − 13.8100I
u = −0.254207 − 0.093976I
a = −0.02448 + 12.67700I
b = −0.775297 + 0.496292I
−3.15119 + 2.08241I −30.9227 + 13.8100I
u = −0.197015 + 0.025110I
a = 2.85799 + 5.76242I
b = 0.903883 − 0.528559I
−1.74590 + 2.04516I −12.58558 − 2.81237I
u = −0.197015 − 0.025110I
a = 2.85799 − 5.76242I
b = 0.903883 + 0.528559I
−1.74590 − 2.04516I −12.58558 + 2.81237I
14
II. I
u
2
= hb + u, −5u
3
+ u
2
+ 3a + u + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
u
2
+ 1
a
7
=
5
3
u
3
−
1
3
u
2
−
1
3
u −
1
3
−u
a
2
=
−
1
3
u
3
+
4
3
u
2
−
1
3
u −
2
3
−u
2
a
1
=
−
1
3
u
3
+
1
3
u
2
−
1
3
u −
2
3
−u
2
a
11
=
−
1
3
u
3
−
1
3
u
2
−
4
3
u
−
5
3
u
3
−
2
3
u
2
+
4
3
u +
1
3
a
6
=
1
3
u
3
+
1
3
u
2
+
1
3
u −
2
3
u
3
− u
a
8
=
−
2
3
u
2
−
1
3
u
3
−
1
3
u
2
+
2
3
u +
2
3
a
12
=
−
1
3
u
3
+
1
3
u
2
−
4
3
u −
2
3
−2u
3
− u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
2
− 16
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
6
, c
9
u
4
− u
2
+ 1
c
5
, c
12
(u
2
+ 1)
2
c
8
9(9u
4
+ 4)
c
10
9(9u
4
− 18u
3
+ 18u
2
− 6u + 1)
c
11
(u
2
+ u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
11
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
6
, c
9
(y
2
− y + 1)
2
c
5
, c
12
(y + 1)
4
c
8
81(9y
2
+ 4)
2
c
10
81(81y
4
+ 126y
2
+ 1)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.78868 + 1.21132I
b = −0.866025 − 0.500000I
−1.64493 − 4.05977I −12.00000 + 6.92820I
u = 0.866025 − 0.500000I
a = −0.78868 − 1.21132I
b = −0.866025 + 0.500000I
−1.64493 + 4.05977I −12.00000 − 6.92820I
u = −0.866025 + 0.500000I
a = −0.21132 + 1.78868I
b = 0.866025 − 0.500000I
−1.64493 + 4.05977I −12.00000 − 6.92820I
u = −0.866025 − 0.500000I
a = −0.21132 − 1.78868I
b = 0.866025 + 0.500000I
−1.64493 − 4.05977I −12.00000 + 6.92820I
18
III. I
u
3
= hu
3
+ b − u, −2u
3
− 2u
2
+ 3a + u + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
u
2
+ 1
a
7
=
2
3
u
3
+
2
3
u
2
−
1
3
u −
1
3
−u
3
+ u
a
2
=
−
1
3
u
3
−
2
3
u
2
−
1
3
u +
4
3
u
2
− 1
a
1
=
−
1
3
u
3
+
1
3
u
2
−
1
3
u +
1
3
u
2
− 1
a
11
=
−
2
3
u
3
+
1
3
u
2
−
2
3
u −
1
3
−
2
3
u
3
+
1
3
u
2
+
4
3
u −
2
3
a
6
=
−
2
3
u
3
+
1
3
u
2
+
1
3
u −
2
3
u
a
8
=
−
2
3
u
3
+
2
3
u
2
+
1
3
u −
2
3
−
1
3
u
3
−
1
3
u
2
+
5
3
u −
1
3
a
12
=
−
1
3
u
3
+
1
3
u
2
−
4
3
u +
1
3
−2u
3
+ u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
6
, c
9
u
4
− u
2
+ 1
c
5
, c
12
(u
2
+ 1)
2
c
8
9(9u
4
+ 18u
3
+ 9u
2
+ 1)
c
10
9(9u
4
− 18u
3
+ 18u
2
− 12u + 4)
c
11
(u
2
+ u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
11
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
6
, c
9
(y
2
− y + 1)
2
c
5
, c
12
(y + 1)
4
c
8
81(81y
4
− 162y
3
+ 99y
2
+ 18y + 1)
c
10
81(81y
4
− 36y
2
+ 16)
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.288675 + 1.077350I
b = 0.866025 − 0.500000I
−1.64493 −12.0000
u = 0.866025 − 0.500000I
a = −0.288675 − 1.077350I
b = 0.866025 + 0.500000I
−1.64493 −12.0000
u = −0.866025 + 0.500000I
a = 0.288675 − 0.077350I
b = −0.866025 − 0.500000I
−1.64493 −12.0000
u = −0.866025 − 0.500000I
a = 0.288675 + 0.077350I
b = −0.866025 + 0.500000I
−1.64493 −12.0000
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
95
+ 45u
94
+ ··· + 5812u + 169)
c
2
, c
6
((u
4
− u
2
+ 1)
2
)(u
95
− 3u
94
+ ··· − 64u − 13)
c
3
, c
4
, c
9
((u
4
− u
2
+ 1)
2
)(u
95
− u
94
+ ··· + 14u − 1)
c
5
, c
12
((u
2
+ 1)
4
)(u
95
− 3u
94
+ ··· − 544u − 52)
c
7
((u
2
− u + 1)
4
)(u
95
+ 5u
94
+ ··· − 22u − 1)
c
8
42849(9u
4
+ 4)(9u
4
+ 18u
3
+ 9u
2
+ 1)
· (529u
95
− 345u
94
+ ··· − 101241168u + 12252224)
c
10
42849(9u
4
− 18u
3
+ ··· − 12u + 4)(9u
4
− 18u
3
+ ··· − 6u + 1)
· (529u
95
+ 1035u
94
+ ··· + 66519920u + 12600800)
c
11
((u
2
+ u + 1)
4
)(u
95
+ 5u
94
+ ··· − 22u − 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
95
+ 15y
94
+ ··· + 2924000y −28561)
c
2
, c
6
((y
2
− y + 1)
4
)(y
95
− 45y
94
+ ··· + 5812y −169)
c
3
, c
4
, c
9
((y
2
− y + 1)
4
)(y
95
− 93y
94
+ ··· + 88y −1)
c
5
, c
12
((y + 1)
8
)(y
95
+ 83y
94
+ ··· − 1192y −2704)
c
7
, c
11
((y
2
+ y + 1)
4
)(y
95
− 57y
94
+ ··· + 304y −1)
c
8
1836036801(9y
2
+ 4)
2
(81y
4
− 162y
3
+ 99y
2
+ 18y + 1)
· (2.80 × 10
5
y
95
− 2.19 × 10
7
y
94
+ ··· + 8.54 × 10
15
y −1.50 × 10
14
)
c
10
1836036801(81y
4
− 36y
2
+ 16)(81y
4
+ 126y
2
+ 1)
· (2.80 × 10
5
y
95
− 1.01 × 10
7
y
94
+ ··· + 2.53 × 10
16
y −1.59 × 10
14
)
24
