12n
0132
(K12n
0132
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 4 10 7 12 8 5 9
Solving Sequence
7,10
8
4,11
3 6 5 12 2 1 9
c
7
c
10
c
3
c
6
c
5
c
11
c
2
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.14796 × 10
52
u
43
+ 9.58738 × 10
52
u
42
+ ··· + 1.56185 × 10
54
b + 8.78201 × 10
53
,
− 4.29892 × 10
54
u
43
+ 3.28755 × 10
55
u
42
+ ··· + 1.56185 × 10
54
a + 7.83354 × 10
55
,
u
44
− 7u
43
+ ··· − 83u − 1i
I
u
2
= hb, 3u
8
− 5u
7
− u
6
+ 9u
5
− 6u
4
− 3u
3
+ 10u
2
+ a − 8u + 4, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
u
3
= h−u
2
a − 2u
2
+ b + 1, a
2
+ au + 2u
2
+ 2a − 2u + 3, u
3
− u
2
+ 1i
I
u
4
= h2b + a − 2, a
2
− 2a − 4, u + 1i
I
u
5
= hu
2
+ b, u
2
+ a − 2u + 1, u
3
− u
2
+ 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
= h−2.15 × 10
52
u
43
+ 9.59 × 10
52
u
42
+ · · · + 1.56 × 10
54
b + 8.78 ×
10
53
, −4.30 × 10
54
u
43
+ 3.29 × 10
55
u
42
+ · · · + 1.56 × 10
54
a + 7.83 ×
10
55
, u
44
− 7u
43
+ · · · − 83u − 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
4
=
2.75245u
43
− 21.0490u
42
+ ··· − 383.045u − 50.1555
0.0137527u
43
− 0.0613847u
42
+ ··· + 4.13777u − 0.562282
a
11
=
u
−u
3
+ u
a
3
=
2.76620u
43
− 21.1104u
42
+ ··· − 378.907u − 50.7178
0.0137527u
43
− 0.0613847u
42
+ ··· + 4.13777u − 0.562282
a
6
=
0.0964349u
43
− 0.375473u
42
+ ··· − 71.2040u − 27.7159
−0.0727656u
43
+ 0.491309u
42
+ ··· − 2.80714u − 0.409016
a
5
=
0.102399u
43
− 0.502049u
42
+ ··· − 78.0105u − 27.7938
−0.0451246u
43
+ 0.308080u
42
+ ··· − 2.57914u − 0.402041
a
12
=
−0.130388u
43
+ 0.959055u
42
+ ··· + 40.6420u + 9.41950
0.122234u
43
− 0.687069u
42
+ ··· + 11.8008u + 0.252623
a
2
=
2.64549u
43
− 20.3205u
42
+ ··· − 328.997u − 32.6224
−0.0451246u
43
+ 0.308080u
42
+ ··· − 2.57914u − 0.402041
a
1
=
0.124319u
43
− 0.935985u
42
+ ··· − 42.8904u − 9.55951
−0.174640u
43
+ 1.02487u
42
+ ··· − 12.6464u − 0.262253
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −49.8054u
43
+ 389.878u
42
+ ··· + 5096.96u + 52.1441
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
11
u
44
− 3u
43
+ ··· + 4096u − 512
c
7
, c
10
u
44
+ 7u
43
+ ··· + 83u − 1
c
8
u
44
− 33u
43
+ ··· − 6317u + 1
c
9
, c
12
u
44
+ 5u
43
+ ··· − 16u − 4
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
11
y
44
+ 49y
43
+ ··· − 15859712y + 262144
c
7
, c
10
y
44
− 33y
43
+ ··· − 6317y + 1
c
8
y
44
− 37y
43
+ ··· − 39734481y + 1
c
9
, c
12
y
44
− 3y
43
+ ··· − 1304y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.876497 + 0.429976I
a = −0.802254 − 0.743828I
b = 0.076755 − 1.159430I
3.87014 − 2.97279I 3.60919 + 6.63471I
u = −0.876497 − 0.429976I
a = −0.802254 + 0.743828I
b = 0.076755 + 1.159430I
3.87014 + 2.97279I 3.60919 − 6.63471I
u = −1.035690 + 0.011118I
a = 0.98809 − 3.01949I
b = −0.626019 − 0.060302I
0.651471 + 0.106624I −43.8474 − 14.3936I
u = −1.035690 − 0.011118I
a = 0.98809 + 3.01949I
b = −0.626019 + 0.060302I
0.651471 − 0.106624I −43.8474 + 14.3936I
u = 1.04545
a = −1.23357
b = 1.68917
−7.14674 39.2060
u = 0.638907 + 0.623619I
a = 0.054165 − 0.369885I
b = −0.199038 + 0.637626I
−2.03545 + 1.53423I −2.10831 − 3.28440I
u = 0.638907 − 0.623619I
a = 0.054165 + 0.369885I
b = −0.199038 − 0.637626I
−2.03545 − 1.53423I −2.10831 + 3.28440I
u = −0.354769 + 0.792242I
a = 1.153100 + 0.457040I
b = 0.884926 + 0.773845I
2.35471 − 1.62269I 0.78025 + 2.86308I
u = −0.354769 − 0.792242I
a = 1.153100 − 0.457040I
b = 0.884926 − 0.773845I
2.35471 + 1.62269I 0.78025 − 2.86308I
u = 0.883739 + 0.725281I
a = 2.46589 + 0.69772I
b = 0.500417 − 0.051284I
−4.23715 + 2.76938I −48.8073 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.883739 − 0.725281I
a = 2.46589 − 0.69772I
b = 0.500417 + 0.051284I
−4.23715 − 2.76938I −48.8073 + 0.I
u = −0.833904
a = 0.838853
b = −0.0760954
1.20368 8.97050
u = −0.806388
a = 17.4240
b = 0.105321
−0.460937 −368.890
u = 1.112660 + 0.494049I
a = −0.401224 − 0.346268I
b = −0.297482 + 0.701848I
2.13500 + 7.76603I 0
u = 1.112660 − 0.494049I
a = −0.401224 + 0.346268I
b = −0.297482 − 0.701848I
2.13500 − 7.76603I 0
u = 0.309756 + 0.710019I
a = 0.447198 − 0.401576I
b = −0.053147 − 0.769930I
−0.22354 − 3.19884I 0.00447 + 5.55216I
u = 0.309756 − 0.710019I
a = 0.447198 + 0.401576I
b = −0.053147 + 0.769930I
−0.22354 + 3.19884I 0.00447 − 5.55216I
u = 0.073729 + 1.240780I
a = 0.379736 + 0.020924I
b = 0.63482 + 1.93161I
10.77560 − 8.87064I 0
u = 0.073729 − 1.240780I
a = 0.379736 − 0.020924I
b = 0.63482 − 1.93161I
10.77560 + 8.87064I 0
u = −0.132383 + 1.258200I
a = 0.0707679 − 0.1181420I
b = 0.10550 − 2.15662I
11.64120 − 0.54721I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.132383 − 1.258200I
a = 0.0707679 + 0.1181420I
b = 0.10550 + 2.15662I
11.64120 + 0.54721I 0
u = 1.118360 + 0.595860I
a = 0.909006 + 0.370619I
b = −0.644410 − 1.075560I
−0.60424 + 3.28908I 0
u = 1.118360 − 0.595860I
a = 0.909006 − 0.370619I
b = −0.644410 + 1.075560I
−0.60424 − 3.28908I 0
u = −1.353770 + 0.147916I
a = 0.380791 − 1.326250I
b = 0.573832 + 1.158340I
5.03100 + 0.55063I 0
u = −1.353770 − 0.147916I
a = 0.380791 + 1.326250I
b = 0.573832 − 1.158340I
5.03100 − 0.55063I 0
u = −0.608345 + 0.151373I
a = −0.48220 − 1.88435I
b = −0.158567 − 1.356840I
4.00876 − 2.95005I −9.2752 + 14.0588I
u = −0.608345 − 0.151373I
a = −0.48220 + 1.88435I
b = −0.158567 + 1.356840I
4.00876 + 2.95005I −9.2752 − 14.0588I
u = 1.405350 + 0.093871I
a = 0.454924 + 1.244670I
b = −1.19138 − 1.51744I
4.40564 + 2.10618I 0
u = 1.405350 − 0.093871I
a = 0.454924 − 1.244670I
b = −1.19138 + 1.51744I
4.40564 − 2.10618I 0
u = 1.45332 + 0.14450I
a = −0.11796 − 1.93576I
b = −0.46438 + 2.32992I
10.46410 + 4.58464I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45332 − 0.14450I
a = −0.11796 + 1.93576I
b = −0.46438 − 2.32992I
10.46410 − 4.58464I 0
u = 1.46913 + 0.29367I
a = −0.488382 + 0.902569I
b = 1.91388 − 0.67361I
8.25016 + 5.56575I 0
u = 1.46913 − 0.29367I
a = −0.488382 − 0.902569I
b = 1.91388 + 0.67361I
8.25016 − 5.56575I 0
u = 1.40535 + 0.62626I
a = 1.00047 + 1.55409I
b = 0.88791 − 1.82835I
14.9516 + 15.4441I 0
u = 1.40535 − 0.62626I
a = 1.00047 − 1.55409I
b = 0.88791 + 1.82835I
14.9516 − 15.4441I 0
u = −1.41723 + 0.69052I
a = 1.12597 − 1.25429I
b = 0.53080 + 2.12848I
15.5975 − 6.3488I 0
u = −1.41723 − 0.69052I
a = 1.12597 + 1.25429I
b = 0.53080 − 2.12848I
15.5975 + 6.3488I 0
u = 1.51754 + 0.53920I
a = −0.84332 − 1.48882I
b = −0.35692 + 2.33329I
16.9016 + 6.9619I 0
u = 1.51754 − 0.53920I
a = −0.84332 + 1.48882I
b = −0.35692 − 2.33329I
16.9016 − 6.9619I 0
u = −0.270791 + 0.261743I
a = −4.22835 + 0.15470I
b = −0.526256 + 0.439239I
−0.967972 − 0.798268I −5.17338 − 0.48170I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270791 − 0.261743I
a = −4.22835 − 0.15470I
b = −0.526256 − 0.439239I
−0.967972 + 0.798268I −5.17338 + 0.48170I
u = −1.53465 + 0.55119I
a = −0.87468 + 1.14741I
b = 0.35572 − 2.21568I
15.8788 + 2.3692I 0
u = −1.53465 − 0.55119I
a = −0.87468 − 1.14741I
b = 0.35572 + 2.21568I
15.8788 − 2.3692I 0
u = −0.0125953
a = −45.4128
b = −0.612334
−1.00318 −10.1720
9
II.
I
u
2
= hb, 3u
8
− 5u
7
+ · · · + a + 4, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
4
=
−3u
8
+ 5u
7
+ u
6
− 9u
5
+ 6u
4
+ 3u
3
− 10u
2
+ 8u − 4
0
a
11
=
u
−u
3
+ u
a
3
=
−3u
8
+ 5u
7
+ u
6
− 9u
5
+ 6u
4
+ 3u
3
− 10u
2
+ 8u − 4
0
a
6
=
1
0
a
5
=
u
4
− u
2
+ 1
−u
6
+ 2u
4
− u
2
a
12
=
u
7
− 2u
5
+ 2u
3
−u
8
+ u
7
+ 3u
6
− 2u
5
− 3u
4
+ 2u
3
+ 1
a
2
=
−3u
8
+ 5u
7
+ u
6
− 9u
5
+ 5u
4
+ 3u
3
− 9u
2
+ 8u − 5
u
6
− 2u
4
+ u
2
a
1
=
−u
4
+ u
2
− 1
u
6
− 2u
4
+ u
2
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 42u
8
− 82u
7
− 19u
6
+ 153u
5
− 83u
4
− 70u
3
+ 143u
2
− 120u + 48
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
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
8
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
9
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
10
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
12
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ 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
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
, c
10
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
8
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
9
, c
12
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −0.920144 − 0.598375I
b = 0
−3.42837 + 2.09337I −7.68972 − 3.82038I
u = 0.772920 − 0.510351I
a = −0.920144 + 0.598375I
b = 0
−3.42837 − 2.09337I −7.68972 + 3.82038I
u = −0.825933
a = −14.5113
b = 0
−0.446489 211.240
u = −1.173910 + 0.391555I
a = 0.719281 + 0.119276I
b = 0
2.72642 − 1.33617I 1.56769 + 0.26615I
u = −1.173910 − 0.391555I
a = 0.719281 − 0.119276I
b = 0
2.72642 + 1.33617I 1.56769 − 0.26615I
u = 0.141484 + 0.739668I
a = 0.590648 + 0.449402I
b = 0
−1.02799 − 2.45442I −5.04100 + 1.69416I
u = 0.141484 − 0.739668I
a = 0.590648 − 0.449402I
b = 0
−1.02799 + 2.45442I −5.04100 − 1.69416I
u = 1.172470 + 0.500383I
a = 0.365868 − 0.247975I
b = 0
1.95319 + 7.08493I −0.45449 − 1.34000I
u = 1.172470 − 0.500383I
a = 0.365868 + 0.247975I
b = 0
1.95319 − 7.08493I −0.45449 + 1.34000I
13
III. I
u
3
= h−u
2
a − 2u
2
+ b + 1, a
2
+ au + 2u
2
+ 2a − 2u + 3, u
3
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
4
=
a
u
2
a + 2u
2
− 1
a
11
=
u
−u
2
+ u + 1
a
3
=
u
2
a + 2u
2
+ a − 1
u
2
a + 2u
2
− 1
a
6
=
u
2
a + 3u
2
− 2u + 1
au + u
2
+ a + u + 2
a
5
=
u
2
a + 3u
2
− 2u + 1
au + u
2
+ a + u + 2
a
12
=
u
−u
2
+ u + 1
a
2
=
u
2
a + au + 4u
2
+ a − u + 1
au + u
2
+ a + u + 2
a
1
=
−1
0
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 16u
2
a − 11au + 16u
2
− 11a − 30u
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
8
c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
10
(u
3
+ u
2
− 1)
2
c
4
, c
7
(u
3
− u
2
+ 1)
2
c
5
, c
11
u
6
c
6
, c
9
(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
8
, c
9
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
, c
7
c
10
(y
3
− y
2
+ 2y −1)
2
c
5
, c
11
y
6
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.930160 − 0.424452I
b = −0.215080 + 1.307140I
5.65624I −1.47396 − 5.95889I
u = 0.877439 + 0.744862I
a = −1.94728 − 0.32041I
b = −0.569840
−4.13758 + 2.82812I 14.7077 − 20.6881I
u = 0.877439 − 0.744862I
a = −0.930160 + 0.424452I
b = −0.215080 − 1.307140I
− 5.65624I −1.47396 + 5.95889I
u = 0.877439 − 0.744862I
a = −1.94728 + 0.32041I
b = −0.569840
−4.13758 − 2.82812I 14.7077 + 20.6881I
u = −0.754878
a = −0.62256 + 2.29387I
b = −0.215080 + 1.307140I
4.13758 + 2.82812I 27.7662 + 14.7292I
u = −0.754878
a = −0.62256 − 2.29387I
b = −0.215080 − 1.307140I
4.13758 − 2.82812I 27.7662 − 14.7292I
17
IV. I
u
4
= h2b + a − 2, a
2
− 2a − 4, u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
−1
a
8
=
1
−1
a
4
=
a
−
1
2
a + 1
a
11
=
−1
0
a
3
=
1
2
a + 1
−
1
2
a + 1
a
6
=
3
1
2
a − 2
a
5
=
1
2
a + 1
1
2
a − 2
a
12
=
0
3
2
a − 5
a
2
=
1
1
2
a − 2
a
1
=
0
3
2
a − 5
a
9
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −49
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
6
u
2
− u − 1
c
5
u
2
+ 3u + 1
c
7
(u + 1)
2
c
8
, c
10
(u − 1)
2
c
9
, c
12
u
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
y
2
− 7y + 1
c
2
, c
3
, c
4
c
6
y
2
− 3y + 1
c
7
, c
8
, c
10
(y −1)
2
c
9
, c
12
y
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.23607
b = 1.61803
−7.23771 −49.0000
u = −1.00000
a = 3.23607
b = −0.618034
0.657974 −49.0000
21
V. I
u
5
= hu
2
+ b, u
2
+ a − 2u + 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
4
=
−u
2
+ 2u − 1
−u
2
a
11
=
u
−u
2
+ u + 1
a
3
=
−2u
2
+ 2u − 1
−u
2
a
6
=
u
−u
2
+ u + 1
a
5
=
u
−u
2
+ u + 1
a
12
=
u
−u
2
+ u + 1
a
2
=
−u
2
+ 2u − 1
−u
2
+ u + 1
a
1
=
−1
0
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
8
c
12
u
3
− u
2
+ 2u − 1
c
2
, c
10
u
3
+ u
2
− 1
c
4
, c
7
u
3
− u
2
+ 1
c
5
, c
11
u
3
c
6
, c
9
u
3
+ u
2
+ 2u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
, c
9
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
, c
7
c
10
y
3
− y
2
+ 2y −1
c
5
, c
11
y
3
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.539798 + 0.182582I
b = −0.215080 − 1.307140I
0 0
u = 0.877439 − 0.744862I
a = 0.539798 − 0.182582I
b = −0.215080 + 1.307140I
0 0
u = −0.754878
a = −3.07960
b = −0.569840
0 0
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 + 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
8
(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)
c
9
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
10
(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
11
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
12
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)
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
11
y
9
(y
2
− 7y + 1)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
44
+ 49y
43
+ ··· − 15859712y + 262144)
c
7
, c
10
(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
8
(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)
c
9
, c
12
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)
27
