11n
175
(K11n
175
)
A knot diagram
1
Linearized knot diagam
5 8 1 10 9 1 4 6 2 4 8
Solving Sequence
5,9 2,6
10 1 4 3 8 7 11
c
5
c
9
c
1
c
4
c
3
c
8
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
17
− 27u
16
+ ··· + 2b − 4, −u
17
+ 6u
16
+ ··· + 2a − 35, u
18
− 9u
17
+ ··· − 50u + 4i
I
u
2
= h−43u
5
a
3
+ 57u
5
a
2
+ ··· + 93a + 11, −u
5
a
3
− 3u
5
a + ··· − 8a + 28, u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
I
u
3
= h−u
8
− u
7
− 3u
6
− 2u
5
− 4u
4
− 3u
3
− 3u
2
+ b − 2u − 1,
u
9
+ 2u
8
+ 3u
7
+ 5u
6
+ 4u
5
+ 8u
4
+ 3u
3
+ 5u
2
+ 3a + u + 1,
u
10
+ 2u
9
+ 6u
8
+ 8u
7
+ 13u
6
+ 14u
5
+ 15u
4
+ 14u
3
+ 10u
2
+ 7u + 3i
* 3 irreducible components of dim
C
= 0, with total 52 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
=
h3u
17
−27u
16
+· · ·+2b−4, −u
17
+6u
16
+· · ·+2a−35, u
18
−9u
17
+· · ·−50u+4i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
2
=
1
2
u
17
− 3u
16
+ ··· −
273
2
u +
35
2
−
3
2
u
17
+
27
2
u
16
+ ··· −
85
2
u + 2
a
6
=
1
−u
2
a
10
=
9
4
u
17
−
75
4
u
16
+ ··· +
731
4
u − 18
−
3
2
u
17
+
25
2
u
16
+ ··· −
187
2
u + 9
a
1
=
−u
17
+
21
2
u
16
+ ··· − 179u +
39
2
−
3
2
u
17
+
27
2
u
16
+ ··· −
85
2
u + 2
a
4
=
−u
17
+
19
2
u
16
+ ··· − 261u +
55
2
1
2
u
17
−
7
2
u
16
+ ··· +
179
2
u − 10
a
3
=
−
3
2
u
17
+ 14u
16
+ ··· −
331
2
u +
39
2
−
3
2
u
17
+
25
2
u
16
+ ··· +
57
2
u − 4
a
8
=
−u
u
3
+ u
a
7
=
5
4
u
17
−
43
4
u
16
+ ··· +
327
4
u − 7
−
1
2
u
17
+
9
2
u
16
+ ··· −
145
2
u + 7
a
11
=
−u
17
+
21
2
u
16
+ ··· − 198u +
43
2
−
3
2
u
17
+
27
2
u
16
+ ··· + 194u
2
−
47
2
u
a
11
=
−u
17
+
21
2
u
16
+ ··· − 198u +
43
2
−
3
2
u
17
+
27
2
u
16
+ ··· + 194u
2
−
47
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
17
+ 27u
16
− 140u
15
+ 513u
14
− 1455u
13
+ 3348u
12
− 6412u
11
+ 10399u
10
−
14401u
9
+ 17095u
8
−17369u
7
+ 14980u
6
−10819u
5
+ 6362u
4
−2908u
3
+ 949u
2
−170u −2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
18
− 2u
16
+ ··· + 7u
2
− 1
c
2
, c
6
u
18
− 7u
16
+ ··· − 2u − 13
c
3
u
18
− 13u
17
+ ··· − 62u − 52
c
4
, c
10
u
18
+ 13u
17
+ ··· + 608u + 64
c
5
, c
8
u
18
+ 9u
17
+ ··· + 50u + 4
c
7
, c
11
u
18
+ 2u
17
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
18
− 4y
17
+ ··· − 14y + 1
c
2
, c
6
y
18
− 14y
17
+ ··· − 1564y + 169
c
3
y
18
− 19y
17
+ ··· + 6660y + 2704
c
4
, c
10
y
18
+ 9y
17
+ ··· − 17408y + 4096
c
5
, c
8
y
18
+ 13y
17
+ ··· − 364y + 16
c
7
, c
11
y
18
− 26y
17
+ ··· − 21y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.082250 + 0.227691I
a = 0.552560 − 1.011470I
b = −0.828307 + 0.968844I
−2.96562 + 8.53890I −6.56006 − 6.26417I
u = 1.082250 − 0.227691I
a = 0.552560 + 1.011470I
b = −0.828307 − 0.968844I
−2.96562 − 8.53890I −6.56006 + 6.26417I
u = −0.118459 + 1.148360I
a = 0.235904 + 0.462260I
b = 0.558784 − 0.216142I
−1.23970 − 1.97493I −7.15329 + 4.18348I
u = −0.118459 − 1.148360I
a = 0.235904 − 0.462260I
b = 0.558784 + 0.216142I
−1.23970 + 1.97493I −7.15329 − 4.18348I
u = 0.119333 + 1.157960I
a = −0.466244 − 0.909025I
b = −0.996978 + 0.648369I
−3.72560 + 1.35027I −12.38494 − 1.13112I
u = 0.119333 − 1.157960I
a = −0.466244 + 0.909025I
b = −0.996978 − 0.648369I
−3.72560 − 1.35027I −12.38494 + 1.13112I
u = 0.200699 + 1.177200I
a = 0.746983 + 1.092830I
b = 1.13656 − 1.09868I
0.82240 + 4.90619I −8.42983 − 0.71625I
u = 0.200699 − 1.177200I
a = 0.746983 − 1.092830I
b = 1.13656 + 1.09868I
0.82240 − 4.90619I −8.42983 + 0.71625I
u = 1.48738
a = −0.407205
b = 0.605669
−6.56717 −21.0980
u = 0.46203 + 1.43201I
a = −0.460365 − 1.018170I
b = −1.24533 + 1.12967I
−8.1698 + 13.9821I −9.44231 − 6.99967I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.46203 − 1.43201I
a = −0.460365 + 1.018170I
b = −1.24533 − 1.12967I
−8.1698 − 13.9821I −9.44231 + 6.99967I
u = 0.446331 + 0.206443I
a = −1.97819 − 0.97124I
b = 0.682422 + 0.841875I
3.74044 − 2.38337I −9.76739 + 4.47048I
u = 0.446331 − 0.206443I
a = −1.97819 + 0.97124I
b = 0.682422 − 0.841875I
3.74044 + 2.38337I −9.76739 − 4.47048I
u = 0.51935 + 1.48126I
a = 0.115710 + 0.783531I
b = 1.100520 − 0.578325I
−11.82300 + 6.66028I −12.41949 − 4.41908I
u = 0.51935 − 1.48126I
a = 0.115710 − 0.783531I
b = 1.100520 + 0.578325I
−11.82300 − 6.66028I −12.41949 + 4.41908I
u = 0.93646 + 1.42974I
a = 0.302389 − 0.123907I
b = −0.460331 − 0.316302I
−5.89009 − 1.65718I −15.9057 + 11.0160I
u = 0.93646 − 1.42974I
a = 0.302389 + 0.123907I
b = −0.460331 + 0.316302I
−5.89009 + 1.65718I −15.9057 − 11.0160I
u = 0.216637
a = 2.30970
b = −0.500367
−0.728249 −13.7760
6
II. I
u
2
= h−43u
5
a
3
+ 57u
5
a
2
+ · · · + 93a + 11, −u
5
a
3
− 3u
5
a + · · · − 8a +
28, u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
2
=
a
0.394495a
3
u
5
− 0.522936a
2
u
5
+ ··· − 0.853211a − 0.100917
a
6
=
1
−u
2
a
10
=
−a
2
u
0.385321a
3
u
5
− 0.394495a
2
u
5
+ ··· + 0.724771a − 0.935780
a
1
=
0.394495a
3
u
5
− 0.522936a
2
u
5
+ ··· + 0.146789a − 0.100917
0.394495a
3
u
5
− 0.522936a
2
u
5
+ ··· − 0.853211a − 0.100917
a
4
=
0.321101a
3
u
5
− 0.495413a
2
u
5
+ ··· − 0.229358a + 0.220183
0.385321a
3
u
5
− 0.394495a
2
u
5
+ ··· + 0.724771a + 0.0642202
a
3
=
0.798165a
3
u
5
− 1.17431a
2
u
5
+ ··· + 0.715596a − 0.366972
0.862385a
3
u
5
− 1.07339a
2
u
5
+ ··· + 0.669725a − 0.522936
a
8
=
−u
u
3
+ u
a
7
=
0.522936a
3
u
5
− 1.32110a
2
u
5
+ ··· + 0.0550459a + 2.58716
0.146789a
3
u
5
− 1.05505a
2
u
5
+ ··· + 0.752294a − 0.642202
a
11
=
0.0642202a
3
u
5
+ 0.100917a
2
u
5
+ ··· + 0.954128a − 0.155963
−0.385321a
3
u
5
+ 0.394495a
2
u
5
+ ··· − 0.724771a − 0.0642202
a
11
=
0.0642202a
3
u
5
+ 0.100917a
2
u
5
+ ··· + 0.954128a − 0.155963
−0.385321a
3
u
5
+ 0.394495a
2
u
5
+ ··· − 0.724771a − 0.0642202
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
168
109
u
5
a
3
+
172
109
u
5
a
2
+ ··· −
316
109
a −
682
109
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
24
+ 5u
23
+ ··· − 12u + 3
c
2
, c
6
u
24
− u
23
+ ··· − 1976u + 793
c
3
(u
6
+ 5u
5
+ 7u
4
− 2u
2
+ 3u − 1)
4
c
4
, c
10
(u
2
− u + 1)
12
c
5
, c
8
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
c
7
, c
11
u
24
+ u
23
+ ··· + 198u + 93
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
24
+ 3y
23
+ ··· − 156y + 9
c
2
, c
6
y
24
− 17y
23
+ ··· − 2553304y + 628849
c
3
(y
6
− 11y
5
+ 45y
4
− 60y
3
− 10y
2
− 5y + 1)
4
c
4
, c
10
(y
2
+ y + 1)
12
c
5
, c
8
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
4
c
7
, c
11
y
24
− 25y
23
+ ··· + 40776y + 8649
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873214
a = 0.696693 + 0.745196I
b = −0.424035 − 0.969980I
2.72528 − 2.02988I −5.73050 + 3.46410I
u = −0.873214
a = 0.696693 − 0.745196I
b = −0.424035 + 0.969980I
2.72528 + 2.02988I −5.73050 − 3.46410I
u = −0.873214
a = −0.485602 + 1.110820I
b = 0.608362 − 0.650716I
2.72528 + 2.02988I −5.73050 − 3.46410I
u = −0.873214
a = −0.485602 − 1.110820I
b = 0.608362 + 0.650716I
2.72528 − 2.02988I −5.73050 + 3.46410I
u = 0.138835 + 1.234450I
a = 0.047053 − 0.843430I
b = 0.49525 + 2.03273I
−7.89505 − 0.05747I −13.42428 − 0.22068I
u = 0.138835 + 1.234450I
a = −1.67067 + 0.21330I
b = −1.047700 + 0.059012I
−7.89505 − 0.05747I −13.42428 − 0.22068I
u = 0.138835 + 1.234450I
a = 0.010113 + 0.251086I
b = −1.84383 − 1.47696I
−7.89505 + 4.00229I −13.4243 − 7.1489I
u = 0.138835 + 1.234450I
a = 1.34740 − 1.34211I
b = 0.308548 − 0.047344I
−7.89505 + 4.00229I −13.4243 − 7.1489I
u = 0.138835 − 1.234450I
a = 0.047053 + 0.843430I
b = 0.49525 − 2.03273I
−7.89505 + 0.05747I −13.42428 + 0.22068I
u = 0.138835 − 1.234450I
a = −1.67067 − 0.21330I
b = −1.047700 − 0.059012I
−7.89505 + 0.05747I −13.42428 + 0.22068I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.138835 − 1.234450I
a = 0.010113 − 0.251086I
b = −1.84383 + 1.47696I
−7.89505 − 4.00229I −13.4243 + 7.1489I
u = 0.138835 − 1.234450I
a = 1.34740 + 1.34211I
b = 0.308548 + 0.047344I
−7.89505 − 4.00229I −13.4243 + 7.1489I
u = −0.408802 + 1.276380I
a = −0.353289 + 0.834565I
b = −1.20721 − 1.28821I
−1.23922 − 6.62201I −9.41886 + 6.66892I
u = −0.408802 + 1.276380I
a = −0.070379 + 0.682688I
b = −0.269751 − 0.368903I
−1.23922 − 2.56224I −9.41886 − 0.25928I
u = −0.408802 + 1.276380I
a = 0.640625 − 1.150990I
b = 0.920794 + 0.792102I
−1.23922 − 6.62201I −9.41886 + 6.66892I
u = −0.408802 + 1.276380I
a = 0.200742 − 0.275636I
b = 0.842596 + 0.368915I
−1.23922 − 2.56224I −9.41886 − 0.25928I
u = −0.408802 − 1.276380I
a = −0.353289 − 0.834565I
b = −1.20721 + 1.28821I
−1.23922 + 6.62201I −9.41886 − 6.66892I
u = −0.408802 − 1.276380I
a = −0.070379 − 0.682688I
b = −0.269751 + 0.368903I
−1.23922 + 2.56224I −9.41886 + 0.25928I
u = −0.408802 − 1.276380I
a = 0.640625 + 1.150990I
b = 0.920794 − 0.792102I
−1.23922 + 6.62201I −9.41886 − 6.66892I
u = −0.408802 − 1.276380I
a = 0.200742 + 0.275636I
b = 0.842596 − 0.368915I
−1.23922 + 2.56224I −9.41886 + 0.25928I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.413150
a = −0.71019 + 2.16507I
b = −1.176440 − 0.634954I
−4.19595 + 2.02988I −4.58322 − 3.46410I
u = 0.413150
a = −0.71019 − 2.16507I
b = −1.176440 + 0.634954I
−4.19595 − 2.02988I −4.58322 + 3.46410I
u = 0.413150
a = 2.84750 + 1.53686I
b = 0.293413 − 0.894500I
−4.19595 + 2.02988I −4.58322 − 3.46410I
u = 0.413150
a = 2.84750 − 1.53686I
b = 0.293413 + 0.894500I
−4.19595 − 2.02988I −4.58322 + 3.46410I
12
III.
I
u
3
= h−u
8
− u
7
+ · · · + b − 1, u
9
+ 2u
8
+ · · · + 3a + 1, u
10
+ 2u
9
+ · · · + 7u + 3i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
2
=
−
1
3
u
9
−
2
3
u
8
+ ··· −
1
3
u −
1
3
u
8
+ u
7
+ 3u
6
+ 2u
5
+ 4u
4
+ 3u
3
+ 3u
2
+ 2u + 1
a
6
=
1
−u
2
a
10
=
1
3
u
9
+
2
3
u
8
+ ··· −
2
3
u −
5
3
−u
8
− u
7
− 4u
6
− 3u
5
− 6u
4
− 4u
3
− 4u
2
− 3u − 1
a
1
=
−
1
3
u
9
+
1
3
u
8
+ ··· +
5
3
u +
2
3
u
8
+ u
7
+ 3u
6
+ 2u
5
+ 4u
4
+ 3u
3
+ 3u
2
+ 2u + 1
a
4
=
−
2
3
u
9
−
7
3
u
8
+ ··· −
23
3
u −
11
3
u
7
+ u
6
+ 3u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u + 2
a
3
=
2
3
u
9
+
4
3
u
8
+ ··· +
5
3
u −
1
3
u
9
+ 2u
8
+ 5u
7
+ 6u
6
+ 8u
5
+ 8u
4
+ 7u
3
+ 6u
2
+ 3u + 1
a
8
=
−u
u
3
+ u
a
7
=
2
3
u
9
+
4
3
u
8
+ ··· +
11
3
u +
5
3
−u
5
− u
4
− 2u
3
− 2u
2
− 2u − 2
a
11
=
−
1
3
u
9
+
1
3
u
8
+ ··· +
8
3
u +
2
3
u
4
+ u
3
+ 2u
2
+ u + 1
a
11
=
−
1
3
u
9
+
1
3
u
8
+ ··· +
8
3
u +
2
3
u
4
+ u
3
+ 2u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
9
+ 6u
8
+ 16u
7
+ 21u
6
+ 29u
5
+ 34u
4
+ 29u
3
+ 29u
2
+ 16u + 3
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
10
+ u
8
− u
7
+ 6u
6
− 2u
5
+ 4u
4
− 4u
3
+ 5u
2
− 2u + 1
c
2
, c
6
u
10
− 4u
8
+ 3u
7
+ 12u
6
+ u
5
+ 11u
3
+ 2u
2
− 2u + 3
c
3
u
10
+ 8u
9
+ ··· + 26u + 3
c
4
u
10
+ 4u
8
+ 8u
6
+ 2u
5
+ 10u
4
+ 3u
3
+ 7u
2
+ u + 3
c
5
u
10
+ 2u
9
+ 6u
8
+ 8u
7
+ 13u
6
+ 14u
5
+ 15u
4
+ 14u
3
+ 10u
2
+ 7u + 3
c
7
, c
11
u
10
− 4u
8
+ 3u
6
+ u
5
+ 4u
4
+ 4u
2
− u + 1
c
8
u
10
− 2u
9
+ 6u
8
− 8u
7
+ 13u
6
− 14u
5
+ 15u
4
− 14u
3
+ 10u
2
− 7u + 3
c
10
u
10
+ 4u
8
+ 8u
6
− 2u
5
+ 10u
4
− 3u
3
+ 7u
2
− u + 3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
10
+ 2y
9
+ ··· + 6y + 1
c
2
, c
6
y
10
− 8y
9
+ ··· + 8y + 9
c
3
y
10
− 8y
9
+ ··· − 178y + 9
c
4
, c
10
y
10
+ 8y
9
+ ··· + 41y + 9
c
5
, c
8
y
10
+ 8y
9
+ ··· + 11y + 9
c
7
, c
11
y
10
− 8y
9
+ 22y
8
− 16y
7
− 15y
6
− 7y
5
+ 32y
4
+ 40y
3
+ 24y
2
+ 7y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.555224 + 0.913312I
a = 0.348707 + 0.379158I
b = −0.152679 + 0.528996I
−5.66496 − 0.94946I −9.80995 − 0.64578I
u = 0.555224 − 0.913312I
a = 0.348707 − 0.379158I
b = −0.152679 − 0.528996I
−5.66496 + 0.94946I −9.80995 + 0.64578I
u = 0.106413 + 1.166400I
a = −0.965103 + 0.714296I
b = −0.935856 − 1.049690I
−7.32588 + 2.86616I −9.25686 − 0.74854I
u = 0.106413 − 1.166400I
a = −0.965103 − 0.714296I
b = −0.935856 + 1.049690I
−7.32588 − 2.86616I −9.25686 + 0.74854I
u = −0.757440 + 0.211348I
a = −1.029450 + 0.893435I
b = 0.590918 − 0.894294I
4.48505 + 2.09086I 1.20974 − 1.26388I
u = −0.757440 − 0.211348I
a = −1.029450 − 0.893435I
b = 0.590918 + 0.894294I
4.48505 − 2.09086I 1.20974 + 1.26388I
u = −0.333031 + 1.234640I
a = 0.641089 − 1.043630I
b = 1.07501 + 1.13908I
1.20593 − 5.98785I −5.27541 + 6.66552I
u = −0.333031 − 1.234640I
a = 0.641089 + 1.043630I
b = 1.07501 − 1.13908I
1.20593 + 5.98785I −5.27541 − 6.66552I
u = −0.571165 + 1.251720I
a = −0.161914 + 0.535162I
b = −0.577394 − 0.508337I
−0.92481 − 3.39622I −5.36753 + 9.56684I
u = −0.571165 − 1.251720I
a = −0.161914 − 0.535162I
b = −0.577394 + 0.508337I
−0.92481 + 3.39622I −5.36753 − 9.56684I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
10
+ u
8
− u
7
+ 6u
6
− 2u
5
+ 4u
4
− 4u
3
+ 5u
2
− 2u + 1)
· (u
18
− 2u
16
+ ··· + 7u
2
− 1)(u
24
+ 5u
23
+ ··· − 12u + 3)
c
2
, c
6
(u
10
− 4u
8
+ 3u
7
+ 12u
6
+ u
5
+ 11u
3
+ 2u
2
− 2u + 3)
· (u
18
− 7u
16
+ ··· − 2u − 13)(u
24
− u
23
+ ··· − 1976u + 793)
c
3
((u
6
+ 5u
5
+ 7u
4
− 2u
2
+ 3u − 1)
4
)(u
10
+ 8u
9
+ ··· + 26u + 3)
· (u
18
− 13u
17
+ ··· − 62u − 52)
c
4
(u
2
− u + 1)
12
(u
10
+ 4u
8
+ 8u
6
+ 2u
5
+ 10u
4
+ 3u
3
+ 7u
2
+ u + 3)
· (u
18
+ 13u
17
+ ··· + 608u + 64)
c
5
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
· (u
10
+ 2u
9
+ 6u
8
+ 8u
7
+ 13u
6
+ 14u
5
+ 15u
4
+ 14u
3
+ 10u
2
+ 7u + 3)
· (u
18
+ 9u
17
+ ··· + 50u + 4)
c
7
, c
11
(u
10
− 4u
8
+ ··· − u + 1)(u
18
+ 2u
17
+ ··· + u + 1)
· (u
24
+ u
23
+ ··· + 198u + 93)
c
8
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
· (u
10
− 2u
9
+ 6u
8
− 8u
7
+ 13u
6
− 14u
5
+ 15u
4
− 14u
3
+ 10u
2
− 7u + 3)
· (u
18
+ 9u
17
+ ··· + 50u + 4)
c
10
(u
2
− u + 1)
12
(u
10
+ 4u
8
+ 8u
6
− 2u
5
+ 10u
4
− 3u
3
+ 7u
2
− u + 3)
· (u
18
+ 13u
17
+ ··· + 608u + 64)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y
10
+ 2y
9
+ ··· + 6y + 1)(y
18
− 4y
17
+ ··· − 14y + 1)
· (y
24
+ 3y
23
+ ··· − 156y + 9)
c
2
, c
6
(y
10
− 8y
9
+ ··· + 8y + 9)(y
18
− 14y
17
+ ··· − 1564y + 169)
· (y
24
− 17y
23
+ ··· − 2553304y + 628849)
c
3
(y
6
− 11y
5
+ 45y
4
− 60y
3
− 10y
2
− 5y + 1)
4
· (y
10
− 8y
9
+ ··· − 178y + 9)(y
18
− 19y
17
+ ··· + 6660y + 2704)
c
4
, c
10
((y
2
+ y + 1)
12
)(y
10
+ 8y
9
+ ··· + 41y + 9)
· (y
18
+ 9y
17
+ ··· − 17408y + 4096)
c
5
, c
8
((y
6
+ 5y
5
+ ··· − 5y + 1)
4
)(y
10
+ 8y
9
+ ··· + 11y + 9)
· (y
18
+ 13y
17
+ ··· − 364y + 16)
c
7
, c
11
(y
10
− 8y
9
+ 22y
8
− 16y
7
− 15y
6
− 7y
5
+ 32y
4
+ 40y
3
+ 24y
2
+ 7y + 1)
· (y
18
− 26y
17
+ ··· − 21y + 1)(y
24
− 25y
23
+ ··· + 40776y + 8649)
18
