12n
0232
(K12n
0232
)
A knot diagram
1
Linearized knot diagam
3 5 7 6 2 9 4 11 12 6 7 10
Solving Sequence
4,7 8,11
9 12 3 6 5 2 1 10
c
7
c
8
c
11
c
3
c
6
c
4
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.48632 × 10
99
u
33
− 5.79126 × 10
99
u
32
+ ··· + 9.25530 × 10
102
b − 2.38605 × 10
103
,
− 3.67965 × 10
100
u
33
− 2.13068 × 10
101
u
32
+ ··· + 3.70212 × 10
103
a − 8.18316 × 10
104
,
u
34
+ 2u
33
+ ··· − 3072u + 1024i
I
u
2
= hu
8
− 3u
6
− u
5
+ 4u
4
+ 2u
3
− u
2
+ b − 2u − 1, u
8
+ 2u
7
− 2u
6
− 5u
5
+ u
4
+ 5u
3
+ u
2
+ a,
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
I
v
1
= ha, 1728v
9
− 4936v
8
+ 9872v
7
+ 12908v
6
− 24680v
5
− 34552v
4
+ 91527v
3
+ 4936v
2
+ 3335b − 613,
v
10
− 3v
9
+ 6v
8
+ 7v
7
− 16v
6
− 19v
5
+ 58v
4
− 2v
3
− 7v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 53 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−1.49 × 10
99
u
33
− 5.79 × 10
99
u
32
+ · · · + 9.26 × 10
102
b − 2.39 ×
10
103
, −3.68 × 10
100
u
33
− 2.13 × 10
101
u
32
+ · · · + 3.70 × 10
103
a − 8.18 ×
10
104
, u
34
+ 2u
33
+ · · · − 3072u + 1024i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
0.000993930u
33
+ 0.00575530u
32
+ ··· − 34.8075u + 22.1040
0.000160592u
33
+ 0.000625724u
32
+ ··· − 5.64954u + 2.57803
a
9
=
−0.00135334u
33
− 0.00441762u
32
+ ··· + 6.87137u − 7.96186
0.000582441u
33
+ 0.00154725u
32
+ ··· + 2.00787u − 0.0842617
a
12
=
0.000833338u
33
+ 0.00512957u
32
+ ··· − 29.1579u + 19.5259
0.000160592u
33
+ 0.000625724u
32
+ ··· − 5.64954u + 2.57803
a
3
=
−u
u
a
6
=
0.00199895u
33
+ 0.00538241u
32
+ ··· − 0.684374u + 3.58838
−0.00147460u
33
− 0.00388109u
32
+ ··· − 4.51110u + 1.52261
a
5
=
−0.000983560u
33
− 0.00100646u
32
+ ··· − 17.7146u + 4.94069
−0.000685051u
33
− 0.00177065u
32
+ ··· − 1.78423u + 1.03576
a
2
=
−0.000524358u
33
− 0.00150131u
32
+ ··· + 5.19547u − 5.11099
−0.00147460u
33
− 0.00388109u
32
+ ··· − 4.51110u + 1.52261
a
1
=
−0.000790332u
33
− 0.00216412u
32
+ ··· + 2.98921u − 3.69326
−0.00120862u
33
− 0.00321829u
32
+ ··· − 2.30484u + 0.104878
a
10
=
−0.000643181u
33
+ 0.000310006u
32
+ ··· − 24.6133u + 14.9301
0.000927418u
33
+ 0.00308742u
32
+ ··· − 3.88840u + 1.37424
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0110768u
33
+ 0.0125415u
32
+ ··· + 188.174u − 59.8533
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
34
+ 23u
33
+ ··· − 148u + 1
c
2
, c
5
u
34
+ 7u
33
+ ··· − 74u
2
+ 1
c
3
, c
7
u
34
+ 2u
33
+ ··· − 3072u + 1024
c
6
u
34
+ 4u
33
+ ··· − 3u − 1
c
8
u
34
− 3u
33
+ ··· − 5632u + 512
c
9
, c
12
u
34
+ 12u
33
+ ··· − 11u − 1
c
10
u
34
− 4u
33
+ ··· − 666199u + 339173
c
11
u
34
+ 2u
33
+ ··· − 10595u + 25489
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
34
− 17y
33
+ ··· − 14096y + 1
c
2
, c
5
y
34
+ 23y
33
+ ··· − 148y + 1
c
3
, c
7
y
34
+ 50y
33
+ ··· + 1048576y + 1048576
c
6
y
34
− 4y
33
+ ··· − 19y + 1
c
8
y
34
− 51y
33
+ ··· − 3407872y + 262144
c
9
, c
12
y
34
− 4y
33
+ ··· + 65y + 1
c
10
y
34
+ 60y
33
+ ··· − 783443850999y + 115038323929
c
11
y
34
− 36y
33
+ ··· + 7287355609y + 649689121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.01886
a = 0.402417
b = −0.825508
1.38631 7.11490
u = 0.946524 + 0.004818I
a = 0.0881160 − 0.0882313I
b = −0.622736 + 0.920702I
6.54075 + 2.05806I 13.8961 − 2.8397I
u = 0.946524 − 0.004818I
a = 0.0881160 + 0.0882313I
b = −0.622736 − 0.920702I
6.54075 − 2.05806I 13.8961 + 2.8397I
u = −0.764707 + 0.536808I
a = 0.0835054 + 0.0924226I
b = −0.236214 − 0.979802I
6.07730 − 7.11588I 12.1179 + 9.6630I
u = −0.764707 − 0.536808I
a = 0.0835054 − 0.0924226I
b = −0.236214 + 0.979802I
6.07730 + 7.11588I 12.1179 − 9.6630I
u = −0.305197 + 0.863434I
a = 1.356410 − 0.154788I
b = 0.691749 + 0.367275I
0.62542 + 2.57137I 3.17282 − 2.86214I
u = −0.305197 − 0.863434I
a = 1.356410 + 0.154788I
b = 0.691749 − 0.367275I
0.62542 − 2.57137I 3.17282 + 2.86214I
u = −0.642836 + 0.443818I
a = 0.488581 + 0.467682I
b = 0.115474 + 0.349761I
−1.59132 − 1.76956I −2.73476 + 4.21364I
u = −0.642836 − 0.443818I
a = 0.488581 − 0.467682I
b = 0.115474 − 0.349761I
−1.59132 + 1.76956I −2.73476 − 4.21364I
u = −0.732513 + 0.269955I
a = 2.27941 − 2.52971I
b = −0.05782 + 1.46259I
0.72250 + 2.82980I 10.05148 − 3.22591I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.732513 − 0.269955I
a = 2.27941 + 2.52971I
b = −0.05782 − 1.46259I
0.72250 − 2.82980I 10.05148 + 3.22591I
u = 0.678106 + 0.349109I
a = 2.13499 + 2.18985I
b = −0.369797 − 0.819998I
1.56878 + 0.34703I 8.40786 − 0.51532I
u = 0.678106 − 0.349109I
a = 2.13499 − 2.18985I
b = −0.369797 + 0.819998I
1.56878 − 0.34703I 8.40786 + 0.51532I
u = 0.062735 + 0.467390I
a = 0.893723 + 0.003916I
b = 0.331665 − 0.940404I
0.61291 + 1.48611I 4.79533 − 4.74523I
u = 0.062735 − 0.467390I
a = 0.893723 − 0.003916I
b = 0.331665 + 0.940404I
0.61291 − 1.48611I 4.79533 + 4.74523I
u = 0.074045 + 0.443473I
a = 8.71021 + 1.02714I
b = 1.33192 − 0.57161I
2.15188 + 2.20308I −18.1536 + 5.4483I
u = 0.074045 − 0.443473I
a = 8.71021 − 1.02714I
b = 1.33192 + 0.57161I
2.15188 − 2.20308I −18.1536 − 5.4483I
u = 1.12191 + 1.21427I
a = 0.292658 − 0.148357I
b = 0.94260 + 1.15777I
−2.99715 − 2.34695I 4.00000 + 3.07511I
u = 1.12191 − 1.21427I
a = 0.292658 + 0.148357I
b = 0.94260 − 1.15777I
−2.99715 + 2.34695I 4.00000 − 3.07511I
u = 0.305756
a = 4.77767
b = −1.04203
2.29528 1.25710
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.56509 + 2.04215I
a = −0.773555 + 0.263179I
b = −1.39864 − 0.29584I
−7.72558 − 0.90268I 0
u = −0.56509 − 2.04215I
a = −0.773555 − 0.263179I
b = −1.39864 + 0.29584I
−7.72558 + 0.90268I 0
u = 1.02869 + 1.89861I
a = −0.706865 − 0.350243I
b = −1.26804 + 0.74707I
−11.18750 + 7.23815I 0
u = 1.02869 − 1.89861I
a = −0.706865 + 0.350243I
b = −1.26804 − 0.74707I
−11.18750 − 7.23815I 0
u = −1.91642 + 1.10283I
a = 0.054061 + 0.259519I
b = −2.33781 + 0.73216I
−3.63061 − 2.77360I 0
u = −1.91642 − 1.10283I
a = 0.054061 − 0.259519I
b = −2.33781 − 0.73216I
−3.63061 + 2.77360I 0
u = −1.19908 + 1.98984I
a = 0.816613 − 0.366169I
b = 1.73482 + 1.78350I
−10.8926 − 14.7212I 0
u = −1.19908 − 1.98984I
a = 0.816613 + 0.366169I
b = 1.73482 − 1.78350I
−10.8926 + 14.7212I 0
u = 0.77518 + 2.27315I
a = 0.803096 + 0.162714I
b = 2.06341 − 1.43354I
−7.46169 + 8.00267I 0
u = 0.77518 − 2.27315I
a = 0.803096 − 0.162714I
b = 2.06341 + 1.43354I
−7.46169 − 8.00267I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04194 + 2.58121I
a = −0.741302 − 0.045471I
b = −1.88206 − 0.20245I
−13.09350 − 4.80207I 0
u = −0.04194 − 2.58121I
a = −0.741302 + 0.045471I
b = −1.88206 + 0.20245I
−13.09350 + 4.80207I 0
u = −0.18171 + 2.97411I
a = 0.630299 + 0.012157I
b = 2.89525 + 1.03267I
−13.37580 − 1.94532I 0
u = −0.18171 − 2.97411I
a = 0.630299 − 0.012157I
b = 2.89525 − 1.03267I
−13.37580 + 1.94532I 0
8
II. I
u
2
= hu
8
− 3u
6
− u
5
+ 4u
4
+ 2u
3
− u
2
+ b − 2u − 1, u
8
+ 2u
7
− 2u
6
−
5u
5
+ u
4
+ 5u
3
+ u
2
+ a, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
−u
8
− 2u
7
+ 2u
6
+ 5u
5
− u
4
− 5u
3
− u
2
−u
8
+ 3u
6
+ u
5
− 4u
4
− 2u
3
+ u
2
+ 2u + 1
a
9
=
1
−u
2
a
12
=
−2u
7
− u
6
+ 4u
5
+ 3u
4
− 3u
3
− 2u
2
− 2u − 1
−u
8
+ 3u
6
+ u
5
− 4u
4
− 2u
3
+ u
2
+ 2u + 1
a
3
=
−u
u
a
6
=
−u
2
+ 1
u
4
a
5
=
−u
5
+ 2u
3
− u
u
7
− u
5
+ u
a
2
=
−u
4
+ u
2
− 1
u
4
a
1
=
−1
u
2
a
10
=
−2u
7
− u
6
+ 4u
5
+ 3u
4
− 3u
3
− 2u
2
− 2u
−u
8
+ 3u
6
+ u
5
− 4u
4
− 2u
3
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
8
+ 9u
7
− 7u
6
− 22u
5
− 2u
4
+ 23u
3
+ 13u
2
+ u + 3
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
2
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
3
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
6
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
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
c
9
(u + 1)
9
c
10
, c
11
u
9
+ u
8
− 2u
7
− 4u
6
− u
5
+ 9u
4
+ 15u
3
+ 12u
2
+ 5u + 1
c
12
(u − 1)
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
2
, c
5
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
3
, c
7
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
8
y
9
c
9
, c
12
(y −1)
9
c
10
, c
11
y
9
− 5y
8
+ 10y
7
− y
5
− 37y
4
+ 7y
3
− 12y
2
+ y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 0.939568 − 0.981640I
b = 0.457852 + 1.072010I
−0.13850 − 2.09337I 3.38047 + 2.85927I
u = −0.772920 − 0.510351I
a = 0.939568 + 0.981640I
b = 0.457852 − 1.072010I
−0.13850 + 2.09337I 3.38047 − 2.85927I
u = 0.825933
a = −2.14893
b = 1.46592
2.84338 17.4870
u = 1.173910 + 0.391555I
a = −0.119081 + 0.409451I
b = 0.522253 − 0.392004I
6.01628 + 1.33617I 6.48878 + 2.15019I
u = 1.173910 − 0.391555I
a = −0.119081 − 0.409451I
b = 0.522253 + 0.392004I
6.01628 − 1.33617I 6.48878 − 2.15019I
u = −0.141484 + 0.739668I
a = −2.26219 + 2.13290I
b = −1.63880 + 0.65075I
2.26187 + 2.45442I 6.9022 − 12.4598I
u = −0.141484 − 0.739668I
a = −2.26219 − 2.13290I
b = −1.63880 − 0.65075I
2.26187 − 2.45442I 6.9022 + 12.4598I
u = −1.172470 + 0.500383I
a = 0.016164 − 0.378317I
b = 0.425734 + 0.444312I
5.24306 − 7.08493I 2.48514 + 6.49599I
u = −1.172470 − 0.500383I
a = 0.016164 + 0.378317I
b = 0.425734 − 0.444312I
5.24306 + 7.08493I 2.48514 − 6.49599I
12
III. I
v
1
= ha, 1728v
9
− 4936v
8
+ · · · + 3335b − 613, v
10
− 3v
9
+ · · · − v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−0.518141v
9
+ 1.48006v
8
+ ··· − 1.48006v
2
+ 0.183808
a
9
=
1
0.462969v
9
− 1.33373v
8
+ ··· + 1.33373v
2
− 1.81379
a
12
=
0.518141v
9
− 1.48006v
8
+ ··· + 1.48006v
2
− 0.183808
−0.518141v
9
+ 1.48006v
8
+ ··· − 1.48006v
2
+ 0.183808
a
3
=
v
0
a
6
=
0.462969v
9
− 1.33373v
8
+ ··· + 1.33373v
2
− 0.813793
−1.14783v
9
+ 3.29565v
8
+ ··· − 3.29565v
2
+ 1.75652
a
5
=
0.0740630v
9
− 0.148126v
8
+ ··· + 3.77811v − 0.424888
−0.147826v
9
+ 0.295652v
8
+ ··· − 7v + 0.756522
a
2
=
−0.610795v
9
+ 1.75982v
8
+ ··· + v + 0.961619
1.14783v
9
− 3.29565v
8
+ ··· + 3.29565v
2
− 1.75652
a
1
=
−0.462969v
9
+ 1.33373v
8
+ ··· − 1.33373v
2
+ 0.813793
1.14783v
9
− 3.29565v
8
+ ··· + 3.29565v
2
− 1.75652
a
10
=
−0.684858v
9
+ 1.96192v
8
+ ··· − 1.96192v
2
+ 0.942729
1.14783v
9
− 3.29565v
8
+ ··· + 3.29565v
2
− 1.75652
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
1259
667
v
9
−
146
29
v
8
+
6397
667
v
7
+
11075
667
v
6
−
16703
667
v
5
−
29857
667
v
4
+
2799
29
v
3
+
18061
667
v
2
−
151
23
v +
990
667
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
7
u
10
c
6
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
8
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
10
, c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
5
c
3
, c
7
y
10
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
c
8
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
c
9
, c
10
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.38814 + 0.78973I
a = 0
b = 0.339110 + 0.822375I
0.329100 + 0.499304I 3.01153 − 0.88894I
v = 1.38814 − 0.78973I
a = 0
b = 0.339110 − 0.822375I
0.329100 − 0.499304I 3.01153 + 0.88894I
v = −1.37799 + 0.80730I
a = 0
b = 0.339110 + 0.822375I
0.32910 − 3.56046I 3.07628 + 9.77765I
v = −1.37799 − 0.80730I
a = 0
b = 0.339110 − 0.822375I
0.32910 + 3.56046I 3.07628 − 9.77765I
v = −0.294694 + 0.220725I
a = 0
b = −0.455697 − 1.200150I
5.87256 − 6.43072I 6.63163 + 0.01393I
v = −0.294694 − 0.220725I
a = 0
b = −0.455697 + 1.200150I
5.87256 + 6.43072I 6.63163 − 0.01393I
v = 0.338500 + 0.144851I
a = 0
b = −0.455697 − 1.200150I
5.87256 − 2.37095I 3.55752 + 5.27247I
v = 0.338500 − 0.144851I
a = 0
b = −0.455697 + 1.200150I
5.87256 + 2.37095I 3.55752 − 5.27247I
v = 1.44605 + 2.50463I
a = 0
b = −0.766826
2.40108 − 2.02988I 9.72304 − 3.67600I
v = 1.44605 − 2.50463I
a = 0
b = −0.766826
2.40108 + 2.02988I 9.72304 + 3.67600I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)
5
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
34
+ 23u
33
+ ··· − 148u + 1)
c
2
(u
2
+ u + 1)
5
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
34
+ 7u
33
+ ··· − 74u
2
+ 1)
c
3
u
10
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
34
+ 2u
33
+ ··· − 3072u + 1024)
c
5
(u
2
− u + 1)
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
34
+ 7u
33
+ ··· − 74u
2
+ 1)
c
6
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
34
+ 4u
33
+ ··· − 3u − 1)
c
7
u
10
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
34
+ 2u
33
+ ··· − 3072u + 1024)
c
8
u
9
(u
5
+ u
4
+ ··· + u + 1)
2
(u
34
− 3u
33
+ ··· − 5632u + 512)
c
9
((u + 1)
9
)(u
5
− u
4
+ ··· + u + 1)
2
(u
34
+ 12u
33
+ ··· − 11u − 1)
c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
9
+ u
8
− 2u
7
− 4u
6
− u
5
+ 9u
4
+ 15u
3
+ 12u
2
+ 5u + 1)
· (u
34
− 4u
33
+ ··· − 666199u + 339173)
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
· (u
9
+ u
8
− 2u
7
− 4u
6
− u
5
+ 9u
4
+ 15u
3
+ 12u
2
+ 5u + 1)
· (u
34
+ 2u
33
+ ··· − 10595u + 25489)
c
12
((u − 1)
9
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
34
+ 12u
33
+ ··· − 11u − 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
5
)(y
9
+ 7y
8
+ ··· + 13y − 1)
· (y
34
− 17y
33
+ ··· − 14096y + 1)
c
2
, c
5
(y
2
+ y + 1)
5
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
34
+ 23y
33
+ ··· − 148y + 1)
c
3
, c
7
y
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
34
+ 50y
33
+ ··· + 1048576y + 1048576)
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
34
− 4y
33
+ ··· − 19y + 1)
c
8
y
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
· (y
34
− 51y
33
+ ··· − 3407872y + 262144)
c
9
, c
12
((y − 1)
9
)(y
5
− 5y
4
+ ··· − y − 1)
2
(y
34
− 4y
33
+ ··· + 65y + 1)
c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
9
− 5y
8
+ 10y
7
− y
5
− 37y
4
+ 7y
3
− 12y
2
+ y − 1)
· (y
34
+ 60y
33
+ ··· − 783443850999y + 115038323929)
c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
· (y
9
− 5y
8
+ 10y
7
− y
5
− 37y
4
+ 7y
3
− 12y
2
+ y − 1)
· (y
34
− 36y
33
+ ··· + 7287355609y + 649689121)
18
