12n
0087
(K12n
0087
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 8 4 10 5 12 7 9 11
Solving Sequence
8,10
7
4,11
3 6 5 9 12 2 1
c
7
c
10
c
3
c
6
c
5
c
8
c
11
c
2
c
1
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.21397 × 10
102
u
43
− 1.21296 × 10
103
u
42
+ ··· + 5.90528 × 10
102
b − 1.68663 × 10
103
,
2.74407 × 10
102
u
43
− 1.57666 × 10
103
u
42
+ ··· + 2.95264 × 10
102
a − 2.53471 × 10
103
, u
44
− 5u
43
+ ··· + 16u − 4i
I
u
2
= hu
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
+ b − 2u + 1,
3u
8
− 4u
7
+ 8u
6
− 7u
5
+ 13u
4
− 9u
3
+ 11u
2
+ a − 6u + 6, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
u
3
= h−3u
2
a + 4au + u
2
+ 5b + 3a + 7u + 4, −2u
2
a + a
2
− au + 12u
2
− a + 5u + 22, u
3
+ u
2
+ 2u + 1i
I
u
4
= hb − u, a, u
3
+ u
2
+ 2u + 1i
I
v
1
= ha, 3b + v −5, v
2
− 7v + 1i
* 5 irreducible components of dim
C
= 0, with total 64 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
= h2.21 × 10
102
u
43
− 1.21 × 10
103
u
42
+ · · · + 5.91 × 10
102
b − 1.69 ×
10
103
, 2.74 × 10
102
u
43
− 1.58 × 10
103
u
42
+ · · · + 2.95 × 10
102
a − 2.53 ×
10
103
, u
44
− 5u
43
+ · · · + 16u − 4i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
4
=
−0.929363u
43
+ 5.33983u
42
+ ··· − 18.7982u + 8.58457
−0.374913u
43
+ 2.05402u
42
+ ··· − 21.5523u + 2.85613
a
11
=
u
u
3
+ u
a
3
=
−1.07481u
43
+ 6.05592u
42
+ ··· − 25.5449u + 8.66865
−0.409892u
43
+ 2.21633u
42
+ ··· − 21.9557u + 2.81153
a
6
=
0.145102u
43
− 0.707901u
42
+ ··· + 19.1582u + 1.02362
0.147085u
43
− 0.785533u
42
+ ··· + 9.81828u − 1.73382
a
5
=
0.292188u
43
− 1.49343u
42
+ ··· + 28.9765u − 0.710207
0.147085u
43
− 0.785533u
42
+ ··· + 9.81828u − 1.73382
a
9
=
−0.115004u
43
+ 0.603443u
42
+ ··· − 8.54799u + 1.54989
−0.253152u
43
+ 1.35100u
42
+ ··· − 24.4831u + 3.51231
a
12
=
−0.143897u
43
+ 0.773429u
42
+ ··· − 15.0203u + 1.84872
−0.289178u
43
+ 1.53362u
42
+ ··· − 25.0070u + 3.61440
a
2
=
−1.09992u
43
+ 6.16075u
42
+ ··· − 35.4851u + 8.06492
−0.238125u
43
+ 1.32996u
42
+ ··· − 6.84876u + 1.04083
a
1
=
0.138148u
43
− 0.747554u
42
+ ··· + 15.9351u − 1.96242
0.280915u
43
− 1.49627u
42
+ ··· + 25.9447u − 3.73957
(ii) Obstruction class = −1
(iii) Cusp Shapes = 25.5545u
43
− 140.944u
42
+ ··· + 1055.90u − 191.724
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 6u
43
+ ··· + 29830u + 1
c
2
, c
4
u
44
− 14u
43
+ ··· − 166u − 1
c
3
, c
6
u
44
− 5u
43
+ ··· + 3072u + 512
c
5
, c
8
u
44
− 3u
43
+ ··· + 4096u − 512
c
7
, c
10
u
44
+ 5u
43
+ ··· − 16u − 4
c
9
, c
11
u
44
+ 7u
43
+ ··· + 83u − 1
c
12
u
44
− 33u
43
+ ··· − 6317u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
+ 78y
43
+ ··· − 889350874y + 1
c
2
, c
4
y
44
− 6y
43
+ ··· − 29830y + 1
c
3
, c
6
y
44
+ 63y
43
+ ··· − 69206016y + 262144
c
5
, c
8
y
44
+ 49y
43
+ ··· − 15859712y + 262144
c
7
, c
10
y
44
− 3y
43
+ ··· − 1304y + 16
c
9
, c
11
y
44
− 33y
43
+ ··· − 6317y + 1
c
12
y
44
− 37y
43
+ ··· − 39734481y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.048281 + 1.061060I
a = 0.370251 + 0.083303I
b = −0.623557 − 0.693283I
−2.03545 − 1.53423I −2.00000 + 3.28440I
u = 0.048281 − 1.061060I
a = 0.370251 − 0.083303I
b = −0.623557 + 0.693283I
−2.03545 + 1.53423I −2.00000 − 3.28440I
u = −0.444024 + 0.972451I
a = −0.213577 − 0.298798I
b = −0.151321 − 0.361837I
−0.22354 − 3.19884I 0. + 5.55216I
u = −0.444024 − 0.972451I
a = −0.213577 + 0.298798I
b = −0.151321 + 0.361837I
−0.22354 + 3.19884I 0. − 5.55216I
u = 0.874663 + 0.275257I
a = 1.04774 + 1.16816I
b = 0.236448 + 0.150247I
3.87014 − 2.97279I 3.60919 + 6.63471I
u = 0.874663 − 0.275257I
a = 1.04774 − 1.16816I
b = 0.236448 − 0.150247I
3.87014 + 2.97279I 3.60919 − 6.63471I
u = 0.310742 + 1.065360I
a = 0.269693 + 1.146740I
b = −0.465484 + 0.146095I
5.03100 + 0.55063I 1.92030 − 1.63801I
u = 0.310742 − 1.065360I
a = 0.269693 − 1.146740I
b = −0.465484 − 0.146095I
5.03100 − 0.55063I 1.92030 + 1.63801I
u = 0.627914 + 0.971697I
a = −0.330748 − 0.066410I
b = −0.034558 + 0.334761I
2.13500 + 7.76603I 0. − 12.26438I
u = 0.627914 − 0.971697I
a = −0.330748 + 0.066410I
b = −0.034558 − 0.334761I
2.13500 − 7.76603I 0. + 12.26438I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.088600 + 0.454876I
a = 0.415899 − 0.644451I
b = 0.653494 − 0.268396I
2.35471 − 1.62269I 0. + 2.86308I
u = −1.088600 − 0.454876I
a = 0.415899 + 0.644451I
b = 0.653494 + 0.268396I
2.35471 + 1.62269I 0. − 2.86308I
u = 1.171290 + 0.197003I
a = 0.058277 + 0.836682I
b = −1.49981 − 0.37516I
4.40564 + 2.10618I 0
u = 1.171290 − 0.197003I
a = 0.058277 − 0.836682I
b = −1.49981 + 0.37516I
4.40564 − 2.10618I 0
u = −0.625793 + 1.141240I
a = 0.475335 − 0.251871I
b = −1.43711 + 0.62601I
−0.60424 − 3.28908I 0
u = −0.625793 − 1.141240I
a = 0.475335 + 0.251871I
b = −1.43711 − 0.62601I
−0.60424 + 3.28908I 0
u = −0.231224 + 1.281260I
a = 2.55356 − 0.49814I
b = −3.85023 − 0.67062I
−4.23715 − 2.76938I −48.8073 + 0.I
u = −0.231224 − 1.281260I
a = 2.55356 + 0.49814I
b = −3.85023 + 0.67062I
−4.23715 + 2.76938I −48.8073 + 0.I
u = −1.271420 + 0.302065I
a = −0.143630 + 1.274350I
b = 0.295378 − 0.275889I
10.46410 − 4.58464I 0
u = −1.271420 − 0.302065I
a = −0.143630 − 1.274350I
b = 0.295378 + 0.275889I
10.46410 + 4.58464I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.652018 + 0.010138I
a = 0.75783 + 3.15503I
b = 0.1218200 − 0.0058498I
4.00876 − 2.95005I −9.2752 + 14.0588I
u = 0.652018 − 0.010138I
a = 0.75783 − 3.15503I
b = 0.1218200 + 0.0058498I
4.00876 + 2.95005I −9.2752 − 14.0588I
u = −0.585308 + 0.189725I
a = −1.96529 − 0.47582I
b = −1.23447 + 0.72984I
−0.967972 − 0.798268I −5.17338 − 0.48170I
u = −0.585308 − 0.189725I
a = −1.96529 + 0.47582I
b = −1.23447 − 0.72984I
−0.967972 + 0.798268I −5.17338 + 0.48170I
u = 1.30067 + 0.60834I
a = −0.056153 + 0.571188I
b = 0.935749 − 0.007550I
8.25016 + 5.56575I 0
u = 1.30067 − 0.60834I
a = −0.056153 − 0.571188I
b = 0.935749 + 0.007550I
8.25016 − 5.56575I 0
u = −0.531060
a = 16.7494
b = 4.82907
−0.460937 −368.890
u = −0.503995
a = 1.38825
b = 0.276534
1.20368 8.97050
u = −0.311757
a = −0.443655
b = 1.64605
−7.14674 39.2060
u = 1.13348 + 1.25222I
a = 0.883536 + 1.035620I
b = −2.30222 + 0.38639I
14.9516 + 15.4441I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13348 − 1.25222I
a = 0.883536 − 1.035620I
b = −2.30222 − 0.38639I
14.9516 − 15.4441I 0
u = −0.044479 + 0.277185I
a = −13.9186 + 9.4770I
b = 0.649522 − 0.305876I
0.651471 − 0.106624I −43.8474 + 14.3936I
u = −0.044479 − 0.277185I
a = −13.9186 − 9.4770I
b = 0.649522 + 0.305876I
0.651471 + 0.106624I −43.8474 − 14.3936I
u = 1.36977 + 1.10574I
a = −0.621322 − 0.964621I
b = 2.15902 − 0.17933I
16.9016 + 6.9619I 0
u = 1.36977 − 1.10574I
a = −0.621322 + 0.964621I
b = 2.15902 + 0.17933I
16.9016 − 6.9619I 0
u = −1.17136 + 1.33639I
a = 0.817996 − 0.874491I
b = −2.44154 − 0.26744I
10.77560 − 8.87064I 0
u = −1.17136 − 1.33639I
a = 0.817996 + 0.874491I
b = −2.44154 + 0.26744I
10.77560 + 8.87064I 0
u = 1.37757 + 1.14007I
a = −0.503126 − 0.688009I
b = 2.39105 + 0.13674I
15.5975 − 6.3488I 0
u = 1.37757 − 1.14007I
a = −0.503126 + 0.688009I
b = 2.39105 − 0.13674I
15.5975 + 6.3488I 0
u = 1.13292 + 1.40159I
a = 0.854370 + 0.676020I
b = −2.37293 + 0.03727I
15.8788 + 2.3692I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13292 − 1.40159I
a = 0.854370 − 0.676020I
b = −2.37293 − 0.03727I
15.8788 − 2.3692I 0
u = −1.41982 + 1.12122I
a = −0.510761 + 0.835178I
b = 2.37704 + 0.10328I
11.64120 − 0.54721I 0
u = −1.41982 − 1.12122I
a = −0.510761 − 0.835178I
b = 2.37704 − 0.10328I
11.64120 + 0.54721I 0
u = 0.112220
a = 3.82348
b = −0.564184
−1.00318 −10.1720
9
II. I
u
2
= hu
8
− 2u
7
+ · · · + b + 1, 3u
8
− 4u
7
+ · · · + a + 6, u
9
− u
8
+ 2u
7
−
u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
4
=
−3u
8
+ 4u
7
− 8u
6
+ 7u
5
− 13u
4
+ 9u
3
− 11u
2
+ 6u − 6
−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 3u
2
+ 2u − 1
a
11
=
u
u
3
+ u
a
3
=
−3u
8
+ 4u
7
− 8u
6
+ 7u
5
− 13u
4
+ 9u
3
− 11u
2
+ 6u − 6
−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 3u
2
+ 2u − 1
a
6
=
1
u
2
a
5
=
u
2
+ 1
u
2
a
9
=
u
4
+ u
2
+ 1
u
4
a
12
=
−u
6
− u
4
− 2u
2
− 1
−u
8
− 2u
6
− 2u
4
− 2u
2
a
2
=
−3u
8
+ 4u
7
− 8u
6
+ 7u
5
− 13u
4
+ 9u
3
− 12u
2
+ 6u − 7
−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 4u
2
+ 2u − 1
a
1
=
−u
2
− 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 45u
8
−71u
7
+ 127u
6
−112u
5
+ 192u
4
−149u
3
+ 165u
2
−83u + 85
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
9
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
10
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
11
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
12
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
9
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
12
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = −0.920144 + 0.598375I
b = 1.004430 − 0.297869I
−3.42837 − 2.09337I −7.68972 + 3.82038I
u = −0.140343 − 0.966856I
a = −0.920144 − 0.598375I
b = 1.004430 + 0.297869I
−3.42837 + 2.09337I −7.68972 − 3.82038I
u = −0.628449 + 0.875112I
a = 0.590648 + 0.449402I
b = 0.275254 − 0.816341I
−1.02799 − 2.45442I −5.04100 + 1.69416I
u = −0.628449 − 0.875112I
a = 0.590648 − 0.449402I
b = 0.275254 + 0.816341I
−1.02799 + 2.45442I −5.04100 − 1.69416I
u = 0.796005 + 0.733148I
a = 0.719281 + 0.119276I
b = −0.070080 + 0.850995I
2.72642 − 1.33617I 1.56769 + 0.26615I
u = 0.796005 − 0.733148I
a = 0.719281 − 0.119276I
b = −0.070080 − 0.850995I
2.72642 + 1.33617I 1.56769 − 0.26615I
u = 0.728966 + 0.986295I
a = 0.365868 − 0.247975I
b = 0.195086 + 0.635552I
1.95319 + 7.08493I −0.45449 − 1.34000I
u = 0.728966 − 0.986295I
a = 0.365868 + 0.247975I
b = 0.195086 − 0.635552I
1.95319 − 7.08493I −0.45449 + 1.34000I
u = −0.512358
a = −14.5113
b = −3.80937
−0.446489 211.240
13
III. I
u
3
= h−3u
2
a + 4au + u
2
+ 5b + 3a + 7u + 4, −2u
2
a + a
2
− au + 12u
2
−
a + 5u + 22, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
4
=
a
3
5
u
2
a −
1
5
u
2
+ ··· −
3
5
a −
4
5
a
11
=
u
−u
2
− u − 1
a
3
=
−
2
5
u
2
a −
1
5
u
2
+ ··· +
2
5
a −
4
5
6
5
u
2
a +
3
5
u
2
+ ··· −
1
5
a +
2
5
a
6
=
−
1
5
u
2
a −
18
5
u
2
+ ··· +
1
5
a −
27
5
0
a
5
=
−
1
5
u
2
a −
18
5
u
2
+ ··· +
1
5
a −
27
5
0
a
9
=
1
0
a
12
=
−u
2
− 1
−u
2
− u − 1
a
2
=
−u
2
a − au − 4u
2
− 3u − 6
6
5
u
2
a +
3
5
u
2
+ ··· −
1
5
a +
2
5
a
1
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
12
5
u
2
a −
31
5
au +
101
5
u
2
−
37
5
a +
52
5
u +
144
5
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
10
c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
11
(u
3
+ u
2
− 1)
2
c
4
, c
9
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
c
6
, c
7
(u
3
+ u
2
+ 2u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
, c
9
c
11
(y
3
− y
2
+ 2y −1)
2
c
5
, c
8
y
6
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.477322 + 0.078540I
b = 0.622561 − 1.169310I
− 5.65624I −1.47396 + 5.95889I
u = −0.215080 + 1.307140I
a = −2.06248 + 0.10404I
b = 2.91724 + 0.98673I
−4.13758 − 2.82812I 14.7077 + 20.6881I
u = −0.215080 − 1.307140I
a = −0.477322 − 0.078540I
b = 0.622561 + 1.169310I
5.65624I −1.47396 − 5.95889I
u = −0.215080 − 1.307140I
a = −2.06248 − 0.10404I
b = 2.91724 − 0.98673I
−4.13758 + 2.82812I 14.7077 − 20.6881I
u = −0.569840
a = 0.53980 + 4.77033I
b = −0.039798 + 0.241870I
4.13758 − 2.82812I 27.7662 − 14.7292I
u = −0.569840
a = 0.53980 − 4.77033I
b = −0.039798 − 0.241870I
4.13758 + 2.82812I 27.7662 + 14.7292I
17
IV. I
u
4
= hb − u, a, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
4
=
0
u
a
11
=
u
−u
2
− u − 1
a
3
=
u
−u
2
− u − 1
a
6
=
1
0
a
5
=
1
0
a
9
=
1
0
a
12
=
−u
2
− 1
−u
2
− u − 1
a
2
=
−u
2
− 1
−u
2
− u − 1
a
1
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
10
c
12
u
3
− u
2
+ 2u − 1
c
2
, c
11
u
3
+ u
2
− 1
c
4
, c
9
u
3
− u
2
+ 1
c
5
, c
8
u
3
c
6
, c
7
u
3
+ u
2
+ 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
, c
9
c
11
y
3
− y
2
+ 2y −1
c
5
, c
8
y
3
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0
b = −0.215080 + 1.307140I
0 0
u = −0.215080 − 1.307140I
a = 0
b = −0.215080 − 1.307140I
0 0
u = −0.569840
a = 0
b = −0.569840
0 0
21
V. I
v
1
= ha, 3b + v − 5, v
2
− 7v + 1i
(i) Arc colorings
a
8
=
1
0
a
10
=
v
0
a
7
=
1
0
a
4
=
0
−
1
3
v +
5
3
a
11
=
v
0
a
3
=
−
1
3
v +
5
3
−
1
3
v +
5
3
a
6
=
1
1
3
v −
8
3
a
5
=
1
3
v −
5
3
1
3
v −
8
3
a
9
=
−
2
3
v +
16
3
−v + 7
a
12
=
5
3
v −
16
3
v − 7
a
2
=
−1
1
3
v −
8
3
a
1
=
2
3
v −
16
3
v − 7
(ii) Obstruction class = 1
(iii) Cusp Shapes = −49
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
6
u
2
− u − 1
c
7
, c
10
u
2
c
8
u
2
+ 3u + 1
c
9
(u + 1)
2
c
11
, c
12
(u − 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
8
y
2
− 7y + 1
c
2
, c
3
, c
4
c
6
y
2
− 3y + 1
c
7
, c
10
y
2
c
9
, c
11
, c
12
(y − 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.145898
a = 0
b = 1.61803
−7.23771 −49.0000
v = 6.85410
a = 0
b = −0.618034
0.657974 −49.0000
25
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
2
− 3u + 1)(u
3
− u
2
+ 2u − 1)
3
· (u
44
+ 6u
43
+ ··· + 29830u + 1)
c
2
((u − 1)
9
)(u
2
+ u − 1)(u
3
+ u
2
− 1)
3
(u
44
− 14u
43
+ ··· − 166u − 1)
c
3
u
9
(u
2
+ u − 1)(u
3
− u
2
+ 2u − 1)
3
(u
44
− 5u
43
+ ··· + 3072u + 512)
c
4
((u + 1)
9
)(u
2
− u − 1)(u
3
− u
2
+ 1)
3
(u
44
− 14u
43
+ ··· − 166u − 1)
c
5
u
9
(u
2
− 3u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
44
− 3u
43
+ ··· + 4096u − 512)
c
6
u
9
(u
2
− u − 1)(u
3
+ u
2
+ 2u + 1)
3
(u
44
− 5u
43
+ ··· + 3072u + 512)
c
7
u
2
(u
3
+ u
2
+ 2u + 1)
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
44
+ 5u
43
+ ··· − 16u − 4)
c
8
u
9
(u
2
+ 3u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
44
− 3u
43
+ ··· + 4096u − 512)
c
9
(u + 1)
2
(u
3
− u
2
+ 1)
3
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
44
+ 7u
43
+ ··· + 83u − 1)
c
10
u
2
(u
3
− u
2
+ 2u − 1)
3
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
44
+ 5u
43
+ ··· − 16u − 4)
c
11
(u − 1)
2
(u
3
+ u
2
− 1)
3
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
44
+ 7u
43
+ ··· + 83u − 1)
c
12
(u − 1)
2
(u
3
− u
2
+ 2u − 1)
3
· (u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
44
− 33u
43
+ ··· − 6317u + 1)
26
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
9
(y
2
− 7y + 1)(y
3
+ 3y
2
+ 2y − 1)
3
· (y
44
+ 78y
43
+ ··· − 889350874y + 1)
c
2
, c
4
(y − 1)
9
(y
2
− 3y + 1)(y
3
− y
2
+ 2y − 1)
3
· (y
44
− 6y
43
+ ··· − 29830y + 1)
c
3
, c
6
y
9
(y
2
− 3y + 1)(y
3
+ 3y
2
+ 2y − 1)
3
· (y
44
+ 63y
43
+ ··· − 69206016y + 262144)
c
5
, c
8
y
9
(y
2
− 7y + 1)(y
9
+ 7y
8
+ ··· + 13y − 1)
· (y
44
+ 49y
43
+ ··· − 15859712y + 262144)
c
7
, c
10
y
2
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
44
− 3y
43
+ ··· − 1304y + 16)
c
9
, c
11
(y − 1)
2
(y
3
− y
2
+ 2y − 1)
3
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
44
− 33y
43
+ ··· − 6317y + 1)
c
12
(y − 1)
2
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
44
− 37y
43
+ ··· − 39734481y + 1)
27
