11a
109
(K11a
109
)
A knot diagram
1
Linearized knot diagam
5 1 10 9 2 11 3 4 8 6 7
Solving Sequence
4,9 2,5
6 1 8 10 3 7 11
c
4
c
5
c
1
c
8
c
9
c
3
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
45
− 11u
43
+ ··· + 4b − 2u, u
45
− 10u
43
+ ··· + 4a − 4, u
47
+ 2u
46
+ ··· + 4u + 2i
I
u
2
= h110u
5
a
2
− 28u
5
a + ··· − 169a + 180,
− 2u
4
a
2
− u
5
a + 2u
3
a
2
+ 4u
4
a + u
5
+ 2a
2
u
2
+ 2u
3
a + u
4
+ a
3
− 2a
2
u − 5u
2
a − u
3
+ 4au + 2u
2
+ a − 1,
u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
u
3
= hu
3
+ u
2
+ b − u + 1, u
3
− 2u
2
+ 2a + 6, u
4
− 2u
2
+ 2i
I
v
1
= ha, b + 1, v −1i
* 4 irreducible components of dim
C
= 0, with total 70 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
=
hu
45
−11u
43
+· · ·+4b −2u, u
45
−10u
43
+· · ·+4a −4, u
47
+2u
46
+· · ·+4u +2i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−
1
4
u
45
+
5
2
u
43
+ ··· −
1
2
u
3
+ 1
−
1
4
u
45
+
11
4
u
43
+ ··· +
1
2
u
2
+
1
2
u
a
5
=
1
u
2
a
6
=
−
1
2
u
46
+
11
2
u
44
+ ··· −
1
2
u +
1
2
−u
46
− u
45
+ ··· −
7
2
u − 1
a
1
=
−
1
2
u
46
−
3
4
u
45
+ ··· −
1
2
u +
1
2
−
3
4
u
45
+
33
4
u
43
+ ··· −
1
2
u − 1
a
8
=
u
u
a
10
=
−u
3
−u
3
+ u
a
3
=
u
6
− u
4
+ 1
u
6
− 2u
4
+ u
2
a
7
=
−u
11
+ 2u
9
− 2u
7
+ u
3
−u
11
+ 3u
9
− 4u
7
+ 3u
5
− u
3
+ u
a
11
=
−
1
4
u
34
+ 2u
32
+ ··· +
1
2
u +
1
2
−
1
4
u
36
+ 2u
34
+ ··· +
1
2
u
2
+ u
a
11
=
−
1
4
u
34
+ 2u
32
+ ··· +
1
2
u +
1
2
−
1
4
u
36
+ 2u
34
+ ··· +
1
2
u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
46
+ 22u
44
+ ··· − 4u
2
+ 2u
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
47
+ 2u
46
+ ··· − 5u + 5
c
2
u
47
+ 18u
46
+ ··· + 445u + 25
c
3
u
47
+ 6u
46
+ ··· + 736u + 128
c
4
, c
8
u
47
+ 2u
46
+ ··· + 4u + 2
c
6
, c
10
, c
11
u
47
− 2u
46
+ ··· + 23u + 5
c
7
u
47
− 2u
46
+ ··· − 3652u + 3866
c
9
u
47
+ 22u
46
+ ··· + 8u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
47
− 18y
46
+ ··· + 445y −25
c
2
y
47
+ 30y
46
+ ··· − 49175y −625
c
3
y
47
+ 10y
46
+ ··· − 154624y −16384
c
4
, c
8
y
47
− 22y
46
+ ··· + 8y −4
c
6
, c
10
, c
11
y
47
− 50y
46
+ ··· − 211y −25
c
7
y
47
− 14y
46
+ ··· + 245188856y −14945956
c
9
y
47
+ 6y
46
+ ··· − 96y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637057 + 0.718687I
a = −0.721070 + 1.203990I
b = 0.0489452 − 0.0612350I
7.88170 − 7.13370I 4.69775 + 5.86187I
u = 0.637057 − 0.718687I
a = −0.721070 − 1.203990I
b = 0.0489452 + 0.0612350I
7.88170 + 7.13370I 4.69775 − 5.86187I
u = −0.571455 + 0.734273I
a = 0.246152 + 0.401075I
b = 0.880555 + 0.625675I
9.33252 + 1.08584I 6.61100 − 0.78668I
u = −0.571455 − 0.734273I
a = 0.246152 − 0.401075I
b = 0.880555 − 0.625675I
9.33252 − 1.08584I 6.61100 + 0.78668I
u = 1.006040 + 0.471862I
a = 0.029772 − 0.657677I
b = 0.257242 − 0.932477I
−0.11745 − 4.26570I 1.86221 + 7.53589I
u = 1.006040 − 0.471862I
a = 0.029772 + 0.657677I
b = 0.257242 + 0.932477I
−0.11745 + 4.26570I 1.86221 − 7.53589I
u = −0.406762 + 0.786472I
a = 0.118369 − 0.344190I
b = 0.192922 − 0.870022I
8.45114 − 3.90837I 6.00297 + 1.23296I
u = −0.406762 − 0.786472I
a = 0.118369 + 0.344190I
b = 0.192922 + 0.870022I
8.45114 + 3.90837I 6.00297 − 1.23296I
u = 0.359333 + 0.808292I
a = −0.860558 − 0.927434I
b = 2.13804 − 0.70182I
6.36842 + 9.89029I 3.34606 − 5.56719I
u = 0.359333 − 0.808292I
a = −0.860558 + 0.927434I
b = 2.13804 + 0.70182I
6.36842 − 9.89029I 3.34606 + 5.56719I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.099960 + 0.219524I
a = 2.12278 + 0.02040I
b = 1.40098 + 1.56081I
−4.03460 + 3.27231I −6.93849 − 3.87386I
u = 1.099960 − 0.219524I
a = 2.12278 − 0.02040I
b = 1.40098 − 1.56081I
−4.03460 − 3.27231I −6.93849 + 3.87386I
u = 1.117490 + 0.132112I
a = 0.871978 + 0.879966I
b = 0.365572 + 0.512413I
3.39185 + 1.64022I 0.179783 − 0.219910I
u = 1.117490 − 0.132112I
a = 0.871978 − 0.879966I
b = 0.365572 − 0.512413I
3.39185 − 1.64022I 0.179783 + 0.219910I
u = −0.998163 + 0.550991I
a = −0.315047 + 0.102429I
b = −0.898334 − 0.169658I
0.241182 + 1.057240I 0.289576 + 0.557042I
u = −0.998163 − 0.550991I
a = −0.315047 − 0.102429I
b = −0.898334 + 0.169658I
0.241182 − 1.057240I 0.289576 − 0.557042I
u = −0.568933 + 0.644352I
a = −0.15650 − 1.49843I
b = −0.187633 − 0.331112I
1.50796 + 3.62695I 2.13655 − 6.26888I
u = −0.568933 − 0.644352I
a = −0.15650 + 1.49843I
b = −0.187633 + 0.331112I
1.50796 − 3.62695I 2.13655 + 6.26888I
u = 0.951297 + 0.631945I
a = 0.093242 − 0.484467I
b = −0.390493 + 0.618210I
6.94963 + 1.98085I 3.48623 − 0.28252I
u = 0.951297 − 0.631945I
a = 0.093242 + 0.484467I
b = −0.390493 − 0.618210I
6.94963 − 1.98085I 3.48623 + 0.28252I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.108720 + 0.363808I
a = −2.65417 + 0.58730I
b = −2.29701 − 1.20468I
−5.47077 − 3.68113I −9.62046 + 4.56447I
u = 1.108720 − 0.363808I
a = −2.65417 − 0.58730I
b = −2.29701 + 1.20468I
−5.47077 + 3.68113I −9.62046 − 4.56447I
u = −0.365235 + 0.745543I
a = −0.561966 + 1.294290I
b = 1.96786 + 0.35399I
0.49152 − 5.74739I 0.29552 + 5.57964I
u = −0.365235 − 0.745543I
a = −0.561966 − 1.294290I
b = 1.96786 − 0.35399I
0.49152 + 5.74739I 0.29552 − 5.57964I
u = −1.165410 + 0.187983I
a = 2.28007 + 0.42466I
b = 2.08406 − 1.07708I
1.38638 − 7.13549I −2.46560 + 4.47635I
u = −1.165410 − 0.187983I
a = 2.28007 − 0.42466I
b = 2.08406 + 1.07708I
1.38638 + 7.13549I −2.46560 − 4.47635I
u = −1.005960 + 0.623496I
a = 1.24908 + 0.75581I
b = 1.063390 − 0.194010I
8.04432 + 4.08182I 4.48123 − 4.68553I
u = −1.005960 − 0.623496I
a = 1.24908 − 0.75581I
b = 1.063390 + 0.194010I
8.04432 − 4.08182I 4.48123 + 4.68553I
u = −1.111110 + 0.494738I
a = −1.83321 − 1.25072I
b = −2.10148 + 0.95562I
−4.58829 + 3.84650I −8.76666 − 3.56046I
u = −1.111110 − 0.494738I
a = −1.83321 + 1.25072I
b = −2.10148 − 0.95562I
−4.58829 − 3.84650I −8.76666 + 3.56046I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.176480 + 0.396630I
a = −2.40697 − 0.03813I
b = −2.05844 + 1.68830I
−1.23516 + 6.21145I −1.74487 − 7.02826I
u = −1.176480 − 0.396630I
a = −2.40697 + 0.03813I
b = −2.05844 − 1.68830I
−1.23516 − 6.21145I −1.74487 + 7.02826I
u = 0.066156 + 0.753461I
a = 0.967191 + 0.143999I
b = −1.41080 − 0.53958I
2.42833 − 2.22486I 2.96572 + 3.27842I
u = 0.066156 − 0.753461I
a = 0.967191 − 0.143999I
b = −1.41080 + 0.53958I
2.42833 + 2.22486I 2.96572 − 3.27842I
u = −1.111590 + 0.573138I
a = 2.03891 + 1.83979I
b = 3.12984 − 0.32101I
−1.69804 + 10.75150I −2.97142 − 9.27459I
u = −1.111590 − 0.573138I
a = 2.03891 − 1.83979I
b = 3.12984 + 0.32101I
−1.69804 − 10.75150I −2.97142 + 9.27459I
u = 1.168440 + 0.464509I
a = −1.31459 + 1.24173I
b = −2.05354 − 0.47643I
−0.77532 − 2.18171I 0
u = 1.168440 − 0.464509I
a = −1.31459 − 1.24173I
b = −2.05354 + 0.47643I
−0.77532 + 2.18171I 0
u = −1.108280 + 0.598698I
a = −0.816787 + 0.770371I
b = −0.110572 + 0.781750I
6.36874 + 9.11603I 3.03425 − 5.54417I
u = −1.108280 − 0.598698I
a = −0.816787 − 0.770371I
b = −0.110572 − 0.781750I
6.36874 − 9.11603I 3.03425 + 5.54417I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.132790 + 0.591464I
a = 2.36607 − 1.55769I
b = 3.12191 + 1.03804I
4.0697 − 15.1191I 0. + 9.40367I
u = 1.132790 − 0.591464I
a = 2.36607 + 1.55769I
b = 3.12191 − 1.03804I
4.0697 + 15.1191I 0. − 9.40367I
u = −0.664931
a = 1.02381
b = −0.379109
−1.34703 −7.25790
u = 0.448712 + 0.454594I
a = 1.225200 − 0.260236I
b = 0.412150 + 0.326959I
1.43130 + 0.33753I 6.95713 − 1.01845I
u = 0.448712 − 0.454594I
a = 1.225200 + 0.260236I
b = 0.412150 − 0.326959I
1.43130 − 0.33753I 6.95713 + 1.01845I
u = −0.174154 + 0.607070I
a = 1.020160 − 0.035294I
b = −1.365630 + 0.008684I
−2.04844 + 0.43724I −5.38341 − 0.85631I
u = −0.174154 − 0.607070I
a = 1.020160 + 0.035294I
b = −1.365630 − 0.008684I
−2.04844 − 0.43724I −5.38341 + 0.85631I
9
II. I
u
2
= h110u
5
a
2
− 28u
5
a + · · · − 169a + 180, −u
5
a + u
5
+ · · · + a − 1, u
6
−
u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
a
−0.607735a
2
u
5
+ 0.154696au
5
+ ··· + 0.933702a − 0.994475
a
5
=
1
u
2
a
6
=
−0.232044a
2
u
5
− 0.359116au
5
+ ··· + 1.01105a + 0.165746
−0.243094a
2
u
5
+ 0.861878au
5
+ ··· − 1.22652a + 1.60221
a
1
=
−0.607735a
2
u
5
+ 0.154696au
5
+ ··· + 1.93370a − 0.994475
−1.02762a
2
u
5
+ 0.552486au
5
+ ··· − 0.0939227a − 0.408840
a
8
=
u
u
a
10
=
−u
3
−u
3
+ u
a
3
=
u
5
− 2u
3
+ u
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
a
7
=
−1
−u
2
a
11
=
a
−0.607735a
2
u
5
+ 0.154696au
5
+ ··· + 0.933702a − 0.994475
a
11
=
a
−0.607735a
2
u
5
+ 0.154696au
5
+ ··· + 0.933702a − 0.994475
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
4
− 4u
2
+ 4u + 2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
u
18
− 6u
16
+ ··· + u + 1
c
2
u
18
+ 12u
17
+ ··· + u + 1
c
3
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
3
c
4
, c
8
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
3
c
9
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
y
18
− 12y
17
+ ··· − y + 1
c
2
y
18
− 12y
17
+ ··· + 7y + 1
c
3
, c
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
c
4
, c
7
, c
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.348652 − 0.303516I
b = −0.0836886 + 0.0822976I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −1.002190 + 0.295542I
a = 1.54157 − 0.67011I
b = 0.02798 − 1.89773I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −1.002190 + 0.295542I
a = −3.26061 − 1.15289I
b = −2.46071 + 0.67711I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −1.002190 − 0.295542I
a = 0.348652 + 0.303516I
b = −0.0836886 − 0.0822976I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −1.002190 − 0.295542I
a = 1.54157 + 0.67011I
b = 0.02798 + 1.89773I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −1.002190 − 0.295542I
a = −3.26061 + 1.15289I
b = −2.46071 − 0.67711I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = 0.428243 + 0.664531I
a = 0.466201 + 0.792945I
b = −0.025081 + 0.674941I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.428243 + 0.664531I
a = 1.083770 − 0.074988I
b = −1.56679 + 0.56745I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.428243 + 0.664531I
a = 0.285996 − 1.259370I
b = 1.42596 − 0.05764I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.428243 − 0.664531I
a = 0.466201 − 0.792945I
b = −0.025081 − 0.674941I
1.89061 − 0.92430I 3.71672 + 0.79423I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 − 0.664531I
a = 1.083770 + 0.074988I
b = −1.56679 − 0.56745I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 0.428243 − 0.664531I
a = 0.285996 + 1.259370I
b = 1.42596 + 0.05764I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 1.073950 + 0.558752I
a = −0.789928 − 0.420050I
b = −0.640192 − 0.601752I
− 5.69302I 0. + 5.51057I
u = 1.073950 + 0.558752I
a = 1.29540 − 1.82419I
b = 2.40293 − 0.55520I
− 5.69302I 0. + 5.51057I
u = 1.073950 + 0.558752I
a = −1.97105 + 1.48173I
b = −2.08041 − 1.24333I
− 5.69302I 0. + 5.51057I
u = 1.073950 − 0.558752I
a = −0.789928 + 0.420050I
b = −0.640192 + 0.601752I
5.69302I 0. − 5.51057I
u = 1.073950 − 0.558752I
a = 1.29540 + 1.82419I
b = 2.40293 + 0.55520I
5.69302I 0. − 5.51057I
u = 1.073950 − 0.558752I
a = −1.97105 − 1.48173I
b = −2.08041 + 1.24333I
5.69302I 0. − 5.51057I
14
III. I
u
3
= hu
3
+ u
2
+ b − u + 1, u
3
− 2u
2
+ 2a + 6, u
4
− 2u
2
+ 2i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−
1
2
u
3
+ u
2
− 3
−u
3
− u
2
+ u − 1
a
5
=
1
u
2
a
6
=
−
1
2
u
3
+ u
2
− 2
−u
3
+ u − 1
a
1
=
−
1
2
u
3
+ u
2
− 2
−u
3
+ u − 1
a
8
=
u
u
a
10
=
−u
3
−u
3
+ u
a
3
=
−1
−u
2
a
7
=
u
3
u
3
− u
a
11
=
−
3
2
u
3
+ u
2
− 2
−2u
3
+ 2u − 1
a
11
=
−
3
2
u
3
+ u
2
− 2
−2u
3
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
c
11
(u + 1)
4
c
3
, c
7
u
4
+ 2u
2
+ 2
c
4
, c
8
u
4
− 2u
2
+ 2
c
5
, c
6
(u − 1)
4
c
9
(u
2
+ 2u + 2)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
, c
11
(y −1)
4
c
3
, c
7
(y
2
+ 2y + 2)
2
c
4
, c
8
(y
2
− 2y + 2)
2
c
9
(y
2
+ 4)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098680 + 0.455090I
a = −2.32180 + 0.22311I
b = −1.54491 − 2.09868I
−2.46740 − 3.66386I −4.00000 + 4.00000I
u = 1.098680 − 0.455090I
a = −2.32180 − 0.22311I
b = −1.54491 + 2.09868I
−2.46740 + 3.66386I −4.00000 − 4.00000I
u = −1.098680 + 0.455090I
a = −1.67820 − 1.77689I
b = −2.45509 − 0.09868I
−2.46740 + 3.66386I −4.00000 − 4.00000I
u = −1.098680 − 0.455090I
a = −1.67820 + 1.77689I
b = −2.45509 + 0.09868I
−2.46740 − 3.66386I −4.00000 + 4.00000I
18
IV. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
1
0
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
1
=
−1
−1
a
8
=
1
0
a
10
=
1
0
a
3
=
1
0
a
7
=
1
0
a
11
=
0
−1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
11
u − 1
c
2
, c
5
, c
6
u + 1
c
3
, c
4
, c
7
c
8
, c
9
u
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
, c
11
y −1
c
3
, c
4
, c
7
c
8
, c
9
y
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u + 1)
4
(u
18
− 6u
16
+ ··· + u + 1)(u
47
+ 2u
46
+ ··· − 5u + 5)
c
2
((u + 1)
5
)(u
18
+ 12u
17
+ ··· + u + 1)(u
47
+ 18u
46
+ ··· + 445u + 25)
c
3
u(u
4
+ 2u
2
+ 2)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
3
· (u
47
+ 6u
46
+ ··· + 736u + 128)
c
4
, c
8
u(u
4
− 2u
2
+ 2)(u
6
− u
5
+ ··· − u + 1)
3
(u
47
+ 2u
46
+ ··· + 4u + 2)
c
5
((u − 1)
4
)(u + 1)(u
18
− 6u
16
+ ··· + u + 1)(u
47
+ 2u
46
+ ··· − 5u + 5)
c
6
((u − 1)
4
)(u + 1)(u
18
− 6u
16
+ ··· + u + 1)(u
47
− 2u
46
+ ··· + 23u + 5)
c
7
u(u
4
+ 2u
2
+ 2)(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
3
· (u
47
− 2u
46
+ ··· − 3652u + 3866)
c
9
u(u
2
+ 2u + 2)
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
· (u
47
+ 22u
46
+ ··· + 8u + 4)
c
10
, c
11
(u − 1)(u + 1)
4
(u
18
− 6u
16
+ ··· + u + 1)(u
47
− 2u
46
+ ··· + 23u + 5)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y −1)
5
)(y
18
− 12y
17
+ ··· − y + 1)(y
47
− 18y
46
+ ··· + 445y −25)
c
2
((y −1)
5
)(y
18
− 12y
17
+ ··· + 7y + 1)
· (y
47
+ 30y
46
+ ··· − 49175y −625)
c
3
y(y
2
+ 2y + 2)
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
· (y
47
+ 10y
46
+ ··· − 154624y −16384)
c
4
, c
8
y(y
2
− 2y + 2)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· (y
47
− 22y
46
+ ··· + 8y −4)
c
6
, c
10
, c
11
((y −1)
5
)(y
18
− 12y
17
+ ··· − y + 1)(y
47
− 50y
46
+ ··· − 211y −25)
c
7
y(y
2
+ 2y + 2)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· (y
47
− 14y
46
+ ··· + 245188856y −14945956)
c
9
y(y
2
+ 4)
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
· (y
47
+ 6y
46
+ ··· − 96y −16)
24
