12n
0028
(K12n
0028
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 12 4 11 7 6 9 10
Solving Sequence
8,11
9
4,12
7 5 10 1 6 3 2
c
8
c
11
c
7
c
4
c
9
c
12
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.08304 × 10
52
u
37
− 3.92285 × 10
53
u
36
+ ··· + 2.56521 × 10
53
b − 1.92852 × 10
53
,
− 4.66168 × 10
52
u
37
+ 5.98970 × 10
53
u
36
+ ··· + 2.56521 × 10
53
a − 4.47281 × 10
53
,
u
38
− 13u
37
+ ··· − 8u + 1i
I
u
2
= hb, −u
5
a + 2u
4
a + u
5
− 3u
4
− 2u
2
a + 3u
3
+ a
2
+ au − 2u + 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
u
3
= ha
3
+ b + 2a, a
4
− a
3
+ 3a
2
− 2a + 1, u + 1i
I
u
4
= h39a
5
− 213a
4
+ 550a
3
− 390a
2
+ 295b + 748a − 63, a
6
− 5a
5
+ 11a
4
+ 7a
2
+ 2a + 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 60 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
= h3.08 × 10
52
u
37
− 3.92 × 10
53
u
36
+ · · · + 2.57 × 10
53
b − 1.93 ×
10
53
, −4.66 × 10
52
u
37
+ 5.99 × 10
53
u
36
+ · · · + 2.57 × 10
53
a − 4.47 ×
10
53
, u
38
− 13u
37
+ · · · − 8u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
4
=
0.181727u
37
− 2.33497u
36
+ ··· + 20.3488u + 1.74364
−0.120187u
37
+ 1.52925u
36
+ ··· − 5.67119u + 0.751797
a
12
=
u
−u
3
+ u
a
7
=
−0.780745u
37
+ 9.98000u
36
+ ··· − 13.8096u + 4.94182
0.239039u
37
− 3.07898u
36
+ ··· + 2.00450u − 1.30500
a
5
=
1.05713u
37
− 13.6449u
36
+ ··· + 30.2257u − 4.50545
−0.236519u
37
+ 3.03144u
36
+ ··· − 6.54670u + 2.04114
a
10
=
0.187039u
37
− 2.41394u
36
+ ··· − 7.46873u − 2.11666
−0.000250736u
37
+ 0.0152541u
36
+ ··· + 2.70178u + 0.223799
a
1
=
0.0174232u
37
− 0.223414u
36
+ ··· + 2.06976u − 0.961603
0.0147652u
37
− 0.190086u
36
+ ··· + 2.06249u + 0.0414843
a
6
=
−0.758911u
37
+ 9.70005u
36
+ ··· − 13.2564u + 4.74750
0.261495u
37
− 3.36527u
36
+ ··· + 2.54841u − 1.49543
a
3
=
0.858153u
37
− 11.0889u
36
+ ··· + 28.3257u − 4.91506
−0.174044u
37
+ 2.22800u
36
+ ··· − 3.74240u + 1.77583
a
2
=
−0.474366u
37
+ 6.13382u
36
+ ··· + 28.8620u + 0.288063
0.0102207u
37
− 0.155656u
36
+ ··· + 0.659483u − 0.0673376
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.765395u
37
+ 9.83295u
36
+ ··· − 3.08287u + 7.31166
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 28u
37
+ ··· + 159u + 1
c
2
, c
5
u
38
+ 8u
37
+ ··· + 11u + 1
c
3
u
38
− 8u
37
+ ··· + 17360u + 1732
c
4
, c
7
u
38
+ 2u
37
+ ··· − 12288u + 4096
c
6
u
38
− 4u
37
+ ··· − 3u + 1
c
8
, c
11
u
38
+ 13u
37
+ ··· + 8u + 1
c
9
u
38
+ 8u
37
+ ··· − 149993u + 47809
c
10
u
38
+ 2u
37
+ ··· + 575973u + 248449
c
12
u
38
− 3u
37
+ ··· − 11264u + 1024
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
− 28y
37
+ ··· − 10893y + 1
c
2
, c
5
y
38
+ 28y
37
+ ··· + 159y + 1
c
3
y
38
− 84y
37
+ ··· + 436784552y + 2999824
c
4
, c
7
y
38
+ 70y
37
+ ··· + 134217728y + 16777216
c
6
y
38
+ 4y
37
+ ··· + 19y + 1
c
8
, c
11
y
38
+ y
37
+ ··· − 84y + 1
c
9
y
38
+ 48y
37
+ ··· + 51838210455y + 2285700481
c
10
y
38
− 84y
37
+ ··· + 1086486467931y + 61726905601
c
12
y
38
− 69y
37
+ ··· − 7864320y + 1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.872556 + 0.495557I
a = 0.505994 − 0.202943I
b = −0.690714 − 0.617908I
0.91553 + 4.18220I 3.10264 − 7.31279I
u = 0.872556 − 0.495557I
a = 0.505994 + 0.202943I
b = −0.690714 + 0.617908I
0.91553 − 4.18220I 3.10264 + 7.31279I
u = −1.029200 + 0.216658I
a = −0.422423 + 0.457150I
b = −0.209980 + 0.250980I
1.91078 − 0.79833I 4.44525 − 0.45789I
u = −1.029200 − 0.216658I
a = −0.422423 − 0.457150I
b = −0.209980 − 0.250980I
1.91078 + 0.79833I 4.44525 + 0.45789I
u = −0.933302 + 0.093882I
a = −2.24303 + 4.72814I
b = 0.300084 + 0.412662I
1.67684 − 2.65330I 7.7232 − 16.8130I
u = −0.933302 − 0.093882I
a = −2.24303 − 4.72814I
b = 0.300084 − 0.412662I
1.67684 + 2.65330I 7.7232 + 16.8130I
u = −1.130550 + 0.077748I
a = 1.43764 − 2.54970I
b = −0.392217 − 0.325280I
2.15015 + 1.46241I 0. − 14.08993I
u = −1.130550 − 0.077748I
a = 1.43764 + 2.54970I
b = −0.392217 + 0.325280I
2.15015 − 1.46241I 0. + 14.08993I
u = 1.094840 + 0.358324I
a = −0.425261 − 0.241871I
b = 0.269512 + 0.935520I
−0.61516 + 8.47206I −1.23185 − 12.18265I
u = 1.094840 − 0.358324I
a = −0.425261 + 0.241871I
b = 0.269512 − 0.935520I
−0.61516 − 8.47206I −1.23185 + 12.18265I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.851367 + 0.892503I
a = −0.001244 − 0.292263I
b = −0.962152 − 0.487944I
0.067821 − 0.704860I 2.00000 + 2.96425I
u = −0.851367 − 0.892503I
a = −0.001244 + 0.292263I
b = −0.962152 + 0.487944I
0.067821 + 0.704860I 2.00000 − 2.96425I
u = 0.697244 + 0.310286I
a = 0.159158 + 0.892544I
b = 0.334991 − 0.821597I
−3.35491 + 0.78621I −8.48784 − 2.29609I
u = 0.697244 − 0.310286I
a = 0.159158 − 0.892544I
b = 0.334991 + 0.821597I
−3.35491 − 0.78621I −8.48784 + 2.29609I
u = 0.110487 + 0.652381I
a = −0.913173 + 0.555160I
b = 0.154768 + 0.641440I
−1.32113 − 1.32492I −1.95750 + 1.98412I
u = 0.110487 − 0.652381I
a = −0.913173 − 0.555160I
b = 0.154768 − 0.641440I
−1.32113 + 1.32492I −1.95750 − 1.98412I
u = 0.224375 + 1.325980I
a = 0.096188 + 1.029440I
b = 1.75400 + 1.85534I
−6.74677 + 2.59569I 0
u = 0.224375 − 1.325980I
a = 0.096188 − 1.029440I
b = 1.75400 − 1.85534I
−6.74677 − 2.59569I 0
u = −0.281259 + 0.487374I
a = 1.158940 − 0.418649I
b = 1.336190 − 0.226899I
−0.61371 + 2.86891I −0.25435 − 4.83204I
u = −0.281259 − 0.487374I
a = 1.158940 + 0.418649I
b = 1.336190 + 0.226899I
−0.61371 − 2.86891I −0.25435 + 4.83204I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.12152 + 1.66606I
a = 0.019900 − 0.800533I
b = −1.10703 − 1.69579I
−6.26733 − 3.08288I 0
u = 0.12152 − 1.66606I
a = 0.019900 + 0.800533I
b = −1.10703 + 1.69579I
−6.26733 + 3.08288I 0
u = 1.40051 + 1.03446I
a = 1.000780 − 0.696492I
b = −0.98102 − 2.10542I
−16.2164 + 7.5794I 0
u = 1.40051 − 1.03446I
a = 1.000780 + 0.696492I
b = −0.98102 + 2.10542I
−16.2164 − 7.5794I 0
u = 1.24001 + 1.25622I
a = −0.795058 + 0.781650I
b = 0.41366 + 2.27352I
−12.39510 + 1.09723I 0
u = 1.24001 − 1.25622I
a = −0.795058 − 0.781650I
b = 0.41366 − 2.27352I
−12.39510 − 1.09723I 0
u = 1.28856 + 1.21540I
a = 0.770618 − 0.850146I
b = −0.58138 − 2.41986I
−12.2225 + 8.2203I 0
u = 1.28856 − 1.21540I
a = 0.770618 + 0.850146I
b = −0.58138 + 2.41986I
−12.2225 − 8.2203I 0
u = 1.45865 + 1.07373I
a = −0.932042 + 0.820199I
b = 1.14222 + 2.13195I
−15.9377 + 14.9717I 0
u = 1.45865 − 1.07373I
a = −0.932042 − 0.820199I
b = 1.14222 − 2.13195I
−15.9377 − 14.9717I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.137741 + 0.126546I
a = 0.67206 + 4.46519I
b = 0.730737 + 0.068723I
−0.42860 − 2.78462I 1.78865 + 4.97070I
u = −0.137741 − 0.126546I
a = 0.67206 − 4.46519I
b = 0.730737 − 0.068723I
−0.42860 + 2.78462I 1.78865 − 4.97070I
u = 0.135837 + 0.044906I
a = 4.46953 + 0.98915I
b = −0.615656 − 0.694581I
1.12636 + 1.44186I 2.40380 − 3.54555I
u = 0.135837 − 0.044906I
a = 4.46953 − 0.98915I
b = −0.615656 + 0.694581I
1.12636 − 1.44186I 2.40380 + 3.54555I
u = 1.07616 + 1.52432I
a = −0.618148 + 0.747510I
b = −0.22384 + 3.07549I
−17.7767 + 1.7959I 0
u = 1.07616 − 1.52432I
a = −0.618148 − 0.747510I
b = −0.22384 − 3.07549I
−17.7767 − 1.7959I 0
u = 1.14268 + 1.63665I
a = 0.559572 − 0.668950I
b = 0.32782 − 2.75595I
−17.5824 − 5.0951I 0
u = 1.14268 − 1.63665I
a = 0.559572 + 0.668950I
b = 0.32782 + 2.75595I
−17.5824 + 5.0951I 0
8
II. I
u
2
= hb, −u
5
a + u
5
+ · · · + a
2
+ 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
4
=
a
0
a
12
=
u
−u
3
+ u
a
7
=
1
0
a
5
=
a
0
a
10
=
−u
2
+ 1
−u
2
a
1
=
−u
4
+ u
2
− 1
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
a
6
=
u
4
− u
2
+ 1
−u
5
+ u
4
+ 2u
3
− u
2
− u + 1
a
3
=
au + 2a
−2u
5
a + 2u
3
a − 2u
2
a − au + 2a
a
2
=
−u
5
+ 2u
4
+ au − 2u
2
+ 2a + u
−2u
5
a + 2u
3
a − 2u
2
a − au + 2a
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
5
a + 5u
4
a + u
5
+ u
3
a − 7u
4
− 5u
2
a + 3u
3
− au + 4u
2
+ a − 6u − 1
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
7
u
12
c
6
, c
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
8
, c
10
, c
12
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
7
y
12
c
6
, c
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
8
, c
10
, c
11
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.82520 + 2.42341I
b = 0
1.89061 − 2.95419I 11.02954 + 8.16480I
u = −1.002190 + 0.295542I
a = 2.51133 − 0.49706I
b = 0
1.89061 + 1.10558I −0.484082 − 0.231437I
u = −1.002190 − 0.295542I
a = −0.82520 − 2.42341I
b = 0
1.89061 + 2.95419I 11.02954 − 8.16480I
u = −1.002190 − 0.295542I
a = 2.51133 + 0.49706I
b = 0
1.89061 − 1.10558I −0.484082 + 0.231437I
u = 0.428243 + 0.664531I
a = 0.489858 + 0.681154I
b = 0
−1.89061 + 1.10558I −1.04064 − 1.99047I
u = 0.428243 + 0.664531I
a = −0.834826 + 0.083652I
b = 0
−1.89061 − 2.95419I −3.79900 + 4.11613I
u = 0.428243 − 0.664531I
a = 0.489858 − 0.681154I
b = 0
−1.89061 − 1.10558I −1.04064 + 1.99047I
u = 0.428243 − 0.664531I
a = −0.834826 − 0.083652I
b = 0
−1.89061 + 2.95419I −3.79900 − 4.11613I
u = 1.073950 + 0.558752I
a = 0.458424 − 0.081263I
b = 0
7.72290I 2.83009 − 4.64337I
u = 1.073950 + 0.558752I
a = −0.299588 − 0.356375I
b = 0
3.66314I −2.53591 − 3.55776I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = 0.458424 + 0.081263I
b = 0
− 7.72290I 2.83009 + 4.64337I
u = 1.073950 − 0.558752I
a = −0.299588 + 0.356375I
b = 0
− 3.66314I −2.53591 + 3.55776I
13
III. I
u
3
= ha
3
+ b + 2a, a
4
− a
3
+ 3a
2
− 2a + 1, u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
−1
a
9
=
1
−1
a
4
=
a
−a
3
− 2a
a
12
=
−1
0
a
7
=
−a
3
+ a
2
− 2a + 2
a
3
− a
2
+ 3a − 2
a
5
=
−a
3
− a − 1
−a
3
+ a
2
− 2a + 2
a
10
=
−a
2
0
a
1
=
−1
0
a
6
=
a
a
3
− a
2
+ 3a − 2
a
3
=
a
2
+ a + 1
a
3
− a
2
+ 3a − 2
a
2
=
−a
3
+ a
2
− 2a + 2
2a
3
− a
2
+ 5a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7a
2
− 2a − 3
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
7
u
4
+ u
2
− u + 1
c
6
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
8
(u + 1)
4
c
9
, c
10
u
4
− u
3
+ 3u
2
− 2u + 1
c
11
(u − 1)
4
c
12
u
4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
5
c
7
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
8
, c
11
(y −1)
4
c
9
, c
10
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
12
y
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.395123 + 0.506844I
b = −0.547424 − 1.120870I
−0.98010 + 7.64338I −3.08487 − 3.81741I
u = −1.00000
a = 0.395123 − 0.506844I
b = −0.547424 + 1.120870I
−0.98010 − 7.64338I −3.08487 + 3.81741I
u = −1.00000
a = 0.10488 + 1.55249I
b = 0.547424 + 0.585652I
2.62503 + 1.39709I 13.5849 − 5.3845I
u = −1.00000
a = 0.10488 − 1.55249I
b = 0.547424 − 0.585652I
2.62503 − 1.39709I 13.5849 + 5.3845I
17
IV.
I
u
4
= h39a
5
+ 295b + · · · + 748a − 63, a
6
− 5a
5
+ 11a
4
+ 7a
2
+ 2a + 1, u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
−1
a
9
=
1
−1
a
4
=
a
−0.132203a
5
+ 0.722034a
4
+ ··· − 2.53559a + 0.213559
a
12
=
−1
0
a
7
=
0.0610169a
5
− 0.410169a
4
+ ··· + 0.477966a + 1.13220
−0.369492a
5
+ 2.09492a
4
+ ··· − 2.06102a − 0.633898
a
5
=
0.115254a
5
− 0.552542a
4
+ ··· − 1.43051a + 0.583051
−0.593220a
5
+ 2.93220a
4
+ ··· − 2.81356a − 1.11864
a
10
=
0.379661a
5
− 1.99661a
4
+ ··· + 1.64068a + 0.155932
0
a
1
=
−1
0
a
6
=
−0.308475a
5
+ 1.68475a
4
+ ··· − 1.58305a + 0.498305
−0.369492a
5
+ 2.09492a
4
+ ··· − 2.06102a − 0.633898
a
3
=
−0.213559a
5
+ 0.935593a
4
+ ··· + 0.827119a − 0.962712
0.522034a
5
− 2.62034a
4
+ ··· + 1.75593a + 0.464407
a
2
=
0.0813559a
5
− 0.213559a
4
+ ··· + 1.63729a + 0.176271
0.176271a
5
− 0.962712a
4
+ ··· − 0.952542a − 0.284746
(ii) Obstruction class = 1
(iii) Cusp Shapes =
119
59
a
5
−
600
59
a
4
+
1300
59
a
3
+
108
59
a
2
+
411
59
a +
189
59
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
6
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
8
(u + 1)
6
c
9
, c
10
u
6
− 2u
3
+ 4u
2
− 3u + 1
c
11
(u − 1)
6
c
12
u
6
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
5
c
7
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
8
, c
11
(y −1)
6
c
9
, c
10
y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1
c
12
y
6
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.052721 + 0.753034I
b = −0.284920 − 1.115140I
−2.75839 −2.43992 − 2.50363I
u = −1.00000
a = 0.052721 − 0.753034I
b = −0.284920 + 1.115140I
−2.75839 −2.43992 + 2.50363I
u = −1.00000
a = −0.195217 + 0.332027I
b = 0.498832 − 1.001300I
1.37919 − 2.82812I 3.08014 + 1.90022I
u = −1.00000
a = −0.195217 − 0.332027I
b = 0.498832 + 1.001300I
1.37919 + 2.82812I 3.08014 − 1.90022I
u = −1.00000
a = 2.64250 + 2.20145I
b = −0.713912 + 0.305839I
1.37919 + 2.82812I −2.14022 − 3.69351I
u = −1.00000
a = 2.64250 − 2.20145I
b = −0.713912 − 0.305839I
1.37919 − 2.82812I −2.14022 + 3.69351I
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
38
+ 28u
37
+ ··· + 159u + 1)
c
2
(u
2
+ u + 1)
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
38
+ 8u
37
+ ··· + 11u + 1)
c
3
(u
2
− u + 1)
6
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
38
− 8u
37
+ ··· + 17360u + 1732)
c
4
u
12
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
38
+ 2u
37
+ ··· − 12288u + 4096)
c
5
(u
2
− u + 1)
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
38
+ 8u
37
+ ··· + 11u + 1)
c
6
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)(u
38
− 4u
37
+ ··· − 3u + 1)
c
7
u
12
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
38
+ 2u
37
+ ··· − 12288u + 4096)
c
8
((u + 1)
10
)(u
6
− u
5
+ ··· − u + 1)
2
(u
38
+ 13u
37
+ ··· + 8u + 1)
c
9
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
6
− 2u
3
+ 4u
2
− 3u + 1)
· (u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
38
+ 8u
37
+ ··· − 149993u + 47809)
c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
6
− 2u
3
+ 4u
2
− 3u + 1)
· ((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
38
+ 2u
37
+ ··· + 575973u + 248449)
c
11
((u − 1)
10
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
38
+ 13u
37
+ ··· + 8u + 1)
c
12
u
10
(u
6
− u
5
+ ··· − u + 1)
2
(u
38
− 3u
37
+ ··· − 11264u + 1024)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
38
− 28y
37
+ ··· − 10893y + 1)
c
2
, c
5
(y
2
+ y + 1)
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
38
+ 28y
37
+ ··· + 159y + 1)
c
3
(y
2
+ y + 1)
6
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
38
− 84y
37
+ ··· + 436784552y + 2999824)
c
4
, c
7
y
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
38
+ 70y
37
+ ··· + 134217728y + 16777216)
c
6
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· ((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
38
+ 4y
37
+ ··· + 19y + 1)
c
8
, c
11
(y −1)
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
38
+ y
37
+ ··· − 84y + 1)
c
9
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1)
· (y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
38
+ 48y
37
+ ··· + 51838210455y + 2285700481)
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1)
· (y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
38
− 84y
37
+ ··· + 1086486467931y + 61726905601)
c
12
y
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
38
− 69y
37
+ ··· − 7864320y + 1048576)
23
