12n
0315
(K12n
0315
)
A knot diagram
1
Linearized knot diagam
3 6 11 10 2 4 3 12 6 7 8 9
Solving Sequence
4,11 3,7
8 12 6 2 1 5 10 9
c
3
c
7
c
11
c
6
c
2
c
1
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.20606 × 10
53
u
43
− 5.58942 × 10
53
u
42
+ ··· + 5.03135 × 10
53
b + 2.95975 × 10
54
,
− 3.18519 × 10
53
u
43
− 8.78761 × 10
54
u
42
+ ··· + 1.45909 × 10
55
a + 5.45810 × 10
56
,
u
44
− 5u
43
+ ··· + 42u − 29i
I
u
2
= h−u
9
+ u
8
− u
7
+ u
4
+ 2u
3
− u
2
+ b + u, 3u
8
− 3u
7
+ 5u
6
− 2u
5
+ u
4
− 2u
3
− 7u
2
+ a + u − 6,
u
10
− u
9
+ 2u
8
− u
7
+ u
6
− u
5
− 2u
4
− 3u
2
− 1i
I
u
3
= hu
2
+ b + u, a, u
4
+ u
3
+ u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 58 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
= h1.21 × 10
53
u
43
− 5.59 × 10
53
u
42
+ · · · + 5.03 × 10
53
b + 2.96 ×
10
54
, −3.19 × 10
53
u
43
− 8.79 × 10
54
u
42
+ · · · + 1.46 × 10
55
a + 5.46 ×
10
56
, u
44
− 5u
43
+ · · · + 42u − 29i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
3
=
1
−u
2
a
7
=
0.0218300u
43
+ 0.602265u
42
+ ··· + 35.6982u − 37.4075
−0.239709u
43
+ 1.11092u
42
+ ··· + 27.7492u − 5.88261
a
8
=
0.116480u
43
− 0.214561u
42
+ ··· + 34.2011u − 22.6591
0.196318u
43
− 1.07204u
42
+ ··· + 10.5743u + 4.08103
a
12
=
−0.264193u
43
+ 0.881362u
42
+ ··· − 44.3354u + 34.0722
0.396645u
43
− 2.17462u
42
+ ··· − 57.8387u + 23.3029
a
6
=
−0.217879u
43
+ 1.71318u
42
+ ··· + 63.4475u − 43.2901
−0.239709u
43
+ 1.11092u
42
+ ··· + 27.7492u − 5.88261
a
2
=
0.00263508u
43
− 0.985931u
42
+ ··· − 67.9139u + 53.2351
0.161780u
43
− 1.07286u
42
+ ··· − 34.3822u + 20.2044
a
1
=
−0.00400046u
43
− 0.634908u
42
+ ··· − 61.3639u + 45.2296
−0.0666468u
43
+ 0.211695u
42
+ ··· − 20.8403u + 10.9869
a
5
=
−0.136976u
43
− 1.16465u
42
+ ··· − 39.2384u + 65.9737
−0.0834339u
43
+ 0.546656u
42
+ ··· + 17.1001u − 4.86412
a
10
=
−1.27373u
43
+ 6.20997u
42
+ ··· + 44.8550u + 10.4545
−0.337820u
43
+ 1.39778u
42
+ ··· − 9.87916u + 17.6646
a
9
=
0.157901u
43
− 1.21230u
42
+ ··· − 74.0140u + 41.4809
0.325629u
43
− 1.96751u
42
+ ··· − 60.8611u + 31.4254
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.287876u
43
− 2.76272u
42
+ ··· − 100.619u + 56.2787
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 61u
43
+ ··· + 654834u + 3025
c
2
, c
5
u
44
+ u
43
+ ··· + 592u + 55
c
3
u
44
+ 5u
43
+ ··· − 42u − 29
c
4
u
44
+ 2u
43
+ ··· + 583u − 121
c
6
u
44
− 6u
43
+ ··· + 10u − 1
c
7
u
44
− u
43
+ ··· + 295u + 229
c
8
, c
11
, c
12
u
44
− u
43
+ ··· − 113u − 11
c
9
u
44
+ 52u
42
+ ··· − 10437016u − 496609
c
10
u
44
+ 6u
43
+ ··· + 248u + 80
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
− 157y
43
+ ··· − 380470856606y + 9150625
c
2
, c
5
y
44
− 61y
43
+ ··· − 654834y + 3025
c
3
y
44
+ 13y
43
+ ··· + 12678y + 841
c
4
y
44
+ 52y
43
+ ··· − 193721y + 14641
c
6
y
44
+ 4y
43
+ ··· − 18y + 1
c
7
y
44
− y
43
+ ··· − 491439y + 52441
c
8
, c
11
, c
12
y
44
− 33y
43
+ ··· − 24187y + 121
c
9
y
44
+ 104y
43
+ ··· − 91222464416576y + 246620498881
c
10
y
44
− 12y
43
+ ··· − 113984y + 6400
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.646694 + 0.709710I
a = −1.44530 − 0.26000I
b = 0.754661 − 1.033090I
−0.73884 + 3.57823I −2.03363 − 1.23509I
u = −0.646694 − 0.709710I
a = −1.44530 + 0.26000I
b = 0.754661 + 1.033090I
−0.73884 − 3.57823I −2.03363 + 1.23509I
u = 0.560756 + 0.906193I
a = 0.988565 − 0.382204I
b = −0.479339 − 0.355674I
−0.07583 − 2.23571I 0.15264 + 3.25000I
u = 0.560756 − 0.906193I
a = 0.988565 + 0.382204I
b = −0.479339 + 0.355674I
−0.07583 + 2.23571I 0.15264 − 3.25000I
u = −0.931877
a = 0.852980
b = −0.358962
1.95891 7.69720
u = −0.134801 + 1.060870I
a = 0.326691 − 0.405578I
b = −0.036301 − 1.377150I
8.47609 + 2.02964I 8.25034 − 3.54308I
u = −0.134801 − 1.060870I
a = 0.326691 + 0.405578I
b = −0.036301 + 1.377150I
8.47609 − 2.02964I 8.25034 + 3.54308I
u = 0.494156 + 0.966731I
a = −0.87020 + 1.18836I
b = 0.641372 + 0.824984I
0.09327 − 2.72034I 1.39183 + 2.41510I
u = 0.494156 − 0.966731I
a = −0.87020 − 1.18836I
b = 0.641372 − 0.824984I
0.09327 + 2.72034I 1.39183 − 2.41510I
u = 0.229114 + 0.882547I
a = 2.27817 + 0.13416I
b = −1.118850 − 0.022452I
−4.56670 + 1.09587I −0.21127 + 1.60051I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.229114 − 0.882547I
a = 2.27817 − 0.13416I
b = −1.118850 + 0.022452I
−4.56670 − 1.09587I −0.21127 − 1.60051I
u = 0.715929 + 0.820156I
a = 1.31822 − 0.95604I
b = −0.82920 − 1.28038I
−7.86621 − 0.05476I −0.99221 + 1.86582I
u = 0.715929 − 0.820156I
a = 1.31822 + 0.95604I
b = −0.82920 + 1.28038I
−7.86621 + 0.05476I −0.99221 − 1.86582I
u = 0.499429 + 0.740618I
a = −1.013390 + 0.171593I
b = 1.145160 − 0.547724I
−0.68618 − 1.34446I 1.50024 + 5.16811I
u = 0.499429 − 0.740618I
a = −1.013390 − 0.171593I
b = 1.145160 + 0.547724I
−0.68618 + 1.34446I 1.50024 − 5.16811I
u = 0.689773 + 0.925188I
a = 0.426003 − 0.482177I
b = −1.30573 + 1.09475I
−7.53216 − 5.34120I −0.67544 + 3.86207I
u = 0.689773 − 0.925188I
a = 0.426003 + 0.482177I
b = −1.30573 − 1.09475I
−7.53216 + 5.34120I −0.67544 − 3.86207I
u = 0.148274 + 0.828216I
a = −2.47783 − 1.74623I
b = −0.277976 + 0.017995I
−4.75567 − 2.81209I 2.57862 + 7.29704I
u = 0.148274 − 0.828216I
a = −2.47783 + 1.74623I
b = −0.277976 − 0.017995I
−4.75567 + 2.81209I 2.57862 − 7.29704I
u = −0.973154 + 0.747396I
a = 0.544042 + 0.618644I
b = −1.19354 − 0.90568I
−12.93820 − 0.76342I −3.80369 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.973154 − 0.747396I
a = 0.544042 − 0.618644I
b = −1.19354 + 0.90568I
−12.93820 + 0.76342I −3.80369 + 0.I
u = −0.519846 + 1.144310I
a = −1.36543 − 0.79561I
b = 0.887391 − 0.816016I
0.76786 + 6.70478I 0. − 7.25034I
u = −0.519846 − 1.144310I
a = −1.36543 + 0.79561I
b = 0.887391 + 0.816016I
0.76786 − 6.70478I 0. + 7.25034I
u = −0.676167 + 0.306109I
a = −1.147500 − 0.672697I
b = 0.803888 + 0.651455I
−1.75012 − 2.06472I −2.87061 + 3.92303I
u = −0.676167 − 0.306109I
a = −1.147500 + 0.672697I
b = 0.803888 − 0.651455I
−1.75012 + 2.06472I −2.87061 − 3.92303I
u = 1.191210 + 0.490115I
a = 0.654463 − 0.667822I
b = −1.082710 + 0.775736I
−9.49734 + 7.11306I 0
u = 1.191210 − 0.490115I
a = 0.654463 + 0.667822I
b = −1.082710 − 0.775736I
−9.49734 − 7.11306I 0
u = −0.605021 + 1.146520I
a = 1.059940 + 0.253544I
b = −0.731247 + 0.441154I
4.82729 + 5.41905I 0
u = −0.605021 − 1.146520I
a = 1.059940 − 0.253544I
b = −0.731247 − 0.441154I
4.82729 − 5.41905I 0
u = −0.103748 + 0.684443I
a = 1.224370 + 0.560955I
b = −0.043528 + 0.580499I
1.21862 − 0.91087I 6.00533 + 4.55629I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.103748 − 0.684443I
a = 1.224370 − 0.560955I
b = −0.043528 − 0.580499I
1.21862 + 0.91087I 6.00533 − 4.55629I
u = 0.679096
a = −0.424824
b = 0.727825
−1.43381 −8.35220
u = −0.806563 + 1.049120I
a = 1.29333 + 0.62058I
b = −1.01794 + 1.20383I
−11.95870 + 7.26271I 0
u = −0.806563 − 1.049120I
a = 1.29333 − 0.62058I
b = −1.01794 − 1.20383I
−11.95870 − 7.26271I 0
u = −0.042706 + 0.623007I
a = −0.75781 + 1.69326I
b = 0.35910 + 1.52836I
6.53095 − 1.24141I 1.101277 + 0.846650I
u = −0.042706 − 0.623007I
a = −0.75781 − 1.69326I
b = 0.35910 − 1.52836I
6.53095 + 1.24141I 1.101277 − 0.846650I
u = 0.827601 + 1.122030I
a = −1.017800 + 0.089758I
b = 0.781744 + 1.041420I
0.99079 − 7.76049I 0
u = 0.827601 − 1.122030I
a = −1.017800 − 0.089758I
b = 0.781744 − 1.041420I
0.99079 + 7.76049I 0
u = −0.69348 + 1.23762I
a = −0.128890 − 0.232242I
b = 0.593220 + 0.522980I
0.81092 + 1.60255I 0
u = −0.69348 − 1.23762I
a = −0.128890 + 0.232242I
b = 0.593220 − 0.522980I
0.81092 − 1.60255I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.76866 + 1.22958I
a = 1.209600 − 0.452753I
b = −1.12581 − 1.15829I
−7.1426 − 14.0288I 0
u = 0.76866 − 1.22958I
a = 1.209600 + 0.452753I
b = −1.12581 + 1.15829I
−7.1426 + 14.0288I 0
u = 1.70367 + 1.24530I
a = 0.0487407 + 0.1311720I
b = 0.091200 − 0.327127I
−0.527893 + 0.187966I 0
u = 1.70367 − 1.24530I
a = 0.0487407 − 0.1311720I
b = 0.091200 + 0.327127I
−0.527893 − 0.187966I 0
9
II. I
u
2
= h−u
9
+ u
8
− u
7
+ u
4
+ 2u
3
− u
2
+ b + u, 3u
8
− 3u
7
+ · · · + a −
6, u
10
− u
9
+ 2u
8
− u
7
+ u
6
− u
5
− 2u
4
− 3u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
3
=
1
−u
2
a
7
=
−3u
8
+ 3u
7
− 5u
6
+ 2u
5
− u
4
+ 2u
3
+ 7u
2
− u + 6
u
9
− u
8
+ u
7
− u
4
− 2u
3
+ u
2
− u
a
8
=
u
9
− 3u
8
+ 3u
7
− 3u
6
+ u
5
− u
4
− u
3
+ 5u
2
− 2u + 3
2u
9
− 2u
8
+ 2u
7
− u
4
− 4u
3
+ u
2
− 2u − 1
a
12
=
u
7
− u
6
+ u
5
− u
2
− 2u + 1
u
9
+ u
7
+ u
6
− 3u
3
− 3u
2
− 3u − 3
a
6
=
u
9
− 4u
8
+ 4u
7
− 5u
6
+ 2u
5
− 2u
4
+ 8u
2
− 2u + 6
u
9
− u
8
+ u
7
− u
4
− 2u
3
+ u
2
− u
a
2
=
2u
9
− 8u
8
+ 9u
7
− 10u
6
+ 4u
5
− 3u
4
+ 14u
2
− 6u + 11
u
9
− u
8
+ u
7
− u
4
− 2u
3
− u − 1
a
1
=
2u
9
− 5u
8
+ 6u
7
− 5u
6
+ 2u
5
− 2u
4
− 2u
3
+ 7u
2
− 5u + 4
u
9
+ 2u
6
− u
5
− 3u
3
− 2u
2
− u − 4
a
5
=
−5u
9
+ 13u
8
− 17u
7
+ 15u
6
− 6u
5
+ 5u
4
+ 5u
3
− 17u
2
+ 16u − 13
−u
8
+ u
7
− 2u
6
+ u
5
− u
4
+ u
3
+ 2u
2
+ 3
a
10
=
−8u
9
+ 7u
8
− 10u
7
+ u
6
+ 5u
4
+ 17u
3
− u
2
+ 14u + 5
u
9
− u
8
+ 2u
7
− u
6
+ u
5
− u
4
− 2u
3
− 3u
a
9
=
2u
9
+ 2u
7
+ u
6
− u
4
− 6u
3
− 4u
2
− 5u − 3
−u
9
+ 3u
8
− 3u
7
+ 3u
6
− u
5
+ u
4
+ u
3
− 5u
2
+ 2u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
9
− u
8
+ u
7
+ 3u
6
− 2u
5
− 5u
4
− 11u
3
− 2u
2
− 4u − 3
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 10u
9
+ 37u
8
− 58u
7
+ 70u
6
− 51u
5
+ 29u
4
− 27u
3
+ 4u
2
− u + 1
c
2
u
10
+ 6u
9
+ 13u
8
+ 10u
7
− 6u
6
− 19u
5
− 15u
4
− 3u
3
+ 4u
2
+ 3u + 1
c
3
u
10
− u
9
+ 2u
8
− u
7
+ u
6
− u
5
− 2u
4
− 3u
2
− 1
c
4
u
10
+ 3u
8
+ 2u
6
+ u
5
− u
4
+ u
3
− 2u
2
+ u − 1
c
5
u
10
− 6u
9
+ 13u
8
− 10u
7
− 6u
6
+ 19u
5
− 15u
4
+ 3u
3
+ 4u
2
− 3u + 1
c
6
u
10
+ 3u
9
+ 6u
8
+ 7u
7
+ 4u
6
− 3u
5
− 6u
4
− 2u
3
+ 4u
2
+ 4u + 1
c
7
u
10
− 7u
8
− 12u
7
+ 16u
6
+ 40u
5
+ 27u
4
− u
3
+ u − 1
c
8
u
10
− 6u
8
+ 2u
7
+ 13u
6
− 8u
5
− 11u
4
+ 9u
3
+ 2u
2
− 2u + 1
c
9
u
10
+ u
9
+ 15u
8
+ 37u
6
+ 16u
4
− 9u
3
− 8u
2
− u + 1
c
10
u
10
− u
9
+ 2u
8
− 11u
7
+ 16u
6
+ 6u
5
− 17u
4
− 51u
3
+ 104u
2
− 53u + 5
c
11
, c
12
u
10
− 6u
8
− 2u
7
+ 13u
6
+ 8u
5
− 11u
4
− 9u
3
+ 2u
2
+ 2u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
− 26y
9
+ ··· + 7y + 1
c
2
, c
5
y
10
− 10y
9
+ 37y
8
− 58y
7
+ 70y
6
− 51y
5
+ 29y
4
− 27y
3
+ 4y
2
− y + 1
c
3
y
10
+ 3y
9
+ 4y
8
− 3y
7
− 15y
6
− 19y
5
− 6y
4
+ 10y
3
+ 13y
2
+ 6y + 1
c
4
y
10
+ 6y
9
+ 13y
8
+ 10y
7
− 6y
6
− 19y
5
− 15y
4
− 3y
3
+ 4y
2
+ 3y + 1
c
6
y
10
+ 3y
9
+ 2y
8
+ 5y
7
+ 6y
6
− 3y
5
+ 12y
4
− 20y
3
+ 20y
2
− 8y + 1
c
7
y
10
− 14y
9
+ ··· − y + 1
c
8
, c
11
, c
12
y
10
− 12y
9
+ ··· + 18y
2
+ 1
c
9
y
10
+ 29y
9
+ ··· − 17y + 1
c
10
y
10
+ 3y
9
+ ··· − 1769y + 25
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.970948
a = 0.125163
b = 0.485263
−0.629142 4.19170
u = 0.275604 + 0.891818I
a = −0.521340 + 1.227210I
b = 0.12415 + 1.53429I
6.96867 − 2.45082I 2.80943 + 5.14150I
u = 0.275604 − 0.891818I
a = −0.521340 − 1.227210I
b = 0.12415 − 1.53429I
6.96867 + 2.45082I 2.80943 − 5.14150I
u = −0.488238 + 0.958609I
a = −1.23025 − 0.71023I
b = 0.673452 − 0.956870I
0.20069 + 4.40188I 3.38083 − 6.40382I
u = −0.488238 − 0.958609I
a = −1.23025 + 0.71023I
b = 0.673452 + 0.956870I
0.20069 − 4.40188I 3.38083 + 6.40382I
u = 1.26392
a = −0.608152
b = 0.615015
1.41391 −8.87500
u = 0.634722 + 1.144960I
a = −1.149300 + 0.305987I
b = 0.956654 + 0.685271I
4.21151 − 6.16726I 1.23716 + 7.09016I
u = 0.634722 − 1.144960I
a = −1.149300 − 0.305987I
b = 0.956654 − 0.685271I
4.21151 + 6.16726I 1.23716 − 7.09016I
u = −0.068575 + 0.683246I
a = 3.14239 − 1.75200I
b = −0.804393 − 0.314356I
−5.19351 + 2.25286I −4.08574 − 0.02786I
u = −0.068575 − 0.683246I
a = 3.14239 + 1.75200I
b = −0.804393 + 0.314356I
−5.19351 − 2.25286I −4.08574 + 0.02786I
13
III. I
u
3
= hu
2
+ b + u, a, u
4
+ u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
3
=
1
−u
2
a
7
=
0
−u
2
− u
a
8
=
−u
2
− u
−2u
2
− 2u − 1
a
12
=
−u
3
− 2u
2
− 2u − 1
−u
3
− 3u
2
− 3u − 2
a
6
=
−u
2
− u
−u
2
− u
a
2
=
u
2
+ u + 1
u
a
1
=
u
2
+ u
u
2
+ u
a
5
=
1
−u
2
a
10
=
0
u
a
9
=
u
3
+ 2u
2
+ 2u + 1
u
3
+ 2u
2
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
3
+ u + 1
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
4
u
4
+ u
3
+ u
2
+ u + 1
c
5
(u + 1)
4
c
6
, c
7
u
4
+ 2u
3
+ 4u
2
+ 3u + 1
c
8
(u
2
− u − 1)
2
c
9
, c
11
, c
12
(u
2
+ u − 1)
2
c
10
u
4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
y
4
+ y
3
+ y
2
+ y + 1
c
6
, c
7
y
4
+ 4y
3
+ 6y
2
− y + 1
c
8
, c
9
, c
11
c
12
(y
2
− 3y + 1)
2
c
10
y
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309017 + 0.951057I
a = 0
b = 0.50000 − 1.53884I
7.23771 2.92705 + 2.12663I
u = 0.309017 − 0.951057I
a = 0
b = 0.50000 + 1.53884I
7.23771 2.92705 − 2.12663I
u = −0.809017 + 0.587785I
a = 0
b = 0.500000 + 0.363271I
−0.657974 −0.427051 − 1.314328I
u = −0.809017 − 0.587785I
a = 0
b = 0.500000 − 0.363271I
−0.657974 −0.427051 + 1.314328I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
· (u
10
− 10u
9
+ 37u
8
− 58u
7
+ 70u
6
− 51u
5
+ 29u
4
− 27u
3
+ 4u
2
− u + 1)
· (u
44
+ 61u
43
+ ··· + 654834u + 3025)
c
2
(u − 1)
4
· (u
10
+ 6u
9
+ 13u
8
+ 10u
7
− 6u
6
− 19u
5
− 15u
4
− 3u
3
+ 4u
2
+ 3u + 1)
· (u
44
+ u
43
+ ··· + 592u + 55)
c
3
(u
4
+ u
3
+ u
2
+ u + 1)(u
10
− u
9
+ 2u
8
− u
7
+ u
6
− u
5
− 2u
4
− 3u
2
− 1)
· (u
44
+ 5u
43
+ ··· − 42u − 29)
c
4
(u
4
+ u
3
+ u
2
+ u + 1)(u
10
+ 3u
8
+ 2u
6
+ u
5
− u
4
+ u
3
− 2u
2
+ u − 1)
· (u
44
+ 2u
43
+ ··· + 583u − 121)
c
5
(u + 1)
4
· (u
10
− 6u
9
+ 13u
8
− 10u
7
− 6u
6
+ 19u
5
− 15u
4
+ 3u
3
+ 4u
2
− 3u + 1)
· (u
44
+ u
43
+ ··· + 592u + 55)
c
6
(u
4
+ 2u
3
+ 4u
2
+ 3u + 1)
· (u
10
+ 3u
9
+ 6u
8
+ 7u
7
+ 4u
6
− 3u
5
− 6u
4
− 2u
3
+ 4u
2
+ 4u + 1)
· (u
44
− 6u
43
+ ··· + 10u − 1)
c
7
(u
4
+ 2u
3
+ 4u
2
+ 3u + 1)
· (u
10
− 7u
8
− 12u
7
+ 16u
6
+ 40u
5
+ 27u
4
− u
3
+ u − 1)
· (u
44
− u
43
+ ··· + 295u + 229)
c
8
(u
2
− u − 1)
2
· (u
10
− 6u
8
+ 2u
7
+ 13u
6
− 8u
5
− 11u
4
+ 9u
3
+ 2u
2
− 2u + 1)
· (u
44
− u
43
+ ··· − 113u − 11)
c
9
(u
2
+ u − 1)
2
(u
10
+ u
9
+ 15u
8
+ 37u
6
+ 16u
4
− 9u
3
− 8u
2
− u + 1)
· (u
44
+ 52u
42
+ ··· − 10437016u − 496609)
c
10
u
4
· (u
10
− u
9
+ 2u
8
− 11u
7
+ 16u
6
+ 6u
5
− 17u
4
− 51u
3
+ 104u
2
− 53u + 5)
· (u
44
+ 6u
43
+ ··· + 248u + 80)
c
11
, c
12
(u
2
+ u − 1)
2
· (u
10
− 6u
8
− 2u
7
+ 13u
6
+ 8u
5
− 11u
4
− 9u
3
+ 2u
2
+ 2u + 1)
· (u
44
− u
43
+ ··· − 113u − 11)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
4
)(y
10
− 26y
9
+ ··· + 7y + 1)
· (y
44
− 157y
43
+ ··· − 380470856606y + 9150625)
c
2
, c
5
(y −1)
4
· (y
10
− 10y
9
+ 37y
8
− 58y
7
+ 70y
6
− 51y
5
+ 29y
4
− 27y
3
+ 4y
2
− y + 1)
· (y
44
− 61y
43
+ ··· − 654834y + 3025)
c
3
(y
4
+ y
3
+ y
2
+ y + 1)
· (y
10
+ 3y
9
+ 4y
8
− 3y
7
− 15y
6
− 19y
5
− 6y
4
+ 10y
3
+ 13y
2
+ 6y + 1)
· (y
44
+ 13y
43
+ ··· + 12678y + 841)
c
4
(y
4
+ y
3
+ y
2
+ y + 1)
· (y
10
+ 6y
9
+ 13y
8
+ 10y
7
− 6y
6
− 19y
5
− 15y
4
− 3y
3
+ 4y
2
+ 3y + 1)
· (y
44
+ 52y
43
+ ··· − 193721y + 14641)
c
6
(y
4
+ 4y
3
+ 6y
2
− y + 1)
· (y
10
+ 3y
9
+ 2y
8
+ 5y
7
+ 6y
6
− 3y
5
+ 12y
4
− 20y
3
+ 20y
2
− 8y + 1)
· (y
44
+ 4y
43
+ ··· − 18y + 1)
c
7
(y
4
+ 4y
3
+ 6y
2
− y + 1)(y
10
− 14y
9
+ ··· − y + 1)
· (y
44
− y
43
+ ··· − 491439y + 52441)
c
8
, c
11
, c
12
((y
2
− 3y + 1)
2
)(y
10
− 12y
9
+ ··· + 18y
2
+ 1)
· (y
44
− 33y
43
+ ··· − 24187y + 121)
c
9
((y
2
− 3y + 1)
2
)(y
10
+ 29y
9
+ ··· − 17y + 1)
· (y
44
+ 104y
43
+ ··· − 91222464416576y + 246620498881)
c
10
y
4
(y
10
+ 3y
9
+ ··· − 1769y + 25)
· (y
44
− 12y
43
+ ··· − 113984y + 6400)
19
