12a
1205
(K12a
1205
)
A knot diagram
1
Linearized knot diagam
4 11 7 10 9 3 1 12 5 2 6 8
Solving Sequence
6,9
5
2,10
11 3 12 4 1 8 7
c
5
c
9
c
10
c
2
c
11
c
4
c
1
c
8
c
7
c
3
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h73u
10
− 18u
9
+ 462u
8
− 140u
7
+ 1023u
6
− 266u
5
+ 780u
4
+ 66u
3
+ 131u
2
+ 119b + 230u + 144,
− 209u
10
+ 120u
9
+ ··· + 119a − 365, u
11
+ 6u
9
+ 12u
7
+ 2u
6
+ 8u
5
+ 7u
4
+ 3u
3
+ 5u
2
+ 4u + 1i
I
u
2
= h1.25318 × 10
92
u
59
+ 2.44302 × 10
92
u
58
+ ··· + 8.16358 × 10
92
b − 9.04940 × 10
93
,
− 3.40806 × 10
92
u
59
− 3.96269 × 10
92
u
58
+ ··· + 4.08179 × 10
93
a + 7.98134 × 10
94
,
u
60
+ 2u
59
+ ··· − 252u + 36i
I
u
3
= h−au + b − u + 1, 3a
2
− 2au − 2a + u − 2, u
2
− u + 1i
I
u
4
= h−au + b + 2a + 1, 6a
2
+ 3au + 6a + u + 1, u
2
+ 2i
I
u
5
= h3b + 5u + 4, 3a + u − 1, u
2
+ u + 1i
I
v
1
= ha, 3b − v, v
2
+ 3v + 3i
* 6 irreducible components of dim
C
= 0, with total 83 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
= h73u
10
− 18u
9
+ · · · + 119b + 144, −209u
10
+ 120u
9
+ · · · + 119a −
365, u
11
+ 6u
9
+ · · · + 4u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
2
=
1.75630u
10
− 1.00840u
9
+ ··· + 7.21849u + 3.06723
−0.613445u
10
+ 0.151261u
9
+ ··· − 1.93277u − 1.21008
a
10
=
u
u
3
+ u
a
11
=
0.815126u
10
− 0.420168u
9
+ ··· + 3.92437u + 1.36134
−0.815126u
10
+ 0.420168u
9
+ ··· − 3.92437u − 2.36134
a
3
=
8
7
u
10
−
6
7
u
9
+ ··· +
37
7
u +
13
7
9
7
u
10
−
5
7
u
9
+ ··· +
39
7
u +
19
7
a
12
=
−1
−0.815126u
10
+ 0.420168u
9
+ ··· − 3.92437u − 2.36134
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−u
2
− 1
−1.04202u
10
+ 0.722689u
9
+ ··· − 4.78992u − 2.78151
a
8
=
−u
0.420168u
10
− 0.226891u
9
+ ··· + 1.89916u + 0.815126
a
7
=
−u
3
− 2u
8
7
u
10
−
6
7
u
9
+ ··· +
23
7
u +
13
7
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
372
119
u
10
−
20
119
u
9
+
300
17
u
8
+
8
17
u
7
+
3596
119
u
6
+
192
17
u
5
+
1184
119
u
4
+
3088
119
u
3
+
172
119
u
2
+
520
119
u +
1350
119
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
17(17u
11
− 173u
10
+ ··· + 236u − 40)
c
2
, c
3
, c
6
c
10
u
11
+ 2u
10
− 2u
9
− 6u
8
+ 4u
6
+ 2u
5
+ 5u
4
+ 7u
3
+ 3u
2
+ 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
u
11
+ 6u
9
+ 12u
7
− 2u
6
+ 8u
5
− 7u
4
+ 3u
3
− 5u
2
+ 4u − 1
c
11
17(17u
11
− 173u
10
+ ··· + 1920u − 256)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
289(289y
11
− 4463y
10
+ ··· − 8944y −1600)
c
2
, c
3
, c
6
c
10
y
11
− 8y
10
+ ··· − 6y −1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
11
+ 12y
10
+ ··· + 6y −1
c
11
289(289y
11
+ 875y
10
+ ··· + 311296y −65536)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680975 + 0.675052I
a = 0.702616 − 0.178305I
b = 0.09896 + 1.78843I
−7.07216 + 7.70619I −4.42118 − 7.71824I
u = 0.680975 − 0.675052I
a = 0.702616 + 0.178305I
b = 0.09896 − 1.78843I
−7.07216 − 7.70619I −4.42118 + 7.71824I
u = 0.161381 + 1.138270I
a = 0.151626 − 0.748852I
b = −0.166833 − 0.455380I
−4.56283 + 4.40440I −3.38740 − 7.31700I
u = 0.161381 − 1.138270I
a = 0.151626 + 0.748852I
b = −0.166833 + 0.455380I
−4.56283 − 4.40440I −3.38740 + 7.31700I
u = −0.441939 + 0.225736I
a = −0.875079 + 0.513848I
b = −0.189711 + 0.169501I
0.884913 − 0.517986I 8.70917 + 3.40201I
u = −0.441939 − 0.225736I
a = −0.875079 − 0.513848I
b = −0.189711 − 0.169501I
0.884913 + 0.517986I 8.70917 − 3.40201I
u = −0.490964
a = 1.13114
b = −1.04783
−4.15298 7.21490
u = 0.14545 + 1.56334I
a = −0.406442 − 0.035002I
b = 1.119140 + 0.082033I
−11.62950 + 4.58145I −3.17899 − 3.55621I
u = 0.14545 − 1.56334I
a = −0.406442 + 0.035002I
b = 1.119140 − 0.082033I
−11.62950 − 4.58145I −3.17899 + 3.55621I
u = −0.30038 + 1.63421I
a = −0.72653 − 2.10196I
b = −0.74940 + 3.07893I
17.0539 − 15.5687I −8.09374 + 6.58975I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.30038 − 1.63421I
a = −0.72653 + 2.10196I
b = −0.74940 − 3.07893I
17.0539 + 15.5687I −8.09374 − 6.58975I
6
II. I
u
2
= h1.25 × 10
92
u
59
+ 2.44 × 10
92
u
58
+ · · · + 8.16 × 10
92
b − 9.05 ×
10
93
, −3.41 × 10
92
u
59
− 3.96 × 10
92
u
58
+ · · · + 4.08 × 10
93
a + 7.98 ×
10
94
, u
60
+ 2u
59
+ · · · − 252u + 36i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
2
=
0.0834942u
59
+ 0.0970821u
58
+ ··· + 113.120u − 19.5535
−0.153508u
59
− 0.299258u
58
+ ··· − 77.5361u + 11.0851
a
10
=
u
u
3
+ u
a
11
=
0.200490u
59
+ 0.427440u
58
+ ··· + 66.0395u − 10.3644
−0.0334245u
59
− 0.0366283u
58
+ ··· − 43.3403u + 8.64055
a
3
=
−0.114742u
59
− 0.326177u
58
+ ··· + 10.2529u − 5.95573
−0.0790482u
59
− 0.144541u
58
+ ··· − 49.6201u + 7.70720
a
12
=
0.167066u
59
+ 0.390811u
58
+ ··· + 22.6992u − 1.72388
−0.0334245u
59
− 0.0366283u
58
+ ··· − 43.3403u + 8.64055
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
0.0413371u
59
+ 0.0216303u
58
+ ··· + 86.0346u − 13.9193
−0.120341u
59
− 0.219185u
58
+ ··· − 70.0325u + 10.5469
a
8
=
0.0796060u
59
+ 0.168470u
58
+ ··· + 8.25556u + 4.31633
−0.0126674u
59
− 0.0693921u
58
+ ··· + 26.9172u − 3.41367
a
7
=
0.0484754u
59
+ 0.174481u
58
+ ··· − 39.6371u + 10.1820
−0.0492349u
59
− 0.128310u
58
+ ··· − 11.5918u + 1.43518
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.349952u
59
+ 0.763128u
58
+ ··· + 53.7078u − 5.40438
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
9(3u
30
+ 14u
29
+ ··· + 1087u − 223)
2
c
2
, c
3
, c
6
c
10
u
60
+ 4u
59
+ ··· + 649u + 171
c
4
, c
5
, c
7
c
8
, c
9
, c
12
u
60
− 2u
59
+ ··· + 252u + 36
c
11
9(3u
30
+ 10u
29
+ ··· + 1366u + 167)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
81(9y
30
− 274y
29
+ ··· − 2522245y + 49729)
2
c
2
, c
3
, c
6
c
10
y
60
− 48y
59
+ ··· − 61075y + 29241
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
60
+ 66y
59
+ ··· + 27792y + 1296
c
11
81(9y
30
+ 218y
29
+ ··· + 161758y + 27889)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759750 + 0.662027I
a = −0.931053 + 0.172845I
b = −0.09008 + 1.98013I
−1.86631 − 2.71902I 0
u = −0.759750 − 0.662027I
a = −0.931053 − 0.172845I
b = −0.09008 − 1.98013I
−1.86631 + 2.71902I 0
u = −0.314512 + 0.960641I
a = −0.190977 + 0.499858I
b = 0.419438 + 0.858326I
−1.10026 − 2.27454I 0
u = −0.314512 − 0.960641I
a = −0.190977 − 0.499858I
b = 0.419438 − 0.858326I
−1.10026 + 2.27454I 0
u = −0.129337 + 0.950966I
a = −1.60981 − 1.06801I
b = 0.20747 + 1.44586I
−12.50500 − 0.66605I −8.84093 + 0.I
u = −0.129337 − 0.950966I
a = −1.60981 + 1.06801I
b = 0.20747 − 1.44586I
−12.50500 + 0.66605I −8.84093 + 0.I
u = −0.588192 + 0.683594I
a = 1.039310 − 0.418609I
b = −0.102741 − 0.312706I
−9.38994 − 6.05319I −4.32641 + 5.70687I
u = −0.588192 − 0.683594I
a = 1.039310 + 0.418609I
b = −0.102741 + 0.312706I
−9.38994 + 6.05319I −4.32641 − 5.70687I
u = 0.776674 + 0.411211I
a = 1.206490 + 0.140254I
b = 0.23920 + 1.51841I
−6.21939 − 2.80157I −5.28737 + 3.00592I
u = 0.776674 − 0.411211I
a = 1.206490 − 0.140254I
b = 0.23920 − 1.51841I
−6.21939 + 2.80157I −5.28737 − 3.00592I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.916850 + 0.719386I
a = 0.816528 − 0.325861I
b = −0.10977 − 2.54265I
−14.6835 − 11.0154I 0
u = −0.916850 − 0.719386I
a = 0.816528 + 0.325861I
b = −0.10977 + 2.54265I
−14.6835 + 11.0154I 0
u = 0.576968 + 0.560729I
a = −0.802985 − 0.539725I
b = −0.221236 − 0.702999I
−4.48267 + 2.06711I 1.19955 − 3.78893I
u = 0.576968 − 0.560729I
a = −0.802985 + 0.539725I
b = −0.221236 + 0.702999I
−4.48267 − 2.06711I 1.19955 + 3.78893I
u = −0.355589 + 0.707290I
a = −0.035366 + 0.978857I
b = 0.126483 − 1.162340I
−6.21939 − 2.80157I −5.28737 + 3.00592I
u = −0.355589 − 0.707290I
a = −0.035366 − 0.978857I
b = 0.126483 + 1.162340I
−6.21939 + 2.80157I −5.28737 − 3.00592I
u = −1.076620 + 0.557141I
a = 1.321450 − 0.193835I
b = 1.09050 − 2.33731I
−14.0759 + 4.5063I 0
u = −1.076620 − 0.557141I
a = 1.321450 + 0.193835I
b = 1.09050 + 2.33731I
−14.0759 − 4.5063I 0
u = −0.646640 + 0.296075I
a = 0.016407 − 0.488252I
b = 0.682960 − 1.103020I
−8.24661 + 1.82485I −1.78640 − 0.62717I
u = −0.646640 − 0.296075I
a = 0.016407 + 0.488252I
b = 0.682960 + 1.103020I
−8.24661 − 1.82485I −1.78640 + 0.62717I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.278410 + 1.260600I
a = −0.247426 − 0.743643I
b = 1.277450 − 0.383957I
−4.84465 0
u = 0.278410 − 1.260600I
a = −0.247426 + 0.743643I
b = 1.277450 + 0.383957I
−4.84465 0
u = 1.092800 + 0.750740I
a = −1.124120 − 0.436933I
b = −0.32876 − 3.19706I
−8.92368 + 3.64409I 0
u = 1.092800 − 0.750740I
a = −1.124120 + 0.436933I
b = −0.32876 + 3.19706I
−8.92368 − 3.64409I 0
u = 0.06050 + 1.41516I
a = 1.40096 + 0.56694I
b = −1.56146 − 0.59391I
−7.20542 + 0.22364I 0
u = 0.06050 − 1.41516I
a = 1.40096 − 0.56694I
b = −1.56146 + 0.59391I
−7.20542 − 0.22364I 0
u = −0.06398 + 1.43597I
a = −0.171576 − 0.010774I
b = 0.742412 − 0.071303I
−4.48267 − 2.06711I 0
u = −0.06398 − 1.43597I
a = −0.171576 + 0.010774I
b = 0.742412 + 0.071303I
−4.48267 + 2.06711I 0
u = 0.225772 + 0.478556I
a = 2.00278 + 0.98084I
b = −0.296782 + 0.092033I
−1.86631 + 2.71902I −6.02392 − 8.48187I
u = 0.225772 − 0.478556I
a = 2.00278 − 0.98084I
b = −0.296782 − 0.092033I
−1.86631 − 2.71902I −6.02392 + 8.48187I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05387 + 1.52215I
a = 2.31103 + 0.70700I
b = −3.18172 − 0.73741I
−13.6864 0
u = −0.05387 − 1.52215I
a = 2.31103 − 0.70700I
b = −3.18172 + 0.73741I
−13.6864 0
u = 0.05204 + 1.52292I
a = 0.65459 − 2.51222I
b = −0.60287 + 2.55575I
−8.24661 + 1.82485I 0
u = 0.05204 − 1.52292I
a = 0.65459 + 2.51222I
b = −0.60287 − 2.55575I
−8.24661 − 1.82485I 0
u = 0.18810 + 1.51588I
a = −0.87884 + 2.25051I
b = −0.27333 − 2.47353I
−12.50500 + 0.66605I 0
u = 0.18810 − 1.51588I
a = −0.87884 − 2.25051I
b = −0.27333 + 2.47353I
−12.50500 − 0.66605I 0
u = 0.244643 + 0.402854I
a = −0.334643 + 1.093090I
b = 0.256864 − 1.075110I
−1.70488 + 0.85900I −3.09812 + 2.75630I
u = 0.244643 − 0.402854I
a = −0.334643 − 1.093090I
b = 0.256864 + 1.075110I
−1.70488 − 0.85900I −3.09812 − 2.75630I
u = 0.05319 + 1.56037I
a = −0.242202 − 0.185041I
b = −0.623485 + 0.111421I
−8.92368 + 3.64409I 0
u = 0.05319 − 1.56037I
a = −0.242202 + 0.185041I
b = −0.623485 − 0.111421I
−8.92368 − 3.64409I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.045280 + 0.430914I
a = 2.09252 − 1.08737I
b = 1.15217 + 1.56271I
−7.20542 + 0.22364I −9.04537 + 1.25928I
u = 0.045280 − 0.430914I
a = 2.09252 + 1.08737I
b = 1.15217 − 1.56271I
−7.20542 − 0.22364I −9.04537 − 1.25928I
u = 0.264001 + 0.331764I
a = −0.075640 + 0.209812I
b = 0.785454 + 0.369858I
−1.70488 − 0.85900I −3.09812 − 2.75630I
u = 0.264001 − 0.331764I
a = −0.075640 − 0.209812I
b = 0.785454 − 0.369858I
−1.70488 + 0.85900I −3.09812 + 2.75630I
u = 0.415346 + 0.011561I
a = −1.51548 + 1.51134I
b = −0.315561 + 0.009208I
−1.10026 + 2.27454I 6.39783 − 4.86989I
u = 0.415346 − 0.011561I
a = −1.51548 − 1.51134I
b = −0.315561 − 0.009208I
−1.10026 − 2.27454I 6.39783 + 4.86989I
u = −0.19401 + 1.58701I
a = 0.49148 + 2.16389I
b = 0.52046 − 2.62595I
−9.38994 − 6.05319I 0
u = −0.19401 − 1.58701I
a = 0.49148 − 2.16389I
b = 0.52046 + 2.62595I
−9.38994 + 6.05319I 0
u = −0.10187 + 1.60028I
a = −0.36353 − 1.96711I
b = 0.25135 + 2.10282I
−14.0759 − 4.5063I 0
u = −0.10187 − 1.60028I
a = −0.36353 + 1.96711I
b = 0.25135 − 2.10282I
−14.0759 + 4.5063I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.17637 + 1.60289I
a = 0.015923 + 0.384340I
b = −0.632206 − 0.409488I
−17.1000 − 8.9031I 0
u = −0.17637 − 1.60289I
a = 0.015923 − 0.384340I
b = −0.632206 + 0.409488I
−17.1000 + 8.9031I 0
u = 0.20940 + 1.60061I
a = −0.54658 + 2.10296I
b = −0.36822 − 2.53572I
−14.6835 + 11.0154I 0
u = 0.20940 − 1.60061I
a = −0.54658 − 2.10296I
b = −0.36822 + 2.53572I
−14.6835 − 11.0154I 0
u = −0.02241 + 1.64609I
a = −0.32821 + 1.68373I
b = 1.15247 − 1.88578I
18.0731 − 1.1594I 0
u = −0.02241 − 1.64609I
a = −0.32821 − 1.68373I
b = 1.15247 + 1.88578I
18.0731 + 1.1594I 0
u = 0.31119 + 1.69477I
a = 0.41080 − 2.03463I
b = 1.37332 + 3.18776I
−17.1000 + 8.9031I 0
u = 0.31119 − 1.69477I
a = 0.41080 + 2.03463I
b = 1.37332 − 3.18776I
−17.1000 − 8.9031I 0
u = −0.39432 + 1.69567I
a = −0.21517 − 1.69581I
b = −2.06977 + 2.35462I
18.0731 − 1.1594I 0
u = −0.39432 − 1.69567I
a = −0.21517 + 1.69581I
b = −2.06977 − 2.35462I
18.0731 + 1.1594I 0
15
III. I
u
3
= h−au + b − u + 1, 3a
2
− 2au − 2a + u − 2, u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
u − 1
a
2
=
a
au + u − 1
a
10
=
u
u − 1
a
11
=
−a + u
−au
a
3
=
u
u − 1
a
12
=
−au − a + u
−au
a
4
=
u
u − 2
a
1
=
au + a − u
2au − 2a + 1
a
8
=
−2u + 2
a + 1
a
7
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u − 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
4
− 6u
3
+ u
2
+ 2u + 1)
c
2
(u − 1)
4
c
3
, c
4
, c
5
(u
2
− u + 1)
2
c
6
, c
9
(u
2
+ u + 1)
2
c
7
, c
8
, c
12
(u
2
+ 2)
2
c
10
(u + 1)
4
c
11
3(3u
4
+ 4u
2
+ 4u + 1)
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
9(9y
4
− 30y
3
+ 31y
2
− 2y + 1)
c
2
, c
10
(y −1)
4
c
3
, c
4
, c
5
c
6
, c
9
(y
2
+ y + 1)
2
c
7
, c
8
, c
12
(y + 2)
4
c
11
9(9y
4
+ 24y
3
+ 22y
2
− 8y + 1)
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.316500 + 0.288675I
b = −0.09175 + 2.15048I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −0.316497 + 0.288675I
b = −0.908248 + 0.736269I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 1.316500 − 0.288675I
b = −0.09175 − 2.15048I
−6.57974 − 2.02988I −6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −0.316497 − 0.288675I
b = −0.908248 − 0.736269I
−6.57974 − 2.02988I −6.00000 + 3.46410I
19
IV. I
u
4
= h−au + b + 2a + 1, 6a
2
+ 3au + 6a + u + 1, u
2
+ 2i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
−2
a
2
=
a
au − 2a − 1
a
10
=
u
−u
a
11
=
au + a +
3
2
u
−2a − u − 1
a
3
=
au − a −
1
2
u − 2
1
a
12
=
au − a +
1
2
u − 1
−2a − u − 1
a
4
=
−1
0
a
1
=
au − a − 1
au − 2a − 1
a
8
=
au − a − 1
−au + 1
a
7
=
au − a −
1
2
u − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4au − 8a − 4u − 8
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
4
− 6u
3
+ u
2
+ 2u + 1)
c
2
, c
12
(u
2
+ u + 1)
2
c
3
(u + 1)
4
c
4
, c
5
, c
9
(u
2
+ 2)
2
c
6
(u − 1)
4
c
7
, c
8
, c
10
(u
2
− u + 1)
2
c
11
3(3u
4
+ 4u
2
+ 4u + 1)
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
9(9y
4
− 30y
3
+ 31y
2
− 2y + 1)
c
2
, c
7
, c
8
c
10
, c
12
(y
2
+ y + 1)
2
c
3
, c
6
(y −1)
4
c
4
, c
5
, c
9
(y + 2)
4
c
11
9(9y
4
+ 24y
3
+ 22y
2
− 8y + 1)
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −0.704124 − 0.642229I
b = 1.316500 + 0.288675I
−6.57974 − 2.02988I −6.00000 + 3.46410I
u = 1.414210I
a = −0.295876 − 0.064878I
b = −0.316497 − 0.288675I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = − 1.414210I
a = −0.704124 + 0.642229I
b = 1.316500 − 0.288675I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = − 1.414210I
a = −0.295876 + 0.064878I
b = −0.316497 + 0.288675I
−6.57974 − 2.02988I −6.00000 + 3.46410I
23
V. I
u
5
= h3b + 5u + 4, 3a + u − 1, u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
−u − 1
a
2
=
−
1
3
u +
1
3
−
5
3
u −
4
3
a
10
=
u
u + 1
a
11
=
2
3
u +
1
3
−
2
3
u −
1
3
a
3
=
−u
−u − 1
a
12
=
0
−
2
3
u −
1
3
a
4
=
−u
−u − 2
a
1
=
0
−
2
3
u −
1
3
a
8
=
0
u
a
7
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
3
u − 6
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
2
− 3u + 1)
c
2
(u + 1)
2
c
3
, c
9
u
2
− u + 1
c
4
, c
5
, c
6
u
2
+ u + 1
c
7
, c
8
, c
12
u
2
c
10
(u − 1)
2
c
11
3(3u
2
+ 1)
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
9(9y
2
− 3y + 1)
c
2
, c
10
(y −1)
2
c
3
, c
4
, c
5
c
6
, c
9
y
2
+ y + 1
c
7
, c
8
, c
12
y
2
c
11
9(3y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 − 0.288675I
b = −0.50000 − 1.44338I
−1.64493 − 2.02988I −5.33333 − 1.15470I
u = −0.500000 − 0.866025I
a = 0.500000 + 0.288675I
b = −0.50000 + 1.44338I
−1.64493 + 2.02988I −5.33333 + 1.15470I
27
VI. I
v
1
= ha, 3b − v, v
2
+ 3v + 3i
(i) Arc colorings
a
6
=
1
0
a
9
=
v
0
a
5
=
1
0
a
2
=
0
1
3
v
a
10
=
v
0
a
11
=
v
2
3
v + 1
a
3
=
−2v − 3
−1
a
12
=
5
3
v + 1
2
3
v + 1
a
4
=
1
0
a
1
=
1
3
v
1
3
v
a
8
=
5
3
v + 3
−
1
3
v
a
7
=
2v + 4
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4
3
v −
10
3
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
2
− 3u + 1)
c
2
, c
7
, c
8
u
2
+ u + 1
c
3
(u − 1)
2
c
4
, c
5
, c
9
u
2
c
6
(u + 1)
2
c
10
, c
12
u
2
− u + 1
c
11
3(3u
2
+ 1)
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
9(9y
2
− 3y + 1)
c
2
, c
7
, c
8
c
10
, c
12
y
2
+ y + 1
c
3
, c
6
(y − 1)
2
c
4
, c
5
, c
9
y
2
c
11
9(3y + 1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.50000 + 0.86603I
a = 0
b = −0.500000 + 0.288675I
−1.64493 + 2.02988I −5.33333 + 1.15470I
v = −1.50000 − 0.86603I
a = 0
b = −0.500000 − 0.288675I
−1.64493 − 2.02988I −5.33333 − 1.15470I
31
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
12393(3u
2
− 3u + 1)
2
(3u
4
− 6u
3
+ u
2
+ 2u + 1)
2
· (17u
11
− 173u
10
+ ··· + 236u − 40)
· (3u
30
+ 14u
29
+ ··· + 1087u − 223)
2
c
2
, c
6
(u − 1)
4
(u + 1)
2
(u
2
+ u + 1)
3
· (u
11
+ 2u
10
− 2u
9
− 6u
8
+ 4u
6
+ 2u
5
+ 5u
4
+ 7u
3
+ 3u
2
+ 1)
· (u
60
+ 4u
59
+ ··· + 649u + 171)
c
3
, c
10
(u − 1)
2
(u + 1)
4
(u
2
− u + 1)
3
· (u
11
+ 2u
10
− 2u
9
− 6u
8
+ 4u
6
+ 2u
5
+ 5u
4
+ 7u
3
+ 3u
2
+ 1)
· (u
60
+ 4u
59
+ ··· + 649u + 171)
c
4
, c
5
, c
7
c
8
u
2
(u
2
+ 2)
2
(u
2
− u + 1)
2
(u
2
+ u + 1)
· (u
11
+ 6u
9
+ 12u
7
− 2u
6
+ 8u
5
− 7u
4
+ 3u
3
− 5u
2
+ 4u − 1)
· (u
60
− 2u
59
+ ··· + 252u + 36)
c
9
, c
12
u
2
(u
2
+ 2)
2
(u
2
− u + 1)(u
2
+ u + 1)
2
· (u
11
+ 6u
9
+ 12u
7
− 2u
6
+ 8u
5
− 7u
4
+ 3u
3
− 5u
2
+ 4u − 1)
· (u
60
− 2u
59
+ ··· + 252u + 36)
c
11
12393(3u
2
+ 1)
2
(3u
4
+ 4u
2
+ 4u + 1)
2
· (17u
11
− 173u
10
+ ··· + 1920u − 256)
· (3u
30
+ 10u
29
+ ··· + 1366u + 167)
2
32
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
153586449(9y
2
− 3y + 1)
2
(9y
4
− 30y
3
+ 31y
2
− 2y + 1)
2
· (289y
11
− 4463y
10
+ ··· − 8944y − 1600)
· (9y
30
− 274y
29
+ ··· − 2522245y + 49729)
2
c
2
, c
3
, c
6
c
10
((y − 1)
6
)(y
2
+ y + 1)
3
(y
11
− 8y
10
+ ··· − 6y − 1)
· (y
60
− 48y
59
+ ··· − 61075y + 29241)
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
2
(y + 2)
4
(y
2
+ y + 1)
3
(y
11
+ 12y
10
+ ··· + 6y − 1)
· (y
60
+ 66y
59
+ ··· + 27792y + 1296)
c
11
153586449(3y + 1)
4
(9y
4
+ 24y
3
+ 22y
2
− 8y + 1)
2
· (289y
11
+ 875y
10
+ ··· + 311296y − 65536)
· (9y
30
+ 218y
29
+ ··· + 161758y + 27889)
2
33
