12a
1179
(K12a
1179
)
A knot diagram
1
Linearized knot diagam
4 10 8 9 12 11 3 1 2 7 6 5
Solving Sequence
5,12
6
1,9
4 2 8 3 11 7 10
c
5
c
12
c
4
c
1
c
8
c
3
c
11
c
6
c
10
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
21
− 20u
20
+ ··· + 2b − 36, 3u
21
+ 17u
20
+ ··· + 4a − 10, u
22
+ 7u
21
+ ··· + 88u + 8i
I
u
2
= h−1208412097a
5
u
5
+ 1863706926u
5
a
4
+ ··· + 88241195076a − 13422878124,
6a
5
u
5
+ 4u
5
a
4
+ ··· − 38a − 32, u
6
− u
5
+ 5u
4
− 4u
3
+ 6u
2
− 3u + 1i
I
u
3
= h−u
12
− 9u
10
− 30u
8
− 45u
6
− 29u
4
+ u
3
− 6u
2
+ b + 2u,
− u
12
− u
11
− 9u
10
− 9u
9
− 30u
8
− 30u
7
− 45u
6
− 45u
5
− 29u
4
− 28u
3
− 5u
2
+ a − 4u + 2,
u
13
+ 10u
11
+ 38u
9
+ 68u
7
+ 57u
5
− u
4
+ 18u
3
− 3u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 71 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−3u
21
− 20u
20
+ · · · + 2b − 36, 3u
21
+ 17u
20
+ · · · + 4a − 10, u
22
+
7u
21
+ · · · + 88u + 8i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
−
3
4
u
21
−
17
4
u
20
+ ··· + 8u +
5
2
3
2
u
21
+ 10u
20
+ ··· +
365
2
u + 18
a
4
=
1
2
u
21
+
15
4
u
20
+ ··· +
461
4
u + 13
−
1
4
u
21
−
5
4
u
20
+ ··· − 48u − 6
a
2
=
3
8
u
21
+
19
8
u
20
+ ··· +
115
2
u +
13
2
1
4
u
21
+
7
4
u
20
+ ··· +
23
2
u + 1
a
8
=
−
5
4
u
21
−
31
4
u
20
+ ··· − 106u −
19
2
u
21
+
13
2
u
20
+ ··· +
137
2
u + 6
a
3
=
−
3
8
u
21
−
19
8
u
20
+ ··· −
55
2
u −
5
2
−
1
4
u
21
−
7
4
u
20
+ ··· −
53
2
u − 3
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−u
3
− 2u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
20
+ 6u
19
+ 32u
18
+ 116u
17
+ 363u
16
+ 934u
15
+ 2100u
14
+
4092u
13
+ 7035u
12
+ 10658u
11
+ 14285u
10
+ 16890u
9
+ 17584u
8
+ 15990u
7
+ 12628u
6
+
8526u
5
+ 4861u
4
+ 2276u
3
+ 846u
2
+ 236u + 42
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 19u
21
+ ··· − 800u + 64
c
2
, c
3
, c
7
c
9
u
22
− u
21
+ ··· + 6u
2
+ 1
c
4
, c
8
u
22
+ 6u
20
+ ··· − u + 1
c
5
, c
6
, c
10
c
11
, c
12
u
22
− 7u
21
+ ··· − 88u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− y
21
+ ··· − 1024y + 4096
c
2
, c
3
, c
7
c
9
y
22
− 25y
21
+ ··· + 12y + 1
c
4
, c
8
y
22
+ 12y
21
+ ··· − 7y + 1
c
5
, c
6
, c
10
c
11
, c
12
y
22
+ 29y
21
+ ··· + 32y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.214951 + 0.955332I
a = −0.39803 − 1.38319I
b = 0.670593 − 0.921685I
−2.60701 − 2.88422I −0.19154 + 3.17334I
u = −0.214951 − 0.955332I
a = −0.39803 + 1.38319I
b = 0.670593 + 0.921685I
−2.60701 + 2.88422I −0.19154 − 3.17334I
u = −0.813603 + 0.334821I
a = −0.391314 + 0.249585I
b = −0.463678 − 0.959425I
−6.77494 + 2.66525I −5.93834 − 2.44908I
u = −0.813603 − 0.334821I
a = −0.391314 − 0.249585I
b = −0.463678 + 0.959425I
−6.77494 − 2.66525I −5.93834 + 2.44908I
u = −0.722432 + 0.499538I
a = −0.667442 − 0.524436I
b = 0.702002 − 1.099620I
−7.31468 − 7.59742I −4.88198 + 6.88559I
u = −0.722432 − 0.499538I
a = −0.667442 + 0.524436I
b = 0.702002 + 1.099620I
−7.31468 + 7.59742I −4.88198 − 6.88559I
u = −0.386869 + 1.238110I
a = 0.29217 + 1.62873I
b = −0.85810 + 1.29508I
−12.8000 − 11.4299I −6.89165 + 6.89710I
u = −0.386869 − 1.238110I
a = 0.29217 − 1.62873I
b = −0.85810 − 1.29508I
−12.8000 + 11.4299I −6.89165 − 6.89710I
u = −0.518713 + 1.209380I
a = 0.749140 + 0.553517I
b = 0.141219 + 0.931028I
−11.52230 − 1.93620I −10.29123 + 1.11937I
u = −0.518713 − 1.209380I
a = 0.749140 − 0.553517I
b = 0.141219 − 0.931028I
−11.52230 + 1.93620I −10.29123 − 1.11937I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.188904 + 0.563822I
a = 0.341201 − 0.743824I
b = 0.487380 + 0.071622I
−0.321406 − 1.315600I 0.42346 + 6.52764I
u = −0.188904 − 0.563822I
a = 0.341201 + 0.743824I
b = 0.487380 − 0.071622I
−0.321406 + 1.315600I 0.42346 − 6.52764I
u = 0.03206 + 1.53855I
a = −0.320508 + 0.481993I
b = −0.440190 + 0.193391I
−7.43727 − 1.58134I 0.15073 + 4.91907I
u = 0.03206 − 1.53855I
a = −0.320508 − 0.481993I
b = −0.440190 − 0.193391I
−7.43727 + 1.58134I 0.15073 − 4.91907I
u = −0.398382 + 0.163640I
a = 1.041370 − 0.104922I
b = −0.526173 + 0.495850I
0.836027 − 0.793326I 6.74273 + 3.41727I
u = −0.398382 − 0.163640I
a = 1.041370 + 0.104922I
b = −0.526173 − 0.495850I
0.836027 + 0.793326I 6.74273 − 3.41727I
u = −0.05207 + 1.70520I
a = −0.13197 + 1.64255I
b = −0.83496 + 1.17436I
−12.05740 − 3.92251I 0.689774 + 0.408842I
u = −0.05207 − 1.70520I
a = −0.13197 − 1.64255I
b = −0.83496 − 1.17436I
−12.05740 + 3.92251I 0.689774 − 0.408842I
u = −0.10228 + 1.79386I
a = 0.12610 − 1.92859I
b = 0.95775 − 1.44210I
15.7405 − 13.6253I −7.26879 + 5.92995I
u = −0.10228 − 1.79386I
a = 0.12610 + 1.92859I
b = 0.95775 + 1.44210I
15.7405 + 13.6253I −7.26879 − 5.92995I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13386 + 1.80777I
a = −0.390730 − 1.046170I
b = 0.164157 − 0.996452I
17.1171 − 4.8585I −9.54317 + 2.73303I
u = −0.13386 − 1.80777I
a = −0.390730 + 1.046170I
b = 0.164157 + 0.996452I
17.1171 + 4.8585I −9.54317 − 2.73303I
7
II. I
u
2
= h−1.21 × 10
9
a
5
u
5
+ 1.86 × 10
9
a
4
u
5
+ · · · + 8.82 × 10
10
a − 1.34 ×
10
10
, 6a
5
u
5
+ 4u
5
a
4
+ · · · − 38a − 32, u
6
− u
5
+ 5u
4
− 4u
3
+ 6u
2
− 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
a
0.372194a
5
u
5
− 0.574026a
4
u
5
+ ··· − 27.1785a + 4.13428
a
4
=
−0.145773a
5
u
5
+ 2.18213a
4
u
5
+ ··· + 17.8628a − 21.1907
0.312265a
5
u
5
− 1.60138a
4
u
5
+ ··· − 34.5790a + 1.77561
a
2
=
−0.206418a
5
u
5
− 2.57431a
4
u
5
+ ··· − 10.7722a + 16.8693
0.110381a
5
u
5
− 0.378957a
4
u
5
+ ··· − 20.5376a − 6.45733
a
8
=
0.132970a
5
u
5
+ 1.05447a
4
u
5
+ ··· + 1.43345a − 5.94094
0.505164a
5
u
5
+ 0.480448a
4
u
5
+ ··· − 26.7451a − 1.80666
a
3
=
−0.0660601a
5
u
5
+ 1.04617a
4
u
5
+ ··· + 12.8011a − 4.58028
−0.295252a
5
u
5
+ 0.333319a
4
u
5
+ ··· + 13.4971a + 1.63976
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−u
3
− 2u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
10836912
649345301
a
5
u
5
+
6217485248
649345301
u
5
a
4
+ ···+
27178566568
649345301
a −
51617037366
649345301
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
12
c
2
, c
3
, c
7
c
9
u
36
+ u
35
+ ··· − 334u + 77
c
4
, c
8
u
36
+ 3u
35
+ ··· + 244u + 271
c
5
, c
6
, c
10
c
11
, c
12
(u
6
+ u
5
+ 5u
4
+ 4u
3
+ 6u
2
+ 3u + 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
12
c
2
, c
3
, c
7
c
9
y
36
− 33y
35
+ ··· + 209380y + 5929
c
4
, c
8
y
36
+ 11y
35
+ ··· + 1542616y + 73441
c
5
, c
6
, c
10
c
11
, c
12
(y
6
+ 9y
5
+ 29y
4
+ 40y
3
+ 22y
2
+ 3y + 1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.142924 + 1.159520I
a = 0.020396 − 0.755302I
b = −0.624535 − 0.897322I
−6.55350 − 0.17216I −6.07139 − 0.41864I
u = 0.142924 + 1.159520I
a = −0.90019 + 1.20470I
b = −0.072498 + 0.768105I
−6.55350 − 0.17216I −6.07139 − 0.41864I
u = 0.142924 + 1.159520I
a = −1.09844 + 1.21563I
b = −1.70363 + 1.17475I
−10.69110 + 2.65597I −12.60066 − 3.39809I
u = 0.142924 + 1.159520I
a = 0.71837 − 1.49821I
b = −0.702328 − 0.883472I
−6.55350 + 5.48409I −6.07139 − 6.37753I
u = 0.142924 + 1.159520I
a = 0.09177 + 2.06359I
b = 0.91585 + 1.55946I
−6.55350 + 5.48409I −6.07139 − 6.37753I
u = 0.142924 + 1.159520I
a = 0.85867 + 2.27785I
b = 0.039086 + 0.707567I
−10.69110 + 2.65597I −12.60066 − 3.39809I
u = 0.142924 − 1.159520I
a = 0.020396 + 0.755302I
b = −0.624535 + 0.897322I
−6.55350 + 0.17216I −6.07139 + 0.41864I
u = 0.142924 − 1.159520I
a = −0.90019 − 1.20470I
b = −0.072498 − 0.768105I
−6.55350 + 0.17216I −6.07139 + 0.41864I
u = 0.142924 − 1.159520I
a = −1.09844 − 1.21563I
b = −1.70363 − 1.17475I
−10.69110 − 2.65597I −12.60066 + 3.39809I
u = 0.142924 − 1.159520I
a = 0.71837 + 1.49821I
b = −0.702328 + 0.883472I
−6.55350 − 5.48409I −6.07139 + 6.37753I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.142924 − 1.159520I
a = 0.09177 − 2.06359I
b = 0.91585 − 1.55946I
−6.55350 − 5.48409I −6.07139 + 6.37753I
u = 0.142924 − 1.159520I
a = 0.85867 − 2.27785I
b = 0.039086 − 0.707567I
−10.69110 − 2.65597I −12.60066 + 3.39809I
u = 0.321608 + 0.359079I
a = −0.541913 − 0.991237I
b = 1.134260 − 0.815115I
−5.79017 + 1.10871I −7.48336 − 6.18117I
u = 0.321608 + 0.359079I
a = −0.573836 − 1.111540I
b = −0.036630 + 0.730558I
−1.65258 − 1.71942I −0.95409 − 3.20172I
u = 0.321608 + 0.359079I
a = 1.120820 − 0.796180I
b = −0.727819 − 1.151300I
−1.65258 + 3.93683I −0.95409 − 9.16062I
u = 0.321608 + 0.359079I
a = 1.56692 + 0.28239I
b = 0.488689 − 0.785333I
−1.65258 − 1.71942I −0.95409 − 3.20172I
u = 0.321608 + 0.359079I
a = −2.31941 + 0.30926I
b = 0.467021 + 0.778019I
−1.65258 + 3.93683I −0.95409 − 9.16062I
u = 0.321608 + 0.359079I
a = −0.16556 − 3.53944I
b = −0.475830 − 0.658521I
−5.79017 + 1.10871I −7.48336 − 6.18117I
u = 0.321608 − 0.359079I
a = −0.541913 + 0.991237I
b = 1.134260 + 0.815115I
−5.79017 − 1.10871I −7.48336 + 6.18117I
u = 0.321608 − 0.359079I
a = −0.573836 + 1.111540I
b = −0.036630 − 0.730558I
−1.65258 + 1.71942I −0.95409 + 3.20172I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.321608 − 0.359079I
a = 1.120820 + 0.796180I
b = −0.727819 + 1.151300I
−1.65258 − 3.93683I −0.95409 + 9.16062I
u = 0.321608 − 0.359079I
a = 1.56692 − 0.28239I
b = 0.488689 + 0.785333I
−1.65258 + 1.71942I −0.95409 + 3.20172I
u = 0.321608 − 0.359079I
a = −2.31941 − 0.30926I
b = 0.467021 − 0.778019I
−1.65258 − 3.93683I −0.95409 + 9.16062I
u = 0.321608 − 0.359079I
a = −0.16556 + 3.53944I
b = −0.475830 + 0.658521I
−5.79017 − 1.10871I −7.48336 + 6.18117I
u = 0.03547 + 1.77530I
a = 0.483101 + 1.162360I
b = 0.98695 + 1.09529I
−17.2652 + 0.5991I −6.44525 + 0.72721I
u = 0.03547 + 1.77530I
a = 0.49089 − 1.43550I
b = −0.136931 − 0.892105I
−17.2652 + 0.5991I −6.44525 + 0.72721I
u = 0.03547 + 1.77530I
a = −0.19050 + 1.53203I
b = 0.836637 + 0.957299I
−17.2652 + 6.2553I −6.44525 − 5.23168I
u = 0.03547 + 1.77530I
a = −0.63078 − 1.91690I
b = 0.159090 − 0.769263I
18.0757 + 3.4272I −12.97451 − 2.25224I
u = 0.03547 + 1.77530I
a = 1.57803 − 1.54119I
b = 2.00938 − 1.44296I
18.0757 + 3.4272I −12.97451 − 2.25224I
u = 0.03547 + 1.77530I
a = −0.50833 − 2.26340I
b = −1.05676 − 1.80309I
−17.2652 + 6.2553I −6.44525 − 5.23168I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03547 − 1.77530I
a = 0.483101 − 1.162360I
b = 0.98695 − 1.09529I
−17.2652 − 0.5991I −6.44525 − 0.72721I
u = 0.03547 − 1.77530I
a = 0.49089 + 1.43550I
b = −0.136931 + 0.892105I
−17.2652 − 0.5991I −6.44525 − 0.72721I
u = 0.03547 − 1.77530I
a = −0.19050 − 1.53203I
b = 0.836637 − 0.957299I
−17.2652 − 6.2553I −6.44525 + 5.23168I
u = 0.03547 − 1.77530I
a = −0.63078 + 1.91690I
b = 0.159090 + 0.769263I
18.0757 − 3.4272I −12.97451 + 2.25224I
u = 0.03547 − 1.77530I
a = 1.57803 + 1.54119I
b = 2.00938 + 1.44296I
18.0757 − 3.4272I −12.97451 + 2.25224I
u = 0.03547 − 1.77530I
a = −0.50833 + 2.26340I
b = −1.05676 + 1.80309I
−17.2652 − 6.2553I −6.44525 + 5.23168I
14
III. I
u
3
=
h−u
12
−9u
10
+· · ·+b +2u, −u
12
−u
11
+· · ·+a +2, u
13
+10u
11
+· · ·−3u
2
−1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
u
12
+ u
11
+ ··· + 4u − 2
u
12
+ 9u
10
+ 30u
8
+ 45u
6
+ 29u
4
− u
3
+ 6u
2
− 2u
a
4
=
−u
12
− 10u
10
+ ··· + 5u + 2
u
9
+ 7u
7
+ 16u
5
+ 13u
3
+ 2u − 1
a
2
=
−u
12
− 10u
10
+ ··· − 3u + 2
u
9
− u
8
+ 7u
7
− 6u
6
+ 16u
5
− 11u
4
+ 13u
3
− 6u
2
+ 3u − 1
a
8
=
u
12
+ 9u
10
+ ··· + 4u − 1
u
12
− u
11
+ ··· − 2u + 1
a
3
=
−u
12
− 10u
10
− 38u
8
− 67u
6
− u
5
− 52u
4
− 3u
3
− 11u
2
− u + 2
−u
8
+ u
7
− 6u
6
+ 5u
5
− 11u
4
+ 7u
3
− 6u
2
+ 2u − 1
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−u
3
− 2u
u
5
+ 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
11
+ u
10
− 11u
9
+ 11u
8
− 44u
7
+ 40u
6
− 77u
5
+ 57u
4
− 55u
3
+ 28u
2
− 10u − 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 4u
12
+ 8u
11
− 8u
10
+ u
9
+ 7u
8
− 5u
7
− 3u
6
+ 3u
5
+ 4u
4
− 4u
3
+ 1
c
2
, c
7
u
13
+ u
12
+ ··· + u + 1
c
3
, c
9
u
13
− u
12
+ ··· + u − 1
c
4
, c
8
u
13
+ 2u
11
− u
10
+ 5u
9
− u
8
+ 3u
7
+ 3u
5
+ u
4
+ u
3
− 2u
2
− 1
c
5
, c
6
u
13
+ 10u
11
+ 38u
9
+ 68u
7
+ 57u
5
− u
4
+ 18u
3
− 3u
2
− 1
c
10
, c
11
, c
12
u
13
+ 10u
11
+ 38u
9
+ 68u
7
+ 57u
5
+ u
4
+ 18u
3
+ 3u
2
+ 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ 2y
11
+ ··· − 8y
2
− 1
c
2
, c
3
, c
7
c
9
y
13
− 13y
12
+ ··· + 9y −1
c
4
, c
8
y
13
+ 4y
12
+ ··· − 4y −1
c
5
, c
6
, c
10
c
11
, c
12
y
13
+ 20y
12
+ ··· − 6y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.222851 + 1.128390I
a = −0.528316 + 1.119370I
b = −0.751183 + 0.409643I
−9.46673 + 2.12086I −5.40296 − 0.71019I
u = 0.222851 − 1.128390I
a = −0.528316 − 1.119370I
b = −0.751183 − 0.409643I
−9.46673 − 2.12086I −5.40296 + 0.71019I
u = −0.132288 + 0.825196I
a = −0.80812 − 1.63198I
b = 0.620126 − 1.109460I
−3.74892 − 3.58419I −7.53140 + 5.11211I
u = −0.132288 − 0.825196I
a = −0.80812 + 1.63198I
b = 0.620126 + 1.109460I
−3.74892 + 3.58419I −7.53140 − 5.11211I
u = −0.09053 + 1.45630I
a = 0.446564 + 0.617287I
b = 0.003852 + 0.647453I
−8.20019 + 1.37133I −10.62804 − 1.83848I
u = −0.09053 − 1.45630I
a = 0.446564 − 0.617287I
b = 0.003852 − 0.647453I
−8.20019 − 1.37133I −10.62804 + 1.83848I
u = −0.192457 + 0.338010I
a = −1.90707 + 0.93123I
b = −0.308277 − 0.891137I
−2.11472 + 2.48894I −7.57750 − 5.29863I
u = −0.192457 − 0.338010I
a = −1.90707 − 0.93123I
b = −0.308277 + 0.891137I
−2.11472 − 2.48894I −7.57750 + 5.29863I
u = 0.374429
a = 2.73808
b = 0.745922
−5.68479 −6.08470
u = −0.03925 + 1.68347I
a = −0.05381 + 1.74327I
b = −0.82116 + 1.27338I
−12.70200 − 4.26962I −9.64995 + 5.18333I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03925 − 1.68347I
a = −0.05381 − 1.74327I
b = −0.82116 − 1.27338I
−12.70200 + 4.26962I −9.64995 − 5.18333I
u = 0.04446 + 1.77839I
a = 0.481712 − 1.244350I
b = 0.883684 − 0.737401I
19.3357 + 3.2097I −5.16777 − 0.81655I
u = 0.04446 − 1.77839I
a = 0.481712 + 1.244350I
b = 0.883684 + 0.737401I
19.3357 − 3.2097I −5.16777 + 0.81655I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
12
· (u
13
− 4u
12
+ 8u
11
− 8u
10
+ u
9
+ 7u
8
− 5u
7
− 3u
6
+ 3u
5
+ 4u
4
− 4u
3
+ 1)
· (u
22
− 19u
21
+ ··· − 800u + 64)
c
2
, c
7
(u
13
+ u
12
+ ··· + u + 1)(u
22
− u
21
+ ··· + 6u
2
+ 1)
· (u
36
+ u
35
+ ··· − 334u + 77)
c
3
, c
9
(u
13
− u
12
+ ··· + u − 1)(u
22
− u
21
+ ··· + 6u
2
+ 1)
· (u
36
+ u
35
+ ··· − 334u + 77)
c
4
, c
8
(u
13
+ 2u
11
− u
10
+ 5u
9
− u
8
+ 3u
7
+ 3u
5
+ u
4
+ u
3
− 2u
2
− 1)
· (u
22
+ 6u
20
+ ··· − u + 1)(u
36
+ 3u
35
+ ··· + 244u + 271)
c
5
, c
6
(u
6
+ u
5
+ 5u
4
+ 4u
3
+ 6u
2
+ 3u + 1)
6
· (u
13
+ 10u
11
+ 38u
9
+ 68u
7
+ 57u
5
− u
4
+ 18u
3
− 3u
2
− 1)
· (u
22
− 7u
21
+ ··· − 88u + 8)
c
10
, c
11
, c
12
(u
6
+ u
5
+ 5u
4
+ 4u
3
+ 6u
2
+ 3u + 1)
6
· (u
13
+ 10u
11
+ 38u
9
+ 68u
7
+ 57u
5
+ u
4
+ 18u
3
+ 3u
2
+ 1)
· (u
22
− 7u
21
+ ··· − 88u + 8)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
− y
2
+ 2y −1)
12
)(y
13
+ 2y
11
+ ··· − 8y
2
− 1)
· (y
22
− y
21
+ ··· − 1024y + 4096)
c
2
, c
3
, c
7
c
9
(y
13
− 13y
12
+ ··· + 9y −1)(y
22
− 25y
21
+ ··· + 12y + 1)
· (y
36
− 33y
35
+ ··· + 209380y + 5929)
c
4
, c
8
(y
13
+ 4y
12
+ ··· − 4y −1)(y
22
+ 12y
21
+ ··· − 7y + 1)
· (y
36
+ 11y
35
+ ··· + 1542616y + 73441)
c
5
, c
6
, c
10
c
11
, c
12
(y
6
+ 9y
5
+ 29y
4
+ 40y
3
+ 22y
2
+ 3y + 1)
6
· (y
13
+ 20y
12
+ ··· − 6y −1)(y
22
+ 29y
21
+ ··· + 32y + 64)
21
