11n
144
(K11n
144
)
A knot diagram
1
Linearized knot diagam
6 1 10 7 9 2 10 5 3 5 7
Solving Sequence
7,10 5,8
11 1 4 3 2 6 9
c
7
c
10
c
11
c
4
c
3
c
2
c
6
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h19u
18
− 215u
17
+ ··· + 32b + 896, −14u
18
+ 191u
17
+ ··· + 32a − 1760,
u
19
− 15u
18
+ ··· + 544u − 64i
I
u
2
= h−25111a
11
u + 473518a
10
u + ··· − 96138a − 81801, a
11
u − 6a
10
u + ··· − 155a + 167, u
2
+ u − 1i
I
u
3
= h3u
10
+ 8u
9
+ u
8
− 3u
7
+ 8u
6
− u
5
− u
4
+ 3u
3
− 9u
2
+ b + u − 1,
− u
10
− u
9
+ 4u
8
+ u
7
− 5u
6
+ 5u
5
− 2u
3
+ 5u
2
+ a − 5u + 1,
u
11
+ 4u
10
+ 4u
9
+ 2u
7
+ 3u
6
− u
5
+ u
4
− 2u
3
− 4u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 54 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
= h19u
18
− 215u
17
+ · · · + 32b + 896, −14u
18
+ 191u
17
+ · · · + 32a −
1760, u
19
− 15u
18
+ · · · + 544u − 64i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
5
=
7
16
u
18
−
191
32
u
17
+ ··· −
743
2
u + 55
−
19
32
u
18
+
215
32
u
17
+ ··· + 183u − 28
a
8
=
1
−u
2
a
11
=
−
63
64
u
18
+
883
64
u
17
+ ··· +
1901
4
u − 64
31
32
u
18
−
435
32
u
17
+ ··· −
941
2
u + 63
a
1
=
−
1
64
u
18
+
13
64
u
17
+ ··· +
19
4
u − 1
31
32
u
18
−
435
32
u
17
+ ··· −
941
2
u + 63
a
4
=
−
5
32
u
18
+
3
4
u
17
+ ··· −
377
2
u + 27
−
19
32
u
18
+
215
32
u
17
+ ··· + 183u − 28
a
3
=
−
5
32
u
18
+
3
4
u
17
+ ··· −
377
2
u + 27
115
32
u
18
−
1551
32
u
17
+ ··· − 674u + 74
a
2
=
307
64
u
18
−
3931
64
u
17
+ ··· −
3381
4
u + 100
−
177
32
u
18
+
2313
32
u
17
+ ··· +
2457
2
u − 149
a
6
=
−
137
64
u
18
+
1597
64
u
17
+ ··· − 61u +
37
2
339
32
u
18
−
4473
32
u
17
+ ··· − 2502u + 303
a
9
=
−0.0156250u
18
+ 0.203125u
17
+ ··· − 10.3750u
2
+ 3.75000u
1
32
u
18
−
13
32
u
17
+ ··· −
15
2
u + 1
a
9
=
−0.0156250u
18
+ 0.203125u
17
+ ··· − 10.3750u
2
+ 3.75000u
1
32
u
18
−
13
32
u
17
+ ··· −
15
2
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
107
8
u
18
+
1433
8
u
17
+ ··· + 4122u − 534
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
19
− 5u
18
+ ··· − 14u + 4
c
2
u
19
+ 9u
18
+ ··· + 44u + 16
c
3
, c
5
, c
8
c
9
u
19
+ u
18
+ ··· + 4u + 1
c
4
, c
10
u
19
+ 15u
17
+ ··· + 3u + 1
c
7
u
19
+ 15u
18
+ ··· + 544u + 64
c
11
u
19
− 15u
18
+ ··· − 990u + 196
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
19
− 9y
18
+ ··· + 44y −16
c
2
y
19
+ 3y
18
+ ··· + 2288y −256
c
3
, c
5
, c
8
c
9
y
19
− 9y
18
+ ··· + 12y −1
c
4
, c
10
y
19
+ 30y
18
+ ··· − 25y −1
c
7
y
19
− 11y
18
+ ··· + 95232y −4096
c
11
y
19
+ 3y
18
+ ··· + 237260y −38416
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.068838 + 1.152610I
a = 0.509367 − 0.020838I
b = −0.059082 − 0.585665I
−1.40681 − 1.74274I −5.94701 + 3.80028I
u = 0.068838 − 1.152610I
a = 0.509367 + 0.020838I
b = −0.059082 + 0.585665I
−1.40681 + 1.74274I −5.94701 − 3.80028I
u = −0.655172 + 0.270735I
a = 0.180740 − 0.531477I
b = −0.025474 − 0.397141I
1.11792 − 1.95845I −4.20644 + 5.46350I
u = −0.655172 − 0.270735I
a = 0.180740 + 0.531477I
b = −0.025474 + 0.397141I
1.11792 + 1.95845I −4.20644 − 5.46350I
u = 1.244400 + 0.434239I
a = 0.558407 + 1.198070I
b = −0.17463 − 1.73336I
5.25710 − 1.54392I −8.61355 − 2.51619I
u = 1.244400 − 0.434239I
a = 0.558407 − 1.198070I
b = −0.17463 + 1.73336I
5.25710 + 1.54392I −8.61355 + 2.51619I
u = 0.525160 + 1.295010I
a = −0.477990 − 0.189359I
b = 0.005800 + 0.718444I
−5.26090 + 2.36693I −9.94736 − 1.06990I
u = 0.525160 − 1.295010I
a = −0.477990 + 0.189359I
b = 0.005800 − 0.718444I
−5.26090 − 2.36693I −9.94736 + 1.06990I
u = 1.37929 + 0.44772I
a = −0.340635 − 1.191440I
b = −0.06359 + 1.79584I
6.12748 + 4.38921I −5.85287 − 6.32556I
u = 1.37929 − 0.44772I
a = −0.340635 + 1.191440I
b = −0.06359 − 1.79584I
6.12748 − 4.38921I −5.85287 + 6.32556I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07036 + 1.50415I
a = −0.374863 + 0.006918I
b = −0.015967 + 0.564338I
−4.57325 − 6.41400I −8.03245 + 7.39287I
u = −0.07036 − 1.50415I
a = −0.374863 − 0.006918I
b = −0.015967 − 0.564338I
−4.57325 + 6.41400I −8.03245 − 7.39287I
u = 1.57100 + 0.65066I
a = 0.118849 + 0.926036I
b = 0.41582 − 1.53213I
−1.49409 + 5.07243I −11.25567 − 3.29320I
u = 1.57100 − 0.65066I
a = 0.118849 − 0.926036I
b = 0.41582 + 1.53213I
−1.49409 − 5.07243I −11.25567 + 3.29320I
u = 1.63033 + 0.51703I
a = −0.023365 − 1.061980I
b = −0.51099 + 1.74346I
4.00668 + 8.26944I −5.84435 − 4.36564I
u = 1.63033 − 0.51703I
a = −0.023365 + 1.061980I
b = −0.51099 − 1.74346I
4.00668 − 8.26944I −5.84435 + 4.36564I
u = 1.69551 + 0.51970I
a = −0.052766 + 1.037060I
b = 0.62842 − 1.73093I
1.54987 + 13.80210I −8.55217 − 7.85507I
u = 1.69551 − 0.51970I
a = −0.052766 − 1.037060I
b = 0.62842 + 1.73093I
1.54987 − 13.80210I −8.55217 + 7.85507I
u = 0.222014
a = 1.80451
b = −0.400627
−0.778408 −13.4960
6
II. I
u
2
= h−2.51 × 10
4
a
11
u + 4.74 × 10
5
a
10
u + · · · − 9.61 × 10
4
a − 8.18 ×
10
4
, a
11
u − 6a
10
u + · · · − 155a + 167, u
2
+ u − 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
5
=
a
1.13517a
11
u − 21.4058a
10
u + ··· + 4.34601a + 3.69789
a
8
=
1
u − 1
a
11
=
−a
2
u
−35.3361a
11
u − 18.9502a
10
u + ··· + 8.81063a + 0.563175
a
1
=
−35.3361a
11
u − 18.9502a
10
u + ··· + 8.81063a + 0.563175
−35.3361a
11
u − 18.9502a
10
u + ··· + 8.81063a + 0.563175
a
4
=
1.13517a
11
u − 21.4058a
10
u + ··· + 5.34601a + 3.69789
1.13517a
11
u − 21.4058a
10
u + ··· + 4.34601a + 3.69789
a
3
=
1.13517a
11
u − 21.4058a
10
u + ··· + 5.34601a + 3.69789
−1.83504a
11
u + 34.6362a
10
u + ··· − 7.86737a − 8.59712
a
2
=
22.6625a
11
u + 16.1085a
10
u + ··· − 7.94413a − 2.81597
18.9641a
11
u + 15.2801a
10
u + ··· − 6.71073a − 2.33606
a
6
=
7.69685a
11
u − 29.9099a
10
u + ··· + 6.05140a + 8.17657
−4.02676a
11
u − 39.3625a
10
u + ··· + 8.68333a + 9.01768
a
9
=
−21.8411a
11
u − 11.7229a
10
u + ··· + 4.19271a + 0.957552
a
2
u − a
2
+ 2u
a
9
=
−21.8411a
11
u − 11.7229a
10
u + ··· + 4.19271a + 0.957552
a
2
u − a
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
413176
22121
a
11
u −
1916164
22121
a
10
u + ··· +
545276
22121
a +
178130
22121
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
4
c
2
, c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
4
c
3
, c
5
, c
8
c
9
u
24
+ u
23
+ ··· + 94u + 29
c
4
, c
10
u
24
− u
23
+ ··· + 166u + 79
c
7
(u
2
− u − 1)
12
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
4
c
2
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
4
c
3
, c
5
, c
8
c
9
y
24
− 9y
23
+ ··· − 8372y + 841
c
4
, c
10
y
24
+ 15y
23
+ ··· + 63136y + 6241
c
7
(y
2
− 3y + 1)
12
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.378632 + 0.673935I
b = −1.387580 − 0.061682I
−2.05724 + 0.92430I −4.28328 − 0.79423I
u = 0.618034
a = 0.378632 − 0.673935I
b = −1.387580 + 0.061682I
−2.05724 − 0.92430I −4.28328 + 0.79423I
u = 0.618034
a = −0.347430 + 1.244240I
b = 1.52296 − 0.13510I
−3.94784 − 5.69302I −8.00000 + 5.51057I
u = 0.618034
a = −0.347430 − 1.244240I
b = 1.52296 + 0.13510I
−3.94784 + 5.69302I −8.00000 − 5.51057I
u = 0.618034
a = 0.812996 + 1.057280I
b = 1.195370 − 0.421798I
−5.83845 + 0.92430I −11.71672 − 0.79423I
u = 0.618034
a = 0.812996 − 1.057280I
b = 1.195370 + 0.421798I
−5.83845 − 0.92430I −11.71672 + 0.79423I
u = 0.618034
a = −1.93415 + 0.68248I
b = −0.502459 − 0.653436I
−5.83845 + 0.92430I −11.71672 − 0.79423I
u = 0.618034
a = −1.93415 − 0.68248I
b = −0.502459 + 0.653436I
−5.83845 − 0.92430I −11.71672 + 0.79423I
u = 0.618034
a = 2.24514 + 0.09980I
b = −0.234007 − 0.416515I
−2.05724 + 0.92430I −4.28328 − 0.79423I
u = 0.618034
a = 2.24514 − 0.09980I
b = −0.234007 + 0.416515I
−2.05724 − 0.92430I −4.28328 + 0.79423I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −2.46421 + 0.21859I
b = 0.214724 − 0.768984I
−3.94784 − 5.69302I −8.00000 + 5.51057I
u = 0.618034
a = −2.46421 − 0.21859I
b = 0.214724 + 0.768984I
−3.94784 + 5.69302I −8.00000 − 5.51057I
u = −1.61803
a = 0.086187 + 1.029040I
b = 0.47994 − 1.48236I
5.83845 + 0.92430I −4.28328 − 0.79423I
u = −1.61803
a = 0.086187 − 1.029040I
b = 0.47994 + 1.48236I
5.83845 − 0.92430I −4.28328 + 0.79423I
u = −1.61803
a = −0.417397 + 0.869872I
b = 0.01162 − 1.75281I
3.94784 + 5.69302I −8.00000 − 5.51057I
u = −1.61803
a = −0.417397 − 0.869872I
b = 0.01162 + 1.75281I
3.94784 − 5.69302I −8.00000 + 5.51057I
u = −1.61803
a = 0.296617 + 0.916149I
b = 0.13945 − 1.66501I
5.83845 − 0.92430I −4.28328 + 0.79423I
u = −1.61803
a = 0.296617 − 0.916149I
b = 0.13945 + 1.66501I
5.83845 + 0.92430I −4.28328 − 0.79423I
u = −1.61803
a = 0.007184 + 1.083300I
b = −0.67536 − 1.40748I
3.94784 − 5.69302I −8.00000 + 5.51057I
u = −1.61803
a = 0.007184 − 1.083300I
b = −0.67536 + 1.40748I
3.94784 + 5.69302I −8.00000 − 5.51057I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61803
a = 0.051210 + 0.866179I
b = −0.347529 − 0.990805I
2.05724 + 0.92430I −11.71672 − 0.79423I
u = −1.61803
a = 0.051210 − 0.866179I
b = −0.347529 + 0.990805I
2.05724 − 0.92430I −11.71672 + 0.79423I
u = −1.61803
a = −0.214785 + 0.612351I
b = 0.082860 − 1.401510I
2.05724 − 0.92430I −11.71672 + 0.79423I
u = −1.61803
a = −0.214785 − 0.612351I
b = 0.082860 + 1.401510I
2.05724 + 0.92430I −11.71672 − 0.79423I
12
III.
I
u
3
= h3u
10
+8u
9
+· · ·+b−1, −u
10
−u
9
+· · ·+a+1, u
11
+4u
10
+· · ·−4u
2
−1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
5
=
u
10
+ u
9
− 4u
8
− u
7
+ 5u
6
− 5u
5
+ 2u
3
− 5u
2
+ 5u − 1
−3u
10
− 8u
9
− u
8
+ 3u
7
− 8u
6
+ u
5
+ u
4
− 3u
3
+ 9u
2
− u + 1
a
8
=
1
−u
2
a
11
=
−u
9
− 3u
8
− u
7
+ u
6
− 3u
5
+ u
3
− 2u
2
+ 4u
−u
10
− 3u
9
− u
8
+ u
7
− 3u
6
+ u
4
− 2u
3
+ 4u
2
+ u
a
1
=
−u
10
− 4u
9
− 4u
8
− 2u
6
− 3u
5
+ u
4
− u
3
+ 2u
2
+ 5u
−u
10
− 3u
9
− u
8
+ u
7
− 3u
6
+ u
4
− 2u
3
+ 4u
2
+ u
a
4
=
−2u
10
− 7u
9
− 5u
8
+ 2u
7
− 3u
6
− 4u
5
+ u
4
− u
3
+ 4u
2
+ 4u
−3u
10
− 8u
9
− u
8
+ 3u
7
− 8u
6
+ u
5
+ u
4
− 3u
3
+ 9u
2
− u + 1
a
3
=
−2u
10
− 7u
9
− 5u
8
+ 2u
7
− 3u
6
− 4u
5
+ u
4
− u
3
+ 4u
2
+ 4u
−2u
10
− 6u
9
− 2u
8
+ 3u
7
− 4u
6
− u
5
+ 2u
4
− u
3
+ 5u
2
+ u
a
2
=
−2u
10
− 6u
9
− 3u
8
− 5u
6
− 2u
4
− 3u
3
+ 7u
2
+ u + 2
u
10
+ 2u
9
− u
8
+ 4u
6
− 2u
5
+ u
3
− 3u
2
+ 2u − 1
a
6
=
2u
10
+ 5u
9
− u
8
− 4u
7
+ 6u
6
− 2u
4
+ 3u
3
− 5u
2
+ u + 1
−2u
10
− 6u
9
− 3u
8
− 5u
6
− u
4
− u
3
+ 7u
2
+ 2
a
9
=
u
10
+ 4u
9
+ 4u
8
+ 2u
6
+ 3u
5
− u
4
+ u
3
− 2u
2
− 4u + 1
−u
2
+ 1
a
9
=
u
10
+ 4u
9
+ 4u
8
+ 2u
6
+ 3u
5
− u
4
+ u
3
− 2u
2
− 4u + 1
−u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
10
+ 14u
9
+ 3u
8
−4u
7
+ 15u
6
+ u
5
+ 2u
4
+ 4u
3
−15u
2
+ 3u −16
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 3u
9
+ 5u
7
− 4u
5
+ u
4
+ 2u
3
− 2u
2
+ 1
c
2
u
11
+ 6u
10
+ ··· + 4u + 1
c
3
, c
8
u
11
− u
10
− 3u
9
+ 3u
8
+ 2u
7
− u
6
+ u
5
− 3u
4
− u
3
+ 2u
2
+ 1
c
4
, c
10
u
11
+ 2u
9
+ u
8
− 3u
7
− u
6
− u
5
− 2u
4
+ 3u
3
+ 3u
2
− u − 1
c
5
, c
9
u
11
+ u
10
− 3u
9
− 3u
8
+ 2u
7
+ u
6
+ u
5
+ 3u
4
− u
3
− 2u
2
− 1
c
6
u
11
− 3u
9
+ 5u
7
− 4u
5
− u
4
+ 2u
3
+ 2u
2
− 1
c
7
u
11
+ 4u
10
+ 4u
9
+ 2u
7
+ 3u
6
− u
5
+ u
4
− 2u
3
− 4u
2
− 1
c
11
u
11
+ u
9
+ 4u
8
+ u
7
+ 8u
5
− 5u
4
+ 9u
3
− 3u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
11
− 6y
10
+ ··· + 4y − 1
c
2
y
11
+ 2y
10
+ ··· + 4y − 1
c
3
, c
5
, c
8
c
9
y
11
− 7y
10
+ ··· − 4y − 1
c
4
, c
10
y
11
+ 4y
10
+ ··· + 7y − 1
c
7
y
11
− 8y
10
+ ··· − 8y − 1
c
11
y
11
+ 2y
10
+ ··· + 6y − 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.658661 + 0.780836I
a = 0.334333 − 0.641044I
b = 0.720763 − 0.161171I
−6.99914 + 2.24617I −15.2425 − 3.4100I
u = 0.658661 − 0.780836I
a = 0.334333 + 0.641044I
b = 0.720763 + 0.161171I
−6.99914 − 2.24617I −15.2425 + 3.4100I
u = −0.071195 + 0.899946I
a = −0.435703 − 0.871171I
b = 0.815027 − 0.330086I
−5.80784 − 5.68354I −14.5040 + 4.4186I
u = −0.071195 − 0.899946I
a = −0.435703 + 0.871171I
b = 0.815027 + 0.330086I
−5.80784 + 5.68354I −14.5040 − 4.4186I
u = 0.895531
a = −0.811062
b = −0.726331
−4.44260 −6.63260
u = −1.345990 + 0.064656I
a = 0.175003 − 1.238530I
b = −0.15547 + 1.67836I
5.44803 + 2.65181I −6.56642 − 4.06839I
u = −1.345990 − 0.064656I
a = 0.175003 + 1.238530I
b = −0.15547 − 1.67836I
5.44803 − 2.65181I −6.56642 + 4.06839I
u = 0.049939 + 0.484753I
a = 0.21633 + 1.89590I
b = −0.908242 + 0.199545I
−3.30665 − 0.86798I −12.51115 + 0.41084I
u = 0.049939 − 0.484753I
a = 0.21633 − 1.89590I
b = −0.908242 − 0.199545I
−3.30665 + 0.86798I −12.51115 − 0.41084I
u = −1.73918 + 0.14158I
a = 0.115568 − 0.650407I
b = −0.108908 + 1.147540I
3.01730 − 1.31614I −1.85963 + 5.09190I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.73918 − 0.14158I
a = 0.115568 + 0.650407I
b = −0.108908 − 1.147540I
3.01730 + 1.31614I −1.85963 − 5.09190I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
4
· (u
11
− 3u
9
+ ··· − 2u
2
+ 1)(u
19
− 5u
18
+ ··· − 14u + 4)
c
2
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
4
)(u
11
+ 6u
10
+ ··· + 4u + 1)
· (u
19
+ 9u
18
+ ··· + 44u + 16)
c
3
, c
8
(u
11
− u
10
− 3u
9
+ 3u
8
+ 2u
7
− u
6
+ u
5
− 3u
4
− u
3
+ 2u
2
+ 1)
· (u
19
+ u
18
+ ··· + 4u + 1)(u
24
+ u
23
+ ··· + 94u + 29)
c
4
, c
10
(u
11
+ 2u
9
+ u
8
− 3u
7
− u
6
− u
5
− 2u
4
+ 3u
3
+ 3u
2
− u − 1)
· (u
19
+ 15u
17
+ ··· + 3u + 1)(u
24
− u
23
+ ··· + 166u + 79)
c
5
, c
9
(u
11
+ u
10
− 3u
9
− 3u
8
+ 2u
7
+ u
6
+ u
5
+ 3u
4
− u
3
− 2u
2
− 1)
· (u
19
+ u
18
+ ··· + 4u + 1)(u
24
+ u
23
+ ··· + 94u + 29)
c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
4
· (u
11
− 3u
9
+ ··· + 2u
2
− 1)(u
19
− 5u
18
+ ··· − 14u + 4)
c
7
(u
2
− u − 1)
12
(u
11
+ 4u
10
+ 4u
9
+ 2u
7
+ 3u
6
− u
5
+ u
4
− 2u
3
− 4u
2
− 1)
· (u
19
+ 15u
18
+ ··· + 544u + 64)
c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
4
· (u
11
+ u
9
+ 4u
8
+ u
7
+ 8u
5
− 5u
4
+ 9u
3
− 3u
2
+ 1)
· (u
19
− 15u
18
+ ··· − 990u + 196)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
4
)(y
11
− 6y
10
+ ··· + 4y − 1)
· (y
19
− 9y
18
+ ··· + 44y − 16)
c
2
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
4
)(y
11
+ 2y
10
+ ··· + 4y − 1)
· (y
19
+ 3y
18
+ ··· + 2288y − 256)
c
3
, c
5
, c
8
c
9
(y
11
− 7y
10
+ ··· − 4y − 1)(y
19
− 9y
18
+ ··· + 12y − 1)
· (y
24
− 9y
23
+ ··· − 8372y + 841)
c
4
, c
10
(y
11
+ 4y
10
+ ··· + 7y − 1)(y
19
+ 30y
18
+ ··· − 25y − 1)
· (y
24
+ 15y
23
+ ··· + 63136y + 6241)
c
7
((y
2
− 3y + 1)
12
)(y
11
− 8y
10
+ ··· − 8y − 1)
· (y
19
− 11y
18
+ ··· + 95232y − 4096)
c
11
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
4
)(y
11
+ 2y
10
+ ··· + 6y − 1)
· (y
19
+ 3y
18
+ ··· + 237260y − 38416)
19
