12n
0820
(K12n
0820
)
A knot diagram
1
Linearized knot diagam
4 5 10 8 3 12 1 5 6 4 6 7
Solving Sequence
3,10
4
6,11
12 5 2 1 9 8 7
c
3
c
10
c
11
c
5
c
2
c
1
c
9
c
8
c
7
c
4
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h20309u
19
+ 9314u
18
+ ··· + 12371b − 15594, 980u
19
+ 5579u
18
+ ··· + 12371a − 1467,
u
20
+ u
19
+ ··· − 2u − 1i
I
u
2
= h7.00656 × 10
35
u
35
+ 1.59035 × 10
36
u
34
+ ··· + 1.29954 × 10
37
b − 3.85421 × 10
38
,
1.69263 × 10
47
u
35
− 2.24834 × 10
47
u
34
+ ··· + 5.15433 × 10
47
a + 1.11901 × 10
49
, u
36
− u
35
+ ··· − 50u + 173i
I
u
3
= hu
10
+ u
9
− 4u
8
− 4u
7
+ 4u
6
+ 5u
5
− 2u
4
− 3u
3
+ 2u
2
+ b + u + 1,
u
10
− 6u
8
+ 13u
6
+ u
5
− 15u
4
− 2u
3
+ 12u
2
+ a − 4,
u
11
+ u
10
− 5u
9
− 5u
8
+ 8u
7
+ 9u
6
− 6u
5
− 8u
4
+ 4u
3
+ 4u
2
− u − 1i
* 3 irreducible components of dim
C
= 0, with total 67 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
= h20309u
19
+ 9314u
18
+ · · · + 12371b − 15594, 980u
19
+ 5579u
18
+
· · · + 12371a − 1467, u
20
+ u
19
+ · · · − 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
−0.0792175u
19
− 0.450974u
18
+ ··· − 1.69647u + 0.118584
−1.64166u
19
− 0.752890u
18
+ ··· + 0.958613u + 1.26053
a
11
=
u
−u
3
+ u
a
12
=
0.881416u
19
+ 0.960634u
18
+ ··· + 2.54110u − 0.0663649
1.12651u
19
+ 0.184464u
18
+ ··· − 2.07146u − 2.24549
a
5
=
1.56244u
19
+ 0.301916u
18
+ ··· − 2.65508u − 1.14194
−1.64166u
19
− 0.752890u
18
+ ··· + 0.958613u + 1.26053
a
2
=
−2.04009u
19
− 0.999677u
18
+ ··· − 1.51984u + 2.04777
1.96088u
19
+ 0.548703u
18
+ ··· − 0.176623u − 1.92919
a
1
=
−0.603832u
19
− 0.366098u
18
+ ··· − 1.65573u + 1.15900
0.942042u
19
+ 0.234338u
18
+ ··· − 0.00751758u − 1.12651
a
9
=
0.881416u
19
+ 0.960634u
18
+ ··· + 1.54110u − 0.0663649
−0.371757u
19
− 0.166357u
18
+ ··· − 0.0398513u − 0.0792175
a
8
=
2.14194u
19
+ 0.579500u
18
+ ··· − 0.441840u − 1.62881
−1.26053u
19
+ 0.381133u
18
+ ··· + 1.98294u + 1.56244
a
7
=
−2.36408u
19
− 0.158354u
18
+ ··· + 1.84399u + 3.35316
3.06855u
19
+ 0.418802u
18
+ ··· − 3.07898u − 4.37200
(ii) Obstruction class = −1
(iii) Cusp Shapes =
108774
12371
u
19
+
59182
12371
u
18
+ ··· +
1686
12371
u +
115368
12371
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− u
19
+ ··· + 3u − 1
c
2
, c
5
u
20
+ 12u
19
+ ··· − 288u − 64
c
3
, c
4
, c
8
c
10
u
20
− u
19
+ ··· + 2u − 1
c
6
, c
7
, c
11
c
12
u
20
− 7u
19
+ ··· − 16u + 8
c
9
u
20
− 7u
18
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 9y
19
+ ··· − 23y + 1
c
2
, c
5
y
20
− 12y
19
+ ··· − 41984y + 4096
c
3
, c
4
, c
8
c
10
y
20
− 7y
19
+ ··· − 12y + 1
c
6
, c
7
, c
11
c
12
y
20
− 23y
19
+ ··· − 480y + 64
c
9
y
20
− 14y
19
+ ··· − 47y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531641 + 0.775820I
a = 0.521652 − 0.793900I
b = 0.421927 − 0.879767I
−2.87838 + 0.48775I 4.90275 − 0.25050I
u = 0.531641 − 0.775820I
a = 0.521652 + 0.793900I
b = 0.421927 + 0.879767I
−2.87838 − 0.48775I 4.90275 + 0.25050I
u = −0.780003 + 0.720862I
a = 0.368240 + 0.692494I
b = 0.401381 + 1.125740I
−1.50723 − 4.46688I 9.00256 + 6.89614I
u = −0.780003 − 0.720862I
a = 0.368240 − 0.692494I
b = 0.401381 − 1.125740I
−1.50723 + 4.46688I 9.00256 − 6.89614I
u = −0.918199
a = −1.32642
b = 1.75391
16.1040 18.7100
u = −0.173666 + 0.881491I
a = 0.646323 + 1.135580I
b = 0.621428 + 0.665143I
2.15657 + 2.07163I 8.70820 − 2.09392I
u = −0.173666 − 0.881491I
a = 0.646323 − 1.135580I
b = 0.621428 − 0.665143I
2.15657 − 2.07163I 8.70820 + 2.09392I
u = 0.773890 + 0.398773I
a = −1.14329 + 1.51420I
b = 1.317590 + 0.420622I
4.34968 + 1.79622I 15.4727 − 7.2361I
u = 0.773890 − 0.398773I
a = −1.14329 − 1.51420I
b = 1.317590 − 0.420622I
4.34968 − 1.79622I 15.4727 + 7.2361I
u = −0.964251 + 0.670604I
a = −0.50985 − 1.33705I
b = 1.248990 − 0.652969I
−0.28761 − 6.25899I 10.23267 + 5.61351I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.964251 − 0.670604I
a = −0.50985 + 1.33705I
b = 1.248990 + 0.652969I
−0.28761 + 6.25899I 10.23267 − 5.61351I
u = 0.971344 + 0.669842I
a = 0.253502 − 0.657470I
b = 0.489453 − 1.324130I
6.46708 + 7.19476I 12.8367 − 6.4139I
u = 0.971344 − 0.669842I
a = 0.253502 + 0.657470I
b = 0.489453 + 1.324130I
6.46708 − 7.19476I 12.8367 + 6.4139I
u = −0.783799
a = 0.321973
b = −2.10585
15.5209 28.3760
u = 0.696724
a = 0.426342
b = −1.34554
5.26045 19.7990
u = 1.163650 + 0.737004I
a = −0.392518 + 1.185430I
b = 1.25173 + 0.76023I
1.08242 + 11.20720I 12.2004 − 8.8347I
u = 1.163650 − 0.737004I
a = −0.392518 − 1.185430I
b = 1.25173 − 0.76023I
1.08242 − 11.20720I 12.2004 + 8.8347I
u = −1.32603 + 0.74385I
a = −0.336093 − 1.104220I
b = 1.25227 − 0.82883I
8.8703 − 14.6138I 14.9115 + 7.7101I
u = −1.32603 − 0.74385I
a = −0.336093 + 1.104220I
b = 1.25227 + 0.82883I
8.8703 + 14.6138I 14.9115 − 7.7101I
u = −0.387870
a = 0.762165
b = −0.312052
0.631092 15.5800
6
II. I
u
2
=
h7.01×10
35
u
35
+1.59×10
36
u
34
+· · ·+1.30×10
37
b−3.85×10
38
, 1.69×10
47
u
35
−
2.25 × 10
47
u
34
+ · · · + 5.15 × 10
47
a + 1.12 × 10
49
, u
36
− u
35
+ · · · − 50u + 173i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
−0.328391u
35
+ 0.436204u
34
+ ··· + 113.808u − 21.7102
−0.0539155u
35
− 0.122378u
34
+ ··· + 22.7256u + 29.6582
a
11
=
u
−u
3
+ u
a
12
=
−0.00968600u
35
+ 0.0510508u
34
+ ··· + 1.34871u − 1.93665
0.00857854u
35
− 0.0342699u
34
+ ··· − 13.5525u + 19.8135
a
5
=
−0.274475u
35
+ 0.558582u
34
+ ··· + 91.0822u − 51.3684
−0.0539155u
35
− 0.122378u
34
+ ··· + 22.7256u + 29.6582
a
2
=
−0.0588044u
35
+ 0.0152006u
34
+ ··· + 28.6506u + 1.10313
0.136673u
35
− 0.144683u
34
+ ··· − 51.6170u + 2.13006
a
1
=
0.0979711u
35
− 0.205251u
34
+ ··· − 14.9735u + 10.7766
0.0485802u
35
− 0.0205206u
34
+ ··· − 21.3111u − 8.88587
a
9
=
−0.108106u
35
+ 0.223334u
34
+ ··· + 30.9390u − 35.3423
−0.0516142u
35
+ 0.107338u
34
+ ··· + 7.12661u − 13.4712
a
8
=
0.189528u
35
− 0.272285u
34
+ ··· − 33.3725u + 19.4151
−0.163428u
35
+ 0.181105u
34
+ ··· + 19.8997u + 14.8460
a
7
=
0.420493u
35
− 0.834327u
34
+ ··· − 109.957u + 116.513
−0.177158u
35
+ 0.159116u
34
+ ··· + 31.9669u + 13.1878
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.185352u
35
+ 0.112252u
34
+ ··· + 117.655u + 30.4332
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
− 7u
35
+ ··· + 556u + 23
c
2
, c
5
(u
3
− u
2
+ 1)
12
c
3
, c
4
, c
8
c
10
u
36
+ u
35
+ ··· + 50u + 173
c
6
, c
7
, c
11
c
12
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
c
9
u
36
+ 3u
35
+ ··· − 268u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 15y
35
+ ··· − 395064y + 529
c
2
, c
5
(y
3
− y
2
+ 2y −1)
12
c
3
, c
4
, c
8
c
10
y
36
− 21y
35
+ ··· − 421852y + 29929
c
6
, c
7
, c
11
c
12
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
6
c
9
y
36
+ 7y
35
+ ··· − 70616y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680331 + 0.769624I
a = 0.857359 − 0.939810I
b = −0.877439 − 0.744862I
5.60625 − 1.76400I 13.07138 + 0.22537I
u = 0.680331 − 0.769624I
a = 0.857359 + 0.939810I
b = −0.877439 + 0.744862I
5.60625 + 1.76400I 13.07138 − 0.22537I
u = −0.715828 + 0.752424I
a = −0.440309 − 0.292593I
b = −0.877439 − 0.744862I
−1.049570 + 0.855710I 9.06597 + 0.70533I
u = −0.715828 − 0.752424I
a = −0.440309 + 0.292593I
b = −0.877439 + 0.744862I
−1.049570 − 0.855710I 9.06597 − 0.70533I
u = −0.808909 + 0.653470I
a = −0.279403 + 0.967994I
b = −0.877439 + 0.744862I
2.64952 − 2.82812I 17.9070 + 2.9794I
u = −0.808909 − 0.653470I
a = −0.279403 − 0.967994I
b = −0.877439 − 0.744862I
2.64952 + 2.82812I 17.9070 − 2.9794I
u = −0.902191 + 0.566521I
a = 0.392677 − 1.208180I
b = 0.754878
3.08801 − 1.97241I 15.5952 + 3.6848I
u = −0.902191 − 0.566521I
a = 0.392677 + 1.208180I
b = 0.754878
3.08801 + 1.97241I 15.5952 − 3.6848I
u = −0.907127 + 0.187470I
a = −1.51181 + 1.66928I
b = 0.754878
9.74383 − 4.59213I 19.6006 + 3.2048I
u = −0.907127 − 0.187470I
a = −1.51181 − 1.66928I
b = 0.754878
9.74383 + 4.59213I 19.6006 − 3.2048I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.858363 + 0.219197I
a = 0.55462 − 1.68259I
b = −0.877439 − 0.744862I
9.57076 + 2.82812I 16.7597 − 2.9794I
u = −0.858363 − 0.219197I
a = 0.55462 + 1.68259I
b = −0.877439 + 0.744862I
9.57076 − 2.82812I 16.7597 + 2.9794I
u = −0.927627 + 0.668396I
a = 0.670182 + 0.979419I
b = −0.877439 + 0.744862I
−1.049570 − 0.855710I 9.06597 − 0.70533I
u = −0.927627 − 0.668396I
a = 0.670182 − 0.979419I
b = −0.877439 − 0.744862I
−1.049570 + 0.855710I 9.06597 + 0.70533I
u = 0.462176 + 1.059270I
a = −0.529619 + 0.427825I
b = −0.877439 + 0.744862I
−1.04957 − 4.80053I 9.06597 + 6.66423I
u = 0.462176 − 1.059270I
a = −0.529619 − 0.427825I
b = −0.877439 − 0.744862I
−1.04957 + 4.80053I 9.06597 − 6.66423I
u = 0.823077 + 0.136915I
a = −0.46568 + 1.96947I
b = 0.754878
3.08801 − 1.97241I 15.5952 + 3.6848I
u = 0.823077 − 0.136915I
a = −0.46568 − 1.96947I
b = 0.754878
3.08801 + 1.97241I 15.5952 − 3.6848I
u = 1.076000 + 0.509784I
a = −0.262546 + 0.330297I
b = −0.877439 + 0.744862I
5.60625 + 1.76400I 13.07138 − 0.22537I
u = 1.076000 − 0.509784I
a = −0.262546 − 0.330297I
b = −0.877439 − 0.744862I
5.60625 − 1.76400I 13.07138 + 0.22537I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.720048 + 0.113424I
a = 0.10618 − 1.68037I
b = −0.877439 − 0.744862I
2.64952 + 2.82812I 17.9070 − 2.9794I
u = 0.720048 − 0.113424I
a = 0.10618 + 1.68037I
b = −0.877439 + 0.744862I
2.64952 − 2.82812I 17.9070 + 2.9794I
u = 1.121560 + 0.612290I
a = 0.602203 − 1.093900I
b = −0.877439 − 0.744862I
−1.04957 + 4.80053I 9.06597 − 6.66423I
u = 1.121560 − 0.612290I
a = 0.602203 + 1.093900I
b = −0.877439 + 0.744862I
−1.04957 − 4.80053I 9.06597 + 6.66423I
u = −0.285783 + 1.362540I
a = −0.502070 − 0.521497I
b = −0.877439 − 0.744862I
5.60625 + 7.42025I 13.0714 − 6.1843I
u = −0.285783 − 1.362540I
a = −0.502070 + 0.521497I
b = −0.877439 + 0.744862I
5.60625 − 7.42025I 13.0714 + 6.1843I
u = 1.046170 + 0.922218I
a = −0.293378 − 0.768800I
b = −0.877439 − 0.744862I
9.57076 + 2.82812I 16.7597 − 2.9794I
u = 1.046170 − 0.922218I
a = −0.293378 + 0.768800I
b = −0.877439 + 0.744862I
9.57076 − 2.82812I 16.7597 + 2.9794I
u = −1.294700 + 0.553654I
a = 0.602238 + 1.181210I
b = −0.877439 + 0.744862I
5.60625 − 7.42025I 13.0714 + 6.1843I
u = −1.294700 − 0.553654I
a = 0.602238 − 1.181210I
b = −0.877439 − 0.744862I
5.60625 + 7.42025I 13.0714 − 6.1843I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.14008 + 0.91480I
a = 0.443053 + 0.670343I
b = 0.754878
9.74383 + 4.59213I 19.6006 − 3.2048I
u = 1.14008 − 0.91480I
a = 0.443053 − 0.670343I
b = 0.754878
9.74383 − 4.59213I 19.6006 + 3.2048I
u = 1.46635
a = −0.943085
b = 0.754878
6.78711 24.4360
u = −1.52578
a = −1.32799
b = 0.754878
13.7083 23.2890
u = −1.70178
a = −0.248232
b = 0.754878
6.78711 24.4360
u = 2.02337
a = 0.00186002
b = 0.754878
13.7083 0
13
III.
I
u
3
= hu
10
+ u
9
+ · · · + b + 1, u
10
− 6u
8
+ · · · + a − 4, u
11
+ u
10
+ · · · − u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
−u
10
+ 6u
8
− 13u
6
− u
5
+ 15u
4
+ 2u
3
− 12u
2
+ 4
−u
10
− u
9
+ 4u
8
+ 4u
7
− 4u
6
− 5u
5
+ 2u
4
+ 3u
3
− 2u
2
− u − 1
a
11
=
u
−u
3
+ u
a
12
=
3u
10
+ 2u
9
+ ··· + 4u − 3
−u
10
− 2u
9
+ 4u
8
+ 10u
7
− 3u
6
− 16u
5
− 2u
4
+ 10u
3
+ u
2
− 5u − 1
a
5
=
u
9
+ 2u
8
− 4u
7
− 9u
6
+ 4u
5
+ 13u
4
− u
3
− 10u
2
+ u + 5
−u
10
− u
9
+ 4u
8
+ 4u
7
− 4u
6
− 5u
5
+ 2u
4
+ 3u
3
− 2u
2
− u − 1
a
2
=
−u
10
− 2u
9
+ 3u
8
+ 9u
7
+ 2u
6
− 12u
5
− 10u
4
+ 6u
3
+ 7u
2
− 3u − 5
2u
10
+ 2u
9
− 9u
8
− 9u
7
+ 11u
6
+ 13u
5
− 5u
4
− 8u
3
+ 5u
2
+ 3u + 1
a
1
=
−u
9
− u
8
+ 5u
7
+ 6u
6
− 7u
5
− 12u
4
+ 3u
3
+ 10u
2
− 2u − 5
u
10
+ u
9
− 5u
8
− 5u
7
+ 7u
6
+ 8u
5
− 4u
4
− 5u
3
+ 4u
2
+ 2u + 1
a
9
=
3u
10
+ 2u
9
− 15u
8
− 9u
7
+ 24u
6
+ 14u
5
− 19u
4
− 9u
3
+ 14u
2
+ u − 3
−u
10
− u
9
+ 5u
8
+ 5u
7
− 8u
6
− 9u
5
+ 6u
4
+ 8u
3
− 4u
2
− 3u + 1
a
8
=
4u
10
+ 4u
9
+ ··· + 6u − 3
−u
10
− 2u
9
+ 4u
8
+ 9u
7
− 4u
6
− 13u
5
+ u
4
+ 10u
3
− u
2
− 5u
a
7
=
−u
10
− 2u
9
+ 3u
8
+ 8u
7
− 9u
5
− 4u
4
+ 5u
3
+ 3u
2
− 4u − 2
u
10
+ 3u
9
− 2u
8
− 13u
7
− 4u
6
+ 17u
5
+ 9u
4
− 10u
3
− 6u
2
+ 5u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −2u
10
− 5u
9
+ 3u
8
+ 19u
7
+ 10u
6
− 20u
5
− 13u
4
+ 11u
3
+ 2u
2
− 11u + 10
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
+ 3u
10
+ ··· − 4u + 1
c
2
u
11
+ 3u
10
− u
9
− 11u
8
− 9u
7
+ 8u
6
+ 15u
5
+ 4u
4
− 6u
3
− 4u
2
+ 1
c
3
, c
8
u
11
+ u
10
− 5u
9
− 5u
8
+ 8u
7
+ 9u
6
− 6u
5
− 8u
4
+ 4u
3
+ 4u
2
− u − 1
c
4
, c
10
u
11
− u
10
− 5u
9
+ 5u
8
+ 8u
7
− 9u
6
− 6u
5
+ 8u
4
+ 4u
3
− 4u
2
− u + 1
c
5
u
11
− 3u
10
− u
9
+ 11u
8
− 9u
7
− 8u
6
+ 15u
5
− 4u
4
− 6u
3
+ 4u
2
− 1
c
6
, c
7
u
11
− 8u
9
− u
8
+ 23u
7
+ 6u
6
− 28u
5
− 11u
4
+ 12u
3
+ 6u
2
− 1
c
9
u
11
+ u
9
− u
7
+ 3u
6
+ u
4
− u
3
− 4u
2
+ 1
c
11
, c
12
u
11
− 8u
9
+ u
8
+ 23u
7
− 6u
6
− 28u
5
+ 11u
4
+ 12u
3
− 6u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
+ 3y
10
+ ··· + 44y −1
c
2
, c
5
y
11
− 11y
10
+ ··· + 8y −1
c
3
, c
4
, c
8
c
10
y
11
− 11y
10
+ ··· + 9y −1
c
6
, c
7
, c
11
c
12
y
11
− 16y
10
+ ··· + 12y −1
c
9
y
11
+ 2y
10
− y
9
− 2y
8
− y
7
− 11y
6
− 4y
5
+ 23y
4
+ 3y
3
− 18y
2
+ 8y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.817327 + 0.673187I
a = −0.829096 + 0.875371I
b = −0.429655 + 0.602178I
8.28513 − 5.07300I 13.3655 + 5.6095I
u = −0.817327 − 0.673187I
a = −0.829096 − 0.875371I
b = −0.429655 − 0.602178I
8.28513 + 5.07300I 13.3655 − 5.6095I
u = 0.671261 + 0.485459I
a = −0.54365 − 1.38387I
b = −0.754077 − 0.626003I
1.83297 + 3.34942I 8.74876 − 8.55759I
u = 0.671261 − 0.485459I
a = −0.54365 + 1.38387I
b = −0.754077 + 0.626003I
1.83297 − 3.34942I 8.74876 + 8.55759I
u = 1.27729
a = −0.387060
b = 1.58358
17.5117 21.2400
u = 0.707662
a = 0.996863
b = −2.00315
15.1840 3.15360
u = −0.570810 + 0.224833I
a = 0.94324 + 1.81194I
b = −1.226040 + 0.434225I
4.24437 − 0.92833I 15.1830 − 0.6257I
u = −0.570810 − 0.224833I
a = 0.94324 − 1.81194I
b = −1.226040 − 0.434225I
4.24437 + 0.92833I 15.1830 + 0.6257I
u = −1.38811
a = −0.481020
b = 1.07892
8.15810 21.2750
u = 1.57940
a = −0.599120
b = 0.669115
6.35438 1.73460
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.74249
a = −0.670651
b = 0.491090
12.8934 11.0020
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 3u
10
+ ··· − 4u + 1)(u
20
− u
19
+ ··· + 3u − 1)
· (u
36
− 7u
35
+ ··· + 556u + 23)
c
2
(u
3
− u
2
+ 1)
12
· (u
11
+ 3u
10
− u
9
− 11u
8
− 9u
7
+ 8u
6
+ 15u
5
+ 4u
4
− 6u
3
− 4u
2
+ 1)
· (u
20
+ 12u
19
+ ··· − 288u − 64)
c
3
, c
8
(u
11
+ u
10
− 5u
9
− 5u
8
+ 8u
7
+ 9u
6
− 6u
5
− 8u
4
+ 4u
3
+ 4u
2
− u − 1)
· (u
20
− u
19
+ ··· + 2u − 1)(u
36
+ u
35
+ ··· + 50u + 173)
c
4
, c
10
(u
11
− u
10
− 5u
9
+ 5u
8
+ 8u
7
− 9u
6
− 6u
5
+ 8u
4
+ 4u
3
− 4u
2
− u + 1)
· (u
20
− u
19
+ ··· + 2u − 1)(u
36
+ u
35
+ ··· + 50u + 173)
c
5
(u
3
− u
2
+ 1)
12
· (u
11
− 3u
10
− u
9
+ 11u
8
− 9u
7
− 8u
6
+ 15u
5
− 4u
4
− 6u
3
+ 4u
2
− 1)
· (u
20
+ 12u
19
+ ··· − 288u − 64)
c
6
, c
7
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
· (u
11
− 8u
9
− u
8
+ 23u
7
+ 6u
6
− 28u
5
− 11u
4
+ 12u
3
+ 6u
2
− 1)
· (u
20
− 7u
19
+ ··· − 16u + 8)
c
9
(u
11
+ u
9
+ ··· − 4u
2
+ 1)(u
20
− 7u
18
+ ··· − 3u + 1)
· (u
36
+ 3u
35
+ ··· − 268u − 1)
c
11
, c
12
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
· (u
11
− 8u
9
+ u
8
+ 23u
7
− 6u
6
− 28u
5
+ 11u
4
+ 12u
3
− 6u
2
+ 1)
· (u
20
− 7u
19
+ ··· − 16u + 8)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
11
+ 3y
10
+ ··· + 44y −1)(y
20
− 9y
19
+ ··· − 23y + 1)
· (y
36
+ 15y
35
+ ··· − 395064y + 529)
c
2
, c
5
((y
3
− y
2
+ 2y −1)
12
)(y
11
− 11y
10
+ ··· + 8y −1)
· (y
20
− 12y
19
+ ··· − 41984y + 4096)
c
3
, c
4
, c
8
c
10
(y
11
− 11y
10
+ ··· + 9y −1)(y
20
− 7y
19
+ ··· − 12y + 1)
· (y
36
− 21y
35
+ ··· − 421852y + 29929)
c
6
, c
7
, c
11
c
12
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
6
· (y
11
− 16y
10
+ ··· + 12y −1)(y
20
− 23y
19
+ ··· − 480y + 64)
c
9
(y
11
+ 2y
10
− y
9
− 2y
8
− y
7
− 11y
6
− 4y
5
+ 23y
4
+ 3y
3
− 18y
2
+ 8y −1)
· (y
20
− 14y
19
+ ··· − 47y + 1)(y
36
+ 7y
35
+ ··· − 70616y + 1)
20
