12a
0493
(K12a
0493
)
A knot diagram
1
Linearized knot diagam
3 6 12 10 8 2 11 1 4 5 7 9
Solving Sequence
4,9
10 5
1,11
8 6 7 12 3 2
c
9
c
4
c
10
c
8
c
5
c
7
c
12
c
3
c
2
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.06014 × 10
50
u
36
− 1.13950 × 10
51
u
35
+ ··· + 1.85440 × 10
51
b − 1.47847 × 10
52
,
− 7.67176 × 10
51
u
36
− 2.81819 × 10
52
u
35
+ ··· + 1.48352 × 10
52
a − 4.05802 × 10
53
,
u
37
+ 3u
36
+ ··· + 128u − 32i
I
u
2
= h13u
27
a + 13u
27
+ ··· + 9a − 79, −126u
27
a + 164u
27
+ ··· + 105a − 202, u
28
− u
27
+ ··· − 2u − 1i
I
u
3
= hb − 1, 8a
2
− 2au − 8a + u + 3, u
2
− 2i
I
u
4
= hb − u, 3a − u − 1, u
2
+ 1i
I
v
1
= ha, b + 1, 4v
2
− 2v + 1i
* 5 irreducible components of dim
C
= 0, with total 101 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−3.06 × 10
50
u
36
− 1.14 × 10
51
u
35
+ · · · + 1.85 × 10
51
b − 1.48 ×
10
52
, −7.67 × 10
51
u
36
− 2.82 × 10
52
u
35
+ · · · + 1.48 × 10
52
a − 4.06 ×
10
53
, u
37
+ 3u
36
+ · · · + 128u − 32i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
0.517133u
36
+ 1.89967u
35
+ ··· − 65.6808u + 27.3541
0.165020u
36
+ 0.614485u
35
+ ··· − 22.3411u + 7.97281
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
0.378169u
36
+ 1.38393u
35
+ ··· − 47.6562u + 20.0310
0.116597u
36
+ 0.438884u
35
+ ··· − 15.5080u + 7.33172
a
6
=
−0.260062u
36
− 0.944298u
35
+ ··· + 30.2985u − 13.1873
−0.0118049u
36
− 0.0559693u
35
+ ··· + 2.23444u − 0.782090
a
7
=
0.489111u
36
+ 1.77691u
35
+ ··· − 59.9917u + 24.1822
0.224162u
36
+ 0.829248u
35
+ ··· − 29.6633u + 13.0783
a
12
=
0.352113u
36
+ 1.28518u
35
+ ··· − 43.3397u + 19.3813
0.165020u
36
+ 0.614485u
35
+ ··· − 22.3411u + 7.97281
a
3
=
0.164726u
36
+ 0.616077u
35
+ ··· − 19.8484u + 8.71780
0.160328u
36
+ 0.586036u
35
+ ··· − 20.7819u + 8.37031
a
2
=
0.304049u
36
+ 1.15112u
35
+ ··· − 39.5480u + 15.8740
0.372272u
36
+ 1.37310u
35
+ ··· − 49.4772u + 19.3370
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.647838u
36
− 2.40428u
35
+ ··· + 107.799u − 53.2159
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
37
+ 14u
36
+ ··· + 929u − 64
c
2
, c
6
u
37
− 2u
36
+ ··· + 7u + 8
c
3
, c
5
64(64u
37
− 160u
36
+ ··· − 41u − 19)
c
4
, c
9
, c
10
u
37
− 3u
36
+ ··· + 128u + 32
c
7
, c
8
, c
11
c
12
u
37
+ 2u
36
+ ··· + 39u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 6y
36
+ ··· + 1952449y −4096
c
2
, c
6
y
37
+ 14y
36
+ ··· + 929y −64
c
3
, c
5
4096(4096y
37
− 87040y
36
+ ··· + 1681y −361)
c
4
, c
9
, c
10
y
37
− 37y
36
+ ··· + 10240y −1024
c
7
, c
8
, c
11
c
12
y
37
+ 20y
36
+ ··· − 985y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.717759 + 0.816773I
a = −0.912312 − 0.929862I
b = 0.478496 − 1.321070I
−6.2593 − 13.4401I −5.68141 + 9.41013I
u = 0.717759 − 0.816773I
a = −0.912312 + 0.929862I
b = 0.478496 + 1.321070I
−6.2593 + 13.4401I −5.68141 − 9.41013I
u = 0.415681 + 1.039780I
a = −0.207547 − 0.355306I
b = −0.295825 − 1.226410I
−5.25287 + 7.46721I −6.71313 − 6.59002I
u = 0.415681 − 1.039780I
a = −0.207547 + 0.355306I
b = −0.295825 + 1.226410I
−5.25287 − 7.46721I −6.71313 + 6.59002I
u = −0.795182 + 0.815543I
a = −0.758362 + 0.992112I
b = 0.402574 + 1.213530I
−3.61367 + 7.50969I −3.85082 − 6.86152I
u = −0.795182 − 0.815543I
a = −0.758362 − 0.992112I
b = 0.402574 − 1.213530I
−3.61367 − 7.50969I −3.85082 + 6.86152I
u = −0.780739 + 0.195496I
a = 0.12973 + 1.67958I
b = 0.520268 + 0.618361I
0.70381 + 4.04876I −0.98977 − 8.58412I
u = −0.780739 − 0.195496I
a = 0.12973 − 1.67958I
b = 0.520268 − 0.618361I
0.70381 − 4.04876I −0.98977 + 8.58412I
u = 0.753713 + 1.012550I
a = −0.570904 − 0.720134I
b = 0.144902 − 1.297410I
−10.11250 − 3.50416I −11.13565 + 4.29922I
u = 0.753713 − 1.012550I
a = −0.570904 + 0.720134I
b = 0.144902 + 1.297410I
−10.11250 + 3.50416I −11.13565 − 4.29922I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.364950 + 0.053956I
a = −0.482374 + 0.537077I
b = 0.199987 + 0.285968I
−5.15018 + 2.40489I −8.24367 − 5.51065I
u = −1.364950 − 0.053956I
a = −0.482374 − 0.537077I
b = 0.199987 − 0.285968I
−5.15018 − 2.40489I −8.24367 + 5.51065I
u = 0.633091 + 0.002919I
a = 0.88132 − 1.53274I
b = 0.457881 − 0.454036I
0.564134 + 1.148360I −2.41262 + 1.34947I
u = 0.633091 − 0.002919I
a = 0.88132 + 1.53274I
b = 0.457881 + 0.454036I
0.564134 − 1.148360I −2.41262 − 1.34947I
u = 1.37208
a = 0.234496
b = 0.732338
−3.38199 −0.506720
u = −0.434378 + 1.324040I
a = −0.165219 + 0.603269I
b = −0.115926 + 1.115120I
−2.03465 − 0.92733I −10.61628 + 8.02850I
u = −0.434378 − 1.324040I
a = −0.165219 − 0.603269I
b = −0.115926 − 1.115120I
−2.03465 + 0.92733I −10.61628 − 8.02850I
u = 1.44111 + 0.07312I
a = 0.657076 + 0.293879I
b = 1.138240 + 0.387434I
−3.29453 + 0.35231I −4.03504 + 0.I
u = 1.44111 − 0.07312I
a = 0.657076 − 0.293879I
b = 1.138240 − 0.387434I
−3.29453 − 0.35231I −4.03504 + 0.I
u = 0.248091 + 0.440024I
a = 0.670055 + 0.392554I
b = −0.108331 + 0.395171I
0.042476 − 0.966476I 1.15246 + 6.51275I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248091 − 0.440024I
a = 0.670055 − 0.392554I
b = −0.108331 − 0.395171I
0.042476 + 0.966476I 1.15246 − 6.51275I
u = −1.51529 + 0.03946I
a = 0.916910 − 0.146355I
b = 1.56997 − 0.24762I
−4.83143 + 3.15767I 0
u = −1.51529 − 0.03946I
a = 0.916910 + 0.146355I
b = 1.56997 + 0.24762I
−4.83143 − 3.15767I 0
u = −0.242484 + 0.378477I
a = 0.421990 − 0.025898I
b = −0.940128 + 0.390144I
2.26406 − 1.74820I 5.58765 − 3.71999I
u = −0.242484 − 0.378477I
a = 0.421990 + 0.025898I
b = −0.940128 − 0.390144I
2.26406 + 1.74820I 5.58765 + 3.71999I
u = 0.341813 + 0.196908I
a = 0.510424 + 0.063365I
b = −1.169100 − 0.216448I
1.56390 − 2.42880I −6.3891 + 13.7681I
u = 0.341813 − 0.196908I
a = 0.510424 − 0.063365I
b = −1.169100 + 0.216448I
1.56390 + 2.42880I −6.3891 − 13.7681I
u = −1.61409 + 0.26724I
a = 0.59418 − 1.86265I
b = −0.58352 − 1.43640I
−13.9496 + 17.5003I 0
u = −1.61409 − 0.26724I
a = 0.59418 + 1.86265I
b = −0.58352 + 1.43640I
−13.9496 − 17.5003I 0
u = 1.63110 + 0.25971I
a = 0.52663 + 1.83233I
b = −0.51959 + 1.38080I
−11.6103 − 11.5613I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.63110 − 0.25971I
a = 0.52663 − 1.83233I
b = −0.51959 − 1.38080I
−11.6103 + 11.5613I 0
u = −1.65342 + 0.29506I
a = 0.55360 − 1.67738I
b = −0.35735 − 1.45793I
−18.0870 + 8.2892I 0
u = −1.65342 − 0.29506I
a = 0.55360 + 1.67738I
b = −0.35735 + 1.45793I
−18.0870 − 8.2892I 0
u = −1.73297 + 0.43440I
a = 0.418669 − 1.324280I
b = −0.001916 − 1.266200I
−12.01220 − 1.49842I 0
u = −1.73297 − 0.43440I
a = 0.418669 + 1.324280I
b = −0.001916 + 1.266200I
−12.01220 + 1.49842I 0
u = 1.76511 + 0.30036I
a = 0.32388 + 1.51280I
b = −0.186791 + 1.230020I
−10.04750 − 5.61368I 0
u = 1.76511 − 0.30036I
a = 0.32388 − 1.51280I
b = −0.186791 − 1.230020I
−10.04750 + 5.61368I 0
8
II. I
u
2
= h13u
27
a + 13u
27
+ · · · + 9a − 79, −126u
27
a + 164u
27
+ · · · + 105a −
202, u
28
− u
27
+ · · · − 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
a
−0.147727au
27
− 0.147727u
27
+ ··· − 0.102273a + 0.897727
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
0.147727au
27
+ 1.57630u
27
+ ··· − 0.897727a − 1.75487
−0.147727au
27
− 0.147727u
27
+ ··· − 0.102273a − 1.10227
a
6
=
−1.50974au
27
− 0.183210u
27
+ ··· + 1.72403a − 3.21475
−0.306818au
27
− 0.592532u
27
+ ··· − 0.443182a + 2.12825
a
7
=
0.147727au
27
+ 1.57630u
27
+ ··· − 0.897727a − 2.75487
−1
a
12
=
0.147727au
27
+ 0.147727u
27
+ ··· + 1.10227a − 0.897727
−0.147727au
27
− 0.147727u
27
+ ··· − 0.102273a + 0.897727
a
3
=
−0.592532au
27
+ 0.938080u
27
+ ··· + 2.12825a − 6.64726
0.204545au
27
− 1.50974u
27
+ ··· + 0.295455a + 1.72403
a
2
=
−0.186688au
27
− 0.309137u
27
+ ··· + 1.79383a − 3.10413
0.738636au
27
− 0.404221u
27
+ ··· + 0.511364a + 1.79708
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
26
+ 60u
24
− 384u
22
− 4u
21
+ 1364u
20
+ 48u
19
− 2940u
18
−
236u
17
+ 4000u
16
+ 608u
15
−3604u
14
−884u
13
+ 2428u
12
+ 784u
11
−1376u
10
−560u
9
+
576u
8
+ 384u
7
− 180u
6
− 148u
5
+ 40u
4
+ 52u
3
− 4u
2
− 16u − 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
28
+ 13u
27
+ ··· − 2u + 1)
2
c
2
, c
6
(u
28
− u
27
+ ··· + u
2
− 1)
2
c
3
, c
5
49(49u
56
− 91u
55
+ ··· − 1.53507 × 10
7
u + 3334724)
c
4
, c
9
, c
10
(u
28
+ u
27
+ ··· + 2u − 1)
2
c
7
, c
8
, c
11
c
12
u
56
− 5u
55
+ ··· − 107u + 10
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 5y
27
+ ··· − 26y + 1)
2
c
2
, c
6
(y
28
+ 13y
27
+ ··· − 2y + 1)
2
c
3
, c
5
2401
· (2401y
56
− 79233y
55
+ ··· − 192404715942833y + 11120384156176)
c
4
, c
9
, c
10
(y
28
− 31y
27
+ ··· − 2y + 1)
2
c
7
, c
8
, c
11
c
12
y
56
+ 39y
55
+ ··· + 1011y + 100
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.586405 + 0.574893I
a = 0.934511 − 0.806392I
b = −0.509903 − 1.304970I
−2.17812 + 8.20859I −2.53568 − 8.40980I
u = −0.586405 + 0.574893I
a = −0.428647 + 0.151255I
b = 0.991060 − 0.025480I
−2.17812 + 8.20859I −2.53568 − 8.40980I
u = −0.586405 − 0.574893I
a = 0.934511 + 0.806392I
b = −0.509903 + 1.304970I
−2.17812 − 8.20859I −2.53568 + 8.40980I
u = −0.586405 − 0.574893I
a = −0.428647 − 0.151255I
b = 0.991060 + 0.025480I
−2.17812 − 8.20859I −2.53568 + 8.40980I
u = 0.543996 + 0.566433I
a = 0.925405 + 0.839471I
b = −0.447775 + 1.141120I
−0.24402 − 3.16640I 0.86244 + 4.02500I
u = 0.543996 + 0.566433I
a = −0.286979 + 0.026703I
b = 0.777119 + 0.122141I
−0.24402 − 3.16640I 0.86244 + 4.02500I
u = 0.543996 − 0.566433I
a = 0.925405 − 0.839471I
b = −0.447775 − 1.141120I
−0.24402 + 3.16640I 0.86244 − 4.02500I
u = 0.543996 − 0.566433I
a = −0.286979 − 0.026703I
b = 0.777119 − 0.122141I
−0.24402 + 3.16640I 0.86244 − 4.02500I
u = 0.755212 + 0.133146I
a = −0.540919 + 0.740300I
b = 0.327975 + 1.320330I
−6.69395 − 3.35246I −9.30317 + 5.30916I
u = 0.755212 + 0.133146I
a = −1.287460 − 0.454067I
b = 0.512318 − 1.140390I
−6.69395 − 3.35246I −9.30317 + 5.30916I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.755212 − 0.133146I
a = −0.540919 − 0.740300I
b = 0.327975 − 1.320330I
−6.69395 + 3.35246I −9.30317 − 5.30916I
u = 0.755212 − 0.133146I
a = −1.287460 + 0.454067I
b = 0.512318 + 1.140390I
−6.69395 + 3.35246I −9.30317 − 5.30916I
u = 0.430218 + 0.577744I
a = 0.472399 + 0.979629I
b = −0.260873 + 0.295035I
0.091207 − 0.758227I 2.08172 + 3.18448I
u = 0.430218 + 0.577744I
a = 0.786867 + 0.267464I
b = 0.188478 + 0.847031I
0.091207 − 0.758227I 2.08172 + 3.18448I
u = 0.430218 − 0.577744I
a = 0.472399 − 0.979629I
b = −0.260873 − 0.295035I
0.091207 + 0.758227I 2.08172 − 3.18448I
u = 0.430218 − 0.577744I
a = 0.786867 − 0.267464I
b = 0.188478 − 0.847031I
0.091207 + 0.758227I 2.08172 − 3.18448I
u = −0.567490 + 0.434707I
a = −0.953091 − 0.262766I
b = 0.607189 + 0.445832I
−4.87389 + 1.32970I −6.44616 − 3.85928I
u = −0.567490 + 0.434707I
a = 0.809747 − 1.000910I
b = −0.115321 − 1.301290I
−4.87389 + 1.32970I −6.44616 − 3.85928I
u = −0.567490 − 0.434707I
a = −0.953091 + 0.262766I
b = 0.607189 − 0.445832I
−4.87389 − 1.32970I −6.44616 + 3.85928I
u = −0.567490 − 0.434707I
a = 0.809747 + 1.000910I
b = −0.115321 + 1.301290I
−4.87389 − 1.32970I −6.44616 + 3.85928I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.376046 + 0.601172I
a = 1.089170 + 0.134073I
b = 0.273285 − 1.117400I
−1.56209 − 4.19313I −0.61655 + 2.23475I
u = −0.376046 + 0.601172I
a = 0.56846 − 1.38218I
b = −0.557250 + 0.014188I
−1.56209 − 4.19313I −0.61655 + 2.23475I
u = −0.376046 − 0.601172I
a = 1.089170 − 0.134073I
b = 0.273285 + 1.117400I
−1.56209 + 4.19313I −0.61655 − 2.23475I
u = −0.376046 − 0.601172I
a = 0.56846 + 1.38218I
b = −0.557250 − 0.014188I
−1.56209 + 4.19313I −0.61655 − 2.23475I
u = −0.561801
a = −1.53884 + 1.41722I
b = 0.265812 + 1.100900I
−4.21146 −6.53310
u = −0.561801
a = −1.53884 − 1.41722I
b = 0.265812 − 1.100900I
−4.21146 −6.53310
u = 1.45325 + 0.12481I
a = 0.497932 − 0.933897I
b = −0.092728 + 0.331998I
−7.39140 + 1.71282I −4.00356 − 2.41214I
u = 1.45325 + 0.12481I
a = −1.37354 − 1.92368I
b = 0.022349 − 1.127440I
−7.39140 + 1.71282I −4.00356 − 2.41214I
u = 1.45325 − 0.12481I
a = 0.497932 + 0.933897I
b = −0.092728 − 0.331998I
−7.39140 − 1.71282I −4.00356 + 2.41214I
u = 1.45325 − 0.12481I
a = −1.37354 + 1.92368I
b = 0.022349 + 1.127440I
−7.39140 − 1.71282I −4.00356 + 2.41214I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48911 + 0.14533I
a = −0.006064 + 0.424503I
b = −0.444666 − 0.069093I
−6.17088 + 3.25978I −1.92342 − 3.24223I
u = −1.48911 + 0.14533I
a = −0.75937 + 1.83812I
b = 0.200801 + 1.104680I
−6.17088 + 3.25978I −1.92342 − 3.24223I
u = −1.48911 − 0.14533I
a = −0.006064 − 0.424503I
b = −0.444666 + 0.069093I
−6.17088 − 3.25978I −1.92342 + 3.24223I
u = −1.48911 − 0.14533I
a = −0.75937 − 1.83812I
b = 0.200801 − 1.104680I
−6.17088 − 3.25978I −1.92342 + 3.24223I
u = −1.54219 + 0.16548I
a = −0.467553 − 0.176793I
b = −1.110050 − 0.015985I
−7.18158 + 5.80125I −2.94144 − 3.19136I
u = −1.54219 + 0.16548I
a = −0.37493 + 1.92923I
b = 0.54543 + 1.39509I
−7.18158 + 5.80125I −2.94144 − 3.19136I
u = −1.54219 − 0.16548I
a = −0.467553 + 0.176793I
b = −1.110050 + 0.015985I
−7.18158 − 5.80125I −2.94144 + 3.19136I
u = −1.54219 − 0.16548I
a = −0.37493 − 1.92923I
b = 0.54543 − 1.39509I
−7.18158 − 5.80125I −2.94144 + 3.19136I
u = −0.144411 + 0.424497I
a = 3.71627 + 0.89342I
b = −0.095241 − 1.154760I
−3.83479 + 1.50370I −0.95413 − 4.12502I
u = −0.144411 + 0.424497I
a = 0.92345 − 3.77771I
b = −0.233804 + 0.870476I
−3.83479 + 1.50370I −0.95413 − 4.12502I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.144411 − 0.424497I
a = 3.71627 − 0.89342I
b = −0.095241 + 1.154760I
−3.83479 − 1.50370I −0.95413 + 4.12502I
u = −0.144411 − 0.424497I
a = 0.92345 + 3.77771I
b = −0.233804 − 0.870476I
−3.83479 − 1.50370I −0.95413 + 4.12502I
u = 1.55614 + 0.12966I
a = −0.198340 + 0.485848I
b = −1.093620 + 0.434411I
−12.02270 − 3.39810I −9.35777 + 1.97434I
u = 1.55614 + 0.12966I
a = −0.37182 − 2.05675I
b = 0.28306 − 1.56814I
−12.02270 − 3.39810I −9.35777 + 1.97434I
u = 1.55614 − 0.12966I
a = −0.198340 − 0.485848I
b = −1.093620 − 0.434411I
−12.02270 + 3.39810I −9.35777 − 1.97434I
u = 1.55614 − 0.12966I
a = −0.37182 + 2.05675I
b = 0.28306 + 1.56814I
−12.02270 + 3.39810I −9.35777 − 1.97434I
u = 1.56158
a = 0.21585 + 1.83347I
b = −0.53469 + 1.36297I
−11.5046 −6.31040
u = 1.56158
a = 0.21585 − 1.83347I
b = −0.53469 − 1.36297I
−11.5046 −6.31040
u = 1.55803 + 0.17307I
a = −0.589352 + 0.296556I
b = −1.310590 + 0.010597I
−9.3292 − 10.9377I −6.01109 + 7.20566I
u = 1.55803 + 0.17307I
a = −0.31959 − 1.94804I
b = 0.64841 − 1.51798I
−9.3292 − 10.9377I −6.01109 + 7.20566I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55803 − 0.17307I
a = −0.589352 − 0.296556I
b = −1.310590 − 0.010597I
−9.3292 + 10.9377I −6.01109 − 7.20566I
u = 1.55803 − 0.17307I
a = −0.31959 + 1.94804I
b = 0.64841 + 1.51798I
−9.3292 + 10.9377I −6.01109 − 7.20566I
u = −1.59109 + 0.02596I
a = −0.00141 − 1.54816I
b = −0.83487 − 1.39668I
−14.6422 + 3.8713I −10.42941 − 3.80957I
u = −1.59109 + 0.02596I
a = −0.08503 + 1.90406I
b = −0.50190 + 1.64960I
−14.6422 + 3.8713I −10.42941 − 3.80957I
u = −1.59109 − 0.02596I
a = −0.00141 + 1.54816I
b = −0.83487 + 1.39668I
−14.6422 − 3.8713I −10.42941 + 3.80957I
u = −1.59109 − 0.02596I
a = −0.08503 − 1.90406I
b = −0.50190 − 1.64960I
−14.6422 − 3.8713I −10.42941 + 3.80957I
17
III. I
u
3
= hb − 1, 8a
2
− 2au − 8a + u + 3, u
2
− 2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
2
a
5
=
−u
−u
a
1
=
a
1
a
11
=
−1
0
a
8
=
a + 1
1
a
6
=
2au +
1
2
a −
11
8
u −
1
4
au − u
a
7
=
a
1
a
12
=
a − 1
1
a
3
=
−au +
1
2
a +
5
8
u −
1
4
au
a
2
=
−au + 2a +
3
8
u
au + 2a −
1
2
u −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8au − 4u − 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
2
c
3
16(16u
4
+ 16u
3
− 4u
2
− 4u + 7)
c
4
, c
9
, c
10
(u
2
− 2)
2
c
5
16(16u
4
− 16u
3
− 4u
2
+ 4u + 7)
c
6
(u
2
+ u + 1)
2
c
7
, c
8
(u − 1)
4
c
11
, c
12
(u + 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
256(256y
4
− 384y
3
+ 368y
2
− 72y + 49)
c
4
, c
9
, c
10
(y − 2)
4
c
7
, c
8
, c
11
c
12
(y − 1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 0.676777 + 0.306186I
b = 1.00000
−3.28987 − 2.02988I −2.00000 + 3.46410I
u = 1.41421
a = 0.676777 − 0.306186I
b = 1.00000
−3.28987 + 2.02988I −2.00000 − 3.46410I
u = −1.41421
a = 0.323223 + 0.306186I
b = 1.00000
−3.28987 + 2.02988I −2.00000 − 3.46410I
u = −1.41421
a = 0.323223 − 0.306186I
b = 1.00000
−3.28987 − 2.02988I −2.00000 + 3.46410I
21
IV. I
u
4
= hb − u, 3a − u − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−1
a
5
=
−u
2u
a
1
=
1
3
u +
1
3
u
a
11
=
2
−3
a
8
=
1
3
u +
2
3
−1
a
6
=
−u +
5
9
7
3
u −
2
3
a
7
=
−
5
3
u +
2
3
3u − 1
a
12
=
−
2
3
u +
1
3
u
a
3
=
−
1
3
u +
4
9
5
3
u −
1
3
a
2
=
2
3
u −
1
9
−
2
3
u +
1
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u + 1)
2
c
3
9(9u
2
+ 12u + 5)
c
4
, c
7
, c
8
c
9
, c
10
, c
11
c
12
u
2
+ 1
c
5
9(9u
2
− 12u + 5)
c
6
(u − 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y − 1)
2
c
3
, c
5
81(81y
2
− 54y + 25)
c
4
, c
7
, c
8
c
9
, c
10
, c
11
c
12
(y + 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.333333 + 0.333333I
b = 1.000000I
−1.64493 −4.00000
u = − 1.000000I
a = 0.333333 − 0.333333I
b = − 1.000000I
−1.64493 −4.00000
25
V. I
v
1
= ha, b + 1, 4v
2
− 2v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
10
=
1
0
a
5
=
v
0
a
1
=
0
−1
a
11
=
1
0
a
8
=
1
1
a
6
=
2v
v
a
7
=
0
1
a
12
=
1
−1
a
3
=
2v
−v
a
2
=
2v − 1
−v −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7v −
1
2
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
4(4u
2
+ 2u + 1)
c
4
, c
9
, c
10
u
2
c
5
4(4u
2
− 2u + 1)
c
7
, c
8
(u + 1)
2
c
11
, c
12
(u − 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
2
+ y + 1
c
3
, c
5
16(16y
2
+ 4y + 1)
c
4
, c
9
, c
10
y
2
c
7
, c
8
, c
11
c
12
(y − 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.250000 + 0.433013I
a = 0
b = −1.00000
1.64493 − 2.02988I −2.25000 − 3.03109I
v = 0.250000 − 0.433013I
a = 0
b = −1.00000
1.64493 + 2.02988I −2.25000 + 3.03109I
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u + 1)
2
)(u
2
− u + 1)
3
(u
28
+ 13u
27
+ ··· − 2u + 1)
2
· (u
37
+ 14u
36
+ ··· + 929u − 64)
c
2
((u + 1)
2
)(u
2
− u + 1)
2
(u
2
+ u + 1)(u
28
− u
27
+ ··· + u
2
− 1)
2
· (u
37
− 2u
36
+ ··· + 7u + 8)
c
3
1806336(4u
2
+ 2u + 1)(9u
2
+ 12u + 5)(16u
4
+ 16u
3
+ ··· − 4u + 7)
· (64u
37
− 160u
36
+ ··· − 41u − 19)
· (49u
56
− 91u
55
+ ··· − 15350701u + 3334724)
c
4
, c
9
, c
10
u
2
(u
2
− 2)
2
(u
2
+ 1)(u
28
+ u
27
+ ··· + 2u − 1)
2
· (u
37
− 3u
36
+ ··· + 128u + 32)
c
5
1806336(4u
2
− 2u + 1)(9u
2
− 12u + 5)(16u
4
− 16u
3
+ ··· + 4u + 7)
· (64u
37
− 160u
36
+ ··· − 41u − 19)
· (49u
56
− 91u
55
+ ··· − 15350701u + 3334724)
c
6
((u − 1)
2
)(u
2
− u + 1)(u
2
+ u + 1)
2
(u
28
− u
27
+ ··· + u
2
− 1)
2
· (u
37
− 2u
36
+ ··· + 7u + 8)
c
7
, c
8
((u − 1)
4
)(u + 1)
2
(u
2
+ 1)(u
37
+ 2u
36
+ ··· + 39u + 7)
· (u
56
− 5u
55
+ ··· − 107u + 10)
c
11
, c
12
((u − 1)
2
)(u + 1)
4
(u
2
+ 1)(u
37
+ 2u
36
+ ··· + 39u + 7)
· (u
56
− 5u
55
+ ··· − 107u + 10)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
2
+ y + 1)
3
(y
28
+ 5y
27
+ ··· − 26y + 1)
2
· (y
37
+ 6y
36
+ ··· + 1952449y − 4096)
c
2
, c
6
((y − 1)
2
)(y
2
+ y + 1)
3
(y
28
+ 13y
27
+ ··· − 2y + 1)
2
· (y
37
+ 14y
36
+ ··· + 929y − 64)
c
3
, c
5
3262849744896(16y
2
+ 4y + 1)(81y
2
− 54y + 25)
· (256y
4
− 384y
3
+ 368y
2
− 72y + 49)
· (4096y
37
− 87040y
36
+ ··· + 1681y − 361)
· (2401y
56
− 79233y
55
+ ··· − 192404715942833y + 11120384156176)
c
4
, c
9
, c
10
y
2
(y − 2)
4
(y + 1)
2
(y
28
− 31y
27
+ ··· − 2y + 1)
2
· (y
37
− 37y
36
+ ··· + 10240y − 1024)
c
7
, c
8
, c
11
c
12
((y − 1)
6
)(y + 1)
2
(y
37
+ 20y
36
+ ··· − 985y − 49)
· (y
56
+ 39y
55
+ ··· + 1011y + 100)
31
