12n
0176
(K12n
0176
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 9 4 11 12 5 7 11
Solving Sequence
4,7 8,11
9 12 1 3 2 6 5 10
c
7
c
8
c
11
c
12
c
3
c
1
c
6
c
5
c
10
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3.05361 × 10
37
u
37
− 6.31699 × 10
37
u
36
+ ··· + 7.79069 × 10
38
b − 1.45053 × 10
39
,
6.57951 × 10
37
u
37
− 1.30883 × 10
38
u
36
+ ··· + 7.79069 × 10
38
a + 3.29567 × 10
39
, u
38
− 2u
37
+ ··· − 16u + 64i
I
u
2
= h−u
11
− 2u
9
− 2u
7
+ u
3
+ b, −u
11
+ u
10
− 3u
9
+ 3u
8
− 4u
7
+ 5u
6
− 2u
5
+ 4u
4
+ u
3
+ 2u
2
+ a + u + 1,
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1i
I
u
3
= h−a
2
u
2
− 4a
2
u − 2a
2
+ b + 4u + 2, −4a
2
u
2
+ a
3
− 2a
2
u + 16u
2
a − 6a
2
+ 7au − 8u
2
+ 27a − 3u − 15,
u
3
+ u
2
+ 2u + 1i
I
v
1
= ha, −2v
3
− 3v
2
+ 4b − 8v −3, 2v
4
+ v
3
+ 5v
2
− v + 1i
* 4 irreducible components of dim
C
= 0, with total 63 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
=
h3.05×10
37
u
37
−6.32×10
37
u
36
+· · ·+7.79×10
38
b−1.45×10
39
, 6.58×10
37
u
37
−
1.31 × 10
38
u
36
+ · · · + 7.79 × 10
38
a + 3.30 × 10
39
, u
38
− 2u
37
+ · · · − 16u + 64i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−0.0844535u
37
+ 0.168000u
36
+ ··· − 5.59244u − 4.23026
−0.0391956u
37
+ 0.0810838u
36
+ ··· − 11.2341u + 1.86188
a
9
=
−0.0835952u
37
+ 0.174732u
36
+ ··· − 10.9131u + 0.727986
0.0870239u
37
− 0.136889u
36
+ ··· + 10.6763u + 8.29286
a
12
=
−0.123649u
37
+ 0.249084u
36
+ ··· − 16.8266u − 2.36838
−0.0391956u
37
+ 0.0810838u
36
+ ··· − 11.2341u + 1.86188
a
1
=
−0.100768u
37
+ 0.165433u
36
+ ··· − 8.51486u − 7.59481
−0.0261741u
37
+ 0.0152352u
36
+ ··· − 1.41664u − 8.18193
a
3
=
u
u
3
+ u
a
2
=
−0.0775401u
37
+ 0.125316u
36
+ ··· − 7.03756u − 7.83004
−0.0160423u
37
− 0.00551256u
36
+ ··· − 1.32448u − 8.82286
a
6
=
−0.199765u
37
+ 0.392882u
36
+ ··· − 29.9030u − 7.71626
−0.0575627u
37
+ 0.156935u
36
+ ··· − 18.3766u + 7.51449
a
5
=
−0.0221640u
37
+ 0.0480035u
36
+ ··· − 1.22673u + 2.89771
0.0786038u
37
− 0.117429u
36
+ ··· + 7.28813u + 10.4925
a
10
=
0.0238166u
37
− 0.105781u
36
+ ··· + 18.0697u − 10.6973
0.0874152u
37
− 0.224299u
36
+ ··· + 22.3080u − 6.95902
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.284536u
37
+ 0.695784u
36
+ ··· − 86.8413u + 36.9834
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 16u
37
+ ··· + 49u + 16
c
2
, c
4
u
38
− 4u
37
+ ··· − 35u + 4
c
3
, c
7
u
38
− 2u
37
+ ··· − 16u + 64
c
5
u
38
+ 4u
37
+ ··· − 28u + 49
c
6
, c
10
u
38
− 2u
37
+ ··· + 42u + 9
c
8
u
38
+ 14u
37
+ ··· + 95422u + 43691
c
9
u
38
− 8u
37
+ ··· + 235720u + 204268
c
11
u
38
− 2u
37
+ ··· + 18u + 9
c
12
u
38
+ 2u
37
+ ··· − 576u + 81
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 16y
37
+ ··· + 137023y + 256
c
2
, c
4
y
38
− 16y
37
+ ··· − 49y + 16
c
3
, c
7
y
38
+ 24y
37
+ ··· + 78592y + 4096
c
5
y
38
− 92y
37
+ ··· − 3136y + 2401
c
6
, c
10
y
38
+ 58y
37
+ ··· + 2304y + 81
c
8
y
38
− 48y
37
+ ··· − 15294799908y + 1908903481
c
9
y
38
+ 70y
37
+ ··· + 426020361080y + 41725415824
c
11
y
38
+ 2y
37
+ ··· − 576y + 81
c
12
y
38
+ 82y
37
+ ··· + 166536y + 6561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.988171 + 0.101317I
a = 0.357719 + 0.096343I
b = −0.706300 − 0.532125I
0.60571 + 3.27765I −3.71492 − 6.11137I
u = 0.988171 − 0.101317I
a = 0.357719 − 0.096343I
b = −0.706300 + 0.532125I
0.60571 − 3.27765I −3.71492 + 6.11137I
u = −0.859103 + 0.407305I
a = 0.195881 + 0.507732I
b = −0.415895 − 0.161770I
−0.113764 − 0.661154I −3.22428 + 0.50932I
u = −0.859103 − 0.407305I
a = 0.195881 − 0.507732I
b = −0.415895 + 0.161770I
−0.113764 + 0.661154I −3.22428 − 0.50932I
u = −0.057356 + 0.905930I
a = 0.690281 − 0.347775I
b = −0.294609 − 0.999645I
−0.317569 + 1.038530I −6.65259 − 1.29718I
u = −0.057356 − 0.905930I
a = 0.690281 + 0.347775I
b = −0.294609 + 0.999645I
−0.317569 − 1.038530I −6.65259 + 1.29718I
u = 0.513402 + 1.056580I
a = −0.548129 − 0.950989I
b = 0.629901 − 0.115553I
4.15976 − 1.13418I 1.31812 + 0.91951I
u = 0.513402 − 1.056580I
a = −0.548129 + 0.950989I
b = 0.629901 + 0.115553I
4.15976 + 1.13418I 1.31812 − 0.91951I
u = 0.499541 + 1.066880I
a = 0.678051 + 0.671685I
b = −0.123848 + 1.082220I
−1.77296 − 5.49964I −11.19640 + 5.85708I
u = 0.499541 − 1.066880I
a = 0.678051 − 0.671685I
b = −0.123848 − 1.082220I
−1.77296 + 5.49964I −11.19640 − 5.85708I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.636697 + 0.515733I
a = 1.48373 + 1.08936I
b = 0.050362 + 0.915692I
−3.49167 + 1.02692I −15.5440 − 0.4261I
u = 0.636697 − 0.515733I
a = 1.48373 − 1.08936I
b = 0.050362 − 0.915692I
−3.49167 − 1.02692I −15.5440 + 0.4261I
u = −0.632708 + 1.049740I
a = −0.318350 + 0.929181I
b = 0.386295 + 0.336655I
1.72214 + 6.04516I −1.25225 − 6.03705I
u = −0.632708 − 1.049740I
a = −0.318350 − 0.929181I
b = 0.386295 − 0.336655I
1.72214 − 6.04516I −1.25225 + 6.03705I
u = −0.116308 + 0.741636I
a = −1.59041 + 2.36341I
b = 0.483477 − 0.463055I
−1.04131 − 1.37519I −0.70276 + 2.28236I
u = −0.116308 − 0.741636I
a = −1.59041 − 2.36341I
b = 0.483477 + 0.463055I
−1.04131 + 1.37519I −0.70276 − 2.28236I
u = −0.120470 + 1.245000I
a = 1.85282 + 0.54192I
b = −1.07360 − 1.05803I
8.23228 + 3.92903I −3.32062 − 2.35045I
u = −0.120470 − 1.245000I
a = 1.85282 − 0.54192I
b = −1.07360 + 1.05803I
8.23228 − 3.92903I −3.32062 + 2.35045I
u = 1.330860 + 0.099817I
a = −0.271191 − 0.510477I
b = 1.14380 − 1.00359I
10.21150 − 1.13879I −3.05135 − 0.25663I
u = 1.330860 − 0.099817I
a = −0.271191 + 0.510477I
b = 1.14380 + 1.00359I
10.21150 + 1.13879I −3.05135 + 0.25663I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.316680 + 0.320236I
a = −0.223799 − 0.516251I
b = 1.05336 − 1.13298I
9.76921 − 6.87392I −3.78751 + 4.34762I
u = −1.316680 − 0.320236I
a = −0.223799 + 0.516251I
b = 1.05336 + 1.13298I
9.76921 + 6.87392I −3.78751 − 4.34762I
u = −0.20211 + 1.41718I
a = −1.355950 − 0.243842I
b = 0.995463 + 0.570318I
6.08307 + 2.78224I 0. − 2.28655I
u = −0.20211 − 1.41718I
a = −1.355950 + 0.243842I
b = 0.995463 − 0.570318I
6.08307 − 2.78224I 0. + 2.28655I
u = −0.072001 + 0.547844I
a = −0.238648 − 0.632863I
b = 0.790221 − 0.913835I
5.57535 − 2.98438I 5.83310 − 0.97501I
u = −0.072001 − 0.547844I
a = −0.238648 + 0.632863I
b = 0.790221 + 0.913835I
5.57535 + 2.98438I 5.83310 + 0.97501I
u = 0.52721 + 1.38450I
a = −1.43906 − 0.13679I
b = 0.974228 − 0.765508I
4.71055 − 8.92356I −6.00000 + 7.15584I
u = 0.52721 − 1.38450I
a = −1.43906 + 0.13679I
b = 0.974228 + 0.765508I
4.71055 + 8.92356I −6.00000 − 7.15584I
u = −0.194741 + 0.457992I
a = 0.933635 − 0.070105I
b = −0.245714 − 0.786744I
−0.451389 + 1.231000I −5.01122 − 5.21291I
u = −0.194741 − 0.457992I
a = 0.933635 + 0.070105I
b = −0.245714 + 0.786744I
−0.451389 − 1.231000I −5.01122 + 5.21291I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.74805 + 1.38740I
a = 1.46219 − 0.60021I
b = −0.96971 − 1.27489I
13.1525 + 14.1820I 0
u = −0.74805 − 1.38740I
a = 1.46219 + 0.60021I
b = −0.96971 + 1.27489I
13.1525 − 14.1820I 0
u = 0.53207 + 1.50578I
a = 1.45703 + 0.26277I
b = −1.06014 + 1.24087I
15.4688 − 7.6978I 0
u = 0.53207 − 1.50578I
a = 1.45703 − 0.26277I
b = −1.06014 − 1.24087I
15.4688 + 7.6978I 0
u = 0.64254 + 1.50454I
a = 0.570332 + 0.670108I
b = −1.32203 − 0.83464I
14.6938 − 5.9617I 0
u = 0.64254 − 1.50454I
a = 0.570332 − 0.670108I
b = −1.32203 + 0.83464I
14.6938 + 5.9617I 0
u = −0.35097 + 1.60847I
a = 0.866365 − 0.578189I
b = −1.29525 + 0.97186I
16.4349 − 0.8014I 0
u = −0.35097 − 1.60847I
a = 0.866365 + 0.578189I
b = −1.29525 − 0.97186I
16.4349 + 0.8014I 0
8
II. I
u
2
= h−u
11
− 2u
9
− 2u
7
+ u
3
+ b, −u
11
+ u
10
+ · · · + a + 1, u
12
+ 3u
10
+
5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
u
11
− u
10
+ 3u
9
− 3u
8
+ 4u
7
− 5u
6
+ 2u
5
− 4u
4
− u
3
− 2u
2
− u − 1
u
11
+ 2u
9
+ 2u
7
− u
3
a
9
=
2u
11
− u
10
+ 5u
9
− 3u
8
+ 6u
7
− 5u
6
+ 2u
5
− 4u
4
− 2u
3
− 3u
2
− u − 1
u
11
+ 2u
9
+ 2u
7
− u
3
a
12
=
2u
11
− u
10
+ 5u
9
− 3u
8
+ 6u
7
− 5u
6
+ 2u
5
− 4u
4
− 2u
3
− 2u
2
− u − 1
u
11
+ 2u
9
+ 2u
7
− u
3
a
1
=
u
11
+ 2u
9
+ 2u
7
− u
3
0
a
3
=
u
u
3
+ u
a
2
=
−u
7
− 2u
5
− 2u
3
−u
7
− u
5
+ u
a
6
=
−u
11
− u
10
− 4u
9
− 3u
8
− 6u
7
− 5u
6
− 5u
5
− 4u
4
− u
3
− 2u
2
+ 2
1
a
5
=
u
9
+ 2u
7
+ 3u
5
+ 2u
3
+ u
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
a
10
=
u
11
− u
10
+ 3u
9
− 3u
8
+ 4u
7
− 5u
6
+ 2u
5
− 4u
4
− u
3
− u
2
− u
u
11
+ 2u
9
+ 2u
7
− u
3
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
10
+ 12u
8
+ 16u
6
+ 8u
4
− 4
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
7
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
u
12
− 6u
11
+ ··· − 24u + 9
c
6
, c
10
, c
11
(u
2
+ 1)
6
c
8
u
12
+ 12u
11
+ ··· + 60u + 9
c
9
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
12
(u + 1)
12
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
3
, c
7
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
5
y
12
+ 14y
11
+ ··· + 108y + 81
c
6
, c
10
, c
11
(y + 1)
12
c
8
y
12
− 14y
11
+ ··· − 108y + 81
c
9
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
12
(y − 1)
12
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295542 + 1.002190I
a = −0.272397 − 0.266417I
b = 1.000000I
1.89061 − 0.92430I −2.28328 + 0.79423I
u = 0.295542 − 1.002190I
a = −0.272397 + 0.266417I
b = − 1.000000I
1.89061 + 0.92430I −2.28328 − 0.79423I
u = −0.295542 + 1.002190I
a = −1.26642 + 0.72760I
b = 1.000000I
1.89061 + 0.92430I −2.28328 − 0.79423I
u = −0.295542 − 1.002190I
a = −1.26642 − 0.72760I
b = − 1.000000I
1.89061 − 0.92430I −2.28328 + 0.79423I
u = 0.664531 + 0.428243I
a = −0.79605 − 3.11811I
b = − 1.000000I
−1.89061 + 0.92430I −9.71672 − 0.79423I
u = 0.664531 − 0.428243I
a = −0.79605 + 3.11811I
b = 1.000000I
−1.89061 − 0.92430I −9.71672 + 0.79423I
u = −0.664531 + 0.428243I
a = 2.11811 − 0.20395I
b = − 1.000000I
−1.89061 − 0.92430I −9.71672 + 0.79423I
u = −0.664531 − 0.428243I
a = 2.11811 + 0.20395I
b = 1.000000I
−1.89061 + 0.92430I −9.71672 − 0.79423I
u = 0.558752 + 1.073950I
a = −0.95037 − 1.16713I
b = − 1.000000I
− 5.69302I −6.00000 + 5.51057I
u = 0.558752 − 1.073950I
a = −0.95037 + 1.16713I
b = 1.000000I
5.69302I −6.00000 − 5.51057I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.558752 + 1.073950I
a = 0.167130 − 0.049626I
b = − 1.000000I
5.69302I −6.00000 − 5.51057I
u = −0.558752 − 1.073950I
a = 0.167130 + 0.049626I
b = 1.000000I
− 5.69302I −6.00000 + 5.51057I
13
III. I
u
3
=
h−a
2
u
2
−4a
2
u−2a
2
+b+4u+2, −4a
2
u
2
+16u
2
a+· · ·+27a−15, u
3
+u
2
+2u+1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
a
a
2
u
2
+ 4a
2
u + 2a
2
− 4u − 2
a
9
=
a
2
u
2
+ 4a
2
u + 2a
2
+ a − 4u − 2
a
2
u
2
+ 4a
2
u + 2a
2
− 4u − 2
a
12
=
a
2
u
2
+ 4a
2
u + 2a
2
+ a − 4u − 2
a
2
u
2
+ 4a
2
u + 2a
2
− 4u − 2
a
1
=
1
u
2
a
3
=
u
−u
2
− u − 1
a
2
=
u
2
+ 1
u
2
+ u + 1
a
6
=
−a
2
u
2
+ u
2
a + a
−a
2
u
2
− 4a
2
u + u
2
a − 2a
2
+ 4u + 2
a
5
=
1
0
a
10
=
a
2
u
2
+ 4a
2
u + 2a
2
+ a − 4u − 2
a
2
u
2
+ 4a
2
u + 2a
2
− 4u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 10
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
(u
3
+ u
2
+ 2u + 1)
3
c
2
, c
4
(u
3
− u
2
+ 1)
3
c
5
, c
6
, c
10
c
11
u
9
+ 3u
7
− 3u
6
+ 3u
5
− 6u
4
+ 3u
3
− 3u
2
+ 2u + 1
c
8
u
9
− 6u
8
+ 15u
7
− 15u
6
− 5u
5
+ 24u
4
− 9u
3
− 15u
2
+ 10u + 1
c
9
u
9
c
12
u
9
+ 6u
8
+ 15u
7
+ 15u
6
− 5u
5
− 24u
4
− 9u
3
+ 15u
2
+ 10u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y − 1)
3
c
2
, c
4
(y
3
− y
2
+ 2y − 1)
3
c
5
, c
6
, c
10
c
11
y
9
+ 6y
8
+ 15y
7
+ 15y
6
− 5y
5
− 24y
4
− 9y
3
+ 15y
2
+ 10y − 1
c
8
, c
12
y
9
− 6y
8
+ ··· + 130y − 1
c
9
y
9
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.933500 + 0.242758I
b = 0.550542 − 1.200360I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 + 1.307140I
a = 1.036610 − 0.079466I
b = −0.929255 − 0.157692I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 + 1.307140I
a = −1.182710 + 0.201873I
b = 0.378713 + 1.358050I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = −0.933500 − 0.242758I
b = 0.550542 + 1.200360I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = 1.036610 + 0.079466I
b = −0.929255 + 0.157692I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = −1.182710 − 0.201873I
b = 0.378713 − 1.358050I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.569840
a = 0.644489
b = 0.298201
−1.11345 −9.01950
u = −0.569840
a = 2.75735 + 4.12910I
b = −0.149100 + 1.032810I
−1.11345 −9.01950
u = −0.569840
a = 2.75735 − 4.12910I
b = −0.149100 − 1.032810I
−1.11345 −9.01950
17
IV. I
v
1
= ha, −2v
3
− 3v
2
+ 4b − 8v − 3, 2v
4
+ v
3
+ 5v
2
− v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
1
2
v
3
+
3
4
v
2
+ 2v +
3
4
a
9
=
1
−
3
2
v
3
−
5
4
v
2
−
7
2
v +
1
4
a
12
=
1
2
v
3
+
3
4
v
2
+ 2v +
3
4
1
2
v
3
+
3
4
v
2
+ 2v +
3
4
a
1
=
1
2
v
3
+
3
4
v
2
+ 2v +
3
4
2v
3
+ v
2
+ 5v − 1
a
3
=
v
0
a
2
=
1
2
v
3
+
3
4
v
2
+ 3v +
3
4
2v
3
+ v
2
+ 5v − 1
a
6
=
3
2
v
3
+
5
4
v
2
+
7
2
v +
3
4
v
2
+
1
2
v +
5
2
a
5
=
−
1
2
v
3
−
3
4
v
2
− 2v −
3
4
−2v
3
− v
2
− 5v + 1
a
10
=
3
2
v
3
+
1
4
v
2
+ 3v −
7
4
−v
2
−
1
2
v −
5
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6v
3
− 4v
2
− 12v − 10
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
u
4
+ 5u
3
+ 7u
2
+ 2u + 1
c
6
u
4
− u
3
+ 3u
2
− 2u + 1
c
8
u
4
− u
3
+ u
2
+ 1
c
9
u
4
+ u
3
+ 5u
2
− u + 2
c
10
, c
12
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
11
u
4
+ u
3
+ u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
6
, c
10
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
9
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.130534 + 0.427872I
a = 0
b = 0.851808 + 0.911292I
5.14581 + 3.16396I −10.48546 − 5.24252I
v = 0.130534 − 0.427872I
a = 0
b = 0.851808 − 0.911292I
5.14581 − 3.16396I −10.48546 + 5.24252I
v = −0.38053 + 1.53420I
a = 0
b = −0.351808 + 0.720342I
−1.85594 − 1.41510I −12.38954 + 3.92814I
v = −0.38053 − 1.53420I
a = 0
b = −0.351808 − 0.720342I
−1.85594 + 1.41510I −12.38954 − 3.92814I
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
(u
3
+ u
2
+ 2u + 1)
3
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
38
+ 16u
37
+ ··· + 49u + 16)
c
2
(u − 1)
4
(u
3
− u
2
+ 1)
3
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
· (u
38
− 4u
37
+ ··· − 35u + 4)
c
3
, c
7
u
4
(u
3
+ u
2
+ 2u + 1)
3
(u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1)
· (u
38
− 2u
37
+ ··· − 16u + 64)
c
4
(u + 1)
4
(u
3
− u
2
+ 1)
3
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
38
− 4u
37
+ ··· − 35u + 4)
c
5
(u
4
+ 5u
3
+ 7u
2
+ 2u + 1)
· (u
9
+ 3u
7
− 3u
6
+ 3u
5
− 6u
4
+ 3u
3
− 3u
2
+ 2u + 1)
· (u
12
− 6u
11
+ ··· − 24u + 9)(u
38
+ 4u
37
+ ··· − 28u + 49)
c
6
(u
2
+ 1)
6
(u
4
− u
3
+ 3u
2
− 2u + 1)
· (u
9
+ 3u
7
− 3u
6
+ 3u
5
− 6u
4
+ 3u
3
− 3u
2
+ 2u + 1)
· (u
38
− 2u
37
+ ··· + 42u + 9)
c
8
(u
4
− u
3
+ u
2
+ 1)
· (u
9
− 6u
8
+ 15u
7
− 15u
6
− 5u
5
+ 24u
4
− 9u
3
− 15u
2
+ 10u + 1)
· (u
12
+ 12u
11
+ ··· + 60u + 9)(u
38
+ 14u
37
+ ··· + 95422u + 43691)
c
9
u
9
(u
4
+ u
3
+ 5u
2
− u + 2)(u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1)
· (u
38
− 8u
37
+ ··· + 235720u + 204268)
c
10
(u
2
+ 1)
6
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
· (u
9
+ 3u
7
− 3u
6
+ 3u
5
− 6u
4
+ 3u
3
− 3u
2
+ 2u + 1)
· (u
38
− 2u
37
+ ··· + 42u + 9)
c
11
(u
2
+ 1)
6
(u
4
+ u
3
+ u
2
+ 1)
· (u
9
+ 3u
7
− 3u
6
+ 3u
5
− 6u
4
+ 3u
3
− 3u
2
+ 2u + 1)
· (u
38
− 2u
37
+ ··· + 18u + 9)
c
12
(u + 1)
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
· (u
9
+ 6u
8
+ 15u
7
+ 15u
6
− 5u
5
− 24u
4
− 9u
3
+ 15u
2
+ 10u − 1)
· (u
38
+ 2u
37
+ ··· − 576u + 81)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
4
(y
3
+ 3y
2
+ 2y − 1)
3
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
38
+ 16y
37
+ ··· + 137023y + 256)
c
2
, c
4
(y − 1)
4
(y
3
− y
2
+ 2y − 1)
3
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
38
− 16y
37
+ ··· − 49y + 16)
c
3
, c
7
y
4
(y
3
+ 3y
2
+ 2y − 1)
3
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
· (y
38
+ 24y
37
+ ··· + 78592y + 4096)
c
5
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)
· (y
9
+ 6y
8
+ 15y
7
+ 15y
6
− 5y
5
− 24y
4
− 9y
3
+ 15y
2
+ 10y − 1)
· (y
12
+ 14y
11
+ ··· + 108y + 81)(y
38
− 92y
37
+ ··· − 3136y + 2401)
c
6
, c
10
(y + 1)
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
9
+ 6y
8
+ 15y
7
+ 15y
6
− 5y
5
− 24y
4
− 9y
3
+ 15y
2
+ 10y − 1)
· (y
38
+ 58y
37
+ ··· + 2304y + 81)
c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
9
− 6y
8
+ ··· + 130y − 1)
· (y
12
− 14y
11
+ ··· − 108y + 81)
· (y
38
− 48y
37
+ ··· − 15294799908y + 1908903481)
c
9
y
9
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
· (y
38
+ 70y
37
+ ··· + 426020361080y + 41725415824)
c
11
(y + 1)
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
· (y
9
+ 6y
8
+ 15y
7
+ 15y
6
− 5y
5
− 24y
4
− 9y
3
+ 15y
2
+ 10y − 1)
· (y
38
+ 2y
37
+ ··· − 576y + 81)
c
12
((y − 1)
12
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
9
− 6y
8
+ ··· + 130y − 1)
· (y
38
+ 82y
37
+ ··· + 166536y + 6561)
23
