12n
0274
(K12n
0274
)
A knot diagram
1
Linearized knot diagam
3 4 11 2 10 4 12 3 6 9 8 7
Solving Sequence
8,11 4,12
3 9 2 5 7 1 6 10
c
11
c
3
c
8
c
2
c
4
c
7
c
12
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
12
+ 5u
11
− 18u
10
+ 45u
9
− 87u
8
+ 135u
7
− 162u
6
+ 154u
5
− 100u
4
+ 34u
3
+ 12u
2
+ 4b − 24u + 8,
− u
11
+ 5u
10
− 18u
9
+ 41u
8
− 75u
7
+ 103u
6
− 110u
5
+ 86u
4
− 36u
3
− 2u
2
+ 4a + 20u − 12,
u
13
− 5u
12
+ 18u
11
− 45u
10
+ 89u
9
− 141u
8
+ 178u
7
− 180u
6
+ 134u
5
− 64u
4
+ 4u
3
+ 24u
2
− 16u + 4i
I
u
2
= h−u
11
a − 2u
10
a + ··· − 2a − 3, 3u
12
a − u
12
+ ··· + 2a
2
− 2,
u
13
+ 2u
12
+ 7u
11
+ 10u
10
+ 18u
9
+ 20u
8
+ 21u
7
+ 20u
6
+ 11u
5
+ 10u
4
+ u
3
+ 4u
2
+ 2i
I
u
3
= h−au + 9b + 4a − u + 4, 2a
2
− au + 3u + 5, u
2
+ 2i
I
u
4
= h4b + 2a + u + 2, 2a
2
+ 2au + 5, u
2
+ 2i
I
v
1
= ha, b
2
− b + 1, v + 1i
I
v
2
= ha, b + v −1, v
2
− v + 1i
* 6 irreducible components of dim
C
= 0, with total 51 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−u
12
+5u
11
+· · ·+4b+8, −u
11
+5u
10
+· · ·+4a−12, u
13
−5u
12
+· · ·−16u+4i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
4
=
1
4
u
11
−
5
4
u
10
+ ··· − 5u + 3
1
4
u
12
−
5
4
u
11
+ ··· + 6u − 2
a
12
=
1
u
2
a
3
=
1
4
u
12
− u
11
+ ··· + u + 1
1
4
u
12
−
5
4
u
11
+ ··· + 6u − 2
a
9
=
1
4
u
12
− u
11
+ ··· +
1
2
u
2
− 2u
−
1
4
u
12
+
3
4
u
11
+ ··· − u + 1
a
2
=
1
4
u
12
−
3
2
u
11
+ ··· + 8u − 2
−
1
4
u
12
+
5
4
u
11
+ ··· − 4u + 1
a
5
=
−u
12
+ 5u
11
+ ··· − 20u + 7
u
4
+ 2u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
1
2
u
12
−
9
4
u
11
+ ··· + 10u − 4
1
4
u
12
−
5
4
u
11
+ ··· + 4u − 1
a
10
=
1
2
u
12
−
5
4
u
11
+ ··· −
1
2
u
2
+ u
1
4
u
12
−
3
4
u
11
+ ··· − 2u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
12
−7u
11
+25u
10
−55u
9
+106u
8
−159u
7
+190u
6
−185u
5
+117u
4
−42u
3
−22u
2
+42u−14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
+ 19u
12
+ ··· + 15u − 1
c
2
, c
4
, c
10
u
13
− 3u
12
+ ··· − u + 1
c
3
, c
5
, c
9
u
13
+ u
12
+ 2u
11
+ u
10
+ 6u
9
+ 4u
8
+ 8u
7
+ 3u
6
+ 8u
5
+ 4u
3
+ u
2
+ u + 1
c
6
u
13
+ u
12
+ ··· + 1321u + 181
c
7
, c
11
, c
12
u
13
− 5u
12
+ ··· − 16u + 4
c
8
u
13
− u
12
+ ··· − 39u + 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 61y
12
+ ··· + 287y −1
c
2
, c
4
, c
10
y
13
+ 19y
12
+ ··· + 15y −1
c
3
, c
5
, c
9
y
13
+ 3y
12
+ ··· − y −1
c
6
y
13
+ 39y
12
+ ··· + 2051655y −32761
c
7
, c
11
, c
12
y
13
+ 11y
12
+ ··· + 64y −16
c
8
y
13
− 13y
12
+ ··· + 1191y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.148130 + 0.133771I
a = −0.461030 + 0.761015I
b = −0.953736 − 1.010370I
−12.6764 − 7.1373I −6.57814 + 4.53811I
u = 1.148130 − 0.133771I
a = −0.461030 − 0.761015I
b = −0.953736 + 1.010370I
−12.6764 + 7.1373I −6.57814 − 4.53811I
u = 0.122498 + 1.377410I
a = −0.69924 + 2.04411I
b = −0.201153 − 0.911850I
7.00880 − 3.27286I 6.62507 + 4.15467I
u = 0.122498 − 1.377410I
a = −0.69924 − 2.04411I
b = −0.201153 + 0.911850I
7.00880 + 3.27286I 6.62507 − 4.15467I
u = −0.12567 + 1.42776I
a = −0.020580 − 1.032540I
b = −0.563900 + 0.510841I
3.89768 + 2.33726I −4.18156 − 2.46985I
u = −0.12567 − 1.42776I
a = −0.020580 + 1.032540I
b = −0.563900 − 0.510841I
3.89768 − 2.33726I −4.18156 + 2.46985I
u = −0.534170
a = 0.577891
b = 0.497979
−0.888404 −11.3990
u = 0.67458 + 1.31287I
a = −0.656821 + 0.500993I
b = 0.999822 − 0.879885I
−9.09521 + 0.75227I −5.18637 − 1.36359I
u = 0.67458 − 1.31287I
a = −0.656821 − 0.500993I
b = 0.999822 + 0.879885I
−9.09521 − 0.75227I −5.18637 + 1.36359I
u = 0.420458 + 0.308747I
a = 1.11560 − 0.96767I
b = 0.108686 + 0.774322I
1.70562 − 1.30597I 1.36439 + 5.54852I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.420458 − 0.308747I
a = 1.11560 + 0.96767I
b = 0.108686 − 0.774322I
1.70562 + 1.30597I 1.36439 − 5.54852I
u = 0.52709 + 1.45902I
a = 0.43312 − 1.92910I
b = 0.861292 + 1.076230I
−7.6681 − 13.1014I −3.34370 + 7.13870I
u = 0.52709 − 1.45902I
a = 0.43312 + 1.92910I
b = 0.861292 − 1.076230I
−7.6681 + 13.1014I −3.34370 − 7.13870I
6
II. I
u
2
=
h−u
11
a−2u
10
a+· · ·−2a−3, 3u
12
a−u
12
+· · ·+2a
2
−2, u
13
+2u
12
+· · ·+4u
2
+2i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
4
=
a
1
2
u
11
a + u
10
a + ··· + a +
3
2
a
12
=
1
u
2
a
3
=
1
2
u
11
a + u
10
a + ··· + 2a +
3
2
1
2
u
11
a + u
10
a + ··· + a +
3
2
a
9
=
−
1
2
u
12
a −
3
2
u
11
a + ··· − 3u
2
−
5
2
u
−
1
2
u
12
a +
1
2
u
12
+ ··· + a +
1
2
a
2
=
−
1
2
u
12
a +
1
4
u
12
+ ··· +
3
2
a +
5
2
1
2
u
11
a +
1
2
u
12
+ ··· + 2a −
1
2
a
5
=
u
12
+ u
11
+ ··· + 2a − 3
u
4
+ 2u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
1
2
u
12
a +
1
2
u
11
+ ··· − 2a +
1
2
1
2
u
11
a −
1
2
u
12
+ ··· + 2a −
5
2
a
10
=
1
2
u
12
a −
1
4
u
12
+ ··· +
3
2
a +
5
2
1
2
u
11
a +
1
2
u
12
+ ··· + 2a +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −u
12
− 3u
10
+ 4u
9
+ 2u
8
+ 14u
7
+ 15u
6
+ 12u
5
+ 17u
4
− 2u
3
+ 7u
2
− 6u
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
+ 30u
25
+ ··· − 1609u + 81
c
2
, c
4
, c
10
u
26
− 6u
25
+ ··· − 95u + 9
c
3
, c
5
, c
9
u
26
+ 2u
25
+ ··· − 5u + 3
c
6
u
26
+ 3u
25
+ ··· − 8726u + 1181
c
7
, c
11
, c
12
(u
13
+ 2u
12
+ ··· + 4u
2
+ 2)
2
c
8
u
26
+ u
25
+ ··· − 456u + 241
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
− 50y
25
+ ··· + 5625167y + 6561
c
2
, c
4
, c
10
y
26
+ 30y
25
+ ··· − 1609y + 81
c
3
, c
5
, c
9
y
26
+ 6y
25
+ ··· + 95y + 9
c
6
y
26
+ 37y
25
+ ··· − 40866606y + 1394761
c
7
, c
11
, c
12
(y
13
+ 10y
12
+ ··· − 16y −4)
2
c
8
y
26
− 15y
25
+ ··· − 481230y + 58081
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.190251 + 0.933207I
a = 0.298460 − 0.362265I
b = 0.719395 + 0.860977I
1.31987 + 0.84014I −1.01632 − 1.58660I
u = −0.190251 + 0.933207I
a = −0.31610 − 2.95092I
b = −0.406685 + 1.088750I
1.31987 + 0.84014I −1.01632 − 1.58660I
u = −0.190251 − 0.933207I
a = 0.298460 + 0.362265I
b = 0.719395 − 0.860977I
1.31987 − 0.84014I −1.01632 + 1.58660I
u = −0.190251 − 0.933207I
a = −0.31610 + 2.95092I
b = −0.406685 − 1.088750I
1.31987 − 0.84014I −1.01632 + 1.58660I
u = −0.522806 + 0.734222I
a = 0.408662 + 0.796811I
b = 0.798739 − 0.694333I
−1.83264 + 2.12437I −6.63093 − 3.54511I
u = −0.522806 + 0.734222I
a = 0.671809 − 0.426036I
b = −0.780847 − 0.269963I
−1.83264 + 2.12437I −6.63093 − 3.54511I
u = −0.522806 − 0.734222I
a = 0.408662 − 0.796811I
b = 0.798739 + 0.694333I
−1.83264 − 2.12437I −6.63093 + 3.54511I
u = −0.522806 − 0.734222I
a = 0.671809 + 0.426036I
b = −0.780847 + 0.269963I
−1.83264 − 2.12437I −6.63093 + 3.54511I
u = 0.354216 + 1.088690I
a = 0.804166 − 1.057380I
b = 0.780806 + 0.869479I
1.27349 − 6.51495I −1.32958 + 6.90681I
u = 0.354216 + 1.088690I
a = −0.53542 + 2.66449I
b = −0.376849 − 1.157840I
1.27349 − 6.51495I −1.32958 + 6.90681I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.354216 − 1.088690I
a = 0.804166 + 1.057380I
b = 0.780806 − 0.869479I
1.27349 + 6.51495I −1.32958 − 6.90681I
u = 0.354216 − 1.088690I
a = −0.53542 − 2.66449I
b = −0.376849 + 1.157840I
1.27349 + 6.51495I −1.32958 − 6.90681I
u = −1.16445
a = −0.292211 + 0.542220I
b = −0.996994 − 0.942106I
−12.9066 −6.99580
u = −1.16445
a = −0.292211 − 0.542220I
b = −0.996994 + 0.942106I
−12.9066 −6.99580
u = 0.475729 + 0.397522I
a = 0.255684 + 0.929938I
b = 0.587541 − 0.997816I
−0.73347 + 3.14087I −5.81698 − 0.90558I
u = 0.475729 + 0.397522I
a = 0.907624 + 1.022940I
b = −0.603946 + 0.535433I
−0.73347 + 3.14087I −5.81698 − 0.90558I
u = 0.475729 − 0.397522I
a = 0.255684 − 0.929938I
b = 0.587541 + 0.997816I
−0.73347 − 3.14087I −5.81698 + 0.90558I
u = 0.475729 − 0.397522I
a = 0.907624 − 1.022940I
b = −0.603946 − 0.535433I
−0.73347 − 3.14087I −5.81698 + 0.90558I
u = 0.065416 + 1.409480I
a = −0.944118 + 0.771575I
b = −0.110601 − 0.414458I
5.12373 + 1.84437I 0.90018 − 3.35466I
u = 0.065416 + 1.409480I
a = 0.14726 − 1.84752I
b = −0.534312 + 0.945546I
5.12373 + 1.84437I 0.90018 − 3.35466I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.065416 − 1.409480I
a = −0.944118 − 0.771575I
b = −0.110601 + 0.414458I
5.12373 − 1.84437I 0.90018 + 3.35466I
u = 0.065416 − 1.409480I
a = 0.14726 + 1.84752I
b = −0.534312 − 0.945546I
5.12373 − 1.84437I 0.90018 + 3.35466I
u = −0.60008 + 1.40135I
a = −0.751907 − 0.379224I
b = 1.015400 + 0.803176I
−8.56727 + 6.23778I −4.60847 − 2.87458I
u = −0.60008 + 1.40135I
a = 0.34609 + 1.75574I
b = 0.908351 − 1.039740I
−8.56727 + 6.23778I −4.60847 − 2.87458I
u = −0.60008 − 1.40135I
a = −0.751907 + 0.379224I
b = 1.015400 − 0.803176I
−8.56727 − 6.23778I −4.60847 + 2.87458I
u = −0.60008 − 1.40135I
a = 0.34609 − 1.75574I
b = 0.908351 + 1.039740I
−8.56727 − 6.23778I −4.60847 + 2.87458I
12
III. I
u
3
= h−au + 9b + 4a − u + 4, 2a
2
− au + 3u + 5, u
2
+ 2i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
4
=
a
1
9
au −
4
9
a +
1
9
u −
4
9
a
12
=
1
−2
a
3
=
1
9
au +
5
9
a +
1
9
u −
4
9
1
9
au −
4
9
a +
1
9
u −
4
9
a
9
=
2
3
au +
1
3
a +
1
6
u −
5
3
1
9
au −
4
9
a +
1
9
u +
5
9
a
2
=
2
9
au +
1
9
a −
5
18
u −
17
9
1
9
au −
4
9
a +
1
9
u +
5
9
a
5
=
1
0
a
7
=
u
−u
a
1
=
−1
0
a
6
=
−
5
9
au −
7
9
a −
1
18
u +
20
9
−
1
9
au +
4
9
a −
1
9
u −
5
9
a
10
=
a + u
1
9
au −
4
9
a +
1
9
u −
4
9
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
8
9
au +
32
9
a −
8
9
u −
4
9
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
9
, c
10
(u
2
− u + 1)
2
c
2
, c
5
(u
2
+ u + 1)
2
c
6
u
4
+ 2u
3
+ u
2
− 6u + 3
c
7
, c
11
, c
12
(u
2
+ 2)
2
c
8
u
4
− 2u
3
+ u
2
+ 6u + 3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
c
10
(y
2
+ y + 1)
2
c
6
, c
8
y
4
− 2y
3
+ 31y
2
− 30y + 9
c
7
, c
11
, c
12
(y + 2)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.61237 − 1.37850I
b = −0.500000 + 0.866025I
4.93480 + 4.05977I 0. − 6.92820I
u = 1.414210I
a = −0.61237 + 2.08560I
b = −0.500000 − 0.866025I
4.93480 − 4.05977I 0. + 6.92820I
u = − 1.414210I
a = 0.61237 + 1.37850I
b = −0.500000 − 0.866025I
4.93480 − 4.05977I 0. + 6.92820I
u = − 1.414210I
a = −0.61237 − 2.08560I
b = −0.500000 + 0.866025I
4.93480 + 4.05977I 0. − 6.92820I
16
IV. I
u
4
= h4b + 2a + u + 2, 2a
2
+ 2au + 5, u
2
+ 2i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
4
=
a
−
1
2
a −
1
4
u −
1
2
a
12
=
1
−2
a
3
=
1
2
a −
1
4
u −
1
2
−
1
2
a −
1
4
u −
1
2
a
9
=
1
2
au − a +
1
2
u +
1
2
1
2
a +
1
4
u +
1
2
a
2
=
−
1
4
au −
1
4
u −
7
4
−
1
2
a −
1
4
u +
1
2
a
5
=
1
0
a
7
=
u
−u
a
1
=
−1
0
a
6
=
−
1
2
au +
3
2
a −
1
4
u
−
1
2
a −
1
4
u −
1
2
a
10
=
3
4
au −
1
4
u +
9
4
1
2
a +
1
4
u −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
9
, c
10
(u
2
− u + 1)
2
c
2
, c
5
(u
2
+ u + 1)
2
c
6
u
4
− 4u
3
+ 4u
2
+ 3
c
7
, c
11
, c
12
(u
2
+ 2)
2
c
8
u
4
+ 4u
3
+ 4u
2
+ 3
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
c
10
(y
2
+ y + 1)
2
c
6
, c
8
y
4
− 8y
3
+ 22y
2
+ 24y + 9
c
7
, c
11
, c
12
(y + 2)
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 1.024940I
b = −0.500000 − 0.866025I
4.93480 0
u = 1.414210I
a = − 2.43916I
b = −0.500000 + 0.866025I
4.93480 0
u = − 1.414210I
a = − 1.024940I
b = −0.500000 + 0.866025I
4.93480 0
u = − 1.414210I
a = 2.43916I
b = −0.500000 − 0.866025I
4.93480 0
20
V. I
v
1
= ha, b
2
− b + 1, v + 1i
(i) Arc colorings
a
8
=
−1
0
a
11
=
1
0
a
4
=
0
b
a
12
=
1
0
a
3
=
b
b
a
9
=
−b
−b + 1
a
2
=
b
b − 1
a
5
=
−1
0
a
7
=
−1
0
a
1
=
1
0
a
6
=
−1
−b + 1
a
10
=
0
−b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8b − 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
2
− u + 1
c
2
, c
3
, c
6
c
8
, c
9
u
2
+ u + 1
c
7
, c
11
, c
12
u
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
9
, c
10
y
2
+ y + 1
c
7
, c
11
, c
12
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
v = −1.00000
a = 0
b = 0.500000 − 0.866025I
4.05977I 0. − 6.92820I
24
VI. I
v
2
= ha, b + v − 1, v
2
− v + 1i
(i) Arc colorings
a
8
=
v
0
a
11
=
1
0
a
4
=
0
−v + 1
a
12
=
1
0
a
3
=
−v + 1
−v + 1
a
9
=
1
−v + 1
a
2
=
−v + 1
−v
a
5
=
−1
0
a
7
=
v
0
a
1
=
1
0
a
6
=
v
−v + 1
a
10
=
−v + 2
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
2
− u + 1
c
2
, c
3
, c
9
u
2
+ u + 1
c
6
, c
8
(u − 1)
2
c
7
, c
11
, c
12
u
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
c
10
y
2
+ y + 1
c
6
, c
8
(y − 1)
2
c
7
, c
11
, c
12
y
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
0 −6.00000
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
0 −6.00000
28
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
13
+ 19u
12
+ ··· + 15u − 1)
· (u
26
+ 30u
25
+ ··· − 1609u + 81)
c
2
((u
2
+ u + 1)
6
)(u
13
− 3u
12
+ ··· − u + 1)(u
26
− 6u
25
+ ··· − 95u + 9)
c
3
, c
9
(u
2
− u + 1)
4
(u
2
+ u + 1)
2
· (u
13
+ u
12
+ 2u
11
+ u
10
+ 6u
9
+ 4u
8
+ 8u
7
+ 3u
6
+ 8u
5
+ 4u
3
+ u
2
+ u + 1)
· (u
26
+ 2u
25
+ ··· − 5u + 3)
c
4
, c
10
((u
2
− u + 1)
6
)(u
13
− 3u
12
+ ··· − u + 1)(u
26
− 6u
25
+ ··· − 95u + 9)
c
5
(u
2
− u + 1)
2
(u
2
+ u + 1)
4
· (u
13
+ u
12
+ 2u
11
+ u
10
+ 6u
9
+ 4u
8
+ 8u
7
+ 3u
6
+ 8u
5
+ 4u
3
+ u
2
+ u + 1)
· (u
26
+ 2u
25
+ ··· − 5u + 3)
c
6
(u − 1)
2
(u
2
+ u + 1)(u
4
− 4u
3
+ 4u
2
+ 3)(u
4
+ 2u
3
+ u
2
− 6u + 3)
· (u
13
+ u
12
+ ··· + 1321u + 181)(u
26
+ 3u
25
+ ··· − 8726u + 1181)
c
7
, c
11
, c
12
u
4
(u
2
+ 2)
4
(u
13
− 5u
12
+ ··· − 16u + 4)(u
13
+ 2u
12
+ ··· + 4u
2
+ 2)
2
c
8
(u − 1)
2
(u
2
+ u + 1)(u
4
− 2u
3
+ u
2
+ 6u + 3)(u
4
+ 4u
3
+ 4u
2
+ 3)
· (u
13
− u
12
+ ··· − 39u + 11)(u
26
+ u
25
+ ··· − 456u + 241)
29
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
13
− 61y
12
+ ··· + 287y − 1)
· (y
26
− 50y
25
+ ··· + 5625167y + 6561)
c
2
, c
4
, c
10
((y
2
+ y + 1)
6
)(y
13
+ 19y
12
+ ··· + 15y − 1)
· (y
26
+ 30y
25
+ ··· − 1609y + 81)
c
3
, c
5
, c
9
((y
2
+ y + 1)
6
)(y
13
+ 3y
12
+ ··· − y − 1)(y
26
+ 6y
25
+ ··· + 95y + 9)
c
6
(y − 1)
2
(y
2
+ y + 1)(y
4
− 8y
3
+ 22y
2
+ 24y + 9)
· (y
4
− 2y
3
+ 31y
2
− 30y + 9)(y
13
+ 39y
12
+ ··· + 2051655y − 32761)
· (y
26
+ 37y
25
+ ··· − 40866606y + 1394761)
c
7
, c
11
, c
12
y
4
(y + 2)
8
(y
13
+ 10y
12
+ ··· − 16y − 4)
2
· (y
13
+ 11y
12
+ ··· + 64y − 16)
c
8
(y − 1)
2
(y
2
+ y + 1)(y
4
− 8y
3
+ 22y
2
+ 24y + 9)
· (y
4
− 2y
3
+ 31y
2
− 30y + 9)(y
13
− 13y
12
+ ··· + 1191y − 121)
· (y
26
− 15y
25
+ ··· − 481230y + 58081)
30
