12a
0485
(K12a
0485
)
A knot diagram
1
Linearized knot diagam
3 6 11 12 7 2 10 4 5 1 9 8
Solving Sequence
3,6
2
7,10
8 1 11 4 5 9 12
c
2
c
6
c
7
c
1
c
10
c
3
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h192609591u
55
− 2727061067u
54
+ ··· + 14468204b + 16035728512,
1002233032u
55
− 8827487697u
54
+ ··· + 14468204a + 16773966195, u
56
− 9u
55
+ ··· + 36u − 16i
I
u
2
= h5.06413 × 10
16
a
3
u
26
+ 2.15067 × 10
17
a
2
u
26
+ ··· − 1.13428 × 10
19
a + 9.45090 × 10
18
,
3u
26
a
3
− 9u
26
a
2
+ ··· − 25a + 21, u
27
+ 2u
26
+ ··· − 4u
2
− 1i
I
u
3
= h55u
28
− 252u
27
+ ··· + 21b + 61, 61u
28
− 189u
27
+ ··· + 21a − 32, u
29
− 4u
28
+ ··· − 6u
2
− 1i
I
u
4
= hau + b − 1, a
2
+ au + a + 1, u
2
+ u + 1i
I
u
5
= hau + b − u, a
2
− a − u − 1, u
2
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 201 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
= h1.93 × 10
8
u
55
− 2.73 × 10
9
u
54
+ · · · + 1.45 × 10
7
b + 1.60 × 10
10
, 1.00 ×
10
9
u
55
−8.83×10
9
u
54
+· · ·+1.45×10
7
a+1.68×10
10
, u
56
−9u
55
+· · ·+36u−16i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
10
=
−69.2714u
55
+ 610.130u
54
+ ··· + 2096.44u − 1159.37
−13.3126u
55
+ 188.486u
54
+ ··· + 1334.40u − 1108.34
a
8
=
−8.78193u
55
+ 253.245u
54
+ ··· + 2714.47u − 2326.29
174.208u
55
− 1303.60u
54
+ ··· − 2009.14u − 140.511
a
1
=
u
2
+ 1
u
2
a
11
=
−20.3141u
55
+ 164.851u
54
+ ··· + 477.918u − 272.674
−4.39070u
55
+ 60.8214u
54
+ ··· + 437.619u − 425.076
a
4
=
79.7522u
55
− 623.369u
54
+ ··· − 1262.96u + 253.754
100.284u
55
− 911.993u
54
+ ··· − 3411.74u + 1923.40
a
5
=
u
3
u
5
+ u
3
+ u
a
9
=
−31.3270u
55
+ 292.918u
54
+ ··· + 1098.99u − 564.552
41.0305u
55
− 290.047u
54
+ ··· − 197.308u − 195.175
a
12
=
−32.0066u
55
+ 315.058u
54
+ ··· + 1431.56u − 896.451
66.8287u
55
− 495.324u
54
+ ··· − 647.072u − 154.409
(ii) Obstruction class = −1
(iii) Cusp Shap es = −
1195774015
3617051
u
55
+
10894419483
3617051
u
54
+ ··· +
40309490750
3617051
u −
22849509610
3617051
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
56
+ 17u
55
+ ··· + 2640u + 256
c
2
, c
6
u
56
− 9u
55
+ ··· + 36u − 16
c
3
, c
9
u
56
− u
55
+ ··· + 166u + 34
c
4
, c
8
u
56
− 5u
54
+ ··· + u − 1
c
7
, c
10
u
56
− u
55
+ ··· − 21u + 1
c
11
u
56
+ 43u
55
+ ··· − 34u − 4
c
12
u
56
+ 53u
55
+ ··· − 738197504u − 33554432
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
56
+ 45y
55
+ ··· − 636672y + 65536
c
2
, c
6
y
56
+ 17y
55
+ ··· + 2640y + 256
c
3
, c
9
y
56
− 31y
55
+ ··· − 9332y + 1156
c
4
, c
8
y
56
− 10y
55
+ ··· − 9y + 1
c
7
, c
10
y
56
− 7y
55
+ ··· − 45y + 1
c
11
y
56
− 21y
55
+ ··· − 508y + 16
c
12
y
56
− 9y
55
+ ··· + 19140298416324608y + 1125899906842624
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.148611 + 0.987288I
a = −0.105326 + 0.776858I
b = −0.751329 − 0.219436I
−5.08582 − 0.04483I 0
u = −0.148611 − 0.987288I
a = −0.105326 − 0.776858I
b = −0.751329 + 0.219436I
−5.08582 + 0.04483I 0
u = −1.02530
a = −0.206826
b = 0.212059
1.23312 12.2390
u = −0.388031 + 0.964876I
a = −0.013054 − 0.703235I
b = 0.683600 + 0.260282I
0.66649 − 6.36541I 0
u = −0.388031 − 0.964876I
a = −0.013054 + 0.703235I
b = 0.683600 − 0.260282I
0.66649 + 6.36541I 0
u = 0.754659 + 0.782525I
a = 1.31638 + 1.21329I
b = 0.04399 + 1.94571I
0.734279 + 0.907581I 0
u = 0.754659 − 0.782525I
a = 1.31638 − 1.21329I
b = 0.04399 − 1.94571I
0.734279 − 0.907581I 0
u = 0.410147 + 0.807610I
a = 0.503137 + 0.296621I
b = −0.033194 + 0.527996I
−0.05668 + 1.76377I 0. − 5.48632I
u = 0.410147 − 0.807610I
a = 0.503137 − 0.296621I
b = −0.033194 − 0.527996I
−0.05668 − 1.76377I 0. + 5.48632I
u = −0.461995 + 1.015350I
a = −0.277333 − 0.297378I
b = 0.430069 − 0.144203I
−3.28970 − 5.83406I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.461995 − 1.015350I
a = −0.277333 + 0.297378I
b = 0.430069 + 0.144203I
−3.28970 + 5.83406I 0
u = 0.732257 + 0.863189I
a = −0.56605 − 2.39805I
b = 1.65547 − 2.24459I
2.80607 + 4.77645I 0
u = 0.732257 − 0.863189I
a = −0.56605 + 2.39805I
b = 1.65547 + 2.24459I
2.80607 − 4.77645I 0
u = 0.090367 + 0.856778I
a = 0.141600 + 0.932125I
b = −0.785828 + 0.205553I
−1.45441 + 1.82954I −3.97315 − 5.04709I
u = 0.090367 − 0.856778I
a = 0.141600 − 0.932125I
b = −0.785828 − 0.205553I
−1.45441 − 1.82954I −3.97315 + 5.04709I
u = 0.721081 + 0.885164I
a = −2.05381 − 0.72427I
b = −0.83986 − 2.34021I
2.73433 + 0.76799I 0
u = 0.721081 − 0.885164I
a = −2.05381 + 0.72427I
b = −0.83986 + 2.34021I
2.73433 − 0.76799I 0
u = −0.847184 + 0.024271I
a = 0.512339 + 0.300014I
b = −0.441327 − 0.241732I
5.35540 + 10.65240I 8.10098 − 7.27900I
u = −0.847184 − 0.024271I
a = 0.512339 − 0.300014I
b = −0.441327 + 0.241732I
5.35540 − 10.65240I 8.10098 + 7.27900I
u = −0.756418 + 0.870995I
a = 0.472676 + 0.001674I
b = −0.358999 + 0.410431I
3.13677 − 0.64477I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.756418 − 0.870995I
a = 0.472676 − 0.001674I
b = −0.358999 − 0.410431I
3.13677 + 0.64477I 0
u = −0.315267 + 1.117870I
a = −0.325563 + 0.574726I
b = −0.539830 − 0.545129I
1.6611 − 14.5883I 0
u = −0.315267 − 1.117870I
a = −0.325563 − 0.574726I
b = −0.539830 + 0.545129I
1.6611 + 14.5883I 0
u = −0.752842 + 0.890277I
a = −0.412632 − 0.169367I
b = 0.461431 − 0.239850I
3.07720 − 5.07348I 0
u = −0.752842 − 0.890277I
a = −0.412632 + 0.169367I
b = 0.461431 + 0.239850I
3.07720 + 5.07348I 0
u = 0.910217 + 0.748706I
a = 1.46008 + 1.53528I
b = 0.17952 + 2.49061I
9.9171 − 14.1482I 0
u = 0.910217 − 0.748706I
a = 1.46008 − 1.53528I
b = 0.17952 − 2.49061I
9.9171 + 14.1482I 0
u = −0.265751 + 1.169400I
a = −0.415551 − 0.112866I
b = 0.242420 − 0.455953I
1.27517 + 6.83332I 0
u = −0.265751 − 1.169400I
a = −0.415551 + 0.112866I
b = 0.242420 + 0.455953I
1.27517 − 6.83332I 0
u = 0.734138 + 0.954130I
a = 0.96728 + 1.64674I
b = −0.86109 + 2.13185I
0.21426 + 4.75574I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734138 − 0.954130I
a = 0.96728 − 1.64674I
b = −0.86109 − 2.13185I
0.21426 − 4.75574I 0
u = 0.893467 + 0.810104I
a = −1.68903 − 1.19547I
b = −0.54064 − 2.43639I
8.95532 − 4.37769I 0
u = 0.893467 − 0.810104I
a = −1.68903 + 1.19547I
b = −0.54064 + 2.43639I
8.95532 + 4.37769I 0
u = 0.942592 + 0.754576I
a = 0.312382 + 1.175130I
b = −0.59227 + 1.34338I
9.79014 + 6.70793I 0
u = 0.942592 − 0.754576I
a = 0.312382 − 1.175130I
b = −0.59227 − 1.34338I
9.79014 − 6.70793I 0
u = −0.701393 + 0.337884I
a = −0.066176 − 0.592967I
b = 0.246769 + 0.393543I
2.79814 + 2.42669I 7.0112 − 14.0897I
u = −0.701393 − 0.337884I
a = −0.066176 + 0.592967I
b = 0.246769 − 0.393543I
2.79814 − 2.42669I 7.0112 + 14.0897I
u = 0.953287 + 0.766830I
a = −0.948615 − 0.800138I
b = −0.29073 − 1.49019I
6.49118 − 4.87375I 0
u = 0.953287 − 0.766830I
a = −0.948615 + 0.800138I
b = −0.29073 + 1.49019I
6.49118 + 4.87375I 0
u = 0.013411 + 0.744426I
a = 0.17390 − 1.95972I
b = 1.46120 + 0.10317I
−1.08652 − 1.99360I −2.94814 + 3.49725I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.013411 − 0.744426I
a = 0.17390 + 1.95972I
b = 1.46120 − 0.10317I
−1.08652 + 1.99360I −2.94814 − 3.49725I
u = 0.814580 + 0.991484I
a = −0.94091 − 1.96051I
b = 1.17737 − 2.52990I
8.37962 + 10.69940I 0
u = 0.814580 − 0.991484I
a = −0.94091 + 1.96051I
b = 1.17737 + 2.52990I
8.37962 − 10.69940I 0
u = 0.792855 + 1.029230I
a = 1.25881 + 1.77766I
b = −0.83157 + 2.70503I
9.0363 + 20.4388I 0
u = 0.792855 − 1.029230I
a = 1.25881 − 1.77766I
b = −0.83157 − 2.70503I
9.0363 − 20.4388I 0
u = −0.112713 + 0.673401I
a = 1.041970 + 0.476281I
b = −0.438172 + 0.647982I
−0.99942 + 1.87855I −2.67770 − 3.80115I
u = −0.112713 − 0.673401I
a = 1.041970 − 0.476281I
b = −0.438172 − 0.647982I
−0.99942 − 1.87855I −2.67770 + 3.80115I
u = 0.819918 + 1.039760I
a = −0.595172 − 1.238170I
b = 0.79940 − 1.63403I
5.61955 + 11.37810I 0
u = 0.819918 − 1.039760I
a = −0.595172 + 1.238170I
b = 0.79940 + 1.63403I
5.61955 − 11.37810I 0
u = 0.820110 + 1.044490I
a = 0.919908 + 0.618661I
b = 0.10824 + 1.46820I
8.88440 − 0.23202I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.820110 − 1.044490I
a = 0.919908 − 0.618661I
b = 0.10824 − 1.46820I
8.88440 + 0.23202I 0
u = −0.406216 + 1.276320I
a = 0.102721 − 0.123005I
b = 0.115267 + 0.181071I
−3.08574 − 4.97156I 0
u = −0.406216 − 1.276320I
a = 0.102721 + 0.123005I
b = 0.115267 − 0.181071I
−3.08574 + 4.97156I 0
u = −0.541789 + 0.332536I
a = 0.584596 − 0.319325I
b = −0.210541 + 0.367406I
−1.37335 + 1.75176I −0.47779 − 2.41051I
u = −0.541789 − 0.332536I
a = 0.584596 + 0.319325I
b = −0.210541 − 0.367406I
−1.37335 − 1.75176I −0.47779 + 2.41051I
u = 0.615547
a = 0.989696
b = 0.609204
1.54329 8.12550
10
II. I
u
2
= h5.06 × 10
16
a
3
u
26
+ 2.15 × 10
17
a
2
u
26
+ · · · − 1.13 × 10
19
a + 9.45 ×
10
18
, 3u
26
a
3
− 9u
26
a
2
+ · · · − 25a + 21, u
27
+ 2u
26
+ · · · − 4u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
10
=
a
−0.0194228a
3
u
26
− 0.0824861a
2
u
26
+ ··· + 4.35040a − 3.62477
a
8
=
0.222877a
3
u
26
− 0.426660a
2
u
26
+ ··· + 0.709576a + 1.18860
−0.175602a
3
u
26
+ 0.512669a
2
u
26
+ ··· − 0.00724059a − 1.52161
a
1
=
u
2
+ 1
u
2
a
11
=
0.356153a
3
u
26
+ 0.437054a
2
u
26
+ ··· + 3.71412a − 0.591491
−0.0341233a
3
u
26
+ 0.112725a
2
u
26
+ ··· + 3.57675a − 2.25136
a
4
=
−0.777942a
3
u
26
+ 0.215725a
2
u
26
+ ··· − 2.73581a + 3.08163
0.0221625a
3
u
26
+ 0.670679a
2
u
26
+ ··· + 1.24922a − 2.25944
a
5
=
u
3
u
5
+ u
3
+ u
a
9
=
−0.402197a
3
u
26
+ 0.289264a
2
u
26
+ ··· + 1.48602a + 1.29020
0.356960a
3
u
26
+ 0.574655a
2
u
26
+ ··· + 4.05346a − 3.72719
a
12
=
0.324083a
3
u
26
+ 0.0222001a
2
u
26
+ ··· + 5.02261a − 1.76900
−0.0803756a
3
u
26
− 1.11721a
2
u
26
+ ··· − 1.52529a + 5.87076
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5409149913549089364
2607312645830463659
u
26
a
3
+
584973825734070008
2607312645830463659
u
26
a
2
+ ··· +
12887390798361837140
2607312645830463659
a +
898974269192559217
2607312645830463659
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
27
+ 8u
26
+ ··· − 8u − 1)
4
c
2
, c
6
(u
27
+ 2u
26
+ ··· − 4u
2
− 1)
4
c
3
, c
9
u
108
+ 2u
107
+ ··· + 53770489u + 615212329
c
4
, c
8
u
108
+ 4u
107
+ ··· + u + 1
c
7
, c
10
u
108
− 5u
107
+ ··· − 770948u + 186859
c
11
(u
27
− 13u
26
+ ··· − 10u + 4)
4
c
12
(u
2
− u + 1)
54
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
27
+ 24y
26
+ ··· − 12y −1)
4
c
2
, c
6
(y
27
+ 8y
26
+ ··· − 8y −1)
4
c
3
, c
9
y
108
− 58y
107
+ ··· − 1.51 × 10
19
y + 3.78 × 10
17
c
4
, c
8
y
108
+ 34y
107
+ ··· + 539y + 1
c
7
, c
10
y
108
− 53y
107
+ ··· − 468863324560y + 34916285881
c
11
(y
27
− 5y
26
+ ··· + 236y −16)
4
c
12
(y
2
+ y + 1)
54
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.144711 + 0.987236I
a = 0.162919 + 0.975776I
b = −0.185953 + 0.197380I
−1.79198 + 2.07382I −4.33067 − 4.29744I
u = 0.144711 + 0.987236I
a = −0.102844 + 0.726044I
b = 0.86199 − 1.22813I
−1.79198 + 6.13359I −4.33067 − 11.22564I
u = 0.144711 + 0.987236I
a = −1.09255 − 1.03329I
b = −0.731660 + 0.003536I
−1.79198 + 6.13359I −4.33067 − 11.22564I
u = 0.144711 + 0.987236I
a = 0.168697 + 0.213085I
b = −0.939745 + 0.302045I
−1.79198 + 2.07382I −4.33067 − 4.29744I
u = 0.144711 − 0.987236I
a = 0.162919 − 0.975776I
b = −0.185953 − 0.197380I
−1.79198 − 2.07382I −4.33067 + 4.29744I
u = 0.144711 − 0.987236I
a = −0.102844 − 0.726044I
b = 0.86199 + 1.22813I
−1.79198 − 6.13359I −4.33067 + 11.22564I
u = 0.144711 − 0.987236I
a = −1.09255 + 1.03329I
b = −0.731660 − 0.003536I
−1.79198 − 6.13359I −4.33067 + 11.22564I
u = 0.144711 − 0.987236I
a = 0.168697 − 0.213085I
b = −0.939745 − 0.302045I
−1.79198 − 2.07382I −4.33067 + 4.29744I
u = 0.504183 + 0.966350I
a = −0.395686 + 1.137030I
b = −0.600094 + 0.060154I
0.21047 + 3.60547I 5.54032 + 3.53146I
u = 0.504183 + 0.966350I
a = 1.341760 − 0.156180I
b = 0.339181 + 0.300638I
0.210467 − 0.454298I 5.54032 + 10.45966I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.504183 + 0.966350I
a = −0.205741 + 0.513647I
b = −1.298270 + 0.190898I
0.21047 + 3.60547I 5.54032 + 3.53146I
u = 0.504183 + 0.966350I
a = 0.388483 − 0.148305I
b = 0.82742 + 1.21786I
0.210467 − 0.454298I 5.54032 + 10.45966I
u = 0.504183 − 0.966350I
a = −0.395686 − 1.137030I
b = −0.600094 − 0.060154I
0.21047 − 3.60547I 5.54032 − 3.53146I
u = 0.504183 − 0.966350I
a = 1.341760 + 0.156180I
b = 0.339181 − 0.300638I
0.210467 + 0.454298I 5.54032 − 10.45966I
u = 0.504183 − 0.966350I
a = −0.205741 − 0.513647I
b = −1.298270 − 0.190898I
0.21047 − 3.60547I 5.54032 − 3.53146I
u = 0.504183 − 0.966350I
a = 0.388483 + 0.148305I
b = 0.82742 − 1.21786I
0.210467 + 0.454298I 5.54032 − 10.45966I
u = −0.770533 + 0.784290I
a = −0.490276 + 0.975514I
b = 0.17600 + 1.72828I
4.10422 + 1.06197I 3.95591 − 0.84637I
u = −0.770533 + 0.784290I
a = 1.00912 − 1.21583I
b = −0.387312 − 1.136180I
4.10422 + 1.06197I 3.95591 − 0.84637I
u = −0.770533 + 0.784290I
a = 1.78110 − 1.78074I
b = −0.43134 − 3.24807I
4.10422 + 5.12173I 3.95591 − 7.77457I
u = −0.770533 + 0.784290I
a = −1.83240 + 2.35023I
b = 0.02422 + 2.76901I
4.10422 + 5.12173I 3.95591 − 7.77457I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.770533 − 0.784290I
a = −0.490276 − 0.975514I
b = 0.17600 − 1.72828I
4.10422 − 1.06197I 3.95591 + 0.84637I
u = −0.770533 − 0.784290I
a = 1.00912 + 1.21583I
b = −0.387312 + 1.136180I
4.10422 − 1.06197I 3.95591 + 0.84637I
u = −0.770533 − 0.784290I
a = 1.78110 + 1.78074I
b = −0.43134 + 3.24807I
4.10422 − 5.12173I 3.95591 + 7.77457I
u = −0.770533 − 0.784290I
a = −1.83240 − 2.35023I
b = 0.02422 − 2.76901I
4.10422 − 5.12173I 3.95591 + 7.77457I
u = 0.291946 + 1.107070I
a = 0.181830 + 0.662915I
b = 0.210999 − 0.718219I
1.03822 + 5.71809I 10.8623 − 10.3862I
u = 0.291946 + 1.107070I
a = 0.651923 + 0.130030I
b = −0.091528 − 0.191127I
1.03822 + 1.65832I 10.86231 − 3.45797I
u = 0.291946 + 1.107070I
a = −0.559580 − 0.338159I
b = −0.680809 + 0.394835I
1.03822 + 5.71809I 10.8623 − 10.3862I
u = 0.291946 + 1.107070I
a = −0.181802 + 0.034733I
b = 0.046374 + 0.759687I
1.03822 + 1.65832I 10.86231 − 3.45797I
u = 0.291946 − 1.107070I
a = 0.181830 − 0.662915I
b = 0.210999 + 0.718219I
1.03822 − 5.71809I 10.8623 + 10.3862I
u = 0.291946 − 1.107070I
a = 0.651923 − 0.130030I
b = −0.091528 + 0.191127I
1.03822 − 1.65832I 10.86231 + 3.45797I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.291946 − 1.107070I
a = −0.559580 + 0.338159I
b = −0.680809 − 0.394835I
1.03822 − 5.71809I 10.8623 + 10.3862I
u = 0.291946 − 1.107070I
a = −0.181802 − 0.034733I
b = 0.046374 − 0.759687I
1.03822 − 1.65832I 10.86231 + 3.45797I
u = −0.898179 + 0.746104I
a = −0.54214 + 1.40045I
b = 0.75176 + 1.70293I
9.05837 + 1.20396I 11.98510 + 0.51060I
u = −0.898179 + 0.746104I
a = 0.43666 − 1.53325I
b = −0.55795 − 1.66235I
9.05837 + 1.20396I 11.98510 + 0.51060I
u = −0.898179 + 0.746104I
a = −1.19414 + 1.56565I
b = −0.03647 + 2.44475I
9.05837 + 5.26372I 11.98510 − 6.41760I
u = −0.898179 + 0.746104I
a = 1.36189 − 1.59059I
b = −0.09559 − 2.29719I
9.05837 + 5.26372I 11.98510 − 6.41760I
u = −0.898179 − 0.746104I
a = −0.54214 − 1.40045I
b = 0.75176 − 1.70293I
9.05837 − 1.20396I 11.98510 − 0.51060I
u = −0.898179 − 0.746104I
a = 0.43666 + 1.53325I
b = −0.55795 + 1.66235I
9.05837 − 1.20396I 11.98510 − 0.51060I
u = −0.898179 − 0.746104I
a = −1.19414 − 1.56565I
b = −0.03647 − 2.44475I
9.05837 − 5.26372I 11.98510 + 6.41760I
u = −0.898179 − 0.746104I
a = 1.36189 + 1.59059I
b = −0.09559 + 2.29719I
9.05837 − 5.26372I 11.98510 + 6.41760I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.799598 + 0.863452I
a = −1.64115 − 1.19799I
b = −0.68299 − 2.89905I
7.55270 + 0.49814I 11.51904 − 1.43564I
u = 0.799598 + 0.863452I
a = 0.30170 + 2.08576I
b = −2.52729 + 1.54085I
7.55270 − 3.56162I 11.51904 + 5.49257I
u = 0.799598 + 0.863452I
a = −0.49849 + 2.46534I
b = −1.55972 + 1.92827I
7.55270 − 3.56162I 11.51904 + 5.49257I
u = 0.799598 + 0.863452I
a = −2.20182 − 1.24799I
b = −0.27785 − 2.37496I
7.55270 + 0.49814I 11.51904 − 1.43564I
u = 0.799598 − 0.863452I
a = −1.64115 + 1.19799I
b = −0.68299 + 2.89905I
7.55270 − 0.49814I 11.51904 + 1.43564I
u = 0.799598 − 0.863452I
a = 0.30170 − 2.08576I
b = −2.52729 − 1.54085I
7.55270 + 3.56162I 11.51904 − 5.49257I
u = 0.799598 − 0.863452I
a = −0.49849 − 2.46534I
b = −1.55972 − 1.92827I
7.55270 + 3.56162I 11.51904 − 5.49257I
u = 0.799598 − 0.863452I
a = −2.20182 + 1.24799I
b = −0.27785 + 2.37496I
7.55270 − 0.49814I 11.51904 + 1.43564I
u = 0.802525
a = 0.740539 + 0.485128I
b = −0.333487 + 0.062417I
4.73972 + 2.02988I 15.0178 − 3.4641I
u = 0.802525
a = 0.740539 − 0.485128I
b = −0.333487 − 0.062417I
4.73972 − 2.02988I 15.0178 + 3.4641I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.802525
a = −0.415547 + 0.077776I
b = 0.594301 + 0.389327I
4.73972 + 2.02988I 15.0178 − 3.4641I
u = 0.802525
a = −0.415547 − 0.077776I
b = 0.594301 − 0.389327I
4.73972 − 2.02988I 15.0178 + 3.4641I
u = 0.785462 + 0.911233I
a = 1.84243 + 0.15138I
b = 1.89260 + 2.66876I
7.40416 + 9.51222I 10.8841 − 11.3400I
u = 0.785462 + 0.911233I
a = −0.70561 − 2.17520I
b = 0.83935 − 2.65461I
7.40416 + 5.45245I 10.88411 − 4.41179I
u = 0.785462 + 0.911233I
a = −1.21585 − 1.96915I
b = 1.42789 − 2.35151I
7.40416 + 5.45245I 10.88411 − 4.41179I
u = 0.785462 + 0.911233I
a = 2.70741 + 0.25676I
b = 1.30921 + 1.79779I
7.40416 + 9.51222I 10.8841 − 11.3400I
u = 0.785462 − 0.911233I
a = 1.84243 − 0.15138I
b = 1.89260 − 2.66876I
7.40416 − 9.51222I 10.8841 + 11.3400I
u = 0.785462 − 0.911233I
a = −0.70561 + 2.17520I
b = 0.83935 + 2.65461I
7.40416 − 5.45245I 10.88411 + 4.41179I
u = 0.785462 − 0.911233I
a = −1.21585 + 1.96915I
b = 1.42789 + 2.35151I
7.40416 − 5.45245I 10.88411 + 4.41179I
u = 0.785462 − 0.911233I
a = 2.70741 − 0.25676I
b = 1.30921 − 1.79779I
7.40416 − 9.51222I 10.8841 + 11.3400I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.740227 + 0.958313I
a = −1.004250 + 0.871115I
b = 0.64829 + 1.52871I
3.57298 − 6.78821I 2.48240 + 5.88993I
u = −0.740227 + 0.958313I
a = 0.671829 − 1.195430I
b = −0.09143 − 1.60721I
3.57298 − 6.78821I 2.48240 + 5.88993I
u = −0.740227 + 0.958313I
a = 1.60079 − 1.88829I
b = −0.97104 − 3.37484I
3.57298 − 10.84800I 2.48240 + 12.81813I
u = −0.740227 + 0.958313I
a = −1.71545 + 2.33834I
b = 0.62462 + 2.93183I
3.57298 − 10.84800I 2.48240 + 12.81813I
u = −0.740227 − 0.958313I
a = −1.004250 − 0.871115I
b = 0.64829 − 1.52871I
3.57298 + 6.78821I 2.48240 − 5.88993I
u = −0.740227 − 0.958313I
a = 0.671829 + 1.195430I
b = −0.09143 + 1.60721I
3.57298 + 6.78821I 2.48240 − 5.88993I
u = −0.740227 − 0.958313I
a = 1.60079 + 1.88829I
b = −0.97104 + 3.37484I
3.57298 + 10.84800I 2.48240 − 12.81813I
u = −0.740227 − 0.958313I
a = −1.71545 − 2.33834I
b = 0.62462 − 2.93183I
3.57298 + 10.84800I 2.48240 − 12.81813I
u = −0.818350 + 0.893459I
a = −1.56693 + 0.67484I
b = −0.88903 + 2.53718I
8.10637 − 1.02390I 11.97423 − 0.74985I
u = −0.818350 + 0.893459I
a = −0.62722 + 1.83412I
b = 1.73682 + 1.95046I
8.10637 − 5.08367I 11.97423 + 6.17836I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.818350 + 0.893459I
a = 0.21889 − 2.14442I
b = −1.12542 − 2.06135I
8.10637 − 5.08367I 11.97423 + 6.17836I
u = −0.818350 + 0.893459I
a = 2.03983 − 0.87331I
b = 0.67936 − 1.95224I
8.10637 − 1.02390I 11.97423 − 0.74985I
u = −0.818350 − 0.893459I
a = −1.56693 − 0.67484I
b = −0.88903 − 2.53718I
8.10637 + 1.02390I 11.97423 + 0.74985I
u = −0.818350 − 0.893459I
a = −0.62722 − 1.83412I
b = 1.73682 − 1.95046I
8.10637 + 5.08367I 11.97423 − 6.17836I
u = −0.818350 − 0.893459I
a = 0.21889 + 2.14442I
b = −1.12542 + 2.06135I
8.10637 + 5.08367I 11.97423 − 6.17836I
u = −0.818350 − 0.893459I
a = 2.03983 + 0.87331I
b = 0.67936 + 1.95224I
8.10637 + 1.02390I 11.97423 + 0.74985I
u = −0.194164 + 0.737666I
a = 0.282919 − 0.103964I
b = 1.68593 + 0.47614I
1.79902 − 2.73940I 4.58487 + 7.85357I
u = −0.194164 + 0.737666I
a = −0.04074 + 2.13248I
b = 1.32188 − 1.38731I
1.79902 − 6.79917I 4.5849 + 14.7818I
u = −0.194164 + 0.737666I
a = 0.04105 − 2.29630I
b = 0.021758 + 0.228886I
1.79902 − 2.73940I 4.58487 + 7.85357I
u = −0.194164 + 0.737666I
a = −2.19994 − 1.21292I
b = −1.56515 − 0.44411I
1.79902 − 6.79917I 4.5849 + 14.7818I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.194164 − 0.737666I
a = 0.282919 + 0.103964I
b = 1.68593 − 0.47614I
1.79902 + 2.73940I 4.58487 − 7.85357I
u = −0.194164 − 0.737666I
a = −0.04074 − 2.13248I
b = 1.32188 + 1.38731I
1.79902 + 6.79917I 4.5849 − 14.7818I
u = −0.194164 − 0.737666I
a = 0.04105 + 2.29630I
b = 0.021758 − 0.228886I
1.79902 + 2.73940I 4.58487 − 7.85357I
u = −0.194164 − 0.737666I
a = −2.19994 + 1.21292I
b = −1.56515 + 0.44411I
1.79902 + 6.79917I 4.5849 − 14.7818I
u = −0.786810 + 1.024740I
a = −1.18684 + 0.77153I
b = −0.13781 + 2.02356I
8.18774 − 7.43937I 10.33045 + 4.74153I
u = −0.786810 + 1.024740I
a = 1.30727 − 0.86927I
b = 0.14320 − 1.82325I
8.18774 − 7.43937I 10.33045 + 4.74153I
u = −0.786810 + 1.024740I
a = 1.23532 − 1.62329I
b = −0.52071 − 2.64792I
8.18774 − 11.49910I 10.3304 + 11.6697I
u = −0.786810 + 1.024740I
a = −1.38017 + 1.56786I
b = 0.69149 + 2.54310I
8.18774 − 11.49910I 10.3304 + 11.6697I
u = −0.786810 − 1.024740I
a = −1.18684 − 0.77153I
b = −0.13781 − 2.02356I
8.18774 + 7.43937I 10.33045 − 4.74153I
u = −0.786810 − 1.024740I
a = 1.30727 + 0.86927I
b = 0.14320 + 1.82325I
8.18774 + 7.43937I 10.33045 − 4.74153I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.786810 − 1.024740I
a = 1.23532 + 1.62329I
b = −0.52071 + 2.64792I
8.18774 + 11.49910I 10.3304 − 11.6697I
u = −0.786810 − 1.024740I
a = −1.38017 − 1.56786I
b = 0.69149 − 2.54310I
8.18774 + 11.49910I 10.3304 − 11.6697I
u = 0.522984 + 0.315101I
a = 1.033620 + 0.005607I
b = 0.906076 − 0.080080I
1.87589 + 0.34577I 7.69627 − 1.59195I
u = 0.522984 + 0.315101I
a = 0.812617 + 1.107510I
b = −1.013690 + 0.291758I
1.87589 + 4.40553I 7.69627 − 8.52015I
u = 0.522984 + 0.315101I
a = 1.20340 − 0.87818I
b = 0.538800 + 0.328627I
1.87589 + 0.34577I 7.69627 − 1.59195I
u = 0.522984 + 0.315101I
a = −1.17546 + 1.26609I
b = 0.076008 + 0.835268I
1.87589 + 4.40553I 7.69627 − 8.52015I
u = 0.522984 − 0.315101I
a = 1.033620 − 0.005607I
b = 0.906076 + 0.080080I
1.87589 − 0.34577I 7.69627 + 1.59195I
u = 0.522984 − 0.315101I
a = 0.812617 − 1.107510I
b = −1.013690 − 0.291758I
1.87589 − 4.40553I 7.69627 + 8.52015I
u = 0.522984 − 0.315101I
a = 1.20340 + 0.87818I
b = 0.538800 − 0.328627I
1.87589 − 0.34577I 7.69627 + 1.59195I
u = 0.522984 − 0.315101I
a = −1.17546 − 1.26609I
b = 0.076008 − 0.835268I
1.87589 − 4.40553I 7.69627 + 8.52015I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.241884 + 0.503654I
a = 1.039760 − 0.018154I
b = 1.074950 + 0.695362I
2.43974 + 0.80218I 8.50674 + 4.74457I
u = −0.241884 + 0.503654I
a = 1.37398 − 0.98256I
b = −1.63834 − 0.82035I
2.43974 + 4.86195I 8.50674 − 2.18363I
u = −0.241884 + 0.503654I
a = 0.28897 − 2.27308I
b = −0.242357 + 0.528068I
2.43974 + 0.80218I 8.50674 + 4.74457I
u = −0.241884 + 0.503654I
a = −0.05408 + 3.27888I
b = 0.162526 + 0.929674I
2.43974 + 4.86195I 8.50674 − 2.18363I
u = −0.241884 − 0.503654I
a = 1.039760 + 0.018154I
b = 1.074950 − 0.695362I
2.43974 − 0.80218I 8.50674 − 4.74457I
u = −0.241884 − 0.503654I
a = 1.37398 + 0.98256I
b = −1.63834 + 0.82035I
2.43974 − 4.86195I 8.50674 + 2.18363I
u = −0.241884 − 0.503654I
a = 0.28897 + 2.27308I
b = −0.242357 − 0.528068I
2.43974 − 0.80218I 8.50674 − 4.74457I
u = −0.241884 − 0.503654I
a = −0.05408 − 3.27888I
b = 0.162526 − 0.929674I
2.43974 − 4.86195I 8.50674 + 2.18363I
24
III. I
u
3
= h55u
28
− 252u
27
+ · · · + 21b + 61, 61u
28
− 189u
27
+ · · · + 21a −
32, u
29
− 4u
28
+ · · · − 6u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
10
=
−2.90476u
28
+ 9u
27
+ ··· − 0.619048u + 1.52381
−2.61905u
28
+ 12u
27
+ ··· + 1.52381u − 2.90476
a
8
=
−1.90476u
28
+ 5u
27
+ ··· − 3.61905u − 3.47619
−2.61905u
28
+ 9u
27
+ ··· − 2.47619u − 1.90476
a
1
=
u
2
+ 1
u
2
a
11
=
−
5
7
u
28
+ 2u
27
+ ··· +
8
7
u +
32
7
−0.380952u
28
+ 3u
27
+ ··· + 1.47619u − 1.09524
a
4
=
−
44
7
u
28
+ 26u
27
+ ··· +
62
7
u −
32
7
2.04762u
28
− 2u
27
+ ··· − 5.80952u − 5.23810
a
5
=
u
3
u
5
+ u
3
+ u
a
9
=
−
23
7
u
28
+ 10u
27
+ ··· +
6
7
u +
17
7
−1.61905u
28
+ 8u
27
+ ··· + 1.52381u − 2.90476
a
12
=
30
7
u
28
− 14u
27
+ ··· −
13
7
u +
39
7
2.61905u
28
− 10u
27
+ ··· + 4.47619u + 3.90476
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4
21
u
28
+ 16u
27
+ ··· +
16
21
u −
146
21
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
29
− 10u
28
+ ··· − 12u + 1
c
2
u
29
− 4u
28
+ ··· − 6u
2
− 1
c
3
, c
9
u
29
+ u
28
+ ··· + 2u − 2
c
4
, c
8
u
29
+ 5u
27
+ ··· + u + 1
c
6
u
29
+ 4u
28
+ ··· + 6u
2
+ 1
c
7
, c
10
u
29
+ 7u
28
+ ··· + 11u + 1
c
11
u
29
− 20u
28
+ ··· + 3738u − 441
c
12
u
29
− 10u
28
+ ··· + 24u − 2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
29
+ 22y
28
+ ··· + 16y −1
c
2
, c
6
y
29
+ 10y
28
+ ··· − 12y −1
c
3
, c
9
y
29
− 15y
28
+ ··· + 24y −4
c
4
, c
8
y
29
+ 10y
28
+ ··· − 11y −1
c
7
, c
10
y
29
− 15y
28
+ ··· + 25y −1
c
11
y
29
− 16y
28
+ ··· + 797328y −194481
c
12
y
29
− 10y
28
+ ··· + 60y −4
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.381046 + 0.994636I
a = 0.394422 − 0.036263I
b = −0.114224 + 0.406124I
0.380435 − 0.893832I 3.98943 − 2.64300I
u = −0.381046 − 0.994636I
a = 0.394422 + 0.036263I
b = −0.114224 − 0.406124I
0.380435 + 0.893832I 3.98943 + 2.64300I
u = 0.933476
a = 0.470002
b = 0.438735
0.839659 −11.2680
u = 0.102637 + 0.920918I
a = −0.921307 − 0.423879I
b = 0.295797 − 0.891953I
0.77087 − 5.12193I 0.80745 + 4.16902I
u = 0.102637 − 0.920918I
a = −0.921307 + 0.423879I
b = 0.295797 + 0.891953I
0.77087 + 5.12193I 0.80745 − 4.16902I
u = −0.302805 + 1.032930I
a = 0.252124 − 0.612762I
b = 0.556595 + 0.445973I
0.14121 − 5.25589I 0.91305 + 5.96486I
u = −0.302805 − 1.032930I
a = 0.252124 + 0.612762I
b = 0.556595 − 0.445973I
0.14121 + 5.25589I 0.91305 − 5.96486I
u = 0.739534 + 0.818554I
a = 0.81317 + 2.64099I
b = −1.56043 + 2.61872I
5.00038 − 3.87176I 8.07245 + 2.05460I
u = 0.739534 − 0.818554I
a = 0.81317 − 2.64099I
b = −1.56043 − 2.61872I
5.00038 + 3.87176I 8.07245 − 2.05460I
u = 0.717708 + 0.930722I
a = 2.23453 + 0.96250I
b = 0.70792 + 2.77052I
4.64934 + 9.43078I 6.92090 − 8.42058I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.717708 − 0.930722I
a = 2.23453 − 0.96250I
b = 0.70792 − 2.77052I
4.64934 − 9.43078I 6.92090 + 8.42058I
u = 0.892893 + 0.774986I
a = −1.37205 − 1.37025I
b = −0.16318 − 2.28681I
8.08954 − 4.12661I 6.25922 + 1.62386I
u = 0.892893 − 0.774986I
a = −1.37205 + 1.37025I
b = −0.16318 + 2.28681I
8.08954 + 4.12661I 6.25922 − 1.62386I
u = −0.817743 + 0.884003I
a = 0.296499 + 0.102921I
b = −0.333443 + 0.177943I
6.98004 + 1.96846I 8.21768 − 1.67839I
u = −0.817743 − 0.884003I
a = 0.296499 − 0.102921I
b = −0.333443 − 0.177943I
6.98004 − 1.96846I 8.21768 + 1.67839I
u = −0.803936 + 0.898254I
a = −0.343383 + 0.030655I
b = 0.248522 − 0.333090I
6.93049 − 8.02852I 7.93809 + 6.50291I
u = −0.803936 − 0.898254I
a = −0.343383 − 0.030655I
b = 0.248522 + 0.333090I
6.93049 + 8.02852I 7.93809 − 6.50291I
u = 0.814198 + 0.892612I
a = −1.39320 − 1.71325I
b = 0.39493 − 2.63852I
8.03691 + 3.04142I 12.07509 − 2.75183I
u = 0.814198 − 0.892612I
a = −1.39320 + 1.71325I
b = 0.39493 + 2.63852I
8.03691 − 3.04142I 12.07509 + 2.75183I
u = 0.795789 + 1.009530I
a = −1.13869 − 1.65579I
b = 0.76542 − 2.46720I
7.35018 + 10.38150I 5.17331 − 6.23608I
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.795789 − 1.009530I
a = −1.13869 + 1.65579I
b = 0.76542 + 2.46720I
7.35018 − 10.38150I 5.17331 + 6.23608I
u = 0.093113 + 0.676164I
a = −0.91249 + 2.19288I
b = −1.56771 − 0.41280I
1.73448 + 5.99989I 2.11994 − 3.13699I
u = 0.093113 − 0.676164I
a = −0.91249 − 2.19288I
b = −1.56771 + 0.41280I
1.73448 − 5.99989I 2.11994 + 3.13699I
u = 0.441114 + 1.253380I
a = −0.159594 + 0.165424I
b = −0.277739 − 0.127061I
−3.12845 + 4.78394I −2.9636 + 14.9800I
u = 0.441114 − 1.253380I
a = −0.159594 − 0.165424I
b = −0.277739 + 0.127061I
−3.12845 − 4.78394I −2.9636 − 14.9800I
u = −0.590522 + 0.197460I
a = −0.447464 − 0.749791I
b = 0.412292 + 0.354412I
2.96129 + 1.89751I 11.45632 − 0.75702I
u = −0.590522 − 0.197460I
a = −0.447464 + 0.749791I
b = 0.412292 − 0.354412I
2.96129 − 1.89751I 11.45632 + 0.75702I
u = −0.167670 + 0.470199I
a = −0.53757 − 1.75616I
b = 0.915879 + 0.041690I
2.32133 − 1.86969I 9.65457 + 2.80785I
u = −0.167670 − 0.470199I
a = −0.53757 + 1.75616I
b = 0.915879 − 0.041690I
2.32133 + 1.86969I 9.65457 − 2.80785I
30
IV. I
u
4
= hau + b − 1, a
2
+ au + a + 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u − 1
a
7
=
u
u + 1
a
10
=
a
−au + 1
a
8
=
−au + u
−au − a + 1
a
1
=
−u
−u − 1
a
11
=
a − u − 1
−au
a
4
=
2a − u + 1
−au − u − 1
a
5
=
1
0
a
9
=
au + a − 1
−au + 1
a
12
=
a − u − 1
−au
(ii) Obstruction class = 1
(iii) Cusp Shapes = 13u + 5
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
(u
2
− u + 1)
2
c
2
, c
7
, c
10
c
12
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
u
4
+ 2u
3
− u + 1
c
11
u
4
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
12
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
y
4
− 4y
3
+ 6y
2
− y + 1
c
11
y
4
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.148403 + 0.632502I
b = 1.47356 + 0.44477I
− 4.05977I −1.50000 + 11.25833I
u = −0.500000 + 0.866025I
a = −0.35160 − 1.49853I
b = −0.473561 − 0.444772I
− 4.05977I −1.50000 + 11.25833I
u = −0.500000 − 0.866025I
a = −0.148403 − 0.632502I
b = 1.47356 − 0.44477I
4.05977I −1.50000 − 11.25833I
u = −0.500000 − 0.866025I
a = −0.35160 + 1.49853I
b = −0.473561 + 0.444772I
4.05977I −1.50000 − 11.25833I
34
V. I
u
5
= hau + b − u, a
2
− a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u − 1
a
7
=
u
u + 1
a
10
=
a
−au + u
a
8
=
au + a + u
a + u
a
1
=
−u
−u − 1
a
11
=
a + 1
−au
a
4
=
2au
au + a + u
a
5
=
1
0
a
9
=
au + a − u
−au + u
a
12
=
a + 1
−au
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u + 1
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
(u
2
− u + 1)
2
c
2
, c
7
, c
10
c
12
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
u
4
− u
3
+ 2u + 1
c
11
u
4
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
12
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
y
4
− y
3
+ 6y
2
− 4y + 1
c
11
y
4
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.473561 − 0.444772I
b = −1.12196 + 1.05376I
0 −1.50000 + 4.33013I
u = −0.500000 + 0.866025I
a = 1.47356 + 0.44477I
b = 0.621964 − 0.187730I
0 −1.50000 + 4.33013I
u = −0.500000 − 0.866025I
a = −0.473561 + 0.444772I
b = −1.12196 − 1.05376I
0 −1.50000 − 4.33013I
u = −0.500000 − 0.866025I
a = 1.47356 − 0.44477I
b = 0.621964 + 0.187730I
0 −1.50000 − 4.33013I
38
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
2
− u + 1)
4
)(u
27
+ 8u
26
+ ··· − 8u − 1)
4
· (u
29
− 10u
28
+ ··· − 12u + 1)(u
56
+ 17u
55
+ ··· + 2640u + 256)
c
2
((u
2
+ u + 1)
4
)(u
27
+ 2u
26
+ ··· − 4u
2
− 1)
4
(u
29
− 4u
28
+ ··· − 6u
2
− 1)
· (u
56
− 9u
55
+ ··· + 36u − 16)
c
3
, c
9
(u
4
− u
3
+ 2u + 1)(u
4
+ 2u
3
− u + 1)(u
29
+ u
28
+ ··· + 2u − 2)
· (u
56
− u
55
+ ··· + 166u + 34)
· (u
108
+ 2u
107
+ ··· + 53770489u + 615212329)
c
4
, c
8
(u
4
− u
3
+ 2u + 1)(u
4
+ 2u
3
− u + 1)(u
29
+ 5u
27
+ ··· + u + 1)
· (u
56
− 5u
54
+ ··· + u − 1)(u
108
+ 4u
107
+ ··· + u + 1)
c
6
((u
2
− u + 1)
4
)(u
27
+ 2u
26
+ ··· − 4u
2
− 1)
4
(u
29
+ 4u
28
+ ··· + 6u
2
+ 1)
· (u
56
− 9u
55
+ ··· + 36u − 16)
c
7
, c
10
((u
2
+ u + 1)
4
)(u
29
+ 7u
28
+ ··· + 11u + 1)(u
56
− u
55
+ ··· − 21u + 1)
· (u
108
− 5u
107
+ ··· − 770948u + 186859)
c
11
u
8
(u
27
− 13u
26
+ ··· − 10u + 4)
4
(u
29
− 20u
28
+ ··· + 3738u − 441)
· (u
56
+ 43u
55
+ ··· − 34u − 4)
c
12
((u
2
− u + 1)
54
)(u
2
+ u + 1)
4
(u
29
− 10u
28
+ ··· + 24u − 2)
· (u
56
+ 53u
55
+ ··· − 738197504u − 33554432)
39
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
4
)(y
27
+ 24y
26
+ ··· − 12y −1)
4
· (y
29
+ 22y
28
+ ··· + 16y −1)(y
56
+ 45y
55
+ ··· − 636672y + 65536)
c
2
, c
6
((y
2
+ y + 1)
4
)(y
27
+ 8y
26
+ ··· − 8y −1)
4
· (y
29
+ 10y
28
+ ··· − 12y −1)(y
56
+ 17y
55
+ ··· + 2640y + 256)
c
3
, c
9
(y
4
− 4y
3
+ 6y
2
− y + 1)(y
4
− y
3
+ 6y
2
− 4y + 1)
· (y
29
− 15y
28
+ ··· + 24y −4)(y
56
− 31y
55
+ ··· − 9332y + 1156)
· (y
108
− 58y
107
+ ··· − 1.51 × 10
19
y + 3.78 × 10
17
)
c
4
, c
8
(y
4
− 4y
3
+ 6y
2
− y + 1)(y
4
− y
3
+ 6y
2
− 4y + 1)
· (y
29
+ 10y
28
+ ··· − 11y −1)(y
56
− 10y
55
+ ··· − 9y + 1)
· (y
108
+ 34y
107
+ ··· + 539y + 1)
c
7
, c
10
((y
2
+ y + 1)
4
)(y
29
− 15y
28
+ ··· + 25y −1)(y
56
− 7y
55
+ ··· − 45y + 1)
· (y
108
− 53y
107
+ ··· − 468863324560y + 34916285881)
c
11
y
8
(y
27
− 5y
26
+ ··· + 236y −16)
4
· (y
29
− 16y
28
+ ··· + 797328y −194481)
· (y
56
− 21y
55
+ ··· − 508y + 16)
c
12
((y
2
+ y + 1)
58
)(y
29
− 10y
28
+ ··· + 60y −4)
· (y
56
− 9y
55
+ ··· + 19140298416324608y + 1125899906842624)
40
