11a
123
(K11a
123
)
A knot diagram
1
Linearized knot diagam
5 1 9 6 2 10 3 11 7 4 8
Solving Sequence
1,5
2 3 6
4,8
7 11 9 10
c
1
c
2
c
5
c
4
c
7
c
11
c
8
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h31496267249u
24
− 1954119851u
23
+ ··· + 353576605306b − 294716823050,
− 258242463245u
24
+ 140426199118u
23
+ ··· + 707153210612a + 177949498093,
u
25
− 2u
24
+ ··· + 17u − 4i
I
u
2
= h−5u
18
a − 45u
18
+ ··· + 27a + 5, −6u
18
a + 26u
18
+ ··· − 6a + 39, u
19
− u
18
+ ··· + u
2
− 1i
I
u
3
= hb + 1, 2a + 2u + 1, u
3
+ u
2
− 1i
I
u
4
= hb − a − 1, a
2
+ 2a + 2, u − 1i
* 4 irreducible components of dim
C
= 0, with total 68 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
=
h3.15×10
10
u
24
−1.95×10
9
u
23
+· · ·+3.54×10
11
b−2.95×10
11
, −2.58×10
11
u
24
+
1.40 × 10
11
u
23
+ · · · + 7.07 × 10
11
a + 1.78 × 10
11
, u
25
− 2u
24
+ · · · + 17u − 4i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
4
=
u
3
u
5
− u
3
+ u
a
8
=
0.365186u
24
− 0.198580u
23
+ ··· − 5.28891u − 0.251642
−0.0890790u
24
+ 0.00552672u
23
+ ··· − 1.23519u + 0.833530
a
7
=
0.267603u
24
− 0.170382u
23
+ ··· − 4.06703u − 0.0336839
−0.227826u
24
+ 0.244721u
23
+ ··· + 1.30904u + 0.0124582
a
11
=
−0.361710u
24
+ 0.276963u
23
+ ··· + 5.53501u + 0.291576
0.135603u
24
− 0.0416754u
23
+ ··· + 1.55999u − 0.715415
a
9
=
0.690139u
24
− 0.455342u
23
+ ··· − 9.24059u − 0.0115544
−0.314729u
24
+ 0.224657u
23
+ ··· − 1.21944u + 0.939187
a
10
=
−0.323410u
24
+ 0.155971u
23
+ ··· + 3.99738u + 0.846565
0.110684u
24
− 0.103445u
23
+ ··· + 0.590987u − 0.502652
a
10
=
−0.323410u
24
+ 0.155971u
23
+ ··· + 3.99738u + 0.846565
0.110684u
24
− 0.103445u
23
+ ··· + 0.590987u − 0.502652
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
781324937945
707153210612
u
24
−
104635078433
707153210612
u
23
+ ··· +
4120329941333
176788302653
u −
3444311623734
176788302653
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
25
+ 2u
24
+ ··· + 17u + 4
c
2
, c
4
u
25
+ 8u
24
+ ··· + 241u + 16
c
3
u
25
− 3u
24
+ ··· − 96u + 128
c
6
, c
8
, c
9
c
11
u
25
+ 3u
24
+ ··· + 2u + 1
c
7
, c
10
8(8u
25
+ 4u
24
+ ··· + 2u + 2)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
25
− 8y
24
+ ··· + 241y −16
c
2
, c
4
y
25
+ 20y
24
+ ··· + 19233y −256
c
3
y
25
+ 9y
24
+ ··· − 72704y −16384
c
6
, c
8
, c
9
c
11
y
25
+ 17y
24
+ ··· + 16y −1
c
7
, c
10
64(64y
25
+ 1072y
24
+ ··· + 20y −4)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.831869 + 0.519995I
a = 0.60247 − 1.53377I
b = 0.604789 + 0.633838I
−0.94821 − 3.43572I −13.2032 + 6.7534I
u = 0.831869 − 0.519995I
a = 0.60247 + 1.53377I
b = 0.604789 − 0.633838I
−0.94821 + 3.43572I −13.2032 − 6.7534I
u = −0.096629 + 0.930099I
a = 0.10164 + 1.51799I
b = −0.269095 − 1.312200I
7.47156 − 5.57189I −2.30391 + 4.65826I
u = −0.096629 − 0.930099I
a = 0.10164 − 1.51799I
b = −0.269095 + 1.312200I
7.47156 + 5.57189I −2.30391 − 4.65826I
u = −0.873066 + 0.713586I
a = −0.343451 − 0.174556I
b = −0.321236 − 0.053568I
2.48771 + 2.73173I −3.19620 − 2.74281I
u = −0.873066 − 0.713586I
a = −0.343451 + 0.174556I
b = −0.321236 + 0.053568I
2.48771 − 2.73173I −3.19620 + 2.74281I
u = 0.890108 + 0.788825I
a = −0.718513 − 0.942420I
b = 1.43833 − 0.04819I
2.16301 − 2.96631I −1.51503 + 3.55668I
u = 0.890108 − 0.788825I
a = −0.718513 + 0.942420I
b = 1.43833 + 0.04819I
2.16301 + 2.96631I −1.51503 − 3.55668I
u = 0.746418 + 0.296773I
a = −0.848177 + 0.452473I
b = 0.188697 − 0.408041I
−0.644117 − 0.222126I −12.29988 − 0.69416I
u = 0.746418 − 0.296773I
a = −0.848177 − 0.452473I
b = 0.188697 + 0.408041I
−0.644117 + 0.222126I −12.29988 + 0.69416I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.791605 + 0.124227I
a = 1.178100 + 0.337562I
b = 1.040980 + 0.275015I
−2.97368 + 0.31797I −15.9411 − 13.1085I
u = −0.791605 − 0.124227I
a = 1.178100 − 0.337562I
b = 1.040980 − 0.275015I
−2.97368 − 0.31797I −15.9411 + 13.1085I
u = −1.142430 + 0.382078I
a = −1.268030 − 0.422167I
b = −0.409233 + 1.264710I
3.90197 + 10.08690I −8.02551 − 8.45672I
u = −1.142430 − 0.382078I
a = −1.268030 + 0.422167I
b = −0.409233 − 1.264710I
3.90197 − 10.08690I −8.02551 + 8.45672I
u = 0.770950 + 0.937113I
a = 0.30856 − 1.63900I
b = −0.48655 + 1.44328I
12.8491 + 9.5213I −4.07416 − 4.01278I
u = 0.770950 − 0.937113I
a = 0.30856 + 1.63900I
b = −0.48655 − 1.44328I
12.8491 − 9.5213I −4.07416 + 4.01278I
u = −0.749482 + 1.006980I
a = −0.24489 − 1.53795I
b = 0.065690 + 1.341370I
11.66030 + 0.32743I −0.684836 − 0.302346I
u = −0.749482 − 1.006980I
a = −0.24489 + 1.53795I
b = 0.065690 − 1.341370I
11.66030 − 0.32743I −0.684836 + 0.302346I
u = 1.286720 + 0.219140I
a = 0.295022 − 0.018174I
b = −0.140637 + 1.182510I
2.59539 + 1.53840I −3.54408 − 4.89308I
u = 1.286720 − 0.219140I
a = 0.295022 + 0.018174I
b = −0.140637 − 1.182510I
2.59539 − 1.53840I −3.54408 + 4.89308I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.033460 + 0.815877I
a = −1.39808 + 1.83834I
b = −0.53103 − 1.43134I
12.0149 − 15.9713I −5.35626 + 8.57789I
u = 1.033460 − 0.815877I
a = −1.39808 − 1.83834I
b = −0.53103 + 1.43134I
12.0149 + 15.9713I −5.35626 − 8.57789I
u = −1.076920 + 0.848675I
a = 1.04834 + 1.34169I
b = 0.153566 − 1.310870I
10.62700 + 6.42707I −2.25103 − 5.26300I
u = −1.076920 − 0.848675I
a = 1.04834 − 1.34169I
b = 0.153566 + 1.310870I
10.62700 − 6.42707I −2.25103 + 5.26300I
u = 0.341201
a = −1.17598
b = 0.331472
−0.684794 −14.4600
7
II. I
u
2
= h−5u
18
a − 45u
18
+ · · · + 27a + 5, −6u
18
a + 26u
18
+ · · · − 6a +
39, u
19
− u
18
+ · · · + u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
4
=
u
3
u
5
− u
3
+ u
a
8
=
a
0.147059au
18
+ 1.32353u
18
+ ··· − 0.794118a − 0.147059
a
7
=
0.176471au
18
+ 0.588235u
18
+ ··· + 0.647059a − 0.176471
0.205882au
18
+ 1.85294u
18
+ ··· − 0.911765a − 0.205882
a
11
=
1.32353au
18
− 4.08824u
18
+ ··· − 0.147059a − 6.32353
−0.205882au
18
+ 0.147059u
18
+ ··· − 0.0882353a + 0.205882
a
9
=
u
18
− 3u
16
+ 8u
14
− 13u
12
+ 17u
10
− 15u
8
+ 10u
6
− 2u
4
− u
2
+ 1
−u
18
+ 2u
16
− 5u
14
+ 6u
12
− 5u
10
+ 2u
8
+ 2u
6
− 4u
4
+ u
2
a
10
=
0.794118au
18
− 3.85294u
18
+ ··· − 0.0882353a − 5.79412
0.323529au
18
+ 1.91176u
18
+ ··· − 0.147059a + 2.67647
a
10
=
0.794118au
18
− 3.85294u
18
+ ··· − 0.0882353a − 5.79412
0.323529au
18
+ 1.91176u
18
+ ··· − 0.147059a + 2.67647
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
18
+ 12u
16
− 4u
15
− 32u
14
+ 8u
13
+ 56u
12
− 20u
11
− 72u
10
+
24u
9
+ 76u
8
− 24u
7
− 52u
6
+ 12u
5
+ 24u
4
− 4u
3
− 4u
2
− 8u − 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
19
+ u
18
+ ··· − u
2
+ 1)
2
c
2
, c
4
(u
19
+ 5u
18
+ ··· + 2u + 1)
2
c
3
(u
19
+ u
18
+ ··· + 2u − 1)
2
c
6
, c
8
, c
9
c
11
u
38
− 7u
37
+ ··· − 19u + 2
c
7
, c
10
u
38
− 5u
37
+ ··· + 8230u + 15341
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
19
− 5y
18
+ ··· + 2y −1)
2
c
2
, c
4
(y
19
+ 19y
18
+ ··· + 10y −1)
2
c
3
(y
19
+ 7y
18
+ ··· + 2y −1)
2
c
6
, c
8
, c
9
c
11
y
38
+ 27y
37
+ ··· − 21y + 4
c
7
, c
10
y
38
+ 23y
37
+ ··· + 2526338154y + 235346281
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964317 + 0.230449I
a = −0.985016 − 0.274220I
b = 0.134173 − 0.930763I
−0.332249 − 0.168160I −14.1683 + 0.9143I
u = 0.964317 + 0.230449I
a = −0.491180 + 0.989591I
b = −0.217752 − 0.156279I
−0.332249 − 0.168160I −14.1683 + 0.9143I
u = 0.964317 − 0.230449I
a = −0.985016 + 0.274220I
b = 0.134173 + 0.930763I
−0.332249 + 0.168160I −14.1683 − 0.9143I
u = 0.964317 − 0.230449I
a = −0.491180 − 0.989591I
b = −0.217752 + 0.156279I
−0.332249 + 0.168160I −14.1683 − 0.9143I
u = −0.978202 + 0.313897I
a = −0.849902 − 0.223654I
b = −0.852454 − 0.070284I
0.16029 + 5.52702I −12.4279 − 7.0025I
u = −0.978202 + 0.313897I
a = 1.41152 + 0.19798I
b = 0.462406 − 1.206880I
0.16029 + 5.52702I −12.4279 − 7.0025I
u = −0.978202 − 0.313897I
a = −0.849902 + 0.223654I
b = −0.852454 + 0.070284I
0.16029 − 5.52702I −12.4279 + 7.0025I
u = −0.978202 − 0.313897I
a = 1.41152 − 0.19798I
b = 0.462406 + 1.206880I
0.16029 − 5.52702I −12.4279 + 7.0025I
u = −0.820272 + 0.802988I
a = 0.377406 + 0.541506I
b = 0.357882 + 0.461087I
6.12368 + 1.53005I −8.20605 − 2.54963I
u = −0.820272 + 0.802988I
a = −0.09753 + 2.28421I
b = −0.052144 − 1.206600I
6.12368 + 1.53005I −8.20605 − 2.54963I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.820272 − 0.802988I
a = 0.377406 − 0.541506I
b = 0.357882 − 0.461087I
6.12368 − 1.53005I −8.20605 + 2.54963I
u = −0.820272 − 0.802988I
a = −0.09753 − 2.28421I
b = −0.052144 + 1.206600I
6.12368 − 1.53005I −8.20605 + 2.54963I
u = 0.809650 + 0.858173I
a = 0.565390 + 0.425293I
b = −1.179350 + 0.174669I
7.70394 + 3.71612I −5.80100 − 2.45937I
u = 0.809650 + 0.858173I
a = −0.62274 + 1.72512I
b = 0.48129 − 1.51282I
7.70394 + 3.71612I −5.80100 − 2.45937I
u = 0.809650 − 0.858173I
a = 0.565390 − 0.425293I
b = −1.179350 − 0.174669I
7.70394 − 3.71612I −5.80100 + 2.45937I
u = 0.809650 − 0.858173I
a = −0.62274 − 1.72512I
b = 0.48129 + 1.51282I
7.70394 − 3.71612I −5.80100 + 2.45937I
u = −0.635698 + 0.450549I
a = −0.230067 + 0.608858I
b = −0.213170 − 1.280760I
4.70093 + 1.72326I −4.18035 − 5.18112I
u = −0.635698 + 0.450549I
a = −1.94079 − 0.02901I
b = −0.463625 + 0.999486I
4.70093 + 1.72326I −4.18035 − 5.18112I
u = −0.635698 − 0.450549I
a = −0.230067 − 0.608858I
b = −0.213170 + 1.280760I
4.70093 − 1.72326I −4.18035 + 5.18112I
u = −0.635698 − 0.450549I
a = −1.94079 + 0.02901I
b = −0.463625 − 0.999486I
4.70093 − 1.72326I −4.18035 + 5.18112I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.949254 + 0.773576I
a = 0.620189 − 0.094867I
b = 0.423801 − 0.309302I
5.72757 + 4.39903I −8.93348 − 2.80289I
u = −0.949254 + 0.773576I
a = −1.61357 − 1.95000I
b = −0.116946 + 1.190010I
5.72757 + 4.39903I −8.93348 − 2.80289I
u = −0.949254 − 0.773576I
a = 0.620189 + 0.094867I
b = 0.423801 + 0.309302I
5.72757 − 4.39903I −8.93348 + 2.80289I
u = −0.949254 − 0.773576I
a = −1.61357 + 1.95000I
b = −0.116946 − 1.190010I
5.72757 − 4.39903I −8.93348 + 2.80289I
u = 0.903405 + 0.838368I
a = 0.86034 − 1.32154I
b = −0.60508 + 1.51193I
11.59750 − 3.11880I −2.41376 + 2.69239I
u = 0.903405 + 0.838368I
a = −0.98440 + 2.02627I
b = −0.66723 − 1.46348I
11.59750 − 3.11880I −2.41376 + 2.69239I
u = 0.903405 − 0.838368I
a = 0.86034 + 1.32154I
b = −0.60508 − 1.51193I
11.59750 + 3.11880I −2.41376 − 2.69239I
u = 0.903405 − 0.838368I
a = −0.98440 − 2.02627I
b = −0.66723 + 1.46348I
11.59750 + 3.11880I −2.41376 − 2.69239I
u = 0.975971 + 0.799116I
a = 0.229088 + 0.972721I
b = −1.211890 − 0.090804I
7.18622 − 9.88550I −6.86128 + 7.31129I
u = 0.975971 + 0.799116I
a = 1.30550 − 2.02733I
b = 0.54897 + 1.49405I
7.18622 − 9.88550I −6.86128 + 7.31129I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975971 − 0.799116I
a = 0.229088 − 0.972721I
b = −1.211890 + 0.090804I
7.18622 + 9.88550I −6.86128 − 7.31129I
u = 0.975971 − 0.799116I
a = 1.30550 + 2.02733I
b = 0.54897 − 1.49405I
7.18622 + 9.88550I −6.86128 − 7.31129I
u = 0.667698
a = 6.45400 + 5.52977I
b = 0.072948 − 1.007950I
2.38250 −15.4720
u = 0.667698
a = 6.45400 − 5.52977I
b = 0.072948 + 1.007950I
2.38250 −15.4720
u = −0.103765 + 0.589022I
a = 0.054068 − 0.769378I
b = −0.625152 − 0.214266I
2.82151 − 2.32534I −6.27174 + 3.09456I
u = −0.103765 + 0.589022I
a = −0.56231 − 1.56828I
b = 0.223313 + 1.232590I
2.82151 − 2.32534I −6.27174 + 3.09456I
u = −0.103765 − 0.589022I
a = 0.054068 + 0.769378I
b = −0.625152 + 0.214266I
2.82151 + 2.32534I −6.27174 − 3.09456I
u = −0.103765 − 0.589022I
a = −0.56231 + 1.56828I
b = 0.223313 − 1.232590I
2.82151 + 2.32534I −6.27174 − 3.09456I
14
III. I
u
3
= hb + 1, 2a + 2u + 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
u
2
+ u − 1
a
4
=
−u
2
+ 1
u
2
a
8
=
−u −
1
2
−1
a
7
=
−
3
2
u
1
2
u
2
+
1
2
u −
3
2
a
11
=
−u +
1
2
−1
a
9
=
−2u
−2
a
10
=
−
1
2
u
−
1
2
u
2
−
1
2
u −
1
2
a
10
=
−
1
2
u
−
1
2
u
2
−
1
2
u −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17
4
u
2
+
17
4
u −
41
4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
u
3
+ u
2
+ 2u + 1
c
3
u
3
c
4
u
3
− u
2
+ 2u − 1
c
5
u
3
− u
2
+ 1
c
6
, c
8
(u − 1)
3
c
7
8(8u
3
+ 4u
2
+ 4u + 1)
c
9
, c
11
(u + 1)
3
c
10
8(8u
3
− 4u
2
+ 4u − 1)
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
3
− y
2
+ 2y −1
c
2
, c
4
y
3
+ 3y
2
+ 2y −1
c
3
y
3
c
6
, c
8
, c
9
c
11
(y −1)
3
c
7
, c
10
64(64y
3
+ 48y
2
+ 8y −1)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.377439 − 0.744862I
b = −1.00000
1.37919 + 2.82812I −13.06503 − 2.38969I
u = −0.877439 − 0.744862I
a = 0.377439 + 0.744862I
b = −1.00000
1.37919 − 2.82812I −13.06503 + 2.38969I
u = 0.754878
a = −1.25488
b = −1.00000
−2.75839 −4.61990
18
IV. I
u
4
= hb − a − 1, a
2
+ 2a + 2, u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
3
=
0
1
a
6
=
−1
0
a
4
=
1
1
a
8
=
a
a + 1
a
7
=
a
1
a
11
=
a + 3
1
a
9
=
−a − 1
0
a
10
=
1
−a − 1
a
10
=
1
−a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u − 1)
2
c
2
, c
5
(u + 1)
2
c
3
, c
6
, c
8
c
9
, c
11
u
2
+ 1
c
7
u
2
+ 2u + 2
c
10
u
2
− 2u + 2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y −1)
2
c
3
, c
6
, c
8
c
9
, c
11
(y + 1)
2
c
7
, c
10
y
2
+ 4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000 + 1.00000I
b = 1.000000I
1.64493 −8.00000
u = 1.00000
a = −1.00000 − 1.00000I
b = − 1.000000I
1.64493 −8.00000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
3
+ u
2
− 1)(u
19
+ u
18
+ ··· − u
2
+ 1)
2
· (u
25
+ 2u
24
+ ··· + 17u + 4)
c
2
((u + 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
19
+ 5u
18
+ ··· + 2u + 1)
2
· (u
25
+ 8u
24
+ ··· + 241u + 16)
c
3
u
3
(u
2
+ 1)(u
19
+ u
18
+ ··· + 2u − 1)
2
(u
25
− 3u
24
+ ··· − 96u + 128)
c
4
((u − 1)
2
)(u
3
− u
2
+ 2u − 1)(u
19
+ 5u
18
+ ··· + 2u + 1)
2
· (u
25
+ 8u
24
+ ··· + 241u + 16)
c
5
((u + 1)
2
)(u
3
− u
2
+ 1)(u
19
+ u
18
+ ··· − u
2
+ 1)
2
· (u
25
+ 2u
24
+ ··· + 17u + 4)
c
6
, c
8
((u − 1)
3
)(u
2
+ 1)(u
25
+ 3u
24
+ ··· + 2u + 1)(u
38
− 7u
37
+ ··· − 19u + 2)
c
7
64(u
2
+ 2u + 2)(8u
3
+ 4u
2
+ 4u + 1)(8u
25
+ 4u
24
+ ··· + 2u + 2)
· (u
38
− 5u
37
+ ··· + 8230u + 15341)
c
9
, c
11
((u + 1)
3
)(u
2
+ 1)(u
25
+ 3u
24
+ ··· + 2u + 1)(u
38
− 7u
37
+ ··· − 19u + 2)
c
10
64(u
2
− 2u + 2)(8u
3
− 4u
2
+ 4u − 1)(8u
25
+ 4u
24
+ ··· + 2u + 2)
· (u
38
− 5u
37
+ ··· + 8230u + 15341)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y −1)
2
)(y
3
− y
2
+ 2y −1)(y
19
− 5y
18
+ ··· + 2y −1)
2
· (y
25
− 8y
24
+ ··· + 241y −16)
c
2
, c
4
((y −1)
2
)(y
3
+ 3y
2
+ 2y −1)(y
19
+ 19y
18
+ ··· + 10y −1)
2
· (y
25
+ 20y
24
+ ··· + 19233y −256)
c
3
y
3
(y + 1)
2
(y
19
+ 7y
18
+ ··· + 2y −1)
2
· (y
25
+ 9y
24
+ ··· − 72704y −16384)
c
6
, c
8
, c
9
c
11
((y −1)
3
)(y + 1)
2
(y
25
+ 17y
24
+ ··· + 16y −1)
· (y
38
+ 27y
37
+ ··· − 21y + 4)
c
7
, c
10
4096(y
2
+ 4)(64y
3
+ 48y
2
+ 8y −1)(64y
25
+ 1072y
24
+ ··· + 20y −4)
· (y
38
+ 23y
37
+ ··· + 2526338154y + 235346281)
24
