12n
0701
(K12n
0701
)
A knot diagram
1
Linearized knot diagam
4 5 9 12 11 10 3 12 7 6 2 9
Solving Sequence
6,10
7
2,11
12 5 3 4 1 9 8
c
6
c
10
c
11
c
5
c
2
c
4
c
1
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hu
22
− 5u
21
+ ··· + b − 3, −3u
22
+ 13u
21
+ ··· + 2a + 22, u
23
− 5u
22
+ ··· − 18u + 2i
I
u
2
= h−u
7
− 5u
5
− 7u
3
+ u
2
+ b − 2u + 1, −u
7
− u
6
− 6u
5
− 6u
4
− 11u
3
− 8u
2
+ 2a − 5u − 1,
u
8
+ u
7
+ 6u
6
+ 4u
5
+ 11u
4
+ 4u
3
+ 7u
2
+ u + 2i
I
u
3
= h−u
8
a + u
8
− 6u
6
a + u
7
+ 6u
6
− 10u
4
a + 5u
5
− u
3
a + 10u
4
− 2u
2
a + 7u
3
− 3au + 3u
2
+ b + a + 2u,
2u
9
+ 3u
8
+ ··· − 2a + 7, u
10
+ u
9
+ 7u
8
+ 6u
7
+ 16u
6
+ 11u
5
+ 13u
4
+ 6u
3
+ 3u
2
+ u − 1i
I
u
4
= h−u
3
− u
2
+ b − 2u − 1, u
3
+ a + 3u + 2, u
4
+ u
3
+ 3u
2
+ 3u + 1i
* 4 irreducible components of dim
C
= 0, with total 55 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
22
−5u
21
+· · ·+b−3, −3u
22
+13u
21
+· · ·+2a+22, u
23
−5u
22
+· · ·−18u+2i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
3
2
u
22
−
13
2
u
21
+ ··· +
121
2
u − 11
−u
22
+ 5u
21
+ ··· − 18u + 3
a
11
=
u
u
a
12
=
−
3
2
u
22
+
13
2
u
21
+ ··· −
83
2
u + 6
u
22
− 5u
21
+ ··· + 24u − 3
a
5
=
u
2
+ 1
u
2
a
3
=
1
2
u
22
−
3
2
u
21
+ ··· +
63
2
u − 6
−u
22
+ 5u
21
+ ··· − 16u + 3
a
4
=
1
2
u
22
−
3
2
u
21
+ ··· +
61
2
u − 6
−u
22
+ 5u
21
+ ··· − 15u + 3
a
1
=
3
2
u
22
−
13
2
u
21
+ ··· +
81
2
u − 6
−u
22
+ 5u
21
+ ··· − 23u + 3
a
9
=
−u
u
3
+ u
a
8
=
−
1
2
u
22
+
5
2
u
21
+ ··· −
51
2
u + 4
−u
15
+ 3u
14
+ ··· + 5u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
22
−29u
21
+ 157u
20
−513u
19
+ 1582u
18
−3829u
17
+ 8406u
16
−
15713u
15
+ 26319u
14
− 38607u
13
+ 50328u
12
− 57710u
11
+ 57948u
10
− 50468u
9
+
37196u
8
− 22606u
7
+ 10398u
6
− 2892u
5
− 338u
4
+ 958u
3
− 571u
2
+ 212u − 30
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 14u
22
+ ··· + 212u − 58
c
2
, c
11
u
23
+ u
22
+ ··· + 11u − 1
c
3
, c
8
, c
12
u
23
+ 17u
21
+ ··· + u − 1
c
4
u
23
+ 20u
22
+ ··· − 7680u − 1024
c
5
, c
6
, c
9
c
10
u
23
+ 5u
22
+ ··· − 18u − 2
c
7
u
23
+ u
22
+ ··· + 75u − 76
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 30y
22
+ ··· + 95172y −3364
c
2
, c
11
y
23
+ 15y
22
+ ··· + 49y −1
c
3
, c
8
, c
12
y
23
+ 34y
22
+ ··· − 13y −1
c
4
y
23
+ 2y
22
+ ··· + 1835008y −1048576
c
5
, c
6
, c
9
c
10
y
23
+ 29y
22
+ ··· + 48y −4
c
7
y
23
+ 27y
22
+ ··· + 24929y −5776
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642236 + 0.877944I
a = 0.197001 − 0.148547I
b = 0.793532 + 0.638924I
−9.94522 − 0.85971I 0.652008 + 0.263340I
u = 0.642236 − 0.877944I
a = 0.197001 + 0.148547I
b = 0.793532 − 0.638924I
−9.94522 + 0.85971I 0.652008 − 0.263340I
u = 0.525547 + 0.958461I
a = −0.231366 + 0.083953I
b = −1.63498 + 0.17452I
−10.7803 + 10.1203I 2.47270 − 6.58788I
u = 0.525547 − 0.958461I
a = −0.231366 − 0.083953I
b = −1.63498 − 0.17452I
−10.7803 − 10.1203I 2.47270 + 6.58788I
u = 0.808860 + 0.080850I
a = 0.686984 + 1.110200I
b = −0.207591 − 0.160006I
−7.60162 + 5.68429I 4.92336 − 4.37173I
u = 0.808860 − 0.080850I
a = 0.686984 − 1.110200I
b = −0.207591 + 0.160006I
−7.60162 − 5.68429I 4.92336 + 4.37173I
u = 0.024745 + 0.801676I
a = 0.174801 − 0.754525I
b = −0.740668 − 0.583637I
−2.37077 − 1.03630I 2.58342 + 3.76841I
u = 0.024745 − 0.801676I
a = 0.174801 + 0.754525I
b = −0.740668 + 0.583637I
−2.37077 + 1.03630I 2.58342 − 3.76841I
u = 0.180111 + 0.768204I
a = −0.047351 + 0.934860I
b = 1.47339 + 0.21993I
−1.38871 + 3.48902I 1.80255 − 2.01978I
u = 0.180111 − 0.768204I
a = −0.047351 − 0.934860I
b = 1.47339 − 0.21993I
−1.38871 − 3.48902I 1.80255 + 2.01978I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140649 + 1.391640I
a = 0.471307 − 0.261563I
b = 0.444719 − 0.537456I
−3.65805 − 1.94631I 9.97208 + 4.88462I
u = −0.140649 − 1.391640I
a = 0.471307 + 0.261563I
b = 0.444719 + 0.537456I
−3.65805 + 1.94631I 9.97208 − 4.88462I
u = −0.448926
a = 0.547375
b = 0.215725
0.770537 11.8930
u = 0.01173 + 1.65517I
a = −1.58298 − 0.41772I
b = −2.18998 − 0.09600I
−10.99720 − 0.87329I 2.30677 + 2.57929I
u = 0.01173 − 1.65517I
a = −1.58298 + 0.41772I
b = −2.18998 + 0.09600I
−10.99720 + 0.87329I 2.30677 − 2.57929I
u = 0.04187 + 1.65682I
a = 2.31152 + 0.13555I
b = 3.10043 − 0.45940I
−9.94661 + 4.28907I 2.32600 − 1.89884I
u = 0.04187 − 1.65682I
a = 2.31152 − 0.13555I
b = 3.10043 + 0.45940I
−9.94661 − 4.28907I 2.32600 + 1.89884I
u = 0.286093 + 0.114349I
a = −0.56165 + 2.23126I
b = 0.330646 − 0.563761I
0.49230 − 1.78185I 2.91759 + 6.16768I
u = 0.286093 − 0.114349I
a = −0.56165 − 2.23126I
b = 0.330646 + 0.563761I
0.49230 + 1.78185I 2.91759 − 6.16768I
u = 0.14816 + 1.70012I
a = −2.42737 − 0.12733I
b = −3.34541 + 0.35416I
19.4914 + 12.8043I 0. − 5.39440I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14816 − 1.70012I
a = −2.42737 + 0.12733I
b = −3.34541 − 0.35416I
19.4914 − 12.8043I 0. + 5.39440I
u = 0.19576 + 1.69910I
a = 1.23542 + 0.76867I
b = 1.86806 + 0.82472I
−18.7857 + 2.4887I 0
u = 0.19576 − 1.69910I
a = 1.23542 − 0.76867I
b = 1.86806 − 0.82472I
−18.7857 − 2.4887I 0
7
II.
I
u
2
= h−u
7
−5u
5
−7u
3
+u
2
+b−2u+1, −u
7
−u
6
+· · ·+2a−1, u
8
+u
7
+· · ·+u+2i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
1
2
u
7
+
1
2
u
6
+ ··· +
5
2
u +
1
2
u
7
+ 5u
5
+ 7u
3
− u
2
+ 2u − 1
a
11
=
u
u
a
12
=
−
1
2
u
7
−
3
2
u
6
+ ··· −
5
2
u −
3
2
−u
6
− u
5
− 3u
4
− 2u
3
− u
2
+ 1
a
5
=
u
2
+ 1
u
2
a
3
=
1
2
u
7
+
3
2
u
6
+ ··· +
5
2
u +
3
2
u
5
+ 2u
3
− u
2
− 1
a
4
=
1
2
u
7
+
3
2
u
6
+ ··· +
3
2
u +
3
2
u
7
+ u
6
+ 5u
5
+ 3u
4
+ 6u
3
+ u
2
+ u − 1
a
1
=
−
1
2
u
7
−
3
2
u
6
+ ··· −
3
2
u −
3
2
−u
7
− 2u
6
− 5u
5
− 6u
4
− 6u
3
− 3u
2
− u + 1
a
9
=
−u
u
3
+ u
a
8
=
1
2
u
7
+
1
2
u
6
+ ··· −
5
2
u −
5
2
−u
5
− 2u
4
− 4u
3
− 5u
2
− 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
7
− 5u
6
+ 5u
5
− 22u
4
+ 9u
3
− 27u
2
+ 7u − 6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 6u
7
+ 16u
6
− 28u
5
+ 37u
4
− 36u
3
+ 26u
2
− 13u + 4
c
2
, c
11
u
8
+ 2u
7
+ 2u
6
− 2u
5
− 3u
4
− 2u
3
+ 2u
2
+ u + 1
c
3
, c
8
u
8
− u
7
+ 3u
6
− 2u
5
+ 2u
3
− 2u + 1
c
4
u
8
+ u
7
+ 2u
6
− 2u
5
− 3u
4
− 2u
3
+ 2u
2
+ 2u + 1
c
5
, c
6
u
8
+ u
7
+ 6u
6
+ 4u
5
+ 11u
4
+ 4u
3
+ 7u
2
+ u + 2
c
7
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 11u
3
+ 8u
2
+ 4u + 1
c
9
, c
10
u
8
− u
7
+ 6u
6
− 4u
5
+ 11u
4
− 4u
3
+ 7u
2
− u + 2
c
12
u
8
+ u
7
+ 3u
6
+ 2u
5
− 2u
3
+ 2u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 4y
7
− 6y
6
+ 20y
5
+ 37y
4
+ 28y
3
+ 36y
2
+ 39y + 16
c
2
, c
11
y
8
+ 6y
6
− 4y
5
+ 7y
4
− 8y
3
+ 2y
2
+ 3y + 1
c
3
, c
8
, c
12
y
8
+ 5y
7
+ 5y
6
+ 6y
4
− 6y
3
+ 8y
2
− 4y + 1
c
4
y
8
+ 3y
7
+ 2y
6
− 8y
5
+ 7y
4
− 4y
3
+ 6y
2
+ 1
c
5
, c
6
, c
9
c
10
y
8
+ 11y
7
+ 50y
6
+ 122y
5
+ 175y
4
+ 154y
3
+ 85y
2
+ 27y + 4
c
7
y
8
+ 8y
7
+ 26y
6
+ 40y
5
+ 27y
4
+ 3y
3
− 2y
2
+ 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369565 + 0.771008I
a = −0.155753 − 0.334209I
b = 1.184060 + 0.040896I
−0.59040 − 4.34638I 8.24002 + 7.81362I
u = −0.369565 − 0.771008I
a = −0.155753 + 0.334209I
b = 1.184060 − 0.040896I
−0.59040 + 4.34638I 8.24002 − 7.81362I
u = 0.201988 + 0.673846I
a = −1.34000 + 1.00726I
b = −1.271480 − 0.352014I
−7.52705 + 0.72220I 2.71603 − 0.15399I
u = 0.201988 − 0.673846I
a = −1.34000 − 1.00726I
b = −1.271480 + 0.352014I
−7.52705 − 0.72220I 2.71603 + 0.15399I
u = −0.23773 + 1.39832I
a = −0.278315 + 0.491837I
b = −0.648364 + 0.685778I
−4.19999 − 1.68332I −2.66072 − 1.09034I
u = −0.23773 − 1.39832I
a = −0.278315 − 0.491837I
b = −0.648364 − 0.685778I
−4.19999 + 1.68332I −2.66072 + 1.09034I
u = −0.09469 + 1.65500I
a = 2.02407 + 0.03178I
b = 2.73579 + 0.57245I
−9.06671 − 6.06893I 5.70467 + 5.25665I
u = −0.09469 − 1.65500I
a = 2.02407 − 0.03178I
b = 2.73579 − 0.57245I
−9.06671 + 6.06893I 5.70467 − 5.25665I
11
III.
I
u
3
= h−u
8
a + u
8
+ · · · + b + a, 2u
9
+ 3u
8
+ · · · − 2a + 7, u
10
+ u
9
+ · · · + u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
a
u
8
a − u
8
+ ··· − a − 2u
a
11
=
u
u
a
12
=
−u
7
+ u
5
a − 4u
5
+ 3u
3
a − 4u
3
+ au − 2u
2
+ a − 2u − 2
−u
8
a − u
8
+ ··· + a − u
a
5
=
u
2
+ 1
u
2
a
3
=
−u
9
a − u
8
a + ··· + 2a − 1
−u
8
− 2u
7
− 6u
6
− 8u
5
− 10u
4
− 8u
3
+ au − 4u
2
− 2u
a
4
=
−u
7
+ u
5
a − 4u
5
+ 3u
3
a − 4u
3
+ au − u
2
+ a − 2u − 1
−u
8
a − u
8
+ ··· + a − u
a
1
=
−u
9
a − u
8
a + ··· + 3u + 2
2u
8
a + 2u
7
a + ··· + 3au − 2a
a
9
=
−u
u
3
+ u
a
8
=
−2u
9
a − 2u
8
a + ··· + a + 2
−u
8
a − u
8
+ ··· + a − u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
8
+ 4u
7
+ 24u
6
+ 20u
5
+ 44u
4
+ 28u
3
+ 24u
2
+ 8u + 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 9u
9
+ 31u
8
+ 48u
7
+ 28u
6
+ 5u
5
+ 17u
4
+ 8u
3
− 9u
2
+ 5u − 1)
2
c
2
, c
11
u
20
+ 9u
19
+ ··· + 55u + 14
c
3
, c
8
, c
12
u
20
− u
19
+ ··· − 109u + 142
c
4
(u − 1)
20
c
5
, c
6
, c
9
c
10
(u
10
− u
9
+ 7u
8
− 6u
7
+ 16u
6
− 11u
5
+ 13u
4
− 6u
3
+ 3u
2
− u − 1)
2
c
7
u
20
+ u
19
+ ··· − 2452u + 1723
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
− 19y
9
+ ··· − 7y + 1)
2
c
2
, c
11
y
20
− y
19
+ ··· + 2771y + 196
c
3
, c
8
, c
12
y
20
+ 27y
19
+ ··· + 125859y + 20164
c
4
(y −1)
20
c
5
, c
6
, c
9
c
10
(y
10
+ 13y
9
+ ··· − 7y + 1)
2
c
7
y
20
+ 23y
19
+ ··· + 12716706y + 2968729
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.420834 + 0.842935I
a = 0.198910 − 0.456820I
b = 1.075440 − 0.460885I
−1.99815 − 3.55946I 1.64226 + 4.06361I
u = −0.420834 + 0.842935I
a = 0.291275 − 0.161939I
b = −1.021720 − 0.224140I
−1.99815 − 3.55946I 1.64226 + 4.06361I
u = −0.420834 − 0.842935I
a = 0.198910 + 0.456820I
b = 1.075440 + 0.460885I
−1.99815 + 3.55946I 1.64226 − 4.06361I
u = −0.420834 − 0.842935I
a = 0.291275 + 0.161939I
b = −1.021720 + 0.224140I
−1.99815 + 3.55946I 1.64226 − 4.06361I
u = 0.153406 + 0.833677I
a = 0.02090 − 1.60050I
b = 0.877616 + 0.641363I
−8.43900 + 1.60532I −3.05654 − 5.03395I
u = 0.153406 + 0.833677I
a = −1.42752 + 1.20623I
b = −2.23360 + 1.38307I
−8.43900 + 1.60532I −3.05654 − 5.03395I
u = 0.153406 − 0.833677I
a = 0.02090 + 1.60050I
b = 0.877616 − 0.641363I
−8.43900 − 1.60532I −3.05654 + 5.03395I
u = 0.153406 − 0.833677I
a = −1.42752 − 1.20623I
b = −2.23360 − 1.38307I
−8.43900 − 1.60532I −3.05654 + 5.03395I
u = −0.635590
a = 0.447489 + 0.710048I
b = 0.228085 − 0.214031I
0.553628 6.04860
u = −0.635590
a = 0.447489 − 0.710048I
b = 0.228085 + 0.214031I
0.553628 6.04860
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10787 + 1.66265I
a = 1.69613 − 0.79881I
b = 2.25201 − 0.48002I
−10.67790 − 5.55652I −0.20810 + 2.88175I
u = −0.10787 + 1.66265I
a = −2.12347 − 0.22802I
b = −3.08847 − 0.66832I
−10.67790 − 5.55652I −0.20810 + 2.88175I
u = −0.10787 − 1.66265I
a = 1.69613 + 0.79881I
b = 2.25201 + 0.48002I
−10.67790 + 5.55652I −0.20810 − 2.88175I
u = −0.10787 − 1.66265I
a = −2.12347 + 0.22802I
b = −3.08847 + 0.66832I
−10.67790 + 5.55652I −0.20810 − 2.88175I
u = 0.03425 + 1.67211I
a = 1.66374 + 1.57382I
b = 2.49623 + 2.91801I
−17.3000 + 2.2863I −3.60221 − 2.91176I
u = 0.03425 + 1.67211I
a = −3.01845 + 1.45580I
b = −3.46263 + 1.43734I
−17.3000 + 2.2863I −3.60221 − 2.91176I
u = 0.03425 − 1.67211I
a = 1.66374 − 1.57382I
b = 2.49623 − 2.91801I
−17.3000 − 2.2863I −3.60221 + 2.91176I
u = 0.03425 − 1.67211I
a = −3.01845 − 1.45580I
b = −3.46263 − 1.43734I
−17.3000 − 2.2863I −3.60221 + 2.91176I
u = 0.317683
a = 2.25101 + 3.10693I
b = −0.622963 + 0.916801I
−5.97021 8.40060
u = 0.317683
a = 2.25101 − 3.10693I
b = −0.622963 − 0.916801I
−5.97021 8.40060
16
IV. I
u
4
= h−u
3
− u
2
+ b − 2u − 1, u
3
+ a + 3u + 2, u
4
+ u
3
+ 3u
2
+ 3u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
−u
3
− 3u − 2
u
3
+ u
2
+ 2u + 1
a
11
=
u
u
a
12
=
−u
3
− u
2
− 2u − 1
−u
2
+ u
a
5
=
u
2
+ 1
u
2
a
3
=
−u
u
3
+ u + 1
a
4
=
u
2
− u
2u
3
+ 2u
2
+ 4u + 2
a
1
=
−u
3
− 2u
2
− 2u − 1
−u
3
− 3u
2
− 2u − 1
a
9
=
−u
u
3
+ u
a
8
=
u
2
+ u + 1
u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
3
+ 2u
2
− 3u + 8
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 5u
3
+ 9u
2
− 7u + 3
c
2
, c
11
u
4
− u
3
+ 1
c
3
, c
5
, c
6
c
8
u
4
+ u
3
+ 3u
2
+ 3u + 1
c
4
u
4
− u + 1
c
7
u
4
− 3u
3
+ 6u
2
− 4u + 1
c
9
, c
10
, c
12
u
4
− u
3
+ 3u
2
− 3u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 7y
3
+ 17y
2
+ 5y + 9
c
2
, c
11
y
4
− y
3
+ 2y
2
+ 1
c
3
, c
5
, c
6
c
8
, c
9
, c
10
c
12
y
4
+ 5y
3
+ 5y
2
− 3y + 1
c
4
y
4
+ 2y
2
− y + 1
c
7
y
4
+ 3y
3
+ 14y
2
− 4y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.552038 + 0.242275I
a = −0.272864 − 0.934099I
b = 0.070951 + 0.424335I
1.07586 + 1.18968I 10.21923 − 1.46908I
u = −0.552038 − 0.242275I
a = −0.272864 + 0.934099I
b = 0.070951 − 0.424335I
1.07586 − 1.18968I 10.21923 + 1.46908I
u = 0.05204 + 1.65794I
a = −1.72714 − 0.43001I
b = −2.07095 − 1.05537I
−15.8803 + 1.6928I 2.78077 − 0.08491I
u = 0.05204 − 1.65794I
a = −1.72714 + 0.43001I
b = −2.07095 + 1.05537I
−15.8803 − 1.6928I 2.78077 + 0.08491I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− 5u
3
+ 9u
2
− 7u + 3)
· (u
8
− 6u
7
+ 16u
6
− 28u
5
+ 37u
4
− 36u
3
+ 26u
2
− 13u + 4)
· (u
10
+ 9u
9
+ 31u
8
+ 48u
7
+ 28u
6
+ 5u
5
+ 17u
4
+ 8u
3
− 9u
2
+ 5u − 1)
2
· (u
23
− 14u
22
+ ··· + 212u − 58)
c
2
, c
11
(u
4
− u
3
+ 1)(u
8
+ 2u
7
+ 2u
6
− 2u
5
− 3u
4
− 2u
3
+ 2u
2
+ u + 1)
· (u
20
+ 9u
19
+ ··· + 55u + 14)(u
23
+ u
22
+ ··· + 11u − 1)
c
3
, c
8
(u
4
+ u
3
+ 3u
2
+ 3u + 1)(u
8
− u
7
+ 3u
6
− 2u
5
+ 2u
3
− 2u + 1)
· (u
20
− u
19
+ ··· − 109u + 142)(u
23
+ 17u
21
+ ··· + u − 1)
c
4
((u − 1)
20
)(u
4
− u + 1)(u
8
+ u
7
+ ··· + 2u + 1)
· (u
23
+ 20u
22
+ ··· − 7680u − 1024)
c
5
, c
6
(u
4
+ u
3
+ 3u
2
+ 3u + 1)(u
8
+ u
7
+ ··· + u + 2)
· (u
10
− u
9
+ 7u
8
− 6u
7
+ 16u
6
− 11u
5
+ 13u
4
− 6u
3
+ 3u
2
− u − 1)
2
· (u
23
+ 5u
22
+ ··· − 18u − 2)
c
7
(u
4
− 3u
3
+ 6u
2
− 4u + 1)
· (u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 11u
3
+ 8u
2
+ 4u + 1)
· (u
20
+ u
19
+ ··· − 2452u + 1723)(u
23
+ u
22
+ ··· + 75u − 76)
c
9
, c
10
(u
4
− u
3
+ 3u
2
− 3u + 1)(u
8
− u
7
+ ··· − u + 2)
· (u
10
− u
9
+ 7u
8
− 6u
7
+ 16u
6
− 11u
5
+ 13u
4
− 6u
3
+ 3u
2
− u − 1)
2
· (u
23
+ 5u
22
+ ··· − 18u − 2)
c
12
(u
4
− u
3
+ 3u
2
− 3u + 1)(u
8
+ u
7
+ 3u
6
+ 2u
5
− 2u
3
+ 2u + 1)
· (u
20
− u
19
+ ··· − 109u + 142)(u
23
+ 17u
21
+ ··· + u − 1)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
− 7y
3
+ 17y
2
+ 5y + 9)
· (y
8
− 4y
7
− 6y
6
+ 20y
5
+ 37y
4
+ 28y
3
+ 36y
2
+ 39y + 16)
· ((y
10
− 19y
9
+ ··· − 7y + 1)
2
)(y
23
− 30y
22
+ ··· + 95172y −3364)
c
2
, c
11
(y
4
− y
3
+ 2y
2
+ 1)(y
8
+ 6y
6
− 4y
5
+ 7y
4
− 8y
3
+ 2y
2
+ 3y + 1)
· (y
20
− y
19
+ ··· + 2771y + 196)(y
23
+ 15y
22
+ ··· + 49y −1)
c
3
, c
8
, c
12
(y
4
+ 5y
3
+ 5y
2
− 3y + 1)(y
8
+ 5y
7
+ ··· − 4y + 1)
· (y
20
+ 27y
19
+ ··· + 125859y + 20164)(y
23
+ 34y
22
+ ··· − 13y −1)
c
4
((y −1)
20
)(y
4
+ 2y
2
− y + 1)(y
8
+ 3y
7
+ ··· + 6y
2
+ 1)
· (y
23
+ 2y
22
+ ··· + 1835008y −1048576)
c
5
, c
6
, c
9
c
10
(y
4
+ 5y
3
+ 5y
2
− 3y + 1)
· (y
8
+ 11y
7
+ 50y
6
+ 122y
5
+ 175y
4
+ 154y
3
+ 85y
2
+ 27y + 4)
· ((y
10
+ 13y
9
+ ··· − 7y + 1)
2
)(y
23
+ 29y
22
+ ··· + 48y −4)
c
7
(y
4
+ 3y
3
+ 14y
2
− 4y + 1)
· (y
8
+ 8y
7
+ 26y
6
+ 40y
5
+ 27y
4
+ 3y
3
− 2y
2
+ 1)
· (y
20
+ 23y
19
+ ··· + 12716706y + 2968729)
· (y
23
+ 27y
22
+ ··· + 24929y −5776)
22
