12a
1144
(K12a
1144
)
A knot diagram
1
Linearized knot diagam
4 8 9 11 10 12 3 2 1 5 7 6
Solving Sequence
6,10
5 11
1,4
2 9 3 8 12 7
c
5
c
10
c
4
c
1
c
9
c
3
c
8
c
12
c
6
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −u
31
+ u
30
+ ··· + 32a + 1, u
32
+ 20u
30
+ ··· + 2u + 1i
I
u
2
= h−5.88169 × 10
23
u
41
+ 2.40634 × 10
24
u
40
+ ··· + 2.85857 × 10
25
b − 1.53616 × 10
25
,
− 2.91738 × 10
25
u
41
+ 3.09920 × 10
25
u
40
+ ··· + 2.85857 × 10
25
a + 4.18097 × 10
25
, u
42
− u
41
+ ··· − 2u + 1i
I
u
3
= hb + u, a
5
− a
4
+ 2a
3
− a
2
+ a − 1, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 84 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
= hb − u, −u
31
+ u
30
+ · · · + 32a + 1, u
32
+ 20u
30
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
u
u
3
+ u
a
1
=
0.0312500u
31
− 0.0312500u
30
+ ··· + 2.96875u − 0.0312500
u
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
0.0312500u
31
− 0.0312500u
30
+ ··· + 1.96875u − 0.0312500
0.0312500u
31
− 0.0312500u
30
+ ··· + 0.968750u − 0.0312500
a
9
=
0.0312500u
31
− 0.0312500u
30
+ ··· − 0.0937500u − 0.0937500
0.0312500u
31
− 0.0312500u
30
+ ··· + 0.968750u − 0.0312500
a
3
=
9
16
u
31
−
1
4
u
30
+ ··· +
9
4
u +
21
16
3
8
u
31
+
1
4
u
30
+ ··· +
19
16
u +
5
16
a
8
=
−
1
16
u
31
−
1
16
u
30
+ ··· −
7
8
u −
5
8
1
8
u
31
−
7
16
u
30
+ ··· −
1
2
u −
17
16
a
12
=
0.0312500u
31
− 0.0312500u
30
+ ··· + 1.96875u − 0.0312500
u
a
7
=
0.0312500u
31
+ 0.0312500u
30
+ ··· + 0.0937500u + 1.03125
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
11
8
u
31
−
1
8
u
30
+ ··· + 8u +
7
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
− 7u
31
+ ··· − 629u + 136
c
2
, c
7
, c
8
u
32
− 3u
31
+ ··· − 9u + 2
c
3
u
32
+ 3u
31
+ ··· − 45u + 10
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
32
+ 20u
30
+ ··· − 2u + 1
c
9
u
32
− 21u
31
+ ··· − 31521u + 3794
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
+ 9y
31
+ ··· + 185079y + 18496
c
2
, c
7
, c
8
y
32
+ 29y
31
+ ··· + 3y + 4
c
3
y
32
+ y
31
+ ··· + 1795y + 100
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
32
+ 40y
31
+ ··· + 10y + 1
c
9
y
32
+ 9y
31
+ ··· + 46718595y + 14394436
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.606629 + 0.369922I
a = −1.66986 + 0.58326I
b = −0.606629 + 0.369922I
5.08010 − 7.21382I 6.51491 + 8.36258I
u = −0.606629 − 0.369922I
a = −1.66986 − 0.58326I
b = −0.606629 − 0.369922I
5.08010 + 7.21382I 6.51491 − 8.36258I
u = 0.629670 + 0.175324I
a = 1.56872 + 0.28026I
b = 0.629670 + 0.175324I
6.58025 − 1.12952I 10.00433 − 1.13663I
u = 0.629670 − 0.175324I
a = 1.56872 − 0.28026I
b = 0.629670 − 0.175324I
6.58025 + 1.12952I 10.00433 + 1.13663I
u = 0.546847 + 0.354433I
a = 1.56713 + 0.62149I
b = 0.546847 + 0.354433I
−0.24655 + 3.89301I 1.84831 − 8.81175I
u = 0.546847 − 0.354433I
a = 1.56713 − 0.62149I
b = 0.546847 − 0.354433I
−0.24655 − 3.89301I 1.84831 + 8.81175I
u = −0.046705 + 1.401200I
a = −0.34108 − 1.47427I
b = −0.046705 + 1.401200I
−0.35213 − 5.09138I −0.46090 + 3.41418I
u = −0.046705 − 1.401200I
a = −0.34108 + 1.47427I
b = −0.046705 − 1.401200I
−0.35213 + 5.09138I −0.46090 − 3.41418I
u = 0.02438 + 1.43670I
a = 0.155902 − 1.256460I
b = 0.02438 + 1.43670I
−6.57448 + 2.07353I −3.81450 − 3.36266I
u = 0.02438 − 1.43670I
a = 0.155902 + 1.256460I
b = 0.02438 − 1.43670I
−6.57448 − 2.07353I −3.81450 + 3.36266I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.353670 + 0.399081I
a = −1.25094 + 0.96324I
b = −0.353670 + 0.399081I
1.33414 − 1.26458I 2.44160 + 5.52381I
u = −0.353670 − 0.399081I
a = −1.25094 − 0.96324I
b = −0.353670 − 0.399081I
1.33414 + 1.26458I 2.44160 − 5.52381I
u = −0.103781 + 0.515513I
a = −0.57149 + 1.83224I
b = −0.103781 + 0.515513I
4.24971 + 4.08144I 5.01801 − 1.73350I
u = −0.103781 − 0.515513I
a = −0.57149 − 1.83224I
b = −0.103781 − 0.515513I
4.24971 − 4.08144I 5.01801 + 1.73350I
u = −0.477770 + 0.219464I
a = −1.326770 + 0.440538I
b = −0.477770 + 0.219464I
0.940582 − 0.674762I 6.97731 + 2.54975I
u = −0.477770 − 0.219464I
a = −1.326770 − 0.440538I
b = −0.477770 − 0.219464I
0.940582 + 0.674762I 6.97731 − 2.54975I
u = −0.26977 + 1.48889I
a = −1.178040 − 0.476261I
b = −0.26977 + 1.48889I
−4.22469 − 5.46260I 0
u = −0.26977 − 1.48889I
a = −1.178040 + 0.476261I
b = −0.26977 − 1.48889I
−4.22469 + 5.46260I 0
u = 0.146914 + 0.429589I
a = 0.64149 + 1.38146I
b = 0.146914 + 0.429589I
−0.98864 − 1.13789I −1.40453 + 1.40100I
u = 0.146914 − 0.429589I
a = 0.64149 − 1.38146I
b = 0.146914 − 0.429589I
−0.98864 + 1.13789I −1.40453 − 1.40100I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.28852 + 1.54432I
a = 1.092720 − 0.277920I
b = 0.28852 + 1.54432I
−11.21850 + 6.79287I 0
u = 0.28852 − 1.54432I
a = 1.092720 + 0.277920I
b = 0.28852 − 1.54432I
−11.21850 − 6.79287I 0
u = 0.34148 + 1.53474I
a = 1.241970 − 0.181115I
b = 0.34148 + 1.53474I
−7.3512 + 14.7885I 0
u = 0.34148 − 1.53474I
a = 1.241970 + 0.181115I
b = 0.34148 − 1.53474I
−7.3512 − 14.7885I 0
u = −0.32266 + 1.54438I
a = −1.177440 − 0.201810I
b = −0.32266 + 1.54438I
−12.7964 − 10.9677I 0
u = −0.32266 − 1.54438I
a = −1.177440 + 0.201810I
b = −0.32266 − 1.54438I
−12.7964 + 10.9677I 0
u = 0.24178 + 1.58208I
a = 0.886317 − 0.267032I
b = 0.24178 + 1.58208I
−11.98810 + 6.51283I 0
u = 0.24178 − 1.58208I
a = 0.886317 + 0.267032I
b = 0.24178 − 1.58208I
−11.98810 − 6.51283I 0
u = −0.19813 + 1.59690I
a = −0.728237 − 0.294996I
b = −0.19813 + 1.59690I
−14.7686 − 2.5621I 0
u = −0.19813 − 1.59690I
a = −0.728237 + 0.294996I
b = −0.19813 − 1.59690I
−14.7686 + 2.5621I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15953 + 1.60567I
a = 0.589601 − 0.320624I
b = 0.15953 + 1.60567I
−10.18300 − 1.30058I 0
u = 0.15953 − 1.60567I
a = 0.589601 + 0.320624I
b = 0.15953 − 1.60567I
−10.18300 + 1.30058I 0
8
II.
I
u
2
= h−5.88×10
23
u
41
+2.41×10
24
u
40
+· · ·+2.86×10
25
b−1.54×10
25
, −2.92×
10
25
u
41
+3.10×10
25
u
40
+· · ·+2.86×10
25
a+4.18×10
25
, u
42
−u
41
+· · ·−2u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
u
u
3
+ u
a
1
=
1.02058u
41
− 1.08418u
40
+ ··· − 17.0532u − 1.46261
0.0205757u
41
− 0.0841800u
40
+ ··· − 3.05321u + 0.537389
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
0.982739u
41
− 0.799526u
40
+ ··· − 16.2270u − 1.88182
0.0674687u
41
− 0.121292u
40
+ ··· − 2.75800u + 0.420716
a
9
=
1.03523u
41
− 1.08688u
40
+ ··· − 19.2542u − 0.861618
0.0146583u
41
− 0.00269680u
40
+ ··· − 1.20099u + 0.600993
a
3
=
0.0215507u
41
+ 0.0984422u
40
+ ··· − 16.5835u + 5.10219
0.359884u
41
− 0.273709u
40
+ ··· − 2.93547u + 1.06141
a
8
=
1.19912u
41
− 1.61059u
40
+ ··· − 21.6738u + 1.42196
0.150022u
41
− 0.407409u
40
+ ··· + 3.68385u + 0.0765627
a
12
=
u
41
− u
40
+ ··· − 14u − 2
0.0205757u
41
− 0.0841800u
40
+ ··· − 3.05321u + 0.537389
a
7
=
−0.537389u
41
+ 0.557965u
40
+ ··· − 10.9961u − 0.978429
−0.0636043u
41
+ 0.0576870u
40
+ ··· + 0.578540u + 0.979424
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
72222077540047874114658048
28585672337950454401808201
u
41
+
29500521900029629423443720
28585672337950454401808201
u
40
+
··· −
299812736301611137792225292
28585672337950454401808201
u +
106417593374116830733331718
28585672337950454401808201
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
21
− 5u
20
+ ··· − 11u + 3)
2
c
2
, c
7
, c
8
(u
21
+ u
20
+ ··· − u − 1)
2
c
3
(u
21
− u
20
+ ··· − 3u − 1)
2
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
42
+ u
41
+ ··· + 2u + 1
c
9
(u
21
+ 7u
20
+ ··· + 3u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 3y
20
+ ··· − 41y −9)
2
c
2
, c
7
, c
8
(y
21
+ 19y
20
+ ··· + 3y −1)
2
c
3
(y
21
− y
20
+ ··· + 3y −1)
2
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
42
+ 35y
41
+ ··· − 32y + 1
c
9
(y
21
+ 15y
20
+ ··· + 27y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.142789 + 0.981947I
a = −0.400579 + 1.077330I
b = −0.255559 + 0.080028I
4.29768 + 4.29720I 6.75143 − 3.93304I
u = 0.142789 − 0.981947I
a = −0.400579 − 1.077330I
b = −0.255559 − 0.080028I
4.29768 − 4.29720I 6.75143 + 3.93304I
u = 0.803564 + 0.620127I
a = −0.854334 − 0.849675I
b = −0.07438 − 1.45158I
−4.65974 + 2.68588I −1.85070 − 3.67518I
u = 0.803564 − 0.620127I
a = −0.854334 + 0.849675I
b = −0.07438 + 1.45158I
−4.65974 − 2.68588I −1.85070 + 3.67518I
u = −0.892757 + 0.485854I
a = 1.04420 − 0.99396I
b = 0.18002 − 1.46427I
−6.19421 − 6.51836I −3.49661 + 6.69162I
u = −0.892757 − 0.485854I
a = 1.04420 + 0.99396I
b = 0.18002 + 1.46427I
−6.19421 + 6.51836I −3.49661 − 6.69162I
u = 0.816854 + 0.532908I
a = −0.987760 − 0.874778I
b = −0.12904 − 1.43500I
−4.44976 + 2.73152I −0.80842 − 2.00184I
u = 0.816854 − 0.532908I
a = −0.987760 + 0.874778I
b = −0.12904 + 1.43500I
−4.44976 − 2.73152I −0.80842 + 2.00184I
u = 0.920413 + 0.451372I
a = −1.08540 − 1.03931I
b = −0.20956 − 1.46882I
−0.91901 + 10.18330I 1.25382 − 7.21296I
u = 0.920413 − 0.451372I
a = −1.08540 + 1.03931I
b = −0.20956 + 1.46882I
−0.91901 − 10.18330I 1.25382 + 7.21296I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.769634 + 0.726428I
a = 0.688478 − 0.808047I
b = 0.00133 − 1.45662I
−6.94955 + 0.90110I −5.44354 − 1.25880I
u = −0.769634 − 0.726428I
a = 0.688478 + 0.808047I
b = 0.00133 + 1.45662I
−6.94955 − 0.90110I −5.44354 + 1.25880I
u = −0.405760 + 0.979630I
a = 0.166067 − 0.368101I
b = −0.194828 − 1.239410I
0.10785 − 2.26276I −0.12423 + 3.11409I
u = −0.405760 − 0.979630I
a = 0.166067 + 0.368101I
b = −0.194828 + 1.239410I
0.10785 + 2.26276I −0.12423 − 3.11409I
u = −0.064971 + 1.059860I
a = 0.213265 + 0.829397I
b = 0.155643 − 0.110588I
−1.26832 − 1.59690I 3.13274 + 4.73829I
u = −0.064971 − 1.059860I
a = 0.213265 − 0.829397I
b = 0.155643 + 0.110588I
−1.26832 + 1.59690I 3.13274 − 4.73829I
u = 0.211058 + 1.064720I
a = 0.031919 − 0.161023I
b = 0.211058 − 1.064720I
−4.11368 −8.21539 + 0.I
u = 0.211058 − 1.064720I
a = 0.031919 + 0.161023I
b = 0.211058 + 1.064720I
−4.11368 −8.21539 + 0.I
u = 0.758158 + 0.793503I
a = −0.585546 − 0.804617I
b = 0.04392 − 1.46343I
−1.96895 − 4.48385I −0.56586 + 2.47352I
u = 0.758158 − 0.793503I
a = −0.585546 + 0.804617I
b = 0.04392 + 1.46343I
−1.96895 + 4.48385I −0.56586 − 2.47352I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.726368 + 0.367752I
a = 1.28493 − 0.77998I
b = 0.189110 − 1.334780I
1.85425 − 1.80763I 4.25907 + 2.73625I
u = −0.726368 − 0.367752I
a = 1.28493 + 0.77998I
b = 0.189110 + 1.334780I
1.85425 + 1.80763I 4.25907 − 2.73625I
u = −0.194828 + 1.239410I
a = −0.281989 − 0.192252I
b = −0.405760 − 0.979630I
0.10785 + 2.26276I 0. − 3.11409I
u = −0.194828 − 1.239410I
a = −0.281989 + 0.192252I
b = −0.405760 + 0.979630I
0.10785 − 2.26276I 0. + 3.11409I
u = 0.189110 + 1.334780I
a = −0.830423 + 0.366693I
b = −0.726368 − 0.367752I
1.85425 + 1.80763I 0
u = 0.189110 − 1.334780I
a = −0.830423 − 0.366693I
b = −0.726368 + 0.367752I
1.85425 − 1.80763I 0
u = −0.12904 + 1.43500I
a = 0.879014 + 0.158365I
b = 0.816854 − 0.532908I
−4.44976 − 2.73152I 0
u = −0.12904 − 1.43500I
a = 0.879014 − 0.158365I
b = 0.816854 + 0.532908I
−4.44976 + 2.73152I 0
u = −0.07438 + 1.45158I
a = 0.838772 + 0.066973I
b = 0.803564 − 0.620127I
−4.65974 − 2.68588I 0
u = −0.07438 − 1.45158I
a = 0.838772 − 0.066973I
b = 0.803564 + 0.620127I
−4.65974 + 2.68588I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00133 + 1.45662I
a = −0.770259 − 0.039909I
b = −0.769634 − 0.726428I
−6.94955 − 0.90110I 0
u = 0.00133 − 1.45662I
a = −0.770259 + 0.039909I
b = −0.769634 + 0.726428I
−6.94955 + 0.90110I 0
u = 0.04392 + 1.46343I
a = 0.737670 − 0.110790I
b = 0.758158 − 0.793503I
−1.96895 + 4.48385I 0
u = 0.04392 − 1.46343I
a = 0.737670 + 0.110790I
b = 0.758158 + 0.793503I
−1.96895 − 4.48385I 0
u = 0.18002 + 1.46427I
a = −0.975469 + 0.186914I
b = −0.892757 − 0.485854I
−6.19421 + 6.51836I 0
u = 0.18002 − 1.46427I
a = −0.975469 − 0.186914I
b = −0.892757 + 0.485854I
−6.19421 − 6.51836I 0
u = −0.20956 + 1.46882I
a = 1.015610 + 0.215863I
b = 0.920413 − 0.451372I
−0.91901 − 10.18330I 0
u = −0.20956 − 1.46882I
a = 1.015610 − 0.215863I
b = 0.920413 + 0.451372I
−0.91901 + 10.18330I 0
u = −0.255559 + 0.080028I
a = 3.70633 + 2.09787I
b = 0.142789 + 0.981947I
4.29768 + 4.29720I 6.75143 − 3.93304I
u = −0.255559 − 0.080028I
a = 3.70633 − 2.09787I
b = 0.142789 − 0.981947I
4.29768 − 4.29720I 6.75143 + 3.93304I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.155643 + 0.110588I
a = −4.33450 + 1.97373I
b = −0.064971 − 1.059860I
−1.26832 + 1.59690I 3.13274 − 4.73829I
u = 0.155643 − 0.110588I
a = −4.33450 − 1.97373I
b = −0.064971 + 1.059860I
−1.26832 − 1.59690I 3.13274 + 4.73829I
16
III. I
u
3
= hb + u, a
5
− a
4
+ 2a
3
− a
2
+ a − 1, u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
−1
a
11
=
u
0
a
1
=
a
−u
a
4
=
0
−1
a
2
=
a
a − u
a
9
=
−a
2
u
−a + u
a
3
=
a
4
−a
3
u − a
2
− 1
a
8
=
a
4
u
a
4
u + a
3
+ a
2
u + u
a
12
=
a + u
−u
a
7
=
au
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
3
+ 4a
2
− 4a
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
2
, c
7
, c
8
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
3
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
c
4
, c
5
, c
6
c
10
, c
11
, c
12
(u
2
+ 1)
5
c
9
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
2
, c
7
, c
8
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
3
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
c
4
, c
5
, c
6
c
10
, c
11
, c
12
(y + 1)
10
c
9
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.339110 + 0.822375I
b = − 1.000000I
−2.96077 + 1.53058I −3.48489 − 4.43065I
u = 1.000000I
a = −0.339110 − 0.822375I
b = − 1.000000I
−2.96077 − 1.53058I −3.48489 + 4.43065I
u = 1.000000I
a = 0.766826
b = − 1.000000I
−0.888787 −2.51890
u = 1.000000I
a = 0.455697 + 1.200150I
b = − 1.000000I
2.58269 − 4.40083I 0.74431 + 3.49859I
u = 1.000000I
a = 0.455697 − 1.200150I
b = − 1.000000I
2.58269 + 4.40083I 0.74431 − 3.49859I
u = − 1.000000I
a = −0.339110 + 0.822375I
b = 1.000000I
−2.96077 + 1.53058I −3.48489 − 4.43065I
u = − 1.000000I
a = −0.339110 − 0.822375I
b = 1.000000I
−2.96077 − 1.53058I −3.48489 + 4.43065I
u = − 1.000000I
a = 0.766826
b = 1.000000I
−0.888787 −2.51890
u = − 1.000000I
a = 0.455697 + 1.200150I
b = 1.000000I
2.58269 − 4.40083I 0.74431 + 3.49859I
u = − 1.000000I
a = 0.455697 − 1.200150I
b = 1.000000I
2.58269 + 4.40083I 0.74431 − 3.49859I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
21
− 5u
20
+ ··· − 11u + 3)
2
· (u
32
− 7u
31
+ ··· − 629u + 136)
c
2
, c
7
, c
8
(u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1)(u
21
+ u
20
+ ··· − u − 1)
2
· (u
32
− 3u
31
+ ··· − 9u + 2)
c
3
(u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1)(u
21
− u
20
+ ··· − 3u − 1)
2
· (u
32
+ 3u
31
+ ··· − 45u + 10)
c
4
, c
5
, c
6
c
10
, c
11
, c
12
((u
2
+ 1)
5
)(u
32
+ 20u
30
+ ··· − 2u + 1)(u
42
+ u
41
+ ··· + 2u + 1)
c
9
(u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1)(u
21
+ 7u
20
+ ··· + 3u − 1)
2
· (u
32
− 21u
31
+ ··· − 31521u + 3794)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
21
+ 3y
20
+ ··· − 41y −9)
2
· (y
32
+ 9y
31
+ ··· + 185079y + 18496)
c
2
, c
7
, c
8
((y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
)(y
21
+ 19y
20
+ ··· + 3y −1)
2
· (y
32
+ 29y
31
+ ··· + 3y + 4)
c
3
((y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
)(y
21
− y
20
+ ··· + 3y −1)
2
· (y
32
+ y
31
+ ··· + 1795y + 100)
c
4
, c
5
, c
6
c
10
, c
11
, c
12
((y + 1)
10
)(y
32
+ 40y
31
+ ··· + 10y + 1)(y
42
+ 35y
41
+ ··· − 32y + 1)
c
9
((y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
)(y
21
+ 15y
20
+ ··· + 27y −1)
2
· (y
32
+ 9y
31
+ ··· + 46718595y + 14394436)
22
