12a
0125
(K12a
0125
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 10 4 12 7 1 9 11
Solving Sequence
2,5
3
6,10
7 1 11 4 8 9 12
c
2
c
5
c
6
c
1
c
10
c
4
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.45958 × 10
63
u
105
+ 1.24016 × 10
64
u
104
+ ··· + 1.23680 × 10
62
b + 3.05806 × 10
63
,
1.13273 × 10
63
u
105
− 4.16667 × 10
63
u
104
+ ··· + 1.23680 × 10
62
a + 4.77555 × 10
62
, u
106
− 7u
105
+ ··· + 11u + 1i
I
u
2
= hb − a, −u
3
a + u
2
a + 2u
3
+ a
2
− 2u
2
− a + u + 2, u
4
− u
3
+ u
2
+ 1i
I
u
3
= h−a
2
− 2au + b − a + u + 1, a
4
+ 3a
3
u − 4a
2
u − 4a
2
+ 3a + 2u, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 122 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−1.46 × 10
63
u
105
+ 1.24 × 10
64
u
104
+ · · · + 1.24 × 10
62
b + 3.06 ×
10
63
, 1.13 × 10
63
u
105
− 4.17 × 10
63
u
104
+ · · · + 1.24 × 10
62
a + 4.78 ×
10
62
, u
106
− 7u
105
+ · · · + 11u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
10
=
−9.15857u
105
+ 33.6892u
104
+ ··· − 78.0000u − 3.86123
11.8013u
105
− 100.272u
104
+ ··· − 296.223u − 24.7257
a
7
=
16.6772u
105
− 80.6901u
104
+ ··· + 74.7375u + 5.64569
−11.0849u
105
+ 100.425u
104
+ ··· + 353.574u + 29.7886
a
1
=
u
2
+ 1
−u
4
a
11
=
−12.1515u
105
+ 46.3650u
104
+ ··· − 82.9557u − 3.61751
15.2241u
105
− 129.122u
104
+ ··· − 378.079u − 31.6912
a
4
=
u
3
u
3
+ u
a
8
=
16.8295u
105
− 91.5401u
104
+ ··· + 41.0065u + 2.64419
−10.2180u
105
+ 87.5744u
104
+ ··· + 321.926u + 27.0475
a
9
=
−15.3972u
105
+ 68.9700u
104
+ ··· − 43.5872u − 1.83722
13.1838u
105
− 116.844u
104
+ ··· − 377.008u − 31.4529
a
12
=
3.05675u
105
− 23.6825u
104
+ ··· + 23.3656u − 0.183695
−0.478044u
105
+ 1.52825u
104
+ ··· + 34.1625u + 2.46930
(ii) Obstruction class = −1
(iii) Cusp Shapes = −23.7616u
105
+ 179.119u
104
+ ··· + 290.283u + 26.9682
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
106
+ 35u
105
+ ··· + 9u + 1
c
2
, c
5
u
106
+ 7u
105
+ ··· − 11u + 1
c
3
, c
7
u
106
− 3u
105
+ ··· − 1152u + 256
c
6
, c
9
u
106
+ 3u
105
+ ··· + 1152u + 256
c
8
, c
11
u
106
− 7u
105
+ ··· + 11u + 1
c
10
, c
12
u
106
− 35u
105
+ ··· − 9u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
10
c
12
y
106
+ 79y
105
+ ··· + 1045y + 1
c
2
, c
5
, c
8
c
11
y
106
+ 35y
105
+ ··· + 9y + 1
c
3
, c
6
, c
7
c
9
y
106
+ 55y
105
+ ··· + 1654784y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.183013 + 0.981284I
a = −0.250624 + 1.170010I
b = 1.19910 + 1.07703I
−8.23499 + 5.48524I 0
u = 0.183013 − 0.981284I
a = −0.250624 − 1.170010I
b = 1.19910 − 1.07703I
−8.23499 − 5.48524I 0
u = −0.608368 + 0.790031I
a = −1.71520 + 2.08278I
b = −2.34512 + 1.92007I
0.476825 + 0.520416I 0
u = −0.608368 − 0.790031I
a = −1.71520 − 2.08278I
b = −2.34512 − 1.92007I
0.476825 − 0.520416I 0
u = −0.070703 + 0.979774I
a = 0.473670 + 1.255400I
b = 0.490461 + 0.187755I
−3.20551 + 0.41176I 0
u = −0.070703 − 0.979774I
a = 0.473670 − 1.255400I
b = 0.490461 − 0.187755I
−3.20551 − 0.41176I 0
u = −0.082433 + 1.016070I
a = −0.536516 − 0.233091I
b = −1.61438 − 0.31423I
−3.79720 − 2.42088I 0
u = −0.082433 − 1.016070I
a = −0.536516 + 0.233091I
b = −1.61438 + 0.31423I
−3.79720 + 2.42088I 0
u = 0.139173 + 1.012920I
a = 0.233853 − 0.977567I
b = −1.15979 − 0.93662I
−8.71380 − 0.62719I 0
u = 0.139173 − 1.012920I
a = 0.233853 + 0.977567I
b = −1.15979 + 0.93662I
−8.71380 + 0.62719I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.121668 + 1.027370I
a = −0.262202 − 1.241630I
b = −0.392812 − 0.212170I
−2.89214 − 5.06693I 0
u = −0.121668 − 1.027370I
a = −0.262202 + 1.241630I
b = −0.392812 + 0.212170I
−2.89214 + 5.06693I 0
u = 0.767026 + 0.703266I
a = 1.02342 + 1.09468I
b = 0.650088 − 0.104330I
1.97848 − 2.25070I 0
u = 0.767026 − 0.703266I
a = 1.02342 − 1.09468I
b = 0.650088 + 0.104330I
1.97848 + 2.25070I 0
u = −0.491542 + 0.815968I
a = 2.89723 − 2.04811I
b = 3.28360 − 1.89164I
− 3.72687I 0
u = −0.491542 − 0.815968I
a = 2.89723 + 2.04811I
b = 3.28360 + 1.89164I
3.72687I 0
u = 0.757210 + 0.725465I
a = 0.44531 + 1.47879I
b = 1.59591 + 1.06021I
2.34132 + 0.87923I 0
u = 0.757210 − 0.725465I
a = 0.44531 − 1.47879I
b = 1.59591 − 1.06021I
2.34132 − 0.87923I 0
u = 0.606407 + 0.862300I
a = 0.849818 − 0.206074I
b = −0.382310 − 1.247890I
−6.30345 − 0.88841I 0
u = 0.606407 − 0.862300I
a = 0.849818 + 0.206074I
b = −0.382310 + 1.247890I
−6.30345 + 0.88841I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.797191 + 0.698686I
a = −0.39788 − 1.50231I
b = −1.58826 − 1.20743I
3.31076 − 4.88109I 0
u = 0.797191 − 0.698686I
a = −0.39788 + 1.50231I
b = −1.58826 + 1.20743I
3.31076 + 4.88109I 0
u = −0.814211 + 0.692591I
a = 1.75987 − 0.39778I
b = 1.38167 + 0.58692I
−2.34132 − 0.87923I 0
u = −0.814211 − 0.692591I
a = 1.75987 + 0.39778I
b = 1.38167 − 0.58692I
−2.34132 + 0.87923I 0
u = 0.866786 + 0.634717I
a = 1.46524 + 1.07764I
b = 1.341270 − 0.241167I
− 5.87854I 0
u = 0.866786 − 0.634717I
a = 1.46524 − 1.07764I
b = 1.341270 + 0.241167I
5.87854I 0
u = −0.200048 + 1.057240I
a = 0.893176 − 0.486577I
b = 1.83864 − 0.23783I
− 5.27517I 0
u = −0.200048 − 1.057240I
a = 0.893176 + 0.486577I
b = 1.83864 + 0.23783I
5.27517I 0
u = −0.361209 + 1.017340I
a = −0.059410 − 0.516497I
b = −0.439695 + 0.151597I
0.93508 − 1.21751I 0
u = −0.361209 − 1.017340I
a = −0.059410 + 0.516497I
b = −0.439695 − 0.151597I
0.93508 + 1.21751I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609367 + 0.892037I
a = −0.672343 + 0.456946I
b = 0.63191 + 1.33120I
−6.40447 + 5.65814I 0
u = 0.609367 − 0.892037I
a = −0.672343 − 0.456946I
b = 0.63191 − 1.33120I
−6.40447 − 5.65814I 0
u = 0.770716 + 0.767655I
a = −0.70064 − 1.22855I
b = −0.280019 − 0.215340I
4.52079 + 2.63581I 0
u = 0.770716 − 0.767655I
a = −0.70064 + 1.22855I
b = −0.280019 + 0.215340I
4.52079 − 2.63581I 0
u = −0.566270 + 0.934854I
a = 1.87881 − 1.90621I
b = 2.08787 − 1.30438I
−0.476825 − 0.520416I 0
u = −0.566270 − 0.934854I
a = 1.87881 + 1.90621I
b = 2.08787 + 1.30438I
−0.476825 + 0.520416I 0
u = −0.726604 + 0.816538I
a = −1.86538 + 1.02911I
b = −1.72394 + 0.15846I
3.20551 − 0.41176I 0
u = −0.726604 − 0.816538I
a = −1.86538 − 1.02911I
b = −1.72394 − 0.15846I
3.20551 + 0.41176I 0
u = 0.842877 + 0.705822I
a = −1.26558 − 1.34601I
b = −1.085060 − 0.187678I
6.94581 − 5.02785I 0
u = 0.842877 − 0.705822I
a = −1.26558 + 1.34601I
b = −1.085060 + 0.187678I
6.94581 + 5.02785I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.892716 + 0.645846I
a = −1.56857 − 1.13159I
b = −1.49793 + 0.16723I
1.28626 − 11.79330I 0
u = 0.892716 − 0.645846I
a = −1.56857 + 1.13159I
b = −1.49793 − 0.16723I
1.28626 + 11.79330I 0
u = −0.831655 + 0.735688I
a = −1.94362 + 0.45302I
b = −1.62921 − 0.57066I
−1.56866 + 4.68963I 0
u = −0.831655 − 0.735688I
a = −1.94362 − 0.45302I
b = −1.62921 + 0.57066I
−1.56866 − 4.68963I 0
u = −0.846903 + 0.235789I
a = −0.406411 + 0.154856I
b = 0.522749 − 0.873838I
−1.10077 − 7.84499I 0
u = −0.846903 − 0.235789I
a = −0.406411 − 0.154856I
b = 0.522749 + 0.873838I
−1.10077 + 7.84499I 0
u = −0.499442 + 0.720382I
a = 0.695312 − 0.877601I
b = 0.396527 − 0.460682I
0.00288 − 1.41429I 0
u = −0.499442 − 0.720382I
a = 0.695312 + 0.877601I
b = 0.396527 + 0.460682I
0.00288 + 1.41429I 0
u = −0.599521 + 0.957553I
a = 0.771353 − 1.121240I
b = 1.47129 − 1.34418I
−0.82280 − 3.12789I 0
u = −0.599521 − 0.957553I
a = 0.771353 + 1.121240I
b = 1.47129 + 1.34418I
−0.82280 + 3.12789I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.637724 + 0.932906I
a = −1.94663 + 1.67788I
b = −2.08360 + 0.92011I
− 5.43693I 0
u = −0.637724 − 0.932906I
a = −1.94663 − 1.67788I
b = −2.08360 − 0.92011I
5.43693I 0
u = −0.066695 + 0.862588I
a = 0.915878 + 1.066430I
b = 1.90466 + 0.87933I
−0.93508 + 1.21751I 0
u = −0.066695 − 0.862588I
a = 0.915878 − 1.066430I
b = 1.90466 − 0.87933I
−0.93508 − 1.21751I 0
u = −0.814464 + 0.288678I
a = 0.605911 − 0.175846I
b = −0.286730 + 0.819490I
−1.97848 − 2.25070I 0
u = −0.814464 − 0.288678I
a = 0.605911 + 0.175846I
b = −0.286730 − 0.819490I
−1.97848 + 2.25070I 0
u = −0.706931 + 0.917155I
a = −0.82138 + 1.95452I
b = −1.70509 + 2.01187I
2.89214 − 5.06693I 0
u = −0.706931 − 0.917155I
a = −0.82138 − 1.95452I
b = −1.70509 − 2.01187I
2.89214 + 5.06693I 0
u = −0.135106 + 1.157920I
a = −0.126241 + 0.601309I
b = −1.255940 + 0.283686I
−6.94581 − 5.02785I 0
u = −0.135106 − 1.157920I
a = −0.126241 − 0.601309I
b = −1.255940 − 0.283686I
−6.94581 + 5.02785I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.846366 + 0.807209I
a = −0.210464 − 1.265260I
b = −1.04605 − 1.10106I
8.71380 + 0.62719I 0
u = 0.846366 − 0.807209I
a = −0.210464 + 1.265260I
b = −1.04605 + 1.10106I
8.71380 − 0.62719I 0
u = 0.774318 + 0.876579I
a = 0.680033 + 1.008620I
b = 1.253860 + 0.454713I
5.27854 + 2.91371I 0
u = 0.774318 − 0.876579I
a = 0.680033 − 1.008620I
b = 1.253860 − 0.454713I
5.27854 − 2.91371I 0
u = −0.162545 + 1.173480I
a = 0.162036 − 0.799571I
b = 1.273330 − 0.436696I
−5.99254 − 10.94690I 0
u = −0.162545 − 1.173480I
a = 0.162036 + 0.799571I
b = 1.273330 + 0.436696I
−5.99254 + 10.94690I 0
u = 0.724326 + 0.957520I
a = −0.808980 − 0.583019I
b = −1.76285 − 0.94912I
3.93836 + 3.02552I 0
u = 0.724326 − 0.957520I
a = −0.808980 + 0.583019I
b = −1.76285 + 0.94912I
3.93836 − 3.02552I 0
u = 0.706595 + 0.979712I
a = 1.44150 + 1.08675I
b = 1.77226 + 0.02524I
1.56866 + 4.68963I 0
u = 0.706595 − 0.979712I
a = 1.44150 − 1.08675I
b = 1.77226 − 0.02524I
1.56866 − 4.68963I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.706082 + 0.993444I
a = 0.639854 + 1.066610I
b = 1.73031 + 1.35560I
1.10077 + 7.84499I 0
u = 0.706082 − 0.993444I
a = 0.639854 − 1.066610I
b = 1.73031 − 1.35560I
1.10077 − 7.84499I 0
u = −0.522661 + 1.114150I
a = −0.434161 − 0.452234I
b = 0.309499 − 1.044400I
−4.52079 − 2.63581I 0
u = −0.522661 − 1.114150I
a = −0.434161 + 0.452234I
b = 0.309499 + 1.044400I
−4.52079 + 2.63581I 0
u = −0.489939 + 1.132640I
a = 0.549700 + 0.221371I
b = −0.166076 + 0.880128I
−3.93836 + 3.02552I 0
u = −0.489939 − 1.132640I
a = 0.549700 − 0.221371I
b = −0.166076 − 0.880128I
−3.93836 − 3.02552I 0
u = 0.718362 + 1.003840I
a = −1.57081 − 0.99200I
b = −1.80456 + 0.08368I
2.38453 + 10.59630I 0
u = 0.718362 − 1.003840I
a = −1.57081 + 0.99200I
b = −1.80456 − 0.08368I
2.38453 − 10.59630I 0
u = −0.719884 + 1.009600I
a = 0.23810 − 1.93491I
b = 1.21212 − 2.15144I
−3.31076 − 4.88109I 0
u = −0.719884 − 1.009600I
a = 0.23810 + 1.93491I
b = 1.21212 + 2.15144I
−3.31076 + 4.88109I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.745910 + 0.999607I
a = −0.29151 + 2.10838I
b = −1.30317 + 2.28754I
−2.38453 − 10.59630I 0
u = −0.745910 − 0.999607I
a = −0.29151 − 2.10838I
b = −1.30317 − 2.28754I
−2.38453 + 10.59630I 0
u = 0.795949 + 0.963492I
a = −1.170740 − 0.503153I
b = −1.303770 + 0.227267I
8.23499 + 5.48524I 0
u = 0.795949 − 0.963492I
a = −1.170740 + 0.503153I
b = −1.303770 − 0.227267I
8.23499 − 5.48524I 0
u = 0.741766 + 1.016420I
a = −1.04728 − 1.36665I
b = −2.08849 − 1.51459I
5.99254 + 10.94690I 0
u = 0.741766 − 1.016420I
a = −1.04728 + 1.36665I
b = −2.08849 + 1.51459I
5.99254 − 10.94690I 0
u = 0.895602 + 0.902122I
a = 0.499281 − 0.827980I
b = 0.009136 − 1.083200I
6.40447 + 5.65814I 0
u = 0.895602 − 0.902122I
a = 0.499281 + 0.827980I
b = 0.009136 + 1.083200I
6.40447 − 5.65814I 0
u = 0.724032 + 1.055990I
a = 0.75868 + 1.74992I
b = 1.92533 + 1.84464I
−1.28626 + 11.79330I 0
u = 0.724032 − 1.055990I
a = 0.75868 − 1.74992I
b = 1.92533 − 1.84464I
−1.28626 − 11.79330I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.882666 + 0.934937I
a = −0.782200 + 0.495054I
b = −0.461431 + 0.900066I
6.30345 + 0.88841I 0
u = 0.882666 − 0.934937I
a = −0.782200 − 0.495054I
b = −0.461431 − 0.900066I
6.30345 − 0.88841I 0
u = −0.700805 + 0.103106I
a = −0.347599 + 0.803226I
b = 0.685519 − 0.192768I
3.79720 − 2.42088I 8.03384 + 3.86046I
u = −0.700805 − 0.103106I
a = −0.347599 − 0.803226I
b = 0.685519 + 0.192768I
3.79720 + 2.42088I 8.03384 − 3.86046I
u = 0.737717 + 1.063090I
a = −0.86972 − 1.85842I
b = −2.02279 − 1.91157I
17.8296I 0
u = 0.737717 − 1.063090I
a = −0.86972 + 1.85842I
b = −2.02279 + 1.91157I
− 17.8296I 0
u = 0.591011 + 0.052091I
a = 0.165247 + 0.998865I
b = 0.092280 − 1.103860I
−5.27854 − 2.91371I −3.69090 + 3.04834I
u = 0.591011 − 0.052091I
a = 0.165247 − 0.998865I
b = 0.092280 + 1.103860I
−5.27854 + 2.91371I −3.69090 − 3.04834I
u = −0.250141 + 0.475165I
a = 1.300680 + 0.007167I
b = 0.226506 − 0.170022I
0.004559 − 1.231310I 0.29315 + 4.68261I
u = −0.250141 − 0.475165I
a = 1.300680 − 0.007167I
b = 0.226506 + 0.170022I
0.004559 + 1.231310I 0.29315 − 4.68261I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.510636 + 0.163559I
a = −0.20894 − 2.01670I
b = 0.693169 − 0.805948I
0.82280 − 3.12789I 4.96221 + 2.35512I
u = −0.510636 − 0.163559I
a = −0.20894 + 2.01670I
b = 0.693169 + 0.805948I
0.82280 + 3.12789I 4.96221 − 2.35512I
u = −0.133565 + 0.357143I
a = 1.88642 + 0.19782I
b = 0.212749 − 0.289221I
−0.004559 − 1.231310I −0.29315 + 4.68261I
u = −0.133565 − 0.357143I
a = 1.88642 − 0.19782I
b = 0.212749 + 0.289221I
−0.004559 + 1.231310I −0.29315 − 4.68261I
u = −0.159696 + 0.120542I
a = 1.05065 + 3.71317I
b = 0.237220 + 0.726682I
−0.00288 + 1.41429I 2.00405 − 4.68227I
u = −0.159696 − 0.120542I
a = 1.05065 − 3.71317I
b = 0.237220 − 0.726682I
−0.00288 − 1.41429I 2.00405 + 4.68227I
15
II. I
u
2
= hb − a, −u
3
a + u
2
a + 2u
3
+ a
2
− 2u
2
− a + u + 2, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
10
=
a
a
a
7
=
u
u
a
1
=
u
2
+ 1
−u
3
+ u
2
+ 1
a
11
=
u
3
a − u
2
a − au
2u
3
a
a
4
=
u
3
u
3
+ u
a
8
=
−u
2
− 1
u
3
− u
2
− 1
a
9
=
a
a
a
12
=
u
3
a − u
2
a − u
3
− au + u
2
− 1
2u
3
a − u
3
+ u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
3
a − u
3
− 2au − 5u
2
− a + 7u − 2
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
2
(u
4
− u
3
+ u
2
+ 1)
2
c
5
(u
4
+ u
3
+ u
2
+ 1)
2
c
6
, c
9
u
8
c
7
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
8
, c
12
(u
2
− u + 1)
4
c
10
, c
11
(u
2
+ u + 1)
4
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
2
, c
5
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
6
, c
9
y
8
c
8
, c
10
, c
11
c
12
(y
2
+ y + 1)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351808 + 0.720342I
a = 0.60275 + 1.84505I
b = 0.60275 + 1.84505I
−0.21101 − 3.44499I −4.95650 + 5.37720I
u = −0.351808 + 0.720342I
a = 1.29649 − 1.44452I
b = 1.29649 − 1.44452I
−0.211005 + 0.614778I −0.01166 + 7.13374I
u = −0.351808 − 0.720342I
a = 0.60275 − 1.84505I
b = 0.60275 − 1.84505I
−0.21101 + 3.44499I −4.95650 − 5.37720I
u = −0.351808 − 0.720342I
a = 1.29649 + 1.44452I
b = 1.29649 + 1.44452I
−0.211005 − 0.614778I −0.01166 − 7.13374I
u = 0.851808 + 0.911292I
a = 0.082397 − 0.508565I
b = 0.082397 − 0.508565I
6.79074 + 5.19385I 5.34148 − 0.51945I
u = 0.851808 + 0.911292I
a = −0.481629 + 0.182925I
b = −0.481629 + 0.182925I
6.79074 + 1.13408I 8.12668 − 3.09304I
u = 0.851808 − 0.911292I
a = 0.082397 + 0.508565I
b = 0.082397 + 0.508565I
6.79074 − 5.19385I 5.34148 + 0.51945I
u = 0.851808 − 0.911292I
a = −0.481629 − 0.182925I
b = −0.481629 − 0.182925I
6.79074 − 1.13408I 8.12668 + 3.09304I
19
III.
I
u
3
= h−a
2
− 2au + b − a + u + 1, a
4
+ 3a
3
u − 4a
2
u − 4a
2
+ 3a + 2u, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
10
=
a
a
2
+ 2au + a − u − 1
a
7
=
−a
3
u + 2a
2
u + 2a
2
− a + u
a
3
+ 2a
2
u − au − a − 1
a
1
=
−u
−u
a
11
=
−a
2
u − a
2
+ 3a + u
−a
2
u + 2au + 3a − 1
a
4
=
1
u + 1
a
8
=
−a
3
u + 2a
2
u + 2a
2
− a + u
a
3
+ 2a
2
u − au − a − 1
a
9
=
−a
3
u + 4a
2
u + 4a
2
− 5a − 3u
a
3
+ 4a
2
u + a
2
− 4au − 5a − u + 2
a
12
=
−2a
3
u + 4a
2
u + 4a
2
− 2a
−a
3
u + a
3
+ 4a
2
u + 2a
2
− au − 2a − u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
3
u + 2a
3
+ 8a
2
u − 5au − 6a − 2u − 1
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
3
, c
7
u
8
c
6
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
8
(u
4
+ u
3
+ u
2
+ 1)
2
c
9
, c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
11
(u
4
− u
3
+ u
2
+ 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
4
c
3
, c
7
y
8
c
6
, c
9
, c
10
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
8
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.715106 − 0.583984I
b = 0.68183 − 1.26940I
−6.79074 − 5.19385I −5.34148 + 0.51945I
u = −0.500000 + 0.866025I
a = 0.863298 + 0.327308I
b = −0.428761 + 1.194380I
−6.79074 + 1.13408I −8.12668 − 3.09304I
u = −0.500000 + 0.866025I
a = 0.05207 − 1.53087I
b = −0.189308 − 0.935262I
0.211005 − 0.614778I 0.01166 − 7.13374I
u = −0.500000 + 0.866025I
a = 1.29974 − 0.81053I
b = 1.93624 − 0.72176I
0.21101 − 3.44499I 4.95650 + 5.37720I
u = −0.500000 − 0.866025I
a = −0.715106 + 0.583984I
b = 0.68183 + 1.26940I
−6.79074 + 5.19385I −5.34148 − 0.51945I
u = −0.500000 − 0.866025I
a = 0.863298 − 0.327308I
b = −0.428761 − 1.194380I
−6.79074 − 1.13408I −8.12668 + 3.09304I
u = −0.500000 − 0.866025I
a = 0.05207 + 1.53087I
b = −0.189308 + 0.935262I
0.211005 + 0.614778I 0.01166 + 7.13374I
u = −0.500000 − 0.866025I
a = 1.29974 + 0.81053I
b = 1.93624 + 0.72176I
0.21101 + 3.44499I 4.95650 − 5.37720I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
4
)(u
4
− u
3
+ 3u
2
− 2u + 1)
2
(u
106
+ 35u
105
+ ··· + 9u + 1)
c
2
((u
2
+ u + 1)
4
)(u
4
− u
3
+ u
2
+ 1)
2
(u
106
+ 7u
105
+ ··· − 11u + 1)
c
3
u
8
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
(u
106
− 3u
105
+ ··· − 1152u + 256)
c
5
((u
2
− u + 1)
4
)(u
4
+ u
3
+ u
2
+ 1)
2
(u
106
+ 7u
105
+ ··· − 11u + 1)
c
6
u
8
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
(u
106
+ 3u
105
+ ··· + 1152u + 256)
c
7
u
8
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
(u
106
− 3u
105
+ ··· − 1152u + 256)
c
8
((u
2
− u + 1)
4
)(u
4
+ u
3
+ u
2
+ 1)
2
(u
106
− 7u
105
+ ··· + 11u + 1)
c
9
u
8
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
(u
106
+ 3u
105
+ ··· + 1152u + 256)
c
10
((u
2
+ u + 1)
4
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
(u
106
− 35u
105
+ ··· − 9u + 1)
c
11
((u
2
+ u + 1)
4
)(u
4
− u
3
+ u
2
+ 1)
2
(u
106
− 7u
105
+ ··· + 11u + 1)
c
12
((u
2
− u + 1)
4
)(u
4
− u
3
+ 3u
2
− 2u + 1)
2
(u
106
− 35u
105
+ ··· − 9u + 1)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
10
c
12
(y
2
+ y + 1)
4
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
· (y
106
+ 79y
105
+ ··· + 1045y + 1)
c
2
, c
5
, c
8
c
11
((y
2
+ y + 1)
4
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
(y
106
+ 35y
105
+ ··· + 9y + 1)
c
3
, c
6
, c
7
c
9
y
8
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
· (y
106
+ 55y
105
+ ··· + 1654784y + 65536)
25
