12a
0011
(K12a
0011
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 11 9 4 12 1 7 10
Solving Sequence
4,9
8 5
7,11
12 10 1 6 3 2
c
8
c
4
c
7
c
11
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
= h−7.27315 × 10
120
u
95
+ 1.01058 × 10
120
u
94
+ ··· + 9.05988 × 10
121
b − 5.64489 × 10
122
,
9.19778 × 10
119
u
95
− 1.53124 × 10
120
u
94
+ ··· + 2.83121 × 10
120
a − 2.95068 × 10
120
,
u
96
− 2u
95
+ ··· − 112u + 16i
I
u
2
= hb + 1, −u
3
− u
2
+ a − u + 1, u
4
+ u
2
− u + 1i
I
u
3
= hb + 1, 2u
5
+ u
4
+ 3u
3
+ 2u
2
+ a + 2u + 3, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
I
v
1
= ha, −v
3
+ 8b − 13, v
4
− 3v
3
+ 8v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 110 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−7.27 × 10
120
u
95
+ 1.01 × 10
120
u
94
+ · · · + 9.06 × 10
121
b − 5.64 ×
10
122
, 9.20 × 10
119
u
95
− 1.53 × 10
120
u
94
+ · · · + 2.83 × 10
120
a − 2.95 ×
10
120
, u
96
− 2u
95
+ · · · − 112u + 16i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
5
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
2
a
11
=
−0.324871u
95
+ 0.540842u
94
+ ··· − 14.4927u + 1.04220
0.0802787u
95
− 0.0111544u
94
+ ··· − 30.5199u + 6.23065
a
12
=
−0.207428u
95
+ 0.388117u
94
+ ··· − 12.9586u + 1.57350
0.112780u
95
− 0.0919036u
94
+ ··· − 20.9134u + 4.66415
a
10
=
−0.293420u
95
+ 0.345934u
94
+ ··· + 29.2088u − 7.07180
−0.127753u
95
+ 0.0810802u
94
+ ··· + 33.3471u − 7.46550
a
1
=
−0.248572u
95
+ 0.307437u
94
+ ··· + 34.5855u − 7.95553
−0.0744823u
95
+ 0.00433249u
94
+ ··· + 35.8792u − 7.80797
a
6
=
−0.156252u
95
+ 0.315966u
94
+ ··· − 18.5636u + 2.88775
0.0923201u
95
+ 0.00852920u
94
+ ··· − 53.1492u + 10.8433
a
3
=
0.0558784u
95
+ 0.0316719u
94
+ ··· − 39.1695u + 6.39107
0.273471u
95
− 0.462337u
94
+ ··· + 25.3301u − 0.875238
a
2
=
0.0987072u
95
− 0.0572327u
94
+ ··· − 31.9109u + 5.80866
0.311645u
95
− 0.533355u
94
+ ··· + 31.5399u − 1.40569
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.207765u
95
+ 0.393624u
94
+ ··· − 136.340u + 31.6509
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
96
+ 44u
95
+ ··· − 56u + 1
c
2
, c
5
u
96
+ 4u
95
+ ··· − 28u
2
+ 1
c
3
u
96
− 4u
95
+ ··· − 780u + 36
c
4
, c
8
u
96
− 2u
95
+ ··· − 112u + 16
c
6
, c
11
u
96
− 3u
95
+ ··· + 2048u − 1024
c
7
u
96
+ 30u
95
+ ··· + 2944u + 256
c
9
, c
10
, c
12
u
96
+ 13u
95
+ ··· − 7u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
96
+ 20y
95
+ ··· − 3584y + 1
c
2
, c
5
y
96
+ 44y
95
+ ··· − 56y + 1
c
3
y
96
− 4y
95
+ ··· − 148392y + 1296
c
4
, c
8
y
96
+ 30y
95
+ ··· + 2944y + 256
c
6
, c
11
y
96
− 69y
95
+ ··· − 2621440y + 1048576
c
7
y
96
+ 66y
95
+ ··· − 5578752y + 65536
c
9
, c
10
, c
12
y
96
− 99y
95
+ ··· − 59y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.179865 + 0.981177I
a = 0.400592 + 0.469661I
b = 0.737676 − 0.333905I
−1.89305 + 2.08679I 0
u = 0.179865 − 0.981177I
a = 0.400592 − 0.469661I
b = 0.737676 + 0.333905I
−1.89305 − 2.08679I 0
u = 0.064862 + 1.005660I
a = −1.196160 − 0.222902I
b = 0.176480 + 0.138850I
6.35016 + 2.70358I 0
u = 0.064862 − 1.005660I
a = −1.196160 + 0.222902I
b = 0.176480 − 0.138850I
6.35016 − 2.70358I 0
u = 0.198241 + 0.963841I
a = −0.80496 + 1.16785I
b = −1.53096 + 0.67111I
−1.30704 + 4.75458I 0
u = 0.198241 − 0.963841I
a = −0.80496 − 1.16785I
b = −1.53096 − 0.67111I
−1.30704 − 4.75458I 0
u = 0.956508
a = −0.812407
b = 0.283592
6.97501 13.9200
u = 0.727657 + 0.756348I
a = −0.19023 − 1.61049I
b = 1.25916 − 2.01436I
10.97980 + 2.94589I 0
u = 0.727657 − 0.756348I
a = −0.19023 + 1.61049I
b = 1.25916 + 2.01436I
10.97980 − 2.94589I 0
u = −0.052755 + 0.934065I
a = −0.662357 + 0.538200I
b = −1.91189 − 0.01238I
−1.63144 − 2.08117I 3.21072 + 3.69308I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.052755 − 0.934065I
a = −0.662357 − 0.538200I
b = −1.91189 + 0.01238I
−1.63144 + 2.08117I 3.21072 − 3.69308I
u = 0.506190 + 0.776082I
a = 0.453782 + 0.845346I
b = −1.21115 + 1.39079I
−0.0181181 − 0.1012650I 6.00000 + 0.I
u = 0.506190 − 0.776082I
a = 0.453782 − 0.845346I
b = −1.21115 − 1.39079I
−0.0181181 + 0.1012650I 6.00000 + 0.I
u = 0.732555 + 0.785317I
a = −2.14393 − 0.65735I
b = −0.30613 − 2.06567I
3.34357 − 1.04746I 0
u = 0.732555 − 0.785317I
a = −2.14393 + 0.65735I
b = −0.30613 + 2.06567I
3.34357 + 1.04746I 0
u = −0.640126 + 0.887175I
a = −0.637838 − 0.691592I
b = −0.159222 − 0.593907I
1.50017 − 2.47654I 0
u = −0.640126 − 0.887175I
a = −0.637838 + 0.691592I
b = −0.159222 + 0.593907I
1.50017 + 2.47654I 0
u = −0.043194 + 1.098890I
a = 0.604265 − 0.571418I
b = 0.832969 − 0.162003I
−5.25031 + 1.29319I 0
u = −0.043194 − 1.098890I
a = 0.604265 + 0.571418I
b = 0.832969 + 0.162003I
−5.25031 − 1.29319I 0
u = −0.378146 + 1.034420I
a = 0.250816 + 0.461945I
b = −0.007172 + 0.437665I
−4.01038 − 0.74785I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.378146 − 1.034420I
a = 0.250816 − 0.461945I
b = −0.007172 − 0.437665I
−4.01038 + 0.74785I 0
u = −0.819181 + 0.739492I
a = −0.52219 + 1.62413I
b = 0.86589 + 2.07251I
12.44970 + 2.14786I 0
u = −0.819181 − 0.739492I
a = −0.52219 − 1.62413I
b = 0.86589 − 2.07251I
12.44970 − 2.14786I 0
u = 0.606982 + 0.647554I
a = 0.482836 + 0.124243I
b = −0.1275970 − 0.0182045I
1.29359 + 1.42707I 5.04296 − 3.45734I
u = 0.606982 − 0.647554I
a = 0.482836 − 0.124243I
b = −0.1275970 + 0.0182045I
1.29359 − 1.42707I 5.04296 + 3.45734I
u = −0.826561 + 0.758089I
a = −1.015440 + 0.308143I
b = 0.099788 + 0.182714I
5.34537 + 3.62875I 0
u = −0.826561 − 0.758089I
a = −1.015440 − 0.308143I
b = 0.099788 − 0.182714I
5.34537 − 3.62875I 0
u = −0.837925 + 0.750857I
a = 1.56771 − 1.61603I
b = −0.14758 − 2.27068I
4.82979 + 1.10173I 0
u = −0.837925 − 0.750857I
a = 1.56771 + 1.61603I
b = −0.14758 + 2.27068I
4.82979 − 1.10173I 0
u = −1.118750 + 0.126118I
a = −1.051510 + 0.159099I
b = −0.069491 + 0.255839I
3.98579 + 3.78181I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.118750 − 0.126118I
a = −1.051510 − 0.159099I
b = −0.069491 − 0.255839I
3.98579 − 3.78181I 0
u = 0.572426 + 0.970896I
a = 0.120038 − 0.183375I
b = −0.242684 − 0.284713I
0.30507 + 3.24456I 0
u = 0.572426 − 0.970896I
a = 0.120038 + 0.183375I
b = −0.242684 + 0.284713I
0.30507 − 3.24456I 0
u = −0.249684 + 1.106760I
a = 0.574433 − 0.199646I
b = 1.197250 + 0.405278I
−4.63078 − 6.21392I 0
u = −0.249684 − 1.106760I
a = 0.574433 + 0.199646I
b = 1.197250 − 0.405278I
−4.63078 + 6.21392I 0
u = −0.742235 + 0.861901I
a = −1.81336 + 1.05906I
b = −0.02595 + 2.29423I
4.77127 − 4.14701I 0
u = −0.742235 − 0.861901I
a = −1.81336 − 1.05906I
b = −0.02595 − 2.29423I
4.77127 + 4.14701I 0
u = 0.895738 + 0.705536I
a = 1.89918 + 1.51772I
b = 0.20285 + 2.21158I
3.07743 − 6.16610I 0
u = 0.895738 − 0.705536I
a = 1.89918 − 1.51772I
b = 0.20285 − 2.21158I
3.07743 + 6.16610I 0
u = −0.737566 + 0.438984I
a = 0.699444 − 0.411046I
b = −0.0545657 − 0.1131930I
−0.06859 + 3.07421I 2.78055 − 2.58683I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.737566 − 0.438984I
a = 0.699444 + 0.411046I
b = −0.0545657 + 0.1131930I
−0.06859 − 3.07421I 2.78055 + 2.58683I
u = 0.801875 + 0.817313I
a = −0.727587 − 0.105234I
b = 0.203872 + 0.043495I
6.94878 + 1.52895I 0
u = 0.801875 − 0.817313I
a = −0.727587 + 0.105234I
b = 0.203872 − 0.043495I
6.94878 − 1.52895I 0
u = 0.983067 + 0.593907I
a = −1.04833 − 1.13241I
b = 0.14959 − 1.56719I
6.80439 − 2.73172I 0
u = 0.983067 − 0.593907I
a = −1.04833 + 1.13241I
b = 0.14959 + 1.56719I
6.80439 + 2.73172I 0
u = −0.736893 + 0.881078I
a = 0.81168 − 1.88164I
b = −0.94456 − 2.45732I
4.71166 − 1.47213I 0
u = −0.736893 − 0.881078I
a = 0.81168 + 1.88164I
b = −0.94456 + 2.45732I
4.71166 + 1.47213I 0
u = 0.710431 + 0.942506I
a = 0.49343 + 2.02506I
b = −1.28029 + 2.56757I
2.86050 + 6.56016I 0
u = 0.710431 − 0.942506I
a = 0.49343 − 2.02506I
b = −1.28029 − 2.56757I
2.86050 − 6.56016I 0
u = 0.647089 + 0.994598I
a = −0.749872 − 1.117940I
b = 0.76062 − 2.10880I
−1.06039 + 4.88469I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.647089 − 0.994598I
a = −0.749872 + 1.117940I
b = 0.76062 + 2.10880I
−1.06039 − 4.88469I 0
u = 0.696883 + 0.968308I
a = 1.48900 + 0.31889I
b = 0.20368 + 1.98021I
10.32400 + 2.51546I 0
u = 0.696883 − 0.968308I
a = 1.48900 − 0.31889I
b = 0.20368 − 1.98021I
10.32400 − 2.51546I 0
u = 0.663214 + 0.429650I
a = 1.43183 + 0.39092I
b = −0.142029 + 0.933862I
0.199282 + 0.054914I 5.95141 + 1.45020I
u = 0.663214 − 0.429650I
a = 1.43183 − 0.39092I
b = −0.142029 − 0.933862I
0.199282 − 0.054914I 5.95141 − 1.45020I
u = 0.762855 + 0.939390I
a = −0.214157 + 0.302745I
b = 0.382487 + 0.559471I
6.56862 + 4.35035I 0
u = 0.762855 − 0.939390I
a = −0.214157 − 0.302745I
b = 0.382487 − 0.559471I
6.56862 − 4.35035I 0
u = −0.593981 + 1.068690I
a = −0.023274 + 0.252986I
b = −0.331966 + 0.383447I
−1.90007 − 8.13886I 0
u = −0.593981 − 1.068690I
a = −0.023274 − 0.252986I
b = −0.331966 − 0.383447I
−1.90007 + 8.13886I 0
u = −0.980600 + 0.732809I
a = −1.12281 + 1.60043I
b = 0.15151 + 2.14124I
11.78970 + 4.88988I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.980600 − 0.732809I
a = −1.12281 − 1.60043I
b = 0.15151 − 2.14124I
11.78970 − 4.88988I 0
u = −0.159597 + 0.751118I
a = −0.419266 − 1.331750I
b = −1.265100 − 0.214772I
1.05859 − 1.02125I 7.61187 + 0.05036I
u = −0.159597 − 0.751118I
a = −0.419266 + 1.331750I
b = −1.265100 + 0.214772I
1.05859 + 1.02125I 7.61187 − 0.05036I
u = −0.754185 + 0.986111I
a = −0.036824 − 0.455932I
b = 0.452248 − 0.773019I
4.64082 − 9.55010I 0
u = −0.754185 − 0.986111I
a = −0.036824 + 0.455932I
b = 0.452248 + 0.773019I
4.64082 + 9.55010I 0
u = −0.758090 + 0.018044I
a = 1.40140 + 0.29204I
b = 0.200844 − 0.138201I
−0.87840 + 2.74391I 2.63740 − 6.04113I
u = −0.758090 − 0.018044I
a = 1.40140 − 0.29204I
b = 0.200844 + 0.138201I
−0.87840 − 2.74391I 2.63740 + 6.04113I
u = −0.741529 + 0.998801I
a = 1.47574 − 0.72432I
b = 0.06701 − 2.18200I
11.64830 − 8.01057I 0
u = −0.741529 − 0.998801I
a = 1.47574 + 0.72432I
b = 0.06701 + 2.18200I
11.64830 + 8.01057I 0
u = −0.755636 + 0.994782I
a = −1.16371 + 1.70557I
b = 0.57646 + 2.66065I
4.07325 − 7.05946I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.755636 − 0.994782I
a = −1.16371 − 1.70557I
b = 0.57646 − 2.66065I
4.07325 + 7.05946I 0
u = 0.327809 + 1.223240I
a = −0.488608 − 0.084817I
b = −0.383365 + 0.630574I
2.74232 + 4.46570I 0
u = 0.327809 − 1.223240I
a = −0.488608 + 0.084817I
b = −0.383365 − 0.630574I
2.74232 − 4.46570I 0
u = 1.033530 + 0.740573I
a = −1.33443 − 1.59134I
b = −0.09718 − 2.17128I
9.75556 − 10.08300I 0
u = 1.033530 − 0.740573I
a = −1.33443 + 1.59134I
b = −0.09718 + 2.17128I
9.75556 + 10.08300I 0
u = 0.763723 + 1.038380I
a = −0.94298 − 1.92781I
b = 0.79838 − 2.79461I
2.04041 + 12.30580I 0
u = 0.763723 − 1.038380I
a = −0.94298 + 1.92781I
b = 0.79838 + 2.79461I
2.04041 − 12.30580I 0
u = 0.747775 + 1.102840I
a = 0.828498 + 1.089450I
b = −0.43773 + 2.16511I
5.21813 + 9.00258I 0
u = 0.747775 − 1.102840I
a = 0.828498 − 1.089450I
b = −0.43773 − 2.16511I
5.21813 − 9.00258I 0
u = −0.223963 + 1.321760I
a = −0.661370 + 0.023722I
b = −0.493598 − 0.360114I
−1.46466 − 0.83782I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.223963 − 1.321760I
a = −0.661370 − 0.023722I
b = −0.493598 + 0.360114I
−1.46466 + 0.83782I 0
u = −0.810092 + 1.071990I
a = 1.19835 − 1.42854I
b = −0.32083 − 2.50985I
10.6997 − 11.4421I 0
u = −0.810092 − 1.071990I
a = 1.19835 + 1.42854I
b = −0.32083 + 2.50985I
10.6997 + 11.4421I 0
u = −0.407132 + 1.290330I
a = −0.463759 − 0.102711I
b = −0.610594 − 0.729703I
−0.19623 − 9.22714I 0
u = −0.407132 − 1.290330I
a = −0.463759 + 0.102711I
b = −0.610594 + 0.729703I
−0.19623 + 9.22714I 0
u = 0.830652 + 1.095500I
a = 1.08127 + 1.63799I
b = −0.46328 + 2.61088I
8.5916 + 16.8595I 0
u = 0.830652 − 1.095500I
a = 1.08127 − 1.63799I
b = −0.46328 − 2.61088I
8.5916 − 16.8595I 0
u = −0.457900 + 0.381328I
a = −3.03679 − 2.46911I
b = −0.937516 + 0.031870I
1.98842 − 1.41068I 2.70790 + 7.48837I
u = −0.457900 − 0.381328I
a = −3.03679 + 2.46911I
b = −0.937516 − 0.031870I
1.98842 + 1.41068I 2.70790 − 7.48837I
u = 0.073742 + 0.507409I
a = 2.26010 + 1.46464I
b = −0.177445 − 0.145732I
0.65230 + 2.25194I −2.13457 − 8.32594I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.073742 − 0.507409I
a = 2.26010 − 1.46464I
b = −0.177445 + 0.145732I
0.65230 − 2.25194I −2.13457 + 8.32594I
u = 0.185153 + 0.465023I
a = 0.451736 − 0.268144I
b = 1.94486 − 0.33037I
8.64481 − 1.76125I −0.03733 − 6.99048I
u = 0.185153 − 0.465023I
a = 0.451736 + 0.268144I
b = 1.94486 + 0.33037I
8.64481 + 1.76125I −0.03733 + 6.99048I
u = 0.453811 + 0.103724I
a = −7.23514 + 1.66240I
b = −1.032900 + 0.008082I
1.40994 − 2.35915I 21.8120 − 15.4151I
u = 0.453811 − 0.103724I
a = −7.23514 − 1.66240I
b = −1.032900 − 0.008082I
1.40994 + 2.35915I 21.8120 + 15.4151I
u = 0.362698
a = 1.27387
b = −0.385362
0.845329 11.9590
14
II. I
u
2
= hb + 1, −u
3
− u
2
+ a − u + 1, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
5
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
2
a
11
=
u
3
+ u
2
+ u − 1
−1
a
12
=
u
3
+ u
2
+ u − 1
−1
a
10
=
u
3
+ u
2
+ u
−1
a
1
=
−1
0
a
6
=
u
2
+ 1
u
2
a
3
=
u
3
+ u
2
u
2
a
2
=
u
3
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
3
− 3u
2
− u + 13
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
8
u
4
+ u
2
− u + 1
c
6
, c
11
u
4
c
9
, c
10
(u + 1)
4
c
12
(u − 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
5
c
8
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
6
, c
11
y
4
c
9
, c
10
, c
12
(y −1)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −0.89512 + 1.55249I
b = −1.00000
2.62503 + 1.39709I 14.5787 − 4.1375I
u = 0.547424 − 0.585652I
a = −0.89512 − 1.55249I
b = −1.00000
2.62503 − 1.39709I 14.5787 + 4.1375I
u = −0.547424 + 1.120870I
a = −0.604877 − 0.506844I
b = −1.00000
−0.98010 − 7.64338I 6.92132 + 4.56334I
u = −0.547424 − 1.120870I
a = −0.604877 + 0.506844I
b = −1.00000
−0.98010 + 7.64338I 6.92132 − 4.56334I
18
III.
I
u
3
= hb+1, 2u
5
+u
4
+3u
3
+2u
2
+a+2u+3, u
6
+u
5
+2u
4
+2u
3
+2u
2
+2u+1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
5
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
2
a
11
=
−2u
5
− u
4
− 3u
3
− 2u
2
− 2u − 3
−1
a
12
=
−2u
5
− u
4
− 3u
3
− 2u
2
− 2u − 3
−1
a
10
=
−2u
5
− u
4
− 3u
3
− 2u
2
− 2u − 2
−1
a
1
=
−1
0
a
6
=
u
2
+ 1
u
2
a
3
=
u
5
+ 2u
3
+ u
u
5
+ u
3
+ u
a
2
=
2u
5
+ 3u
3
+ u
2
+ 2u + 1
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ 3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
5
− u
4
− 8u
3
− u
2
− 7u + 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
6
, c
11
u
6
c
9
, c
10
(u + 1)
6
c
12
(u − 1)
6
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
5
c
8
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
6
, c
11
y
6
c
9
, c
10
, c
12
(y −1)
6
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −0.518694 + 0.637866I
b = −1.00000
1.37919 + 2.82812I 10.11473 − 2.08748I
u = 0.498832 − 1.001300I
a = −0.518694 − 0.637866I
b = −1.00000
1.37919 − 2.82812I 10.11473 + 2.08748I
u = −0.284920 + 1.115140I
a = −0.337641 − 0.362106I
b = −1.00000
−2.75839 1.72561 − 0.99756I
u = −0.284920 − 1.115140I
a = −0.337641 + 0.362106I
b = −1.00000
−2.75839 1.72561 + 0.99756I
u = −0.713912 + 0.305839I
a = −2.14366 − 1.20015I
b = −1.00000
1.37919 + 2.82812I 9.65966 − 5.36114I
u = −0.713912 − 0.305839I
a = −2.14366 + 1.20015I
b = −1.00000
1.37919 − 2.82812I 9.65966 + 5.36114I
22
IV. I
v
1
= ha, −v
3
+ 8b − 13, v
4
− 3v
3
+ 8v
2
− 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
8
=
1
0
a
5
=
v
0
a
7
=
1
0
a
11
=
0
1
8
v
3
+
13
8
a
12
=
1
8
v
3
+
13
8
1
8
v
3
+
13
8
a
10
=
−
1
8
v
3
−
13
8
−
1
8
v
3
−
21
8
a
1
=
−1
−
1
8
v
3
−
21
8
a
6
=
1
1
8
v
3
+
21
8
a
3
=
−
3
8
v
3
+ v
2
− 2v +
1
8
−
9
8
v
3
+ 3v
2
− 8v +
3
8
a
2
=
−
1
4
v
3
+ v
2
− 2v −
1
4
−
9
8
v
3
+ 3v
2
− 8v +
3
8
(ii) Obstruction class = 1
(iii) Cusp Shapes =
9
2
v
3
− 13v
2
+ 33v +
17
2
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
4
, c
7
, c
8
u
4
c
6
, c
9
, c
10
(u
2
− u − 1)
2
c
11
, c
12
(u
2
+ u − 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
2
c
4
, c
7
, c
8
y
4
c
6
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.190983 + 0.330792I
a = 0
b = 1.61803
8.88264 − 2.02988I 15.5000 + 9.2736I
v = 0.190983 − 0.330792I
a = 0
b = 1.61803
8.88264 + 2.02988I 15.5000 − 9.2736I
v = 1.30902 + 2.26728I
a = 0
b = −0.618034
0.98696 − 2.02988I 15.5000 − 2.3454I
v = 1.30902 − 2.26728I
a = 0
b = −0.618034
0.98696 + 2.02988I 15.5000 + 2.3454I
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
96
+ 44u
95
+ ··· − 56u + 1)
c
2
(u
2
+ u + 1)
2
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
96
+ 4u
95
+ ··· − 28u
2
+ 1)
c
3
(u
2
− u + 1)
2
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
96
− 4u
95
+ ··· − 780u + 36)
c
4
u
4
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
96
− 2u
95
+ ··· − 112u + 16)
c
5
(u
2
− u + 1)
2
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
96
+ 4u
95
+ ··· − 28u
2
+ 1)
c
6
u
10
(u
2
− u − 1)
2
(u
96
− 3u
95
+ ··· + 2048u − 1024)
c
7
u
4
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
96
+ 30u
95
+ ··· + 2944u + 256)
c
8
u
4
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
96
− 2u
95
+ ··· − 112u + 16)
c
9
, c
10
((u + 1)
10
)(u
2
− u − 1)
2
(u
96
+ 13u
95
+ ··· − 7u − 1)
c
11
u
10
(u
2
+ u − 1)
2
(u
96
− 3u
95
+ ··· + 2048u − 1024)
c
12
((u − 1)
10
)(u
2
+ u − 1)
2
(u
96
+ 13u
95
+ ··· − 7u − 1)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
96
+ 20y
95
+ ··· − 3584y + 1)
c
2
, c
5
(y
2
+ y + 1)
2
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
96
+ 44y
95
+ ··· − 56y + 1)
c
3
(y
2
+ y + 1)
2
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
96
− 4y
95
+ ··· − 148392y + 1296)
c
4
, c
8
y
4
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
96
+ 30y
95
+ ··· + 2944y + 256)
c
6
, c
11
y
10
(y
2
− 3y + 1)
2
(y
96
− 69y
95
+ ··· − 2621440y + 1048576)
c
7
y
4
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
96
+ 66y
95
+ ··· − 5578752y + 65536)
c
9
, c
10
, c
12
((y − 1)
10
)(y
2
− 3y + 1)
2
(y
96
− 99y
95
+ ··· − 59y + 1)
28
