12a
0656
(K12a
0656
)
A knot diagram
1
Linearized knot diagam
3 7 10 12 8 2 11 5 1 6 9 4
Solving Sequence
2,6
7
3,11
8 1 5 10 4 9 12
c
6
c
2
c
7
c
1
c
5
c
10
c
3
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−9540655u
40
− 39881332u
39
+ ··· + 2811062b + 78036718,
177709945u
40
+ 1366370774u
39
+ ··· + 16866372a + 2496378600, u
41
+ 8u
40
+ ··· + 102u + 12i
I
u
2
= h3.46819 × 10
21
au
52
− 3.39067 × 10
24
u
52
+ ··· − 1.10739 × 10
22
a + 2.55339 × 10
24
,
− 2.28935 × 10
21
au
52
+ 1.20458 × 10
21
u
52
+ ··· + 3.67777 × 10
21
a − 1.92411 × 10
20
,
u
53
− 3u
52
+ ··· − 7u + 3i
I
u
3
= h−2u
15
− 2u
14
+ ··· + b + 1,
2u
15
+ 5u
14
− 12u
12
− 10u
11
+ 11u
10
+ 21u
9
− 2u
8
− 26u
7
− 9u
6
+ 19u
5
+ 11u
4
− 5u
3
− 2u
2
+ a + 3u,
u
16
+ 3u
15
+ 2u
14
− 5u
13
− 9u
12
+ 13u
10
+ 8u
9
− 11u
8
− 15u
7
+ 3u
6
+ 13u
5
+ 4u
4
− 4u
3
− u
2
+ 2u + 1i
I
u
4
= h−u
6
a + 3u
5
a − 9u
6
+ 2u
4
a + 6u
5
− 5u
3
a + 11u
4
− 6u
2
a − 3u
3
+ 6au − 19u
2
+ 7b + 3a − 2u + 6,
− u
6
a + 2u
4
a − 3u
5
+ 2u
4
− 3u
2
a + 2u
3
+ a
2
− 2au + 2a − 5u + 1, u
7
− u
6
− u
5
+ u
4
+ 2u
3
− u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 177 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−9.54 × 10
6
u
40
− 3.99 × 10
7
u
39
+ · · · + 2.81 × 10
6
b + 7.80 × 10
7
, 1.78 ×
10
8
u
40
+1.37×10
9
u
39
+· · ·+1.69×10
7
a+2.50×10
9
, u
41
+8u
40
+· · ·+102u+12i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−10.5363u
40
− 81.0115u
39
+ ··· − 1142.34u − 148.009
3.39397u
40
+ 14.1873u
39
+ ··· − 189.050u − 27.7606
a
8
=
11.9344u
40
+ 81.1701u
39
+ ··· + 642.098u + 78.2302
5.42199u
40
+ 44.9429u
39
+ ··· + 841.464u + 112.318
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
2.23943u
40
+ 11.2000u
39
+ ··· − 81.5979u − 12.3360
7.54178u
40
+ 56.4150u
39
+ ··· + 626.918u + 78.4362
a
10
=
−13.9303u
40
− 95.1988u
39
+ ··· − 953.293u − 120.249
3.39397u
40
+ 14.1873u
39
+ ··· − 189.050u − 27.7606
a
4
=
8.93120u
40
+ 49.3410u
39
+ ··· − 43.6295u − 16.1139
10.7792u
40
+ 85.8051u
39
+ ··· + 1221.80u + 158.128
a
9
=
8.17922u
40
+ 62.6496u
39
+ ··· + 848.799u + 110.731
1.12373u
40
+ 13.0388u
39
+ ··· + 341.462u + 45.5333
a
12
=
−16.6903u
40
− 127.083u
39
+ ··· − 1863.89u − 244.521
8.31913u
40
+ 52.5805u
39
+ ··· + 336.750u + 39.1452
(ii) Obstruction class = −1
(iii) Cusp Shapes =
50634926
1405531
u
40
+
355341377
1405531
u
39
+ ··· +
2555447816
1405531
u +
305571258
1405531
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
41
+ 14u
40
+ ··· + 1308u + 144
c
2
, c
6
u
41
− 8u
40
+ ··· + 102u − 12
c
3
, c
10
u
41
+ 12u
39
+ ··· + 13u − 7
c
4
, c
5
, c
8
c
12
u
41
+ u
40
+ ··· + 5u − 1
c
7
, c
9
u
41
+ 3u
40
+ ··· − 10u − 1
c
11
u
41
+ 29u
40
+ ··· − 31212u − 2196
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
+ 18y
40
+ ··· + 259056y −20736
c
2
, c
6
y
41
− 14y
40
+ ··· + 1308y −144
c
3
, c
10
y
41
+ 24y
40
+ ··· − 2197y −49
c
4
, c
5
, c
8
c
12
y
41
+ 41y
40
+ ··· + 13y −1
c
7
, c
9
y
41
− 3y
40
+ ··· − 44y −1
c
11
y
41
− y
40
+ ··· + 18265752y −4822416
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.885459 + 0.468568I
a = 0.74140 + 2.12496I
b = 0.14627 + 1.57300I
−8.61867 − 1.89974I −0.41209 + 3.72876I
u = 0.885459 − 0.468568I
a = 0.74140 − 2.12496I
b = 0.14627 − 1.57300I
−8.61867 + 1.89974I −0.41209 − 3.72876I
u = −0.638864 + 0.751208I
a = 0.138021 + 0.619122I
b = 1.31734 − 1.20105I
−4.97109 − 2.38814I 1.29196 + 2.16768I
u = −0.638864 − 0.751208I
a = 0.138021 − 0.619122I
b = 1.31734 + 1.20105I
−4.97109 + 2.38814I 1.29196 − 2.16768I
u = 1.023760 + 0.040551I
a = −0.89941 + 2.43314I
b = −0.63878 + 1.63015I
−10.53450 − 2.01458I −6.45706 + 3.63025I
u = 1.023760 − 0.040551I
a = −0.89941 − 2.43314I
b = −0.63878 − 1.63015I
−10.53450 + 2.01458I −6.45706 − 3.63025I
u = −0.336434 + 0.998716I
a = −0.244879 − 0.078110I
b = −0.428361 − 0.703700I
−5.98718 + 8.31828I 0.77031 − 8.90553I
u = −0.336434 − 0.998716I
a = −0.244879 + 0.078110I
b = −0.428361 + 0.703700I
−5.98718 − 8.31828I 0.77031 + 8.90553I
u = 0.852689 + 0.638581I
a = −0.665891 − 1.232780I
b = −0.201595 − 1.034500I
3.45937 − 2.49348I 17.3496 + 3.7147I
u = 0.852689 − 0.638581I
a = −0.665891 + 1.232780I
b = −0.201595 + 1.034500I
3.45937 + 2.49348I 17.3496 − 3.7147I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984331 + 0.435389I
a = −1.49599 + 0.52826I
b = 0.247555 + 0.788723I
−8.39285 + 3.15435I −2.00509 − 3.79246I
u = −0.984331 − 0.435389I
a = −1.49599 − 0.52826I
b = 0.247555 − 0.788723I
−8.39285 − 3.15435I −2.00509 + 3.79246I
u = −0.558695 + 0.934797I
a = −0.224063 + 0.056775I
b = −1.00584 + 1.24085I
−4.7480 − 13.5144I 3.83057 + 6.47722I
u = −0.558695 − 0.934797I
a = −0.224063 − 0.056775I
b = −1.00584 − 1.24085I
−4.7480 + 13.5144I 3.83057 − 6.47722I
u = −0.578439 + 0.934242I
a = 0.180422 + 0.011630I
b = 0.828821 − 0.703301I
4.82087 − 2.96510I 11.89661 + 4.32984I
u = −0.578439 − 0.934242I
a = 0.180422 − 0.011630I
b = 0.828821 + 0.703301I
4.82087 + 2.96510I 11.89661 − 4.32984I
u = 0.911339 + 0.643598I
a = 0.442568 + 0.534189I
b = 0.213097 + 0.483788I
−1.08260 − 2.39919I 2.82500 + 2.36815I
u = 0.911339 − 0.643598I
a = 0.442568 − 0.534189I
b = 0.213097 − 0.483788I
−1.08260 + 2.39919I 2.82500 − 2.36815I
u = 0.450241 + 1.042540I
a = 0.082525 + 0.244030I
b = −0.042347 + 0.250005I
0.63600 − 2.52874I 18.1134 + 18.3545I
u = 0.450241 − 1.042540I
a = 0.082525 − 0.244030I
b = −0.042347 − 0.250005I
0.63600 + 2.52874I 18.1134 − 18.3545I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.905940 + 0.723310I
a = −1.206950 + 0.270424I
b = 0.06050 + 1.48050I
−6.88574 + 2.77950I −2.52803 − 2.69400I
u = −0.905940 − 0.723310I
a = −1.206950 − 0.270424I
b = 0.06050 − 1.48050I
−6.88574 − 2.77950I −2.52803 + 2.69400I
u = 1.156170 + 0.163202I
a = 0.054861 + 1.154130I
b = −0.011284 + 0.831483I
−2.60053 − 1.63849I 1.29829 + 3.72995I
u = 1.156170 − 0.163202I
a = 0.054861 − 1.154130I
b = −0.011284 − 0.831483I
−2.60053 + 1.63849I 1.29829 − 3.72995I
u = −1.017490 + 0.598781I
a = −0.48971 + 1.36588I
b = 0.938580 + 0.636689I
0.01859 + 4.99073I 7.41621 − 5.15637I
u = −1.017490 − 0.598781I
a = −0.48971 − 1.36588I
b = 0.938580 − 0.636689I
0.01859 − 4.99073I 7.41621 + 5.15637I
u = −0.582863 + 0.568272I
a = 0.532194 − 0.367975I
b = −0.814843 + 0.187675I
1.313200 − 0.233695I 10.70499 + 1.18118I
u = −0.582863 − 0.568272I
a = 0.532194 + 0.367975I
b = −0.814843 − 0.187675I
1.313200 + 0.233695I 10.70499 − 1.18118I
u = −1.012550 + 0.676105I
a = 1.04077 − 2.00094I
b = −1.44968 − 1.50619I
−6.08547 + 7.82770I 0. − 7.17884I
u = −1.012550 − 0.676105I
a = 1.04077 + 2.00094I
b = −1.44968 + 1.50619I
−6.08547 − 7.82770I 0. + 7.17884I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.255260 + 0.098348I
a = 0.62696 − 1.68689I
b = 0.503775 − 1.234310I
−11.9204 − 11.6017I 0. + 7.20800I
u = 1.255260 − 0.098348I
a = 0.62696 + 1.68689I
b = 0.503775 + 1.234310I
−11.9204 + 11.6017I 0. − 7.20800I
u = −1.097620 + 0.715676I
a = 0.43707 − 1.39878I
b = −0.904534 − 0.976612I
3.20670 + 9.01055I 0
u = −1.097620 − 0.715676I
a = 0.43707 + 1.39878I
b = −0.904534 + 0.976612I
3.20670 − 9.01055I 0
u = −1.110990 + 0.712322I
a = −0.77442 + 1.84377I
b = 1.05657 + 1.43789I
−6.4571 + 19.5586I 0
u = −1.110990 − 0.712322I
a = −0.77442 − 1.84377I
b = 1.05657 − 1.43789I
−6.4571 − 19.5586I 0
u = −1.208090 + 0.536455I
a = 0.835695 − 0.569841I
b = 0.013353 − 0.626817I
−8.96308 − 2.68054I 0
u = −1.208090 − 0.536455I
a = 0.835695 + 0.569841I
b = 0.013353 + 0.626817I
−8.96308 + 2.68054I 0
u = −0.284449 + 0.551332I
a = 0.379709 − 0.836237I
b = 0.419007 + 0.842756I
−6.48873 + 0.58270I 2.21114 − 2.45573I
u = −0.284449 − 0.551332I
a = 0.379709 + 0.836237I
b = 0.419007 − 0.842756I
−6.48873 − 0.58270I 2.21114 + 2.45573I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.436343
a = 1.51826
b = −0.495207
1.00381 8.15590
9
II. I
u
2
= h3.47 × 10
21
au
52
− 3.39 × 10
24
u
52
+ · · · − 1.11 × 10
22
a + 2.55 ×
10
24
, −2.29 × 10
21
au
52
+ 1.20 × 10
21
u
52
+ · · · + 3.68 × 10
21
a − 1.92 ×
10
20
, u
53
− 3u
52
+ · · · − 7u + 3i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
a
−0.00547323au
52
+ 5.35090u
52
+ ··· + 0.0174759a − 4.02956
a
8
=
0.792245au
52
− 3.85460u
52
+ ··· − 10.0550a + 8.50356
−2.56812au
52
+ 6.14017u
52
+ ··· + 10.9405a − 10.5932
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−0.844639au
52
+ 2.51068u
52
+ ··· − 5.12108a + 3.53606
0.662151au
52
− 8.20051u
52
+ ··· + 1.45552a + 14.6696
a
10
=
0.00547323au
52
− 5.35090u
52
+ ··· + 0.982524a + 4.02956
−0.00547323au
52
+ 5.35090u
52
+ ··· + 0.0174759a − 4.02956
a
4
=
5.35090au
52
+ 7.75572u
52
+ ··· − 4.02956a − 31.2778
−1.82420u
52
+ 7.28102u
51
+ ··· − 19.2201u + 14.3168
a
9
=
1.02122u
52
− 6.54669u
51
+ ··· + a − 12.9034
0.00547323au
52
+ 2.07703u
52
+ ··· − 0.0174759a + 2.21423
a
12
=
0.699902au
52
− 5.33229u
52
+ ··· + 8.35283a + 17.7577
4.00241au
52
+ 6.14017u
52
+ ··· − 15.3774a − 9.59325
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
121904372732907815124
10140903080066369147
u
52
+
84784483273909067308
10140903080066369147
u
51
+ ··· −
561107072444840340117
10140903080066369147
u −
235969730948693192607
10140903080066369147
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
53
+ 21u
52
+ ··· + 187u + 9)
2
c
2
, c
6
(u
53
+ 3u
52
+ ··· − 7u − 3)
2
c
3
, c
10
u
106
+ u
105
+ ··· − 102u + 283
c
4
, c
5
, c
8
c
12
u
106
+ 5u
105
+ ··· − 34u + 1
c
7
, c
9
u
106
+ u
105
+ ··· + 38u + 1
c
11
(u
53
− 19u
52
+ ··· + 603u − 55)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
53
+ 27y
52
+ ··· + 1651y −81)
2
c
2
, c
6
(y
53
− 21y
52
+ ··· + 187y −9)
2
c
3
, c
10
y
106
− 9y
105
+ ··· + 484280y + 80089
c
4
, c
5
, c
8
c
12
y
106
+ 75y
105
+ ··· − 698y + 1
c
7
, c
9
y
106
− 3y
105
+ ··· − 230y + 1
c
11
(y
53
+ 27y
52
+ ··· − 30081y −3025)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.761955 + 0.663374I
a = −0.422004 − 0.248213I
b = 1.26884 + 0.75571I
−2.68106 + 4.45453I 6.83454 − 2.23016I
u = 0.761955 + 0.663374I
a = 0.08415 + 2.05127I
b = −1.97665 + 0.42519I
−2.68106 + 4.45453I 6.83454 − 2.23016I
u = 0.761955 − 0.663374I
a = −0.422004 + 0.248213I
b = 1.26884 − 0.75571I
−2.68106 − 4.45453I 6.83454 + 2.23016I
u = 0.761955 − 0.663374I
a = 0.08415 − 2.05127I
b = −1.97665 − 0.42519I
−2.68106 − 4.45453I 6.83454 + 2.23016I
u = −0.739105 + 0.649562I
a = 0.58620 − 1.41792I
b = −1.164340 − 0.733353I
1.99956 − 0.73578I 9.99636 + 2.14125I
u = −0.739105 + 0.649562I
a = 0.261702 + 0.107022I
b = −0.984287 + 0.409104I
1.99956 − 0.73578I 9.99636 + 2.14125I
u = −0.739105 − 0.649562I
a = 0.58620 + 1.41792I
b = −1.164340 + 0.733353I
1.99956 + 0.73578I 9.99636 − 2.14125I
u = −0.739105 − 0.649562I
a = 0.261702 − 0.107022I
b = −0.984287 − 0.409104I
1.99956 + 0.73578I 9.99636 − 2.14125I
u = −0.803695 + 0.553806I
a = −0.471613 − 0.777847I
b = 0.817053 − 0.820052I
−0.914471 − 0.291155I 6.37184 − 2.68973I
u = −0.803695 + 0.553806I
a = −1.04648 + 2.48317I
b = 1.13190 + 1.51872I
−0.914471 − 0.291155I 6.37184 − 2.68973I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.803695 − 0.553806I
a = −0.471613 + 0.777847I
b = 0.817053 + 0.820052I
−0.914471 + 0.291155I 6.37184 + 2.68973I
u = −0.803695 − 0.553806I
a = −1.04648 − 2.48317I
b = 1.13190 − 1.51872I
−0.914471 + 0.291155I 6.37184 + 2.68973I
u = 0.809219 + 0.657477I
a = 0.929581 + 0.655660I
b = −0.054251 + 1.080400I
−0.96806 − 2.57158I 2.36852 + 1.85769I
u = 0.809219 + 0.657477I
a = −0.057982 + 0.463873I
b = 0.404376 − 0.070029I
−0.96806 − 2.57158I 2.36852 + 1.85769I
u = 0.809219 − 0.657477I
a = 0.929581 − 0.655660I
b = −0.054251 − 1.080400I
−0.96806 + 2.57158I 2.36852 − 1.85769I
u = 0.809219 − 0.657477I
a = −0.057982 − 0.463873I
b = 0.404376 + 0.070029I
−0.96806 + 2.57158I 2.36852 − 1.85769I
u = 0.847011 + 0.619709I
a = −0.412637 − 0.614788I
b = −0.770270 − 0.844098I
3.34792 − 2.43380I 12.85093 + 4.05145I
u = 0.847011 + 0.619709I
a = −0.81361 − 1.71549I
b = 0.414434 − 1.083910I
3.34792 − 2.43380I 12.85093 + 4.05145I
u = 0.847011 − 0.619709I
a = −0.412637 + 0.614788I
b = −0.770270 + 0.844098I
3.34792 + 2.43380I 12.85093 − 4.05145I
u = 0.847011 − 0.619709I
a = −0.81361 + 1.71549I
b = 0.414434 + 1.083910I
3.34792 + 2.43380I 12.85093 − 4.05145I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.902087 + 0.562696I
a = −1.211490 − 0.007785I
b = −1.57400 + 1.34383I
−1.24052 + 4.76476I 4.96654 − 5.54371I
u = −0.902087 + 0.562696I
a = 0.92835 − 2.65426I
b = −0.563164 − 0.942103I
−1.24052 + 4.76476I 4.96654 − 5.54371I
u = −0.902087 − 0.562696I
a = −1.211490 + 0.007785I
b = −1.57400 − 1.34383I
−1.24052 − 4.76476I 4.96654 + 5.54371I
u = −0.902087 − 0.562696I
a = 0.92835 + 2.65426I
b = −0.563164 + 0.942103I
−1.24052 − 4.76476I 4.96654 + 5.54371I
u = 0.529209 + 0.925581I
a = −0.140548 − 0.244294I
b = −0.875570 − 1.087590I
0.91880 + 7.85413I 7.41161 − 6.47576I
u = 0.529209 + 0.925581I
a = 0.128027 − 0.146145I
b = 1.029630 + 0.773863I
0.91880 + 7.85413I 7.41161 − 6.47576I
u = 0.529209 − 0.925581I
a = −0.140548 + 0.244294I
b = −0.875570 + 1.087590I
0.91880 − 7.85413I 7.41161 + 6.47576I
u = 0.529209 − 0.925581I
a = 0.128027 + 0.146145I
b = 1.029630 − 0.773863I
0.91880 − 7.85413I 7.41161 + 6.47576I
u = −1.068010 + 0.070510I
a = 0.20788 − 1.77260I
b = 0.392060 − 1.181690I
−6.58685 − 2.11178I −2.20971 + 0.I
u = −1.068010 + 0.070510I
a = −1.13743 + 1.70116I
b = −0.460832 + 1.241750I
−6.58685 − 2.11178I −2.20971 + 0.I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.068010 − 0.070510I
a = 0.20788 + 1.77260I
b = 0.392060 + 1.181690I
−6.58685 + 2.11178I −2.20971 + 0.I
u = −1.068010 − 0.070510I
a = −1.13743 − 1.70116I
b = −0.460832 − 1.241750I
−6.58685 + 2.11178I −2.20971 + 0.I
u = 0.837471 + 0.361490I
a = 0.065083 + 1.154200I
b = −1.56349 + 0.30496I
−2.48325 + 0.50792I −0.045723 + 0.759721I
u = 0.837471 + 0.361490I
a = −2.67691 − 0.70533I
b = −0.178802 − 0.391633I
−2.48325 + 0.50792I −0.045723 + 0.759721I
u = 0.837471 − 0.361490I
a = 0.065083 − 1.154200I
b = −1.56349 − 0.30496I
−2.48325 − 0.50792I −0.045723 − 0.759721I
u = 0.837471 − 0.361490I
a = −2.67691 + 0.70533I
b = −0.178802 + 0.391633I
−2.48325 − 0.50792I −0.045723 − 0.759721I
u = −0.920253 + 0.640465I
a = 0.667286 + 0.588445I
b = 1.48578 − 0.50992I
1.46071 + 5.77097I 6.00000 − 8.48092I
u = −0.920253 + 0.640465I
a = −0.60050 + 1.76608I
b = 0.796743 + 0.614787I
1.46071 + 5.77097I 6.00000 − 8.48092I
u = −0.920253 − 0.640465I
a = 0.667286 − 0.588445I
b = 1.48578 + 0.50992I
1.46071 − 5.77097I 6.00000 + 8.48092I
u = −0.920253 − 0.640465I
a = −0.60050 − 1.76608I
b = 0.796743 − 0.614787I
1.46071 − 5.77097I 6.00000 + 8.48092I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926043 + 0.636364I
a = 0.59546 − 1.29650I
b = 2.19092 + 0.13649I
−3.19040 − 9.51012I 6.00000 + 9.12317I
u = 0.926043 + 0.636364I
a = 1.11316 + 2.24311I
b = −1.12822 + 0.90500I
−3.19040 − 9.51012I 6.00000 + 9.12317I
u = 0.926043 − 0.636364I
a = 0.59546 + 1.29650I
b = 2.19092 − 0.13649I
−3.19040 + 9.51012I 6.00000 − 9.12317I
u = 0.926043 − 0.636364I
a = 1.11316 − 2.24311I
b = −1.12822 − 0.90500I
−3.19040 + 9.51012I 6.00000 − 9.12317I
u = 0.563470 + 0.650779I
a = 0.802413 + 0.694471I
b = −0.607079 − 0.454169I
−1.82739 + 3.33111I 4.53816 − 3.55806I
u = 0.563470 + 0.650779I
a = 0.245333 − 0.331567I
b = 1.15252 + 1.04512I
−1.82739 + 3.33111I 4.53816 − 3.55806I
u = 0.563470 − 0.650779I
a = 0.802413 − 0.694471I
b = −0.607079 + 0.454169I
−1.82739 − 3.33111I 4.53816 + 3.55806I
u = 0.563470 − 0.650779I
a = 0.245333 + 0.331567I
b = 1.15252 − 1.04512I
−1.82739 − 3.33111I 4.53816 + 3.55806I
u = −0.212856 + 0.829020I
a = −0.155685 + 0.859257I
b = −0.532616 + 0.773106I
−0.211705 − 0.528763I 11.05954 − 2.34564I
u = −0.212856 + 0.829020I
a = 0.300917 − 0.092700I
b = −0.880370 − 0.176654I
−0.211705 − 0.528763I 11.05954 − 2.34564I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.212856 − 0.829020I
a = −0.155685 − 0.859257I
b = −0.532616 − 0.773106I
−0.211705 + 0.528763I 11.05954 + 2.34564I
u = −0.212856 − 0.829020I
a = 0.300917 + 0.092700I
b = −0.880370 + 0.176654I
−0.211705 + 0.528763I 11.05954 + 2.34564I
u = 0.545783 + 1.016510I
a = 0.134531 + 0.288899I
b = 0.214856 + 0.429857I
0.66390 − 2.55386I 21.5274 + 0.I
u = 0.545783 + 1.016510I
a = −0.006182 + 0.238215I
b = −0.323074 + 0.067457I
0.66390 − 2.55386I 21.5274 + 0.I
u = 0.545783 − 1.016510I
a = 0.134531 − 0.288899I
b = 0.214856 − 0.429857I
0.66390 + 2.55386I 21.5274 + 0.I
u = 0.545783 − 1.016510I
a = −0.006182 − 0.238215I
b = −0.323074 − 0.067457I
0.66390 + 2.55386I 21.5274 + 0.I
u = 1.165430 + 0.175714I
a = −1.19088 − 1.18311I
b = −0.379117 − 1.235260I
−10.54930 + 2.59097I 0
u = 1.165430 + 0.175714I
a = 0.53528 − 1.99476I
b = 0.054387 − 1.088210I
−10.54930 + 2.59097I 0
u = 1.165430 − 0.175714I
a = −1.19088 + 1.18311I
b = −0.379117 + 1.235260I
−10.54930 − 2.59097I 0
u = 1.165430 − 0.175714I
a = 0.53528 + 1.99476I
b = 0.054387 + 1.088210I
−10.54930 − 2.59097I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.851563 + 0.825849I
a = −0.073086 − 0.590149I
b = 0.183606 + 0.246239I
−2.54747 + 3.04977I 0
u = −0.851563 + 0.825849I
a = −1.06914 + 0.94258I
b = −0.19322 + 1.69960I
−2.54747 + 3.04977I 0
u = −0.851563 − 0.825849I
a = −0.073086 + 0.590149I
b = 0.183606 − 0.246239I
−2.54747 − 3.04977I 0
u = −0.851563 − 0.825849I
a = −1.06914 − 0.94258I
b = −0.19322 − 1.69960I
−2.54747 − 3.04977I 0
u = 1.017210 + 0.627388I
a = −0.841592 − 1.125980I
b = 1.003030 − 0.685688I
−3.12568 − 8.35925I 0
u = 1.017210 + 0.627388I
a = 0.84069 + 2.07433I
b = −1.17258 + 1.39807I
−3.12568 − 8.35925I 0
u = 1.017210 − 0.627388I
a = −0.841592 + 1.125980I
b = 1.003030 + 0.685688I
−3.12568 + 8.35925I 0
u = 1.017210 − 0.627388I
a = 0.84069 − 2.07433I
b = −1.17258 − 1.39807I
−3.12568 + 8.35925I 0
u = 1.100540 + 0.474663I
a = 0.185852 − 1.385000I
b = 1.073590 − 0.557920I
−3.73664 − 3.38760I 0
u = 1.100540 + 0.474663I
a = 1.26944 + 1.03677I
b = 0.046877 + 0.487352I
−3.73664 − 3.38760I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.100540 − 0.474663I
a = 0.185852 + 1.385000I
b = 1.073590 + 0.557920I
−3.73664 + 3.38760I 0
u = 1.100540 − 0.474663I
a = 1.26944 − 1.03677I
b = 0.046877 − 0.487352I
−3.73664 + 3.38760I 0
u = −1.063130 + 0.568697I
a = 1.56510 − 0.47928I
b = −0.138546 − 0.455023I
−8.04966 + 9.90864I 0
u = −1.063130 + 0.568697I
a = 0.57686 − 2.18399I
b = −1.14386 − 1.57633I
−8.04966 + 9.90864I 0
u = −1.063130 − 0.568697I
a = 1.56510 + 0.47928I
b = −0.138546 + 0.455023I
−8.04966 − 9.90864I 0
u = −1.063130 − 0.568697I
a = 0.57686 + 2.18399I
b = −1.14386 + 1.57633I
−8.04966 − 9.90864I 0
u = −0.696627 + 0.209310I
a = 1.31647 + 0.69027I
b = 1.60761 − 0.69970I
−5.84696 − 5.71093I −1.49347 + 4.28887I
u = −0.696627 + 0.209310I
a = −3.02781 + 1.53788I
b = −0.722518 + 0.223372I
−5.84696 − 5.71093I −1.49347 + 4.28887I
u = −0.696627 − 0.209310I
a = 1.31647 − 0.69027I
b = 1.60761 + 0.69970I
−5.84696 + 5.71093I −1.49347 − 4.28887I
u = −0.696627 − 0.209310I
a = −3.02781 − 1.53788I
b = −0.722518 − 0.223372I
−5.84696 + 5.71093I −1.49347 − 4.28887I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.276460 + 0.074097I
a = −0.387601 − 0.942926I
b = −0.323720 − 0.864956I
−6.05943 + 5.69834I 0
u = −1.276460 + 0.074097I
a = 0.53114 + 1.63270I
b = 0.404900 + 1.037470I
−6.05943 + 5.69834I 0
u = −1.276460 − 0.074097I
a = −0.387601 + 0.942926I
b = −0.323720 + 0.864956I
−6.05943 − 5.69834I 0
u = −1.276460 − 0.074097I
a = 0.53114 − 1.63270I
b = 0.404900 − 1.037470I
−6.05943 − 5.69834I 0
u = −0.286837 + 0.649271I
a = 0.295283 + 0.532839I
b = 1.04208 − 1.07030I
−6.04626 − 5.25640I 1.97588 + 3.31648I
u = −0.286837 + 0.649271I
a = −1.50512 − 0.37840I
b = −0.359246 − 0.589546I
−6.04626 − 5.25640I 1.97588 + 3.31648I
u = −0.286837 − 0.649271I
a = 0.295283 − 0.532839I
b = 1.04208 + 1.07030I
−6.04626 + 5.25640I 1.97588 − 3.31648I
u = −0.286837 − 0.649271I
a = −1.50512 + 0.37840I
b = −0.359246 + 0.589546I
−6.04626 + 5.25640I 1.97588 − 3.31648I
u = 1.114990 + 0.698316I
a = 0.37056 + 1.55826I
b = −1.13634 + 1.02615I
−0.88041 − 13.81330I 0
u = 1.114990 + 0.698316I
a = −0.72776 − 1.81101I
b = 0.89886 − 1.28492I
−0.88041 − 13.81330I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.114990 − 0.698316I
a = 0.37056 − 1.55826I
b = −1.13634 − 1.02615I
−0.88041 + 13.81330I 0
u = 1.114990 − 0.698316I
a = −0.72776 + 1.81101I
b = 0.89886 + 1.28492I
−0.88041 + 13.81330I 0
u = 1.086420 + 0.756342I
a = 0.579196 + 1.067940I
b = −0.376750 + 1.016600I
−0.95201 − 3.84201I 0
u = 1.086420 + 0.756342I
a = −0.301202 − 0.504293I
b = 0.493323 − 0.518369I
−0.95201 − 3.84201I 0
u = 1.086420 − 0.756342I
a = 0.579196 − 1.067940I
b = −0.376750 − 1.016600I
−0.95201 + 3.84201I 0
u = 1.086420 − 0.756342I
a = −0.301202 + 0.504293I
b = 0.493323 + 0.518369I
−0.95201 + 3.84201I 0
u = −1.217200 + 0.650248I
a = 0.157075 + 0.700499I
b = 0.829327 + 0.210290I
−3.12919 + 6.08910I 0
u = −1.217200 + 0.650248I
a = −0.49683 + 1.75097I
b = 0.460943 + 1.134740I
−3.12919 + 6.08910I 0
u = −1.217200 − 0.650248I
a = 0.157075 − 0.700499I
b = 0.829327 − 0.210290I
−3.12919 − 6.08910I 0
u = −1.217200 − 0.650248I
a = −0.49683 − 1.75097I
b = 0.460943 − 1.134740I
−3.12919 − 6.08910I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.510512
a = 1.59024 + 0.68134I
b = −0.529767 + 0.296649I
0.958787 4.02350
u = −0.510512
a = 1.59024 − 0.68134I
b = −0.529767 − 0.296649I
0.958787 4.02350
u = 0.488326 + 0.120056I
a = 0.583472 + 0.975215I
b = 0.897245 − 0.451317I
−1.99592 − 2.63154I 0.54415 + 5.66267I
u = 0.488326 + 0.120056I
a = 2.16069 − 1.51977I
b = 0.317808 + 0.436683I
−1.99592 − 2.63154I 0.54415 + 5.66267I
u = 0.488326 − 0.120056I
a = 0.583472 − 0.975215I
b = 0.897245 + 0.451317I
−1.99592 + 2.63154I 0.54415 − 5.66267I
u = 0.488326 − 0.120056I
a = 2.16069 + 1.51977I
b = 0.317808 − 0.436683I
−1.99592 + 2.63154I 0.54415 − 5.66267I
23
III. I
u
3
=
h−2u
15
−2u
14
+· · ·+b +1, 2u
15
+5u
14
+· · ·+a +3u, u
16
+3u
15
+· · ·+2u +1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−2u
15
− 5u
14
+ ··· + 2u
2
− 3u
2u
15
+ 2u
14
+ ··· + 3u − 1
a
8
=
3u
15
+ 9u
14
+ ··· + 3u + 6
−3u
15
− 6u
14
+ ··· − 4u − 3
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−u
15
− 5u
14
+ ··· − 4u − 5
2u
15
+ 6u
14
+ ··· + 2u + 3
a
10
=
−4u
15
− 7u
14
+ ··· − 6u + 1
2u
15
+ 2u
14
+ ··· + 3u − 1
a
4
=
−4u
15
− 10u
14
+ ··· − 6u − 4
2u
15
+ 5u
14
+ ··· + 5u + 2
a
9
=
−3u
15
− 5u
14
+ ··· − 5u + 1
−u
14
− 2u
13
+ ··· + u − 1
a
12
=
4u
15
+ 10u
14
+ ··· + 8u + 6
−u
14
− u
13
+ ··· − u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −27u
15
− 63u
14
− 3u
13
+ 156u
12
+ 138u
11
− 137u
10
− 295u
9
+
18u
8
+ 356u
7
+ 155u
6
− 269u
5
− 194u
4
+ 79u
3
+ 83u
2
− 41u − 27
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 5u
15
+ ··· − 6u + 1
c
2
u
16
− 3u
15
+ ··· − 2u + 1
c
3
, c
10
u
16
− 4u
14
+ ··· − 2u + 1
c
4
, c
8
u
16
− u
15
+ ··· − 2u + 1
c
5
, c
12
u
16
+ u
15
+ ··· + 2u + 1
c
6
u
16
+ 3u
15
+ ··· + 2u + 1
c
7
, c
9
u
16
+ 3u
15
+ ··· + 3u + 1
c
11
u
16
− 12u
15
+ ··· − 121u + 7
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 7y
15
+ ··· + 14y + 1
c
2
, c
6
y
16
− 5y
15
+ ··· − 6y + 1
c
3
, c
10
y
16
− 8y
15
+ ··· + 8y + 1
c
4
, c
5
, c
8
c
12
y
16
+ 13y
15
+ ··· + 14y + 1
c
7
, c
9
y
16
+ y
15
+ ··· + 7y + 1
c
11
y
16
+ 16y
15
+ ··· − 2503y + 49
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.715082 + 0.617273I
a = −0.362225 + 1.332290I
b = 1.71319 − 0.54908I
−3.92884 − 5.06693I 1.20890 + 4.91911I
u = −0.715082 − 0.617273I
a = −0.362225 − 1.332290I
b = 1.71319 + 0.54908I
−3.92884 + 5.06693I 1.20890 − 4.91911I
u = 0.855903 + 0.626934I
a = −0.70077 − 1.38032I
b = −0.196869 − 1.141810I
3.07518 − 2.45620I −3.86955 + 1.80652I
u = 0.855903 − 0.626934I
a = −0.70077 + 1.38032I
b = −0.196869 + 1.141810I
3.07518 + 2.45620I −3.86955 − 1.80652I
u = 1.109480 + 0.168280I
a = −1.07174 − 1.20629I
b = −0.698575 − 0.903116I
−7.46004 + 3.98076I −3.29932 − 4.31107I
u = 1.109480 − 0.168280I
a = −1.07174 + 1.20629I
b = −0.698575 + 0.903116I
−7.46004 − 3.98076I −3.29932 + 4.31107I
u = −0.978068 + 0.620121I
a = 0.72302 − 2.13025I
b = −1.67983 − 0.94245I
−4.76909 + 9.96079I −0.29431 − 10.52022I
u = −0.978068 − 0.620121I
a = 0.72302 + 2.13025I
b = −1.67983 + 0.94245I
−4.76909 − 9.96079I −0.29431 + 10.52022I
u = −0.489195 + 1.118250I
a = −0.0231065 + 0.1339790I
b = −0.082079 + 0.398889I
0.51588 + 2.41846I −18.3848 + 14.8561I
u = −0.489195 − 1.118250I
a = −0.0231065 − 0.1339790I
b = −0.082079 − 0.398889I
0.51588 − 2.41846I −18.3848 − 14.8561I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.664062 + 0.290359I
a = 1.342520 − 0.070390I
b = −0.573558 − 0.232331I
1.068270 + 0.616833I 6.43518 − 10.65020I
u = −0.664062 − 0.290359I
a = 1.342520 + 0.070390I
b = −0.573558 + 0.232331I
1.068270 − 0.616833I 6.43518 + 10.65020I
u = −1.126390 + 0.656058I
a = −0.447640 + 0.880451I
b = 0.433909 + 0.661466I
−1.78072 + 3.65403I −0.38431 − 6.17410I
u = −1.126390 − 0.656058I
a = −0.447640 − 0.880451I
b = 0.433909 − 0.661466I
−1.78072 − 3.65403I −0.38431 + 6.17410I
u = 0.507419 + 0.431087I
a = 1.53994 − 1.09401I
b = 1.083820 − 0.150288I
−4.81491 − 6.68255I 4.08817 + 7.62933I
u = 0.507419 − 0.431087I
a = 1.53994 + 1.09401I
b = 1.083820 + 0.150288I
−4.81491 + 6.68255I 4.08817 − 7.62933I
28
IV. I
u
4
= h−u
6
a − 9u
6
+ · · · + 3a + 6, −u
6
a − 3u
5
+ · · · + 2a + 1, u
7
− u
6
−
u
5
+ u
4
+ 2u
3
− u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
a
1
7
u
6
a +
9
7
u
6
+ ··· −
3
7
a −
6
7
a
8
=
2
7
u
6
a +
11
7
u
6
+ ··· −
6
7
a +
2
7
4
7
u
6
a −
6
7
u
6
+ ··· −
5
7
a +
4
7
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
5
7
u
6
a −
18
7
u
6
+ ··· −
8
7
a +
19
7
−
4
7
u
6
a −
8
7
u
6
+ ··· +
5
7
a −
4
7
a
10
=
−
1
7
u
6
a −
9
7
u
6
+ ··· +
10
7
a +
6
7
1
7
u
6
a +
9
7
u
6
+ ··· −
3
7
a −
6
7
a
4
=
9
7
u
6
a +
4
7
u
6
+ ··· −
6
7
a +
16
7
−u
5
+ u
4
− u
a
9
=
u
5
a − 2u
6
+ u
5
− u
3
a + 2u
4
+ au − 3u
2
+ a + 1
6
7
u
6
a +
5
7
u
6
+ ··· −
4
7
a −
1
7
a
12
=
−u
6
a + 2u
4
a − 3u
2
a + u
3
− au + 2a − 1
3
7
u
6
a +
6
7
u
6
+ ··· −
2
7
a +
3
7
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
6
+ 6u
5
− u
3
− 5u
2
+ u + 5
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
− 3u
6
+ 7u
5
− 9u
4
+ 10u
3
− 7u
2
+ 3u − 1)
2
c
2
(u
7
+ u
6
− u
5
− u
4
+ 2u
3
+ u
2
− u − 1)
2
c
3
, c
10
u
14
+ 2u
12
+ ··· + 8u + 1
c
4
, c
8
u
14
+ 6u
12
+ ··· − 8u + 1
c
5
, c
12
u
14
+ 6u
12
+ ··· + 8u + 1
c
6
(u
7
− u
6
− u
5
+ u
4
+ 2u
3
− u
2
− u + 1)
2
c
7
, c
9
u
14
− 6u
13
+ ··· + 2u + 1
c
11
(u
7
− u
6
+ u
5
− u
3
+ u
2
− u + 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 5y
6
+ 15y
5
+ 23y
4
+ 10y
3
− 7y
2
− 5y −1)
2
c
2
, c
6
(y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 7y
2
+ 3y −1)
2
c
3
, c
10
y
14
+ 4y
13
+ ··· − 20y + 1
c
4
, c
5
, c
8
c
12
y
14
+ 12y
13
+ ··· − 22y + 1
c
7
, c
9
y
14
− 6y
13
+ ··· − 2y + 1
c
11
(y
7
+ y
6
− y
5
− 2y
4
+ y
3
+ y
2
− y −1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.793128 + 0.750889I
a = −1.041400 + 0.521858I
b = −0.374224 + 1.276980I
−0.14750 + 2.89342I 11.30111 − 4.94456I
u = −0.793128 + 0.750889I
a = 0.202445 − 0.608018I
b = 0.245978 + 0.103384I
−0.14750 + 2.89342I 11.30111 − 4.94456I
u = −0.793128 − 0.750889I
a = −1.041400 − 0.521858I
b = −0.374224 − 1.276980I
−0.14750 − 2.89342I 11.30111 + 4.94456I
u = −0.793128 − 0.750889I
a = 0.202445 + 0.608018I
b = 0.245978 − 0.103384I
−0.14750 − 2.89342I 11.30111 + 4.94456I
u = −0.879508
a = −1.08614 + 2.37333I
b = 0.12875 + 1.47876I
−9.61603 −3.61290
u = −0.879508
a = −1.08614 − 2.37333I
b = 0.12875 − 1.47876I
−9.61603 −3.61290
u = 0.610619 + 0.459179I
a = −1.084060 + 0.541554I
b = 0.815763 + 0.636072I
−1.51174 + 1.30245I 3.84837 − 2.49326I
u = 0.610619 + 0.459179I
a = 1.21917 + 1.56352I
b = −1.251260 + 0.609775I
−1.51174 + 1.30245I 3.84837 − 2.49326I
u = 0.610619 − 0.459179I
a = −1.084060 − 0.541554I
b = 0.815763 − 0.636072I
−1.51174 − 1.30245I 3.84837 + 2.49326I
u = 0.610619 − 0.459179I
a = 1.21917 − 1.56352I
b = −1.251260 − 0.609775I
−1.51174 − 1.30245I 3.84837 + 2.49326I
32
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.122260 + 0.611121I
a = 0.157373 − 0.805766I
b = 1.032020 − 0.131730I
−3.40236 − 5.75449I −1.84300 + 2.06964I
u = 1.122260 + 0.611121I
a = 0.63262 + 1.93130I
b = −0.597022 + 1.117100I
−3.40236 − 5.75449I −1.84300 + 2.06964I
u = 1.122260 − 0.611121I
a = 0.157373 + 0.805766I
b = 1.032020 + 0.131730I
−3.40236 + 5.75449I −1.84300 − 2.06964I
u = 1.122260 − 0.611121I
a = 0.63262 − 1.93130I
b = −0.597022 − 1.117100I
−3.40236 + 5.75449I −1.84300 − 2.06964I
33
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
7
− 3u
6
+ 7u
5
− 9u
4
+ 10u
3
− 7u
2
+ 3u − 1)
2
· (u
16
− 5u
15
+ ··· − 6u + 1)(u
41
+ 14u
40
+ ··· + 1308u + 144)
· (u
53
+ 21u
52
+ ··· + 187u + 9)
2
c
2
((u
7
+ u
6
+ ··· − u − 1)
2
)(u
16
− 3u
15
+ ··· − 2u + 1)
· (u
41
− 8u
40
+ ··· + 102u − 12)(u
53
+ 3u
52
+ ··· − 7u − 3)
2
c
3
, c
10
(u
14
+ 2u
12
+ ··· + 8u + 1)(u
16
− 4u
14
+ ··· − 2u + 1)
· (u
41
+ 12u
39
+ ··· + 13u − 7)(u
106
+ u
105
+ ··· − 102u + 283)
c
4
, c
8
(u
14
+ 6u
12
+ ··· − 8u + 1)(u
16
− u
15
+ ··· − 2u + 1)
· (u
41
+ u
40
+ ··· + 5u − 1)(u
106
+ 5u
105
+ ··· − 34u + 1)
c
5
, c
12
(u
14
+ 6u
12
+ ··· + 8u + 1)(u
16
+ u
15
+ ··· + 2u + 1)
· (u
41
+ u
40
+ ··· + 5u − 1)(u
106
+ 5u
105
+ ··· − 34u + 1)
c
6
((u
7
− u
6
+ ··· − u + 1)
2
)(u
16
+ 3u
15
+ ··· + 2u + 1)
· (u
41
− 8u
40
+ ··· + 102u − 12)(u
53
+ 3u
52
+ ··· − 7u − 3)
2
c
7
, c
9
(u
14
− 6u
13
+ ··· + 2u + 1)(u
16
+ 3u
15
+ ··· + 3u + 1)
· (u
41
+ 3u
40
+ ··· − 10u − 1)(u
106
+ u
105
+ ··· + 38u + 1)
c
11
((u
7
− u
6
+ u
5
− u
3
+ u
2
− u + 1)
2
)(u
16
− 12u
15
+ ··· − 121u + 7)
· (u
41
+ 29u
40
+ ··· − 31212u − 2196)
· (u
53
− 19u
52
+ ··· + 603u − 55)
2
34
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 5y
6
+ 15y
5
+ 23y
4
+ 10y
3
− 7y
2
− 5y −1)
2
· (y
16
+ 7y
15
+ ··· + 14y + 1)(y
41
+ 18y
40
+ ··· + 259056y −20736)
· (y
53
+ 27y
52
+ ··· + 1651y −81)
2
c
2
, c
6
(y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 7y
2
+ 3y −1)
2
· (y
16
− 5y
15
+ ··· − 6y + 1)(y
41
− 14y
40
+ ··· + 1308y −144)
· (y
53
− 21y
52
+ ··· + 187y −9)
2
c
3
, c
10
(y
14
+ 4y
13
+ ··· − 20y + 1)(y
16
− 8y
15
+ ··· + 8y + 1)
· (y
41
+ 24y
40
+ ··· − 2197y −49)
· (y
106
− 9y
105
+ ··· + 484280y + 80089)
c
4
, c
5
, c
8
c
12
(y
14
+ 12y
13
+ ··· − 22y + 1)(y
16
+ 13y
15
+ ··· + 14y + 1)
· (y
41
+ 41y
40
+ ··· + 13y −1)(y
106
+ 75y
105
+ ··· − 698y + 1)
c
7
, c
9
(y
14
− 6y
13
+ ··· − 2y + 1)(y
16
+ y
15
+ ··· + 7y + 1)
· (y
41
− 3y
40
+ ··· − 44y −1)(y
106
− 3y
105
+ ··· − 230y + 1)
c
11
(y
7
+ y
6
− y
5
− 2y
4
+ y
3
+ y
2
− y −1)
2
· (y
16
+ 16y
15
+ ··· − 2503y + 49)
· (y
41
− y
40
+ ··· + 18265752y −4822416)
· (y
53
+ 27y
52
+ ··· − 30081y −3025)
2
35
