12n
0330
(K12n
0330
)
A knot diagram
1
Linearized knot diagam
3 5 7 11 2 4 3 12 1 4 10 9
Solving Sequence
4,10
11 5
7,12
3 8 2 1 6 9
c
10
c
4
c
11
c
3
c
7
c
2
c
1
c
6
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.74526 × 10
16
u
25
− 1.33763 × 10
17
u
24
+ ··· + 7.07898 × 10
18
b + 5.73871 × 10
18
,
− 6.55698 × 10
18
u
25
+ 2.22473 × 10
19
u
24
+ ··· + 1.41580 × 10
19
a − 1.02368 × 10
20
, u
26
− 3u
25
+ ··· + 6u + 8i
I
u
2
= hu
13
+ u
12
− u
11
− 2u
10
+ 4u
9
+ 5u
8
− 3u
7
− 6u
6
+ 4u
5
+ 6u
4
− u
2
a − 2u
3
− 2u
2
+ b + a + 2u + 1,
u
13
+ 2u
12
− 3u
10
+ 2u
9
+ 9u
8
+ 2u
7
− 9u
6
− 2u
5
+ 10u
4
+ 4u
3
+ a
2
+ au − 3u
2
+ 3,
u
14
+ u
13
− u
12
− 2u
11
+ 4u
10
+ 5u
9
− 3u
8
− 6u
7
+ 4u
6
+ 6u
5
− 2u
4
− 2u
3
+ 2u
2
+ u − 1i
I
u
3
= h−u
9
+ u
8
+ 3u
7
− 2u
6
− 4u
5
+ u
4
+ u
3
+ 2u
2
+ b + u − 1, −u
8
+ 2u
6
− u
4
− 2u
2
+ a + 1,
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1i
I
v
1
= ha, 2b + 1, v −2i
* 4 irreducible components of dim
C
= 0, with total 65 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
= h7.75×10
16
u
25
−1.34×10
17
u
24
+· · ·+7.08×10
18
b+5.74×10
18
, −6.56×
10
18
u
25
+2.22×10
19
u
24
+· · ·+1.42×10
19
a−1.02×10
20
, u
26
−3u
25
+· · ·+6u+8i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
7
=
0.463130u
25
− 1.57137u
24
+ ··· − 7.38977u + 7.23041
−0.0109412u
25
+ 0.0188959u
24
+ ··· + 0.948527u − 0.810670
a
12
=
−u
2
+ 1
u
2
a
3
=
−0.452189u
25
+ 1.55247u
24
+ ··· + 6.44124u − 6.41974
−0.139816u
25
+ 0.520475u
24
+ ··· + 3.39062u − 2.37790
a
8
=
1.05514u
25
− 3.64431u
24
+ ··· − 16.2216u + 16.0280
0.00913190u
25
− 0.0544808u
24
+ ··· + 0.384691u − 0.813121
a
2
=
−0.257452u
25
+ 0.942913u
24
+ ··· + 3.82805u − 4.96393
−0.288157u
25
+ 0.949849u
24
+ ··· + 4.59799u − 3.63094
a
1
=
−1.06427u
25
+ 3.69879u
24
+ ··· + 15.8369u − 15.2149
−0.283474u
25
+ 1.06311u
24
+ ··· + 5.86288u − 4.86106
a
6
=
0.463130u
25
− 1.57137u
24
+ ··· − 7.38977u + 7.23041
0.183796u
25
− 0.590662u
24
+ ··· − 1.66466u + 0.645138
a
9
=
1.28428u
25
− 4.51273u
24
+ ··· − 21.0928u + 19.1876
0.0634646u
25
− 0.249171u
24
+ ··· − 0.606969u + 0.888390
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2235431246280387471
2022564411084206648
u
25
−
50383957546292106623
14157950877589446536
u
24
+ ··· −
96855145260069592069
14157950877589446536
u +
73272041333640892293
7078975438794723268
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
+ 5u
25
+ ··· − 5u + 1
c
2
, c
3
, c
5
c
6
, c
7
u
26
− u
25
+ ··· − 3u − 1
c
4
, c
10
u
26
− 3u
25
+ ··· + 6u + 8
c
8
, c
9
, c
12
u
26
− 2u
25
+ ··· + 7u − 4
c
11
u
26
+ 9u
25
+ ··· + 436u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 37y
25
+ ··· − 157y + 1
c
2
, c
3
, c
5
c
6
, c
7
y
26
+ 5y
25
+ ··· − 5y + 1
c
4
, c
10
y
26
− 9y
25
+ ··· − 436y + 64
c
8
, c
9
, c
12
y
26
− 22y
25
+ ··· − 65y + 16
c
11
y
26
+ 15y
25
+ ··· − 142352y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.982745 + 0.211485I
a = 0.402843 − 0.499085I
b = −0.232498 + 0.875894I
−1.77257 + 0.70535I −4.40558 + 0.51415I
u = −0.982745 − 0.211485I
a = 0.402843 + 0.499085I
b = −0.232498 − 0.875894I
−1.77257 − 0.70535I −4.40558 − 0.51415I
u = 0.010508 + 1.069030I
a = −0.600779 − 0.379610I
b = 0.115449 + 0.616202I
−3.79097 − 1.46714I −5.06055 + 4.75413I
u = 0.010508 − 1.069030I
a = −0.600779 + 0.379610I
b = 0.115449 − 0.616202I
−3.79097 + 1.46714I −5.06055 − 4.75413I
u = 0.734341 + 0.797765I
a = 1.257320 − 0.172643I
b = 0.228017 + 1.091210I
2.81865 − 0.76966I −3.02229 + 2.23661I
u = 0.734341 − 0.797765I
a = 1.257320 + 0.172643I
b = 0.228017 − 1.091210I
2.81865 + 0.76966I −3.02229 − 2.23661I
u = 1.074650 + 0.168126I
a = −0.355808 + 0.706778I
b = 0.039591 − 1.309980I
−1.79599 − 3.76105I −4.80263 + 8.00937I
u = 1.074650 − 0.168126I
a = −0.355808 − 0.706778I
b = 0.039591 + 1.309980I
−1.79599 + 3.76105I −4.80263 − 8.00937I
u = −0.745967 + 0.945276I
a = −1.129930 − 0.091852I
b = −0.012396 + 1.135900I
6.07946 − 3.67877I −0.12041 + 2.47120I
u = −0.745967 − 0.945276I
a = −1.129930 + 0.091852I
b = −0.012396 − 1.135900I
6.07946 + 3.67877I −0.12041 − 2.47120I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.021750 + 0.716695I
a = −0.081674 + 1.052890I
b = −0.92093 − 2.01835I
1.91220 − 4.97774I −4.59322 + 4.08967I
u = 1.021750 − 0.716695I
a = −0.081674 − 1.052890I
b = −0.92093 + 2.01835I
1.91220 + 4.97774I −4.59322 − 4.08967I
u = 0.755105 + 1.061790I
a = 1.036650 − 0.033748I
b = −0.151747 + 1.120760I
1.48699 + 8.04356I −4.72322 − 5.24092I
u = 0.755105 − 1.061790I
a = 1.036650 + 0.033748I
b = −0.151747 − 1.120760I
1.48699 − 8.04356I −4.72322 + 5.24092I
u = −1.062230 + 0.805325I
a = −0.007950 + 1.055910I
b = 1.20574 − 1.93593I
5.07466 + 10.13450I −2.10298 − 6.96057I
u = −1.062230 − 0.805325I
a = −0.007950 − 1.055910I
b = 1.20574 + 1.93593I
5.07466 − 10.13450I −2.10298 + 6.96057I
u = 1.279790 + 0.462764I
a = −0.302749 − 0.444518I
b = 0.042614 + 0.739956I
−7.94739 − 3.73170I −5.56768 − 0.86519I
u = 1.279790 − 0.462764I
a = −0.302749 + 0.444518I
b = 0.042614 − 0.739956I
−7.94739 + 3.73170I −5.56768 + 0.86519I
u = 0.175064 + 0.597925I
a = 0.812678 − 0.972268I
b = 0.082343 + 0.525293I
1.28130 + 0.88301I 4.68220 − 2.63665I
u = 0.175064 − 0.597925I
a = 0.812678 + 0.972268I
b = 0.082343 − 0.525293I
1.28130 − 0.88301I 4.68220 + 2.63665I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.355470 + 0.349551I
a = 0.160592 + 0.704597I
b = 0.398277 − 1.175870I
−8.58893 + 6.63218I −8.67236 − 8.09999I
u = −1.355470 − 0.349551I
a = 0.160592 − 0.704597I
b = 0.398277 + 1.175870I
−8.58893 − 6.63218I −8.67236 + 8.09999I
u = 1.109820 + 0.856025I
a = 0.068276 + 1.033520I
b = −1.36937 − 1.78727I
0.3265 − 14.9979I −5.89395 + 8.70861I
u = 1.109820 − 0.856025I
a = 0.068276 − 1.033520I
b = −1.36937 + 1.78727I
0.3265 + 14.9979I −5.89395 − 8.70861I
u = −0.541106
a = −2.33904
b = −0.621412
−0.468550 −16.1730
u = −0.488142
a = 0.570097
b = −0.728748
−1.21370 −9.51190
7
II.
I
u
2
= hu
13
+ u
12
+ · · · + a + 1, u
13
+ 2u
12
+ · · · + a
2
+ 3, u
14
+ u
13
+ · · · + u − 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
7
=
a
−u
13
− u
12
+ ··· − a − 1
a
12
=
−u
2
+ 1
u
2
a
3
=
u
13
+ u
12
+ ··· + 2u + 1
−u
13
− u
12
+ ··· + a − 1
a
8
=
u
5
+ u
u
7
− u
5
+ 2u
3
− u
a
2
=
u
13
+ u
12
+ ··· + 2u + 1
−u
13
− u
12
+ ··· + a − 1
a
1
=
−u
7
− 2u
3
−u
9
+ u
7
− 3u
5
+ 2u
3
− u
a
6
=
a
−u
13
− u
12
+ ··· − a − 1
a
9
=
−u
11
+ 2u
9
− 4u
7
+ 6u
5
− 3u
3
+ 2u
u
11
− u
9
+ 4u
7
− 3u
5
+ 3u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
12
− 4u
11
+ 4u
10
+ 8u
9
− 16u
8
− 16u
7
+ 12u
6
+ 20u
5
− 16u
4
− 12u
3
+ 8u
2
− 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
+ 11u
27
+ ··· + 2888u + 289
c
2
, c
3
, c
5
c
6
, c
7
u
28
+ 3u
27
+ ··· + 74u + 17
c
4
, c
10
(u
14
+ u
13
+ ··· + u − 1)
2
c
8
, c
9
, c
12
(u
14
− u
13
+ ··· − 3u − 1)
2
c
11
(u
14
+ 3u
13
+ ··· + 5u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 11y
27
+ ··· + 1428812y + 83521
c
2
, c
3
, c
5
c
6
, c
7
y
28
+ 11y
27
+ ··· + 2888y + 289
c
4
, c
10
(y
14
− 3y
13
+ ··· − 5y + 1)
2
c
8
, c
9
, c
12
(y
14
− 11y
13
+ ··· − 5y + 1)
2
c
11
(y
14
+ 17y
13
+ ··· − y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.919323 + 0.470231I
a = −0.404207 + 0.774825I
b = −1.380120 − 0.199773I
−6.26948 − 4.88256I −7.68599 + 6.44337I
u = 0.919323 + 0.470231I
a = −0.515117 − 1.245060I
b = 0.407942 + 0.463734I
−6.26948 − 4.88256I −7.68599 + 6.44337I
u = 0.919323 − 0.470231I
a = −0.404207 − 0.774825I
b = −1.380120 + 0.199773I
−6.26948 + 4.88256I −7.68599 − 6.44337I
u = 0.919323 − 0.470231I
a = −0.515117 + 1.245060I
b = 0.407942 − 0.463734I
−6.26948 + 4.88256I −7.68599 − 6.44337I
u = −0.924961
a = 0.46248 + 1.34555I
b = 1.014320 − 0.194361I
−8.84982 −12.7050
u = −0.924961
a = 0.46248 − 1.34555I
b = 1.014320 + 0.194361I
−8.84982 −12.7050
u = −0.726911 + 0.518054I
a = 0.725706 − 1.116820I
b = −0.465841 + 0.930039I
−1.93761 + 1.98638I −0.65592 − 5.08636I
u = −0.726911 + 0.518054I
a = 0.001206 + 0.598768I
b = 1.362390 + 0.206201I
−1.93761 + 1.98638I −0.65592 − 5.08636I
u = −0.726911 − 0.518054I
a = 0.725706 + 1.116820I
b = −0.465841 − 0.930039I
−1.93761 − 1.98638I −0.65592 + 5.08636I
u = −0.726911 − 0.518054I
a = 0.001206 − 0.598768I
b = 1.362390 − 0.206201I
−1.93761 − 1.98638I −0.65592 + 5.08636I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.879333 + 0.897049I
a = 0.981434 + 0.058694I
b = −0.362451 − 1.040360I
2.51115 − 1.51934I −3.12222 + 0.64840I
u = −0.879333 + 0.897049I
a = −0.102101 − 0.955743I
b = −0.84520 + 1.71540I
2.51115 − 1.51934I −3.12222 + 0.64840I
u = −0.879333 − 0.897049I
a = 0.981434 − 0.058694I
b = −0.362451 + 1.040360I
2.51115 + 1.51934I −3.12222 − 0.64840I
u = −0.879333 − 0.897049I
a = −0.102101 + 0.955743I
b = −0.84520 − 1.71540I
2.51115 + 1.51934I −3.12222 − 0.64840I
u = 0.405736 + 0.602281I
a = 0.914419 + 0.321246I
b = −2.02195 + 1.20408I
−4.70274 + 0.85224I −3.59802 − 0.38712I
u = 0.405736 + 0.602281I
a = −1.32016 − 0.92353I
b = 1.26370 + 1.60335I
−4.70274 + 0.85224I −3.59802 − 0.38712I
u = 0.405736 − 0.602281I
a = 0.914419 − 0.321246I
b = −2.02195 − 1.20408I
−4.70274 − 0.85224I −3.59802 + 0.38712I
u = 0.405736 − 0.602281I
a = −1.32016 + 0.92353I
b = 1.26370 − 1.60335I
−4.70274 − 0.85224I −3.59802 + 0.38712I
u = 0.924969 + 0.883501I
a = −0.980532 + 0.152079I
b = 0.093102 − 1.203290I
6.36134 − 3.26499I 0.09314 + 2.49004I
u = 0.924969 + 0.883501I
a = 0.055563 − 1.035580I
b = 1.07584 + 1.58872I
6.36134 − 3.26499I 0.09314 + 2.49004I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.924969 − 0.883501I
a = −0.980532 − 0.152079I
b = 0.093102 + 1.203290I
6.36134 + 3.26499I 0.09314 − 2.49004I
u = 0.924969 − 0.883501I
a = 0.055563 + 1.035580I
b = 1.07584 − 1.58872I
6.36134 + 3.26499I 0.09314 − 2.49004I
u = −0.961925 + 0.860252I
a = 0.966136 + 0.234062I
b = 0.177845 − 1.273080I
2.24783 + 8.01486I −3.63204 − 5.37427I
u = −0.961925 + 0.860252I
a = −0.004211 − 1.094310I
b = −1.23004 + 1.41511I
2.24783 + 8.01486I −3.63204 − 5.37427I
u = −0.961925 − 0.860252I
a = 0.966136 − 0.234062I
b = 0.177845 + 1.273080I
2.24783 − 8.01486I −3.63204 + 5.37427I
u = −0.961925 − 0.860252I
a = −0.004211 + 1.094310I
b = −1.23004 − 1.41511I
2.24783 − 8.01486I −3.63204 + 5.37427I
u = 0.561243
a = −0.28062 + 1.84686I
b = −1.58953 − 1.26511I
−4.02051 −10.0930
u = 0.561243
a = −0.28062 − 1.84686I
b = −1.58953 + 1.26511I
−4.02051 −10.0930
13
III. I
u
3
=
h−u
9
+u
8
+· · ·+b−1, −u
8
+2u
6
−u
4
−2u
2
+a+1, u
10
−3u
8
+4u
6
−u
4
−u
2
+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
7
=
u
8
− 2u
6
+ u
4
+ 2u
2
− 1
u
9
− u
8
− 3u
7
+ 2u
6
+ 4u
5
− u
4
− u
3
− 2u
2
− u + 1
a
12
=
−u
2
+ 1
u
2
a
3
=
−u
9
+ 3u
7
− 4u
5
+ u
3
+ u
u
9
+ u
8
− 3u
7
− 2u
6
+ 4u
5
+ u
4
− u
3
+ 2u
2
− 1
a
8
=
0
−u
8
+ 3u
6
− 3u
4
+ 1
a
2
=
−u
9
− u
8
+ 3u
7
+ 3u
6
− 4u
5
− 3u
4
+ u
3
+ u + 1
u
9
+ 2u
8
− 3u
7
− 4u
6
+ 4u
5
+ 3u
4
− u
3
+ 2u
2
− 1
a
1
=
−u
8
+ 3u
6
− 3u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
6
=
u
8
− 2u
6
+ u
4
+ 2u
2
− 1
u
9
− 3u
7
− u
6
+ 4u
5
+ 2u
4
− u
3
− 2u
2
− u
a
9
=
u
4
− u
2
+ 1
u
6
− 2u
4
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
8
− 8u
6
+ 8u
4
+ 4u
2
− 12
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
c
2
, c
3
, c
5
c
6
, c
7
(u
2
+ 1)
5
c
4
, c
10
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
8
, c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
10
c
2
, c
3
, c
5
c
6
, c
7
(y + 1)
10
c
4
, c
10
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
8
, c
9
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822375 + 0.339110I
a = 0.428550 − 1.039280I
b = 0.61073 + 1.46782I
−3.61897 + 1.53058I −8.51511 − 4.43065I
u = −0.822375 − 0.339110I
a = 0.428550 + 1.039280I
b = 0.61073 − 1.46782I
−3.61897 − 1.53058I −8.51511 + 4.43065I
u = 0.822375 + 0.339110I
a = 0.428550 + 1.039280I
b = −1.46782 − 0.61073I
−3.61897 − 1.53058I −8.51511 + 4.43065I
u = 0.822375 − 0.339110I
a = 0.428550 − 1.039280I
b = −1.46782 + 0.61073I
−3.61897 + 1.53058I −8.51511 − 4.43065I
u = 0.766826I
a = −1.30408
b = 1.30408 + 1.30408I
−5.69095 −9.48110
u = − 0.766826I
a = −1.30408
b = 1.30408 − 1.30408I
−5.69095 −9.48110
u = −1.200150 + 0.455697I
a = −0.276511 + 0.728237I
b = 1.004750 − 0.451726I
−9.16243 + 4.40083I −12.74431 − 3.49859I
u = −1.200150 − 0.455697I
a = −0.276511 − 0.728237I
b = 1.004750 + 0.451726I
−9.16243 − 4.40083I −12.74431 + 3.49859I
u = 1.200150 + 0.455697I
a = −0.276511 − 0.728237I
b = −0.451726 + 1.004750I
−9.16243 − 4.40083I −12.74431 + 3.49859I
u = 1.200150 − 0.455697I
a = −0.276511 + 0.728237I
b = −0.451726 − 1.004750I
−9.16243 + 4.40083I −12.74431 − 3.49859I
17
IV. I
v
1
= ha, 2b + 1, v − 2i
(i) Arc colorings
a
4
=
2
0
a
10
=
1
0
a
11
=
1
0
a
5
=
2
0
a
7
=
0
−0.5
a
12
=
1
0
a
3
=
2
0.5
a
8
=
−2
−1
a
2
=
0
0.5
a
1
=
2
1
a
6
=
2
−0.5
a
9
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2.25
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
12
u + 1
c
4
, c
10
, c
11
u
c
5
, c
6
, c
7
c
8
, c
9
u − 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
9
, c
12
y −1
c
4
, c
10
, c
11
y
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 2.00000
a = 0
b = −0.500000
0 2.25000
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u + 1)(u
26
+ 5u
25
+ ··· − 5u + 1)
· (u
28
+ 11u
27
+ ··· + 2888u + 289)
c
2
, c
3
(u + 1)(u
2
+ 1)
5
(u
26
− u
25
+ ··· − 3u − 1)(u
28
+ 3u
27
+ ··· + 74u + 17)
c
4
, c
10
u(u
10
− 3u
8
+ ··· − u
2
+ 1)(u
14
+ u
13
+ ··· + u − 1)
2
· (u
26
− 3u
25
+ ··· + 6u + 8)
c
5
, c
6
, c
7
(u − 1)(u
2
+ 1)
5
(u
26
− u
25
+ ··· − 3u − 1)(u
28
+ 3u
27
+ ··· + 74u + 17)
c
8
, c
9
(u − 1)(u
5
+ u
4
+ ··· + u − 1)
2
(u
14
− u
13
+ ··· − 3u − 1)
2
· (u
26
− 2u
25
+ ··· + 7u − 4)
c
11
u(u
5
+ 3u
4
+ ··· − u − 1)
2
(u
14
+ 3u
13
+ ··· + 5u + 1)
2
· (u
26
+ 9u
25
+ ··· + 436u + 64)
c
12
(u + 1)(u
5
− u
4
+ ··· + u + 1)
2
(u
14
− u
13
+ ··· − 3u − 1)
2
· (u
26
− 2u
25
+ ··· + 7u − 4)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
11
)(y
26
+ 37y
25
+ ··· − 157y + 1)
· (y
28
+ 11y
27
+ ··· + 1428812y + 83521)
c
2
, c
3
, c
5
c
6
, c
7
(y −1)(y + 1)
10
(y
26
+ 5y
25
+ ··· − 5y + 1)
· (y
28
+ 11y
27
+ ··· + 2888y + 289)
c
4
, c
10
y(y
5
− 3y
4
+ ··· − y + 1)
2
(y
14
− 3y
13
+ ··· − 5y + 1)
2
· (y
26
− 9y
25
+ ··· − 436y + 64)
c
8
, c
9
, c
12
(y −1)(y
5
− 5y
4
+ ··· − y −1)
2
(y
14
− 11y
13
+ ··· − 5y + 1)
2
· (y
26
− 22y
25
+ ··· − 65y + 16)
c
11
y(y
5
− y
4
+ ··· + 3y −1)
2
(y
14
+ 17y
13
+ ··· − y + 1)
2
· (y
26
+ 15y
25
+ ··· − 142352y + 4096)
23
