12n
0069
(K12n
0069
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 8 10 3 12 6 1 9 11
Solving Sequence
9,12 3,8
4 7 11 1 2 5 10 6
c
8
c
3
c
7
c
11
c
12
c
1
c
4
c
10
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.25022 × 10
15
u
50
+ 6.32707 × 10
15
u
49
+ ··· + 5.27740 × 10
14
b + 1.09741 × 10
15
,
− 315570811462394u
50
+ 885003680032642u
49
+ ··· + 263870210392814a − 2615309819180911,
u
51
− 5u
50
+ ··· + 12u + 1i
I
u
2
= h−u
6
+ u
5
− u
4
− u
2
+ b, −u
4
+ u
3
− u
2
+ a − 1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
u
3
= h−a
2
u − au + b + u, a
3
− a
2
u + 2a
2
− au − a + u − 2, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 66 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−1.25 × 10
15
u
50
+ 6.33 × 10
15
u
49
+ · · · + 5.28 × 10
14
b + 1.10 ×
10
15
, −3.16 × 10
14
u
50
+ 8.85 × 10
14
u
49
+ · · · + 2.64 × 10
14
a − 2.62 ×
10
15
, u
51
− 5u
50
+ · · · + 12u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
3
=
1.19593u
50
− 3.35394u
49
+ ··· + 22.7516u + 9.91135
2.36901u
50
− 11.9890u
49
+ ··· − 33.0652u − 2.07945
a
8
=
1
u
2
a
4
=
2.03208u
50
− 6.11447u
49
+ ··· + 23.1122u + 9.36508
3.57786u
50
− 18.1788u
49
+ ··· − 50.9440u − 3.49968
a
7
=
−0.655866u
50
+ 0.100505u
49
+ ··· − 30.5833u − 5.33675
−2.04168u
50
+ 11.1347u
49
+ ··· + 35.7500u + 2.53294
a
11
=
−u
u
a
1
=
−u
3
u
3
+ u
a
2
=
2.38515u
50
− 7.53764u
49
+ ··· + 6.70994u + 6.22567
4.11391u
50
− 20.5592u
49
+ ··· − 49.6817u − 3.68437
a
5
=
−0.280392u
50
− 0.591852u
49
+ ··· − 1.39584u + 2.65716
−2.25255u
50
+ 11.2149u
49
+ ··· + 29.5667u + 2.69754
a
10
=
−u
5
− u
u
5
+ u
3
+ u
a
6
=
0.694241u
50
− 0.897617u
49
+ ··· − 3.96472u − 3.36089
2.79370u
50
− 14.0251u
49
+ ··· − 36.9379u − 3.27732
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
255965214862211
131935105196407
u
50
+
1522307809078135
263870210392814
u
49
+ ··· −
2747389394610787
131935105196407
u −
1408076674646089
131935105196407
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
51
+ 10u
50
+ ··· − 5u + 1
c
2
, c
4
u
51
− 12u
50
+ ··· − 9u + 1
c
3
, c
7
u
51
− 3u
50
+ ··· − 512u + 512
c
5
u
51
+ 4u
50
+ ··· − u + 1
c
6
, c
9
u
51
− 2u
50
+ ··· + 32u + 64
c
8
, c
11
u
51
+ 5u
50
+ ··· + 12u − 1
c
10
, c
12
u
51
+ 15u
50
+ ··· + 132u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
51
+ 74y
50
+ ··· − 5y −1
c
2
, c
4
y
51
− 10y
50
+ ··· − 5y −1
c
3
, c
7
y
51
+ 63y
50
+ ··· − 1310720y −262144
c
5
y
51
− 66y
50
+ ··· + 55y −1
c
6
, c
9
y
51
− 40y
50
+ ··· + 33792y −4096
c
8
, c
11
y
51
+ 15y
50
+ ··· + 132y −1
c
10
, c
12
y
51
+ 47y
50
+ ··· + 21000y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.536812 + 0.848543I
a = −3.28628 − 1.11420I
b = 0.02773 + 3.59095I
−1.34634 − 2.15686I −38.8808 − 5.4252I
u = −0.536812 − 0.848543I
a = −3.28628 + 1.11420I
b = 0.02773 − 3.59095I
−1.34634 + 2.15686I −38.8808 + 5.4252I
u = −0.094060 + 1.010250I
a = −0.112437 + 0.884543I
b = 0.240148 − 0.241280I
−2.30980 − 2.34904I −1.63391 + 4.30826I
u = −0.094060 − 1.010250I
a = −0.112437 − 0.884543I
b = 0.240148 + 0.241280I
−2.30980 + 2.34904I −1.63391 − 4.30826I
u = 0.742640 + 0.708697I
a = −0.254347 − 0.182338I
b = 0.276012 + 0.545830I
3.40321 − 2.16441I 5.02879 + 4.36220I
u = 0.742640 − 0.708697I
a = −0.254347 + 0.182338I
b = 0.276012 − 0.545830I
3.40321 + 2.16441I 5.02879 − 4.36220I
u = −0.671229 + 0.780928I
a = −0.409812 − 0.918047I
b = −0.370682 + 1.062140I
1.10678 − 2.18307I 1.75585 + 4.26435I
u = −0.671229 − 0.780928I
a = −0.409812 + 0.918047I
b = −0.370682 − 1.062140I
1.10678 + 2.18307I 1.75585 − 4.26435I
u = −0.343157 + 0.972562I
a = −1.52133 + 0.33833I
b = 0.746603 + 0.561119I
−0.84537 − 2.80643I 0.19319 + 7.33231I
u = −0.343157 − 0.972562I
a = −1.52133 − 0.33833I
b = 0.746603 − 0.561119I
−0.84537 + 2.80643I 0.19319 − 7.33231I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.906899 + 0.049738I
a = −0.05164 + 1.55010I
b = −0.207366 − 0.576620I
10.08960 − 3.82704I 3.71077 + 2.41179I
u = −0.906899 − 0.049738I
a = −0.05164 − 1.55010I
b = −0.207366 + 0.576620I
10.08960 + 3.82704I 3.71077 − 2.41179I
u = −0.634734 + 0.940518I
a = −1.031740 − 0.008845I
b = 0.734442 + 0.646858I
0.59171 − 2.88116I 1.02571 + 2.36792I
u = −0.634734 − 0.940518I
a = −1.031740 + 0.008845I
b = 0.734442 − 0.646858I
0.59171 + 2.88116I 1.02571 − 2.36792I
u = −0.231781 + 0.820128I
a = 1.19571 + 1.76809I
b = 0.08039 − 2.15413I
−2.70466 − 1.62087I −0.49766 + 1.58102I
u = −0.231781 − 0.820128I
a = 1.19571 − 1.76809I
b = 0.08039 + 2.15413I
−2.70466 + 1.62087I −0.49766 − 1.58102I
u = 0.281941 + 0.765767I
a = 2.01085 + 0.32244I
b = −0.827511 − 0.669898I
2.53081 + 4.23664I −4.52353 + 0.13902I
u = 0.281941 − 0.765767I
a = 2.01085 − 0.32244I
b = −0.827511 + 0.669898I
2.53081 − 4.23664I −4.52353 − 0.13902I
u = 0.946253 + 0.718970I
a = 0.29613 + 1.52046I
b = −2.57630 − 0.83741I
14.2145 − 8.1932I 2.56257 + 3.05589I
u = 0.946253 − 0.718970I
a = 0.29613 − 1.52046I
b = −2.57630 + 0.83741I
14.2145 + 8.1932I 2.56257 − 3.05589I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.818205 + 0.870861I
a = 0.71161 + 1.65346I
b = −1.57668 − 0.05628I
3.54064 + 1.51067I 0. − 2.09785I
u = 0.818205 − 0.870861I
a = 0.71161 − 1.65346I
b = −1.57668 + 0.05628I
3.54064 − 1.51067I 0. + 2.09785I
u = 0.869595 + 0.828375I
a = 0.627708 + 0.017566I
b = −1.261280 + 0.334121I
7.00223 − 0.65691I 3.27323 + 0.I
u = 0.869595 − 0.828375I
a = 0.627708 − 0.017566I
b = −1.261280 − 0.334121I
7.00223 + 0.65691I 3.27323 + 0.I
u = 0.703781 + 0.984612I
a = 0.766481 + 0.030963I
b = −0.309574 + 0.323070I
2.57944 + 7.69347I 4.07652 − 9.82403I
u = 0.703781 − 0.984612I
a = 0.766481 − 0.030963I
b = −0.309574 − 0.323070I
2.57944 − 7.69347I 4.07652 + 9.82403I
u = −0.839716 + 0.871954I
a = −1.06327 + 2.00567I
b = 3.24142 − 0.39313I
9.25314 + 0.69544I 0
u = −0.839716 − 0.871954I
a = −1.06327 − 2.00567I
b = 3.24142 + 0.39313I
9.25314 − 0.69544I 0
u = −0.277519 + 1.189370I
a = −1.44184 − 0.41933I
b = 1.239660 − 0.206290I
5.79395 − 7.83565I 0. + 5.73327I
u = −0.277519 − 1.189370I
a = −1.44184 + 0.41933I
b = 1.239660 + 0.206290I
5.79395 + 7.83565I 0. − 5.73327I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.803600 + 0.919882I
a = −0.473301 − 0.798618I
b = 1.99513 + 0.47998I
3.38835 + 4.55859I 0. − 3.21833I
u = 0.803600 − 0.919882I
a = −0.473301 + 0.798618I
b = 1.99513 − 0.47998I
3.38835 − 4.55859I 0. + 3.21833I
u = 0.951705 + 0.774303I
a = −0.44896 − 1.74202I
b = 2.48425 + 0.81897I
15.3068 − 0.2972I 0
u = 0.951705 − 0.774303I
a = −0.44896 + 1.74202I
b = 2.48425 − 0.81897I
15.3068 + 0.2972I 0
u = −0.348613 + 1.179410I
a = 0.874337 + 0.615537I
b = −0.753430 + 0.266431I
6.24476 − 0.53865I 0
u = −0.348613 − 1.179410I
a = 0.874337 − 0.615537I
b = −0.753430 − 0.266431I
6.24476 + 0.53865I 0
u = −0.817892 + 0.928643I
a = 1.28285 − 2.22579I
b = −3.27673 + 0.29519I
9.07395 − 6.87436I 0. + 4.69588I
u = −0.817892 − 0.928643I
a = 1.28285 + 2.22579I
b = −3.27673 − 0.29519I
9.07395 + 6.87436I 0. − 4.69588I
u = 0.815253 + 0.972044I
a = −0.129107 − 1.389170I
b = 0.894314 + 0.620552I
6.55249 + 6.91504I 0
u = 0.815253 − 0.972044I
a = −0.129107 + 1.389170I
b = 0.894314 − 0.620552I
6.55249 − 6.91504I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.382213 + 0.598227I
a = −1.50501 − 0.47756I
b = 0.588819 + 0.737449I
3.06808 − 1.61207I −0.16491 + 5.64429I
u = 0.382213 − 0.598227I
a = −1.50501 + 0.47756I
b = 0.588819 − 0.737449I
3.06808 + 1.61207I −0.16491 − 5.64429I
u = 0.793119 + 1.061710I
a = −1.78595 − 1.61228I
b = 2.94405 − 0.44989I
13.1325 + 14.5878I 0
u = 0.793119 − 1.061710I
a = −1.78595 + 1.61228I
b = 2.94405 + 0.44989I
13.1325 − 14.5878I 0
u = 0.827403 + 1.041820I
a = 1.65771 + 1.36481I
b = −2.86877 + 0.33442I
14.4581 + 6.8314I 0
u = 0.827403 − 1.041820I
a = 1.65771 − 1.36481I
b = −2.86877 − 0.33442I
14.4581 − 6.8314I 0
u = −0.105235 + 0.624758I
a = 1.54589 + 1.13818I
b = 0.324601 − 0.482306I
−1.65146 − 0.02846I −5.98427 + 0.19920I
u = −0.105235 − 0.624758I
a = 1.54589 − 1.13818I
b = 0.324601 + 0.482306I
−1.65146 + 0.02846I −5.98427 − 0.19920I
u = −0.586526 + 0.208462I
a = −0.208700 − 0.246043I
b = −0.565071 + 0.589283I
1.50163 − 0.56025I 5.46794 + 1.34072I
u = −0.586526 − 0.208462I
a = −0.208700 + 0.246043I
b = −0.565071 − 0.589283I
1.50163 + 0.56025I 5.46794 − 1.34072I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0830715
a = 8.50895
b = 0.551653
−1.20993 −9.33730
10
II. I
u
2
= h−u
6
+ u
5
− u
4
− u
2
+ b, −u
4
+ u
3
− u
2
+ a − 1, u
9
− u
8
+ 2u
7
−
u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
3
=
u
4
− u
3
+ u
2
+ 1
u
6
− u
5
+ u
4
+ u
2
a
8
=
1
u
2
a
4
=
u
4
− u
3
+ u
2
+ 1
u
6
− u
5
+ u
4
+ u
2
a
7
=
1
u
2
a
11
=
−u
u
a
1
=
−u
3
u
3
+ u
a
2
=
u
4
− 2u
3
+ u
2
+ 1
u
6
− u
5
+ u
4
+ u
3
+ u
2
+ u
a
5
=
u
3
−u
3
− u
a
10
=
−u
5
− u
u
5
+ u
3
+ u
a
6
=
−u
5
− u
−u
7
− u
5
− 2u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
8
− 7u
7
+ 8u
6
− 8u
5
+ 8u
4
− 12u
3
+ 6u
2
− 2u − 2
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
6
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
8
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
6
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
10
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = 0.457852 + 1.072010I
b = −0.128062 − 1.105260I
−3.42837 − 2.09337I −9.96342 + 4.61282I
u = −0.140343 − 0.966856I
a = 0.457852 − 1.072010I
b = −0.128062 + 1.105260I
−3.42837 + 2.09337I −9.96342 − 4.61282I
u = −0.628449 + 0.875112I
a = −1.63880 − 0.65075I
b = −0.10799 + 2.04391I
−1.02799 − 2.45442I −3.17587 + 4.82524I
u = −0.628449 − 0.875112I
a = −1.63880 + 0.65075I
b = −0.10799 − 2.04391I
−1.02799 + 2.45442I −3.17587 − 4.82524I
u = 0.796005 + 0.733148I
a = 0.522253 + 0.392004I
b = −0.407341 + 0.647242I
2.72642 − 1.33617I 0.058077 − 1.140630I
u = 0.796005 − 0.733148I
a = 0.522253 − 0.392004I
b = −0.407341 − 0.647242I
2.72642 + 1.33617I 0.058077 + 1.140630I
u = 0.728966 + 0.986295I
a = 0.425734 − 0.444312I
b = 0.450985 + 0.808297I
1.95319 + 7.08493I −2.55209 − 3.65320I
u = 0.728966 − 0.986295I
a = 0.425734 + 0.444312I
b = 0.450985 − 0.808297I
1.95319 − 7.08493I −2.55209 + 3.65320I
u = −0.512358
a = 1.46592
b = 0.384820
−0.446489 3.26660
14
III. I
u
3
= h−a
2
u − au + b + u, a
3
− a
2
u + 2a
2
− au − a + u − 2, u
2
+ u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
3
=
a
a
2
u + au − u
a
8
=
1
−u − 1
a
4
=
−a
2
u − 2au + u
a
2
u − a
2
+ 2au − a − u + 1
a
7
=
a
2
u + au + a − 3u
0
a
11
=
−u
u
a
1
=
−1
u + 1
a
2
=
a
2
u + au + a − 3u − 2
2u + 2
a
5
=
a
2
u + a
2
+ a − 3u − 3
−a
2
u − a
2
− a + 3u + 3
a
10
=
1
0
a
6
=
a
2
u + au + a − 3u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8a
2
u − 4a
2
− 6au − 7a + 16u + 9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
(u
3
+ 3u
2
+ 2u − 1)
2
c
6
, c
9
u
6
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
8
, c
12
(u
2
+ u + 1)
3
c
10
, c
11
(u
2
− u + 1)
3
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
(y
3
− 5y
2
+ 10y −1)
2
c
6
, c
9
y
6
c
8
, c
10
, c
11
c
12
(y
2
+ y + 1)
3
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.901916 + 0.094973I
b = −0.583789 + 0.478572I
3.02413 + 0.79824I −0.92725 + 3.21674I
u = −0.500000 + 0.866025I
a = −1.362120 + 0.277556I
b = 0.706350 − 0.266290I
3.02413 − 4.85801I 2.65209 + 7.50333I
u = −0.500000 + 0.866025I
a = −2.03980 + 0.49350I
b = 0.87744 + 1.51977I
−1.11345 − 2.02988I −2.22484 − 4.65789I
u = −0.500000 − 0.866025I
a = 0.901916 − 0.094973I
b = −0.583789 − 0.478572I
3.02413 − 0.79824I −0.92725 − 3.21674I
u = −0.500000 − 0.866025I
a = −1.362120 − 0.277556I
b = 0.706350 + 0.266290I
3.02413 + 4.85801I 2.65209 − 7.50333I
u = −0.500000 − 0.866025I
a = −2.03980 − 0.49350I
b = 0.87744 − 1.51977I
−1.11345 + 2.02988I −2.22484 + 4.65789I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
3
− u
2
+ 2u − 1)
2
(u
51
+ 10u
50
+ ··· − 5u + 1)
c
2
((u − 1)
9
)(u
3
+ u
2
− 1)
2
(u
51
− 12u
50
+ ··· − 9u + 1)
c
3
u
9
(u
3
− u
2
+ 2u − 1)
2
(u
51
− 3u
50
+ ··· − 512u + 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)
2
(u
51
− 12u
50
+ ··· − 9u + 1)
c
5
(u
3
+ 3u
2
+ 2u − 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
51
+ 4u
50
+ ··· − u + 1)
c
6
u
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
51
− 2u
50
+ ··· + 32u + 64)
c
7
u
9
(u
3
+ u
2
+ 2u + 1)
2
(u
51
− 3u
50
+ ··· − 512u + 512)
c
8
(u
2
+ u + 1)
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
51
+ 5u
50
+ ··· + 12u − 1)
c
9
u
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
51
− 2u
50
+ ··· + 32u + 64)
c
10
(u
2
− u + 1)
3
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
51
+ 15u
50
+ ··· + 132u − 1)
c
11
(u
2
− u + 1)
3
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
51
+ 5u
50
+ ··· + 12u − 1)
c
12
(u
2
+ u + 1)
3
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
51
+ 15u
50
+ ··· + 132u − 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
3
+ 3y
2
+ 2y −1)
2
(y
51
+ 74y
50
+ ··· − 5y −1)
c
2
, c
4
((y −1)
9
)(y
3
− y
2
+ 2y −1)
2
(y
51
− 10y
50
+ ··· − 5y −1)
c
3
, c
7
y
9
(y
3
+ 3y
2
+ 2y −1)
2
(y
51
+ 63y
50
+ ··· − 1310720y −262144)
c
5
(y
3
− 5y
2
+ 10y −1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
51
− 66y
50
+ ··· + 55y −1)
c
6
, c
9
y
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
51
− 40y
50
+ ··· + 33792y −4096)
c
8
, c
11
(y
2
+ y + 1)
3
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
51
+ 15y
50
+ ··· + 132y −1)
c
10
, c
12
((y
2
+ y + 1)
3
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
51
+ 47y
50
+ ··· + 21000y −1)
20
