11n
161
(K11n
161
)
A knot diagram
1
Linearized knot diagam
9 8 1 10 2 3 1 6 5 4 8
Solving Sequence
2,9 1,6
5 10 4 8 3 7 11
c
1
c
5
c
9
c
4
c
8
c
2
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −32825u
16
− 78351u
15
+ ··· + 149349a + 108694,
u
17
+ u
16
− u
15
− u
14
+ 9u
13
+ 7u
12
− 5u
11
− 2u
10
+ 18u
9
+ 12u
8
− 4u
7
− 5u
6
+ 5u
5
− u
4
− u
3
− u
2
+ u − 1i
I
u
2
= h1.70203 × 10
30
u
23
+ 4.57303 × 10
30
u
22
+ ··· + 8.77268 × 10
30
b + 5.47196 × 10
31
,
− 6.45612 × 10
27
u
23
− 1.61756 × 10
28
u
22
+ ··· + 5.13568 × 10
28
a − 1.36907 × 10
29
,
u
24
+ 3u
23
+ ··· + 46u + 11i
I
u
3
= hb + u, −14u
9
− u
8
+ 16u
7
− 3u
6
− 69u
5
+ 26u
4
+ 25u
3
− 21u
2
+ 5a − 20u − 12,
u
10
+ u
9
− u
8
− u
7
+ 5u
6
+ 3u
5
− 3u
4
− u
3
+ 3u
2
+ 3u + 1i
* 3 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
= hb − u, −3.28 × 10
4
u
16
− 7.84 × 10
4
u
15
+ · · · + 1.49 × 10
5
a + 1.09 ×
10
5
, u
17
+ u
16
+ · · · + u − 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
1
=
1
u
2
a
6
=
0.219787u
16
+ 0.524617u
15
+ ··· + 1.20532u − 0.727785
u
a
5
=
0.219787u
16
+ 0.524617u
15
+ ··· + 0.205324u − 0.727785
u
a
10
=
0.966327u
16
+ 1.11448u
15
+ ··· − 2.99444u + 1.19912
−0.0803353u
16
− 0.516903u
15
+ ··· + 1.08504u − 0.304830
a
4
=
0.265559u
16
+ 0.586479u
15
+ ··· + 3.63417u + 1.42934
−0.537426u
16
− 0.452303u
15
+ ··· + 0.266865u − 0.452979
a
8
=
0.805657u
16
+ 0.0806701u
15
+ ··· − 2.82436u + 0.589458
−0.0803353u
16
− 0.516903u
15
+ ··· + 1.08504u − 0.304830
a
3
=
0.567001u
16
+ 0.839992u
15
+ ··· + 3.95640u + 0.655438
−0.544229u
16
− 0.276594u
15
+ ··· + 0.616234u − 0.500907
a
7
=
0.385085u
16
− 0.447562u
15
+ ··· − 3.26996u + 1.00962
0.245726u
16
− 0.325151u
15
+ ··· + 0.772131u − 0.412490
a
11
=
0.175562u
16
+ 1.94315u
15
+ ··· + 2.59534u + 1.27888
−0.301442u
16
− 0.253514u
15
+ ··· − 0.322225u + 0.773899
a
11
=
0.175562u
16
+ 1.94315u
15
+ ··· + 2.59534u + 1.27888
−0.301442u
16
− 0.253514u
15
+ ··· − 0.322225u + 0.773899
(ii) Obstruction class = −1
(iii) Cusp Shapes =
163298
149349
u
16
+
580790
149349
u
15
+ ··· +
328192
149349
u −
306609
49783
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
17
− u
16
+ ··· + u + 1
c
2
u
17
− 2u
15
+ ··· − u − 2
c
3
u
17
− 14u
16
+ ··· − 32u − 64
c
4
, c
9
, c
10
u
17
+ 9u
16
+ ··· + 144u + 16
c
6
, c
7
, c
11
u
17
+ u
16
+ ··· + u + 1
c
8
u
17
+ 12u
16
+ ··· + 64u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
17
− 3y
16
+ ··· − y −1
c
2
y
17
− 4y
16
+ ··· + 29y −4
c
3
y
17
− 14y
16
+ ··· + 50688y −4096
c
4
, c
9
, c
10
y
17
+ 15y
16
+ ··· − 128y −256
c
6
, c
7
, c
11
y
17
− 23y
16
+ ··· + 9y −1
c
8
y
17
+ 4y
16
+ ··· − 608y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.736595 + 0.759560I
a = −0.631113 + 0.062721I
b = −0.736595 + 0.759560I
−0.05757 − 2.36290I −6.52154 + 3.94257I
u = −0.736595 − 0.759560I
a = −0.631113 − 0.062721I
b = −0.736595 − 0.759560I
−0.05757 + 2.36290I −6.52154 − 3.94257I
u = −1.008910 + 0.431442I
a = −0.889354 − 0.979858I
b = −1.008910 + 0.431442I
1.14436 − 6.14847I −1.51565 + 5.18000I
u = −1.008910 − 0.431442I
a = −0.889354 + 0.979858I
b = −1.008910 − 0.431442I
1.14436 + 6.14847I −1.51565 − 5.18000I
u = −0.534388 + 0.570811I
a = −2.28268 + 0.49285I
b = −0.534388 + 0.570811I
−5.66005 − 1.97491I −5.96248 + 6.00520I
u = −0.534388 − 0.570811I
a = −2.28268 − 0.49285I
b = −0.534388 − 0.570811I
−5.66005 + 1.97491I −5.96248 − 6.00520I
u = 0.700751
a = 2.48391
b = 0.700751
−3.84845 2.74050
u = 0.902645 + 0.958889I
a = 1.194590 + 0.162669I
b = 0.902645 + 0.958889I
−6.98471 + 8.59095I −7.08514 − 6.35872I
u = 0.902645 − 0.958889I
a = 1.194590 − 0.162669I
b = 0.902645 − 0.958889I
−6.98471 − 8.59095I −7.08514 + 6.35872I
u = 0.482184 + 0.448786I
a = −1.16928 − 1.33243I
b = 0.482184 + 0.448786I
5.38217 + 1.40715I −2.06078 − 4.92367I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.482184 − 0.448786I
a = −1.16928 + 1.33243I
b = 0.482184 − 0.448786I
5.38217 − 1.40715I −2.06078 + 4.92367I
u = 0.175989 + 0.585685I
a = 0.864699 + 0.113620I
b = 0.175989 + 0.585685I
−0.850953 − 0.696665I −8.07292 + 4.89884I
u = 0.175989 − 0.585685I
a = 0.864699 − 0.113620I
b = 0.175989 − 0.585685I
−0.850953 + 0.696665I −8.07292 − 4.89884I
u = 1.14438 + 0.95543I
a = 0.540728 + 0.095251I
b = 1.14438 + 0.95543I
7.19647 + 4.49345I −5.42758 + 0.47721I
u = 1.14438 − 0.95543I
a = 0.540728 − 0.095251I
b = 1.14438 − 0.95543I
7.19647 − 4.49345I −5.42758 − 0.47721I
u = −1.27568 + 1.06823I
a = −0.869544 + 0.210846I
b = −1.27568 + 1.06823I
−0.71290 − 13.72760I −3.72416 + 7.05259I
u = −1.27568 − 1.06823I
a = −0.869544 − 0.210846I
b = −1.27568 − 1.06823I
−0.71290 + 13.72760I −3.72416 − 7.05259I
6
II. I
u
2
= h1.70 × 10
30
u
23
+ 4.57 × 10
30
u
22
+ · · · + 8.77 × 10
30
b + 5.47 ×
10
31
, −6.46 × 10
27
u
23
− 1.62 × 10
28
u
22
+ · · · + 5.14 × 10
28
a − 1.37 ×
10
29
, u
24
+ 3u
23
+ · · · + 46u + 11i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
1
=
1
u
2
a
6
=
0.125711u
23
+ 0.314966u
22
+ ··· + 7.79270u + 2.66581
−0.194014u
23
− 0.521280u
22
+ ··· − 10.4641u − 6.23750
a
5
=
0.319725u
23
+ 0.836246u
22
+ ··· + 18.2568u + 8.90330
−0.194014u
23
− 0.521280u
22
+ ··· − 10.4641u − 6.23750
a
10
=
−0.0116621u
23
− 0.0806554u
22
+ ··· + 4.00812u − 3.44719
−0.175665u
23
− 0.437895u
22
+ ··· − 9.21681u − 2.60383
a
4
=
−0.240478u
23
− 0.644174u
22
+ ··· − 11.8851u − 8.16867
0.0316958u
23
+ 0.103215u
22
+ ··· + 0.735566u + 2.15396
a
8
=
−0.190587u
23
− 0.510517u
22
+ ··· − 7.93355u − 4.80896
−0.00326046u
23
+ 0.00803404u
22
+ ··· − 0.724864u + 1.24206
a
3
=
−0.190071u
23
− 0.496722u
22
+ ··· − 10.2408u − 5.16485
0.0231595u
23
+ 0.0870786u
22
+ ··· + 0.354516u + 2.19543
a
7
=
−0.148842u
23
− 0.367537u
22
+ ··· − 7.93760u − 2.89321
−0.0152103u
23
− 0.0113006u
22
+ ··· − 2.00024u + 1.04689
a
11
=
0.240478u
23
+ 0.644174u
22
+ ··· + 11.8851u + 8.16867
−0.0504074u
23
− 0.147452u
22
+ ··· − 1.64431u − 3.00383
a
11
=
0.240478u
23
+ 0.644174u
22
+ ··· + 11.8851u + 8.16867
−0.0504074u
23
− 0.147452u
22
+ ··· − 1.64431u − 3.00383
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.802694u
23
+ 2.06436u
22
+ ··· + 39.8732u + 14.4982
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
24
− 3u
23
+ ··· − 46u + 11
c
2
u
24
− u
23
+ ··· − 178u + 59
c
3
(u
4
+ 3u
3
+ u
2
− 2u + 1)
6
c
4
, c
9
, c
10
(u
3
− u
2
+ 2u − 1)
8
c
6
, c
7
, c
11
u
24
− u
23
+ ··· − 568u + 89
c
8
(u
4
− u
3
+ u
2
+ 1)
6
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
24
− 5y
23
+ ··· − 1544y + 121
c
2
y
24
− 9y
23
+ ··· − 77232y + 3481
c
3
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
6
c
4
, c
9
, c
10
(y
3
+ 3y
2
+ 2y −1)
8
c
6
, c
7
, c
11
y
24
− 21y
23
+ ··· − 204788y + 7921
c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.726600 + 0.525022I
a = 0.174808 + 1.380500I
b = 0.834345 + 0.058079I
4.88007 + 0.33584I −2.66351 + 0.41465I
u = −0.726600 − 0.525022I
a = 0.174808 − 1.380500I
b = 0.834345 − 0.058079I
4.88007 − 0.33584I −2.66351 − 0.41465I
u = 0.834345 + 0.058079I
a = −1.09167 − 1.01623I
b = −0.726600 + 0.525022I
4.88007 + 0.33584I −2.66351 + 0.41465I
u = 0.834345 − 0.058079I
a = −1.09167 + 1.01623I
b = −0.726600 − 0.525022I
4.88007 − 0.33584I −2.66351 − 0.41465I
u = −0.951037 + 0.715358I
a = 1.032340 − 0.181700I
b = 0.649666 − 0.469539I
0.74248 − 3.16396I −9.19277 + 2.56480I
u = −0.951037 − 0.715358I
a = 1.032340 + 0.181700I
b = 0.649666 + 0.469539I
0.74248 + 3.16396I −9.19277 − 2.56480I
u = 0.649666 + 0.469539I
a = −1.52720 − 0.29894I
b = −0.951037 − 0.715358I
0.74248 + 3.16396I −9.19277 − 2.56480I
u = 0.649666 − 0.469539I
a = −1.52720 + 0.29894I
b = −0.951037 + 0.715358I
0.74248 − 3.16396I −9.19277 + 2.56480I
u = −0.238976 + 1.192720I
a = −0.637456 − 0.167240I
b = −1.72582 − 0.12950I
−2.12168 + 1.41302I −6.31698 + 1.92930I
u = −0.238976 − 1.192720I
a = −0.637456 + 0.167240I
b = −1.72582 + 0.12950I
−2.12168 − 1.41302I −6.31698 − 1.92930I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.168821 + 0.703789I
a = 1.081210 − 0.240521I
b = 1.26487 − 1.00614I
−6.25926 + 1.41510I −12.84625 − 4.90874I
u = 0.168821 − 0.703789I
a = 1.081210 + 0.240521I
b = 1.26487 + 1.00614I
−6.25926 − 1.41510I −12.84625 + 4.90874I
u = −0.939501 + 0.901901I
a = 0.956419 − 0.051833I
b = 1.53236 − 0.89026I
4.88007 − 5.99209I −2.66351 + 5.54425I
u = −0.939501 − 0.901901I
a = 0.956419 + 0.051833I
b = 1.53236 + 0.89026I
4.88007 + 5.99209I −2.66351 − 5.54425I
u = −0.369838 + 0.105617I
a = −1.39380 + 1.54969I
b = −0.99828 − 1.87172I
−2.12168 − 4.24323I −6.31698 + 7.88819I
u = −0.369838 − 0.105617I
a = −1.39380 − 1.54969I
b = −0.99828 + 1.87172I
−2.12168 + 4.24323I −6.31698 − 7.88819I
u = 1.26487 + 1.00614I
a = −0.107103 − 0.484305I
b = 0.168821 − 0.703789I
−6.25926 − 1.41510I −12.84625 + 4.90874I
u = 1.26487 − 1.00614I
a = −0.107103 + 0.484305I
b = 0.168821 + 0.703789I
−6.25926 + 1.41510I −12.84625 − 4.90874I
u = −1.72582 + 0.12950I
a = −0.171564 − 0.430263I
b = −0.238976 − 1.192720I
−2.12168 − 1.41302I −6.31698 − 1.92930I
u = −1.72582 − 0.12950I
a = −0.171564 + 0.430263I
b = −0.238976 + 1.192720I
−2.12168 + 1.41302I −6.31698 + 1.92930I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53236 + 0.89026I
a = −0.673917 − 0.203172I
b = −0.939501 − 0.901901I
4.88007 + 5.99209I −2.66351 − 5.54425I
u = 1.53236 − 0.89026I
a = −0.673917 + 0.203172I
b = −0.939501 + 0.901901I
4.88007 − 5.99209I −2.66351 + 5.54425I
u = −0.99828 + 1.87172I
a = 0.221577 − 0.306137I
b = −0.369838 − 0.105617I
−2.12168 + 4.24323I −5.00000 − 7.88819I
u = −0.99828 − 1.87172I
a = 0.221577 + 0.306137I
b = −0.369838 + 0.105617I
−2.12168 − 4.24323I −5.00000 + 7.88819I
12
III. I
u
3
= hb + u, −14u
9
− u
8
+ · · · + 5a − 12, u
10
+ u
9
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
1
=
1
u
2
a
6
=
14
5
u
9
+
1
5
u
8
+ ··· + 4u +
12
5
−u
a
5
=
14
5
u
9
+
1
5
u
8
+ ··· + 5u +
12
5
−u
a
10
=
−
6
5
u
9
−
4
5
u
8
+ ··· − 2u −
13
5
11
5
u
9
+
4
5
u
8
+ ··· + 6u +
13
5
a
4
=
−
29
5
u
9
−
11
5
u
8
+ ··· − 15u −
42
5
−2u
9
− u
8
+ 3u
7
+ u
6
− 11u
5
− u
4
+ 8u
3
− 2u
2
− 6u − 3
a
8
=
16
5
u
9
+
4
5
u
8
+ ··· + 8u +
13
5
11
5
u
9
+
4
5
u
8
+ ··· + 6u +
13
5
a
3
=
−
28
5
u
9
−
12
5
u
8
+ ··· − 16u −
39
5
−
6
5
u
9
−
4
5
u
8
+ ··· − 5u −
13
5
a
7
=
18
5
u
9
+
7
5
u
8
+ ··· + 10u +
14
5
9
5
u
9
+
6
5
u
8
+ ··· + 5u +
12
5
a
11
=
−
12
5
u
9
+
2
5
u
8
+ ··· − 3u −
11
5
−
1
5
u
9
+
1
5
u
8
+ ··· + u −
3
5
a
11
=
−
12
5
u
9
+
2
5
u
8
+ ··· − 3u −
11
5
−
1
5
u
9
+
1
5
u
8
+ ··· + u −
3
5
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
34
5
u
9
+
16
5
u
8
−
56
5
u
7
−
17
5
u
6
+
184
5
u
5
+
9
5
u
4
− 31u
3
+
31
5
u
2
+ 18u +
42
5
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
10
+ u
9
− u
8
− u
7
+ 5u
6
+ 3u
5
− 3u
4
− u
3
+ 3u
2
+ 3u + 1
c
2
u
10
− 2u
8
+ 4u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 2u
2
+ 2u + 5
c
3
u
10
+ 7u
9
+ ··· + 8u + 5
c
4
u
10
+ 6u
8
− u
7
+ 12u
6
− 3u
5
+ 8u
4
− u
3
+ 2u + 1
c
6
, c
11
u
10
− u
9
− 3u
8
+ 4u
7
− u
5
+ 4u
4
− 3u
3
+ 4u
2
− u + 1
c
7
u
10
+ u
9
− 3u
8
− 4u
7
+ u
5
+ 4u
4
+ 3u
3
+ 4u
2
+ u + 1
c
8
u
10
− 3u
9
+ 6u
8
− 6u
7
+ 6u
6
− 6u
5
+ 9u
4
− 6u
3
+ 3u
2
+ 1
c
9
, c
10
u
10
+ 6u
8
+ u
7
+ 12u
6
+ 3u
5
+ 8u
4
+ u
3
− 2u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
10
− 3y
9
+ 13y
8
− 23y
7
+ 45y
6
− 51y
5
+ 49y
4
− 27y
3
+ 9y
2
− 3y + 1
c
2
y
10
− 4y
9
+ 12y
8
− 8y
7
+ 4y
6
+ 30y
5
− 8y
4
+ 23y
3
+ 24y
2
+ 16y + 25
c
3
y
10
− 7y
9
+ ··· + 246y + 25
c
4
, c
9
, c
10
y
10
+ 12y
9
+ ··· − 4y + 1
c
6
, c
7
, c
11
y
10
− 7y
9
+ 17y
8
− 10y
7
− 14y
6
− y
5
+ 12y
4
+ 21y
3
+ 18y
2
+ 7y + 1
c
8
y
10
+ 3y
9
+ ··· + 6y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.914248 + 0.570518I
a = −1.119990 − 0.219282I
b = −0.914248 − 0.570518I
1.60755 + 3.42301I 1.79285 − 5.67056I
u = 0.914248 − 0.570518I
a = −1.119990 + 0.219282I
b = −0.914248 + 0.570518I
1.60755 − 3.42301I 1.79285 + 5.67056I
u = −0.727640 + 0.146538I
a = 0.66217 + 1.95900I
b = 0.727640 − 0.146538I
6.16667 + 0.45837I 4.93396 + 0.07525I
u = −0.727640 − 0.146538I
a = 0.66217 − 1.95900I
b = 0.727640 + 0.146538I
6.16667 − 0.45837I 4.93396 − 0.07525I
u = 0.914629 + 0.935183I
a = −0.112008 − 0.341459I
b = −0.914629 − 0.935183I
−2.02274 − 3.06369I −5.25989 + 0.93808I
u = 0.914629 − 0.935183I
a = −0.112008 + 0.341459I
b = −0.914629 + 0.935183I
−2.02274 + 3.06369I −5.25989 − 0.93808I
u = −0.380408 + 0.491558I
a = 0.39322 − 1.67428I
b = 0.380408 − 0.491558I
−5.23124 + 0.62784I −5.27518 + 0.19626I
u = −0.380408 − 0.491558I
a = 0.39322 + 1.67428I
b = 0.380408 + 0.491558I
−5.23124 − 0.62784I −5.27518 − 0.19626I
u = −1.22083 + 0.93479I
a = 0.676610 − 0.110678I
b = 1.22083 − 0.93479I
7.70444 − 5.09459I 1.80827 + 6.72626I
u = −1.22083 − 0.93479I
a = 0.676610 + 0.110678I
b = 1.22083 + 0.93479I
7.70444 + 5.09459I 1.80827 − 6.72626I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
10
+ u
9
− u
8
− u
7
+ 5u
6
+ 3u
5
− 3u
4
− u
3
+ 3u
2
+ 3u + 1)
· (u
17
− u
16
+ ··· + u + 1)(u
24
− 3u
23
+ ··· − 46u + 11)
c
2
(u
10
− 2u
8
+ 4u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 2u
2
+ 2u + 5)
· (u
17
− 2u
15
+ ··· − u − 2)(u
24
− u
23
+ ··· − 178u + 59)
c
3
((u
4
+ 3u
3
+ u
2
− 2u + 1)
6
)(u
10
+ 7u
9
+ ··· + 8u + 5)
· (u
17
− 14u
16
+ ··· − 32u − 64)
c
4
(u
3
− u
2
+ 2u − 1)
8
(u
10
+ 6u
8
− u
7
+ 12u
6
− 3u
5
+ 8u
4
− u
3
+ 2u + 1)
· (u
17
+ 9u
16
+ ··· + 144u + 16)
c
6
, c
11
(u
10
− u
9
− 3u
8
+ 4u
7
− u
5
+ 4u
4
− 3u
3
+ 4u
2
− u + 1)
· (u
17
+ u
16
+ ··· + u + 1)(u
24
− u
23
+ ··· − 568u + 89)
c
7
(u
10
+ u
9
− 3u
8
− 4u
7
+ u
5
+ 4u
4
+ 3u
3
+ 4u
2
+ u + 1)
· (u
17
+ u
16
+ ··· + u + 1)(u
24
− u
23
+ ··· − 568u + 89)
c
8
(u
4
− u
3
+ u
2
+ 1)
6
· (u
10
− 3u
9
+ 6u
8
− 6u
7
+ 6u
6
− 6u
5
+ 9u
4
− 6u
3
+ 3u
2
+ 1)
· (u
17
+ 12u
16
+ ··· + 64u + 8)
c
9
, c
10
(u
3
− u
2
+ 2u − 1)
8
(u
10
+ 6u
8
+ u
7
+ 12u
6
+ 3u
5
+ 8u
4
+ u
3
− 2u + 1)
· (u
17
+ 9u
16
+ ··· + 144u + 16)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
10
− 3y
9
+ 13y
8
− 23y
7
+ 45y
6
− 51y
5
+ 49y
4
− 27y
3
+ 9y
2
− 3y + 1)
· (y
17
− 3y
16
+ ··· − y −1)(y
24
− 5y
23
+ ··· − 1544y + 121)
c
2
(y
10
− 4y
9
+ 12y
8
− 8y
7
+ 4y
6
+ 30y
5
− 8y
4
+ 23y
3
+ 24y
2
+ 16y + 25)
· (y
17
− 4y
16
+ ··· + 29y −4)(y
24
− 9y
23
+ ··· − 77232y + 3481)
c
3
((y
4
− 7y
3
+ 15y
2
− 2y + 1)
6
)(y
10
− 7y
9
+ ··· + 246y + 25)
· (y
17
− 14y
16
+ ··· + 50688y −4096)
c
4
, c
9
, c
10
((y
3
+ 3y
2
+ 2y −1)
8
)(y
10
+ 12y
9
+ ··· − 4y + 1)
· (y
17
+ 15y
16
+ ··· − 128y −256)
c
6
, c
7
, c
11
(y
10
− 7y
9
+ 17y
8
− 10y
7
− 14y
6
− y
5
+ 12y
4
+ 21y
3
+ 18y
2
+ 7y + 1)
· (y
17
− 23y
16
+ ··· + 9y −1)(y
24
− 21y
23
+ ··· − 204788y + 7921)
c
8
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
)(y
10
+ 3y
9
+ ··· + 6y + 1)
· (y
17
+ 4y
16
+ ··· − 608y −64)
18
