12n
0580
(K12n
0580
)
A knot diagram
1
Linearized knot diagam
3 7 12 11 10 2 6 12 3 5 8 10
Solving Sequence
2,7
3 1 6
8,10
5 9 12 4 11
c
2
c
1
c
6
c
7
c
5
c
9
c
12
c
3
c
11
c
4
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
20
+ 14u
19
+ ··· + 2b − 4, −u
20
+ 3u
19
+ ··· + 2a + 3, u
21
− 6u
20
+ ··· + 26u − 4i
I
u
2
= h−463u
5
a
3
− 277u
5
a
2
+ ··· − 1475a − 789, −u
5
a
3
− 2u
5
a
2
+ ··· − 2a + 6, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
3
= h−u
11
+ 2u
9
− u
8
− 5u
7
+ u
6
+ 5u
5
− 2u
4
− 5u
3
+ u
2
+ b + u,
− u
10
+ 2u
8
− u
7
− 5u
6
+ u
5
+ 5u
4
− 2u
3
− 5u
2
+ a + u + 1,
u
13
− u
12
− 2u
11
+ 3u
10
+ 4u
9
− 6u
8
− 4u
7
+ 8u
6
+ 3u
5
− 7u
4
+ 3u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 58 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
20
+14u
19
+· · ·+2b−4, −u
20
+3u
19
+· · ·+2a+3, u
21
−6u
20
+· · ·+26u−4i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
10
=
1
2
u
20
−
3
2
u
19
+ ··· + 13u −
3
2
3
2
u
20
− 7u
19
+ ··· −
29
2
u + 2
a
5
=
−
1
4
u
20
+ 3u
19
+ ··· +
79
4
u − 4
3
2
u
20
− 5u
19
+ ··· +
7
2
u − 1
a
9
=
u
20
−
9
2
u
19
+ ··· −
19
2
u +
5
2
3
2
u
20
− 6u
19
+ ··· −
25
2
u + 2
a
12
=
7
4
u
20
− 7u
19
+ ··· −
21
4
u + 2
7
2
u
20
− 16u
19
+ ··· −
89
2
u + 7
a
4
=
u
20
−
5
2
u
19
+ ··· +
25
2
u −
3
2
3
2
u
20
− 6u
19
+ ··· −
25
2
u + 2
a
11
=
15
4
u
20
− 14u
19
+ ··· +
35
4
u − 2
17
2
u
20
− 40u
19
+ ··· −
221
2
u + 17
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
20
+ 15u
19
−25u
18
−10u
17
+ 97u
16
−118u
15
−47u
14
+ 243u
13
−133u
12
−247u
11
+
362u
10
+ 66u
9
− 512u
8
+ 368u
7
+ 162u
6
− 389u
5
+ 165u
4
+ 104u
3
− 120u
2
+ 34u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
21
+ 8u
20
+ ··· + 188u + 16
c
2
, c
6
u
21
− 6u
20
+ ··· + 26u − 4
c
3
u
21
− 2u
20
+ ··· + 5u − 1
c
4
, c
5
, c
9
c
10
u
21
+ 13u
19
+ ··· + u − 1
c
8
, c
11
u
21
− 16u
20
+ ··· + 480u − 64
c
12
u
21
− 3u
20
+ ··· − 11u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
21
+ 12y
20
+ ··· + 9072y −256
c
2
, c
6
y
21
− 8y
20
+ ··· + 188y −16
c
3
y
21
− 36y
20
+ ··· + 47y −1
c
4
, c
5
, c
9
c
10
y
21
+ 26y
20
+ ··· − y −1
c
8
, c
11
y
21
− 6y
20
+ ··· − 7168y −4096
c
12
y
21
+ 33y
20
+ ··· + 43y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.935175 + 0.517534I
a = −1.110460 − 0.861684I
b = −0.59252 − 1.38052I
0.24926 − 3.91469I 2.72764 + 7.21725I
u = 0.935175 − 0.517534I
a = −1.110460 + 0.861684I
b = −0.59252 + 1.38052I
0.24926 + 3.91469I 2.72764 − 7.21725I
u = 0.448329 + 0.989827I
a = −0.363224 − 1.287660I
b = 1.11171 − 0.93682I
−10.43170 + 7.68453I −0.20664 − 3.05097I
u = 0.448329 − 0.989827I
a = −0.363224 + 1.287660I
b = 1.11171 + 0.93682I
−10.43170 − 7.68453I −0.20664 + 3.05097I
u = 0.528861 + 1.017090I
a = −0.085943 + 1.202340I
b = −1.268340 + 0.548462I
−9.86050 − 1.84914I −0.90690 + 1.69467I
u = 0.528861 − 1.017090I
a = −0.085943 − 1.202340I
b = −1.268340 − 0.548462I
−9.86050 + 1.84914I −0.90690 − 1.69467I
u = −0.821760 + 0.209360I
a = 0.270782 − 0.182803I
b = −0.184246 + 0.206911I
−1.40817 + 0.64438I −3.79274 − 1.22685I
u = −0.821760 − 0.209360I
a = 0.270782 + 0.182803I
b = −0.184246 − 0.206911I
−1.40817 − 0.64438I −3.79274 + 1.22685I
u = −0.896473 + 0.746587I
a = −0.309151 + 0.124372I
b = 0.184291 − 0.342305I
4.28731 + 2.84851I 0.39482 − 1.73871I
u = −0.896473 − 0.746587I
a = −0.309151 − 0.124372I
b = 0.184291 + 0.342305I
4.28731 − 2.84851I 0.39482 + 1.73871I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.677418 + 0.397216I
a = 1.51417 + 0.36850I
b = 0.879349 + 0.851081I
1.096940 − 0.102856I 7.06481 + 1.59045I
u = 0.677418 − 0.397216I
a = 1.51417 − 0.36850I
b = 0.879349 − 0.851081I
1.096940 + 0.102856I 7.06481 − 1.59045I
u = 0.904796 + 0.829662I
a = 0.401041 − 0.496617I
b = 0.774885 − 0.116608I
4.71470 − 3.09578I −3.27109 + 3.56536I
u = 0.904796 − 0.829662I
a = 0.401041 + 0.496617I
b = 0.774885 + 0.116608I
4.71470 + 3.09578I −3.27109 − 3.56536I
u = −1.327590 + 0.030849I
a = −0.070884 + 0.549935I
b = 0.077139 − 0.732274I
−17.1548 − 4.6029I −4.70163 + 2.09700I
u = −1.327590 − 0.030849I
a = −0.070884 − 0.549935I
b = 0.077139 + 0.732274I
−17.1548 + 4.6029I −4.70163 − 2.09700I
u = 1.176180 + 0.678965I
a = 1.80081 − 0.07045I
b = 2.16591 + 1.13982I
−12.7012 − 13.7507I −1.99835 + 6.85375I
u = 1.176180 − 0.678965I
a = 1.80081 + 0.07045I
b = 2.16591 − 1.13982I
−12.7012 + 13.7507I −1.99835 − 6.85375I
u = 1.175240 + 0.726178I
a = −1.45480 + 0.41477I
b = −2.01093 − 0.56899I
−11.89320 − 4.50624I −2.44659 + 2.53964I
u = 1.175240 − 0.726178I
a = −1.45480 − 0.41477I
b = −2.01093 + 0.56899I
−11.89320 + 4.50624I −2.44659 − 2.53964I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.399649
a = 1.81531
b = 0.725488
0.927006 12.2730
7
II. I
u
2
= h−463u
5
a
3
− 277u
5
a
2
+ · · · − 1475a − 789, −u
5
a
3
− 2u
5
a
2
+ · · · −
2a + 6, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
10
=
a
0.246670a
3
u
5
+ 0.147576a
2
u
5
+ ··· + 0.785828a + 0.420352
a
5
=
−0.161961a
3
u
5
− 0.461907a
2
u
5
+ ··· − 0.777304a − 0.0340970
−0.621204a
3
u
5
− 1.02824a
2
u
5
+ ··· + 0.604156a − 1.49920
a
9
=
−0.246670a
3
u
5
− 0.147576a
2
u
5
+ ··· + 0.214172a − 0.420352
−0.0223761a
3
u
5
− 0.728290a
2
u
5
+ ··· + 1.28077a + 0.784763
a
12
=
−0.247736a
3
u
5
− 0.420352a
2
u
5
+ ··· + 0.465637a + 0.474161
−0.656367a
3
u
5
− 0.0298348a
2
u
5
+ ··· − 0.0974960a − 2.98029
a
4
=
0.134790a
3
u
5
+ 0.506127a
2
u
5
+ ··· + 0.189664a + 1.34417
1.31700a
3
u
5
− 0.849227a
2
u
5
+ ··· + 1.18913a + 5.38253
a
11
=
−0.228556a
3
u
5
− 0.510389a
2
u
5
+ ··· − 0.0607352a + 0.372936
−0.983484a
3
u
5
− 0.771977a
2
u
5
+ ··· + 0.102291a − 3.36494
(ii) Obstruction class = −1
(iii) Cusp Shapes =
808
1877
u
5
a
3
+
4132
1877
u
5
a
2
+ ··· −
2988
1877
a −
6350
1877
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
4
c
2
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
4
c
3
u
24
− 3u
23
+ ··· + 54u + 43
c
4
, c
5
, c
9
c
10
u
24
− u
23
+ ··· + 148u + 43
c
8
, c
11
(u
2
+ u + 1)
12
c
12
u
24
+ 9u
23
+ ··· + 376u + 229
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
4
c
2
, c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
4
c
3
y
24
− 33y
23
+ ··· − 52280y + 1849
c
4
, c
5
, c
9
c
10
y
24
+ 27y
23
+ ··· + 36576y + 1849
c
8
, c
11
(y
2
+ y + 1)
12
c
12
y
24
+ 27y
23
+ ··· + 65640y + 52441
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −1.050380 + 0.369608I
b = −1.20802 − 1.30034I
−6.82541 − 2.95419I −5.71672 + 4.25833I
u = 1.002190 + 0.295542I
a = −0.081771 + 0.727533I
b = 0.40776 + 1.96764I
−6.82541 + 1.10558I −5.71672 − 2.66988I
u = 1.002190 + 0.295542I
a = −1.46095 − 0.86667I
b = −1.161920 + 0.059986I
−6.82541 − 2.95419I −5.71672 + 4.25833I
u = 1.002190 + 0.295542I
a = 0.90697 + 1.69587I
b = −0.296966 + 0.704962I
−6.82541 + 1.10558I −5.71672 − 2.66988I
u = 1.002190 − 0.295542I
a = −1.050380 − 0.369608I
b = −1.20802 + 1.30034I
−6.82541 + 2.95419I −5.71672 − 4.25833I
u = 1.002190 − 0.295542I
a = −0.081771 − 0.727533I
b = 0.40776 − 1.96764I
−6.82541 − 1.10558I −5.71672 + 2.66988I
u = 1.002190 − 0.295542I
a = −1.46095 + 0.86667I
b = −1.161920 − 0.059986I
−6.82541 + 2.95419I −5.71672 − 4.25833I
u = 1.002190 − 0.295542I
a = 0.90697 − 1.69587I
b = −0.296966 − 0.704962I
−6.82541 − 1.10558I −5.71672 + 2.66988I
u = −0.428243 + 0.664531I
a = 0.820716 − 0.925536I
b = −0.50645 − 1.55897I
−3.04420 − 2.95419I 1.71672 + 4.25833I
u = −0.428243 + 0.664531I
a = 0.481772 − 1.278420I
b = −1.056330 − 0.348684I
−3.04420 + 1.10558I 1.71672 − 2.66988I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 + 0.664531I
a = 0.353054 + 1.362070I
b = 0.643235 + 0.867628I
−3.04420 + 1.10558I 1.71672 − 2.66988I
u = −0.428243 + 0.664531I
a = −1.31057 + 1.60669I
b = 0.263581 + 0.941746I
−3.04420 − 2.95419I 1.71672 + 4.25833I
u = −0.428243 − 0.664531I
a = 0.820716 + 0.925536I
b = −0.50645 + 1.55897I
−3.04420 + 2.95419I 1.71672 − 4.25833I
u = −0.428243 − 0.664531I
a = 0.481772 + 1.278420I
b = −1.056330 + 0.348684I
−3.04420 − 1.10558I 1.71672 + 2.66988I
u = −0.428243 − 0.664531I
a = 0.353054 − 1.362070I
b = 0.643235 − 0.867628I
−3.04420 − 1.10558I 1.71672 + 2.66988I
u = −0.428243 − 0.664531I
a = −1.31057 − 1.60669I
b = 0.263581 − 0.941746I
−3.04420 + 2.95419I 1.71672 − 4.25833I
u = −1.073950 + 0.558752I
a = −1.35473 − 0.44637I
b = −1.82694 + 0.82770I
−4.93480 + 3.66314I −2.00000 − 2.04647I
u = −1.073950 + 0.558752I
a = 1.65432 + 0.08999I
b = 1.70432 − 0.27758I
−4.93480 + 3.66314I −2.00000 − 2.04647I
u = −1.073950 + 0.558752I
a = 1.65472 − 0.61469I
b = 1.97136 − 1.75360I
−4.93480 + 7.72290I −2.00000 − 8.97467I
u = −1.073950 + 0.558752I
a = −2.11314 + 0.53343I
b = −1.43363 + 1.58473I
−4.93480 + 7.72290I −2.00000 − 8.97467I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = −1.35473 + 0.44637I
b = −1.82694 − 0.82770I
−4.93480 − 3.66314I −2.00000 + 2.04647I
u = −1.073950 − 0.558752I
a = 1.65432 − 0.08999I
b = 1.70432 + 0.27758I
−4.93480 − 3.66314I −2.00000 + 2.04647I
u = −1.073950 − 0.558752I
a = 1.65472 + 0.61469I
b = 1.97136 + 1.75360I
−4.93480 − 7.72290I −2.00000 + 8.97467I
u = −1.073950 − 0.558752I
a = −2.11314 − 0.53343I
b = −1.43363 − 1.58473I
−4.93480 − 7.72290I −2.00000 + 8.97467I
13
III.
I
u
3
= h−u
11
+2u
9
+· · ·+b+u, −u
10
+2u
8
+· · ·+a+1, u
13
−u
12
+· · ·+3u
2
−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
10
=
u
10
− 2u
8
+ u
7
+ 5u
6
− u
5
− 5u
4
+ 2u
3
+ 5u
2
− u − 1
u
11
− 2u
9
+ u
8
+ 5u
7
− u
6
− 5u
5
+ 2u
4
+ 5u
3
− u
2
− u
a
5
=
−u
12
− u
11
+ ··· + 4u − 1
−2u
12
+ 5u
10
− u
9
− 11u
8
+ 2u
7
+ 14u
6
− 3u
5
− 13u
4
+ 3u
3
+ 6u
2
− 1
a
9
=
u
12
− u
11
− u
10
+ 3u
9
+ 2u
8
− 5u
7
+ u
6
+ 6u
5
− 2u
4
− 4u
3
+ 5u
2
− 1
u
11
− 2u
9
+ u
8
+ 4u
7
− u
6
− 4u
5
+ 2u
4
+ 3u
3
− u
2
a
12
=
u
12
− 3u
10
+ 7u
8
− 10u
6
+ 11u
4
+ u
3
− 7u
2
+ 3
u
12
− u
11
+ ··· + 2u + 1
a
4
=
−u
11
+ u
10
+ 2u
9
− 4u
8
− 4u
7
+ 7u
6
+ 4u
5
− 10u
4
− 3u
3
+ 8u
2
+ u − 2
−u
12
+ u
11
+ ··· − 2u − 1
a
11
=
u
12
− 3u
10
+ 7u
8
− 11u
6
+ 12u
4
+ u
3
− 8u
2
+ 3
u
12
− u
11
+ ··· + 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
12
− 3u
11
+ 4u
10
+ 4u
9
− 9u
8
− 11u
7
+ 15u
6
+ 9u
5
− 18u
4
− 6u
3
+ 13u
2
− 3u − 5
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 5u
12
+ ··· + 6u − 1
c
2
u
13
− u
12
− 2u
11
+ 3u
10
+ 4u
9
− 6u
8
− 4u
7
+ 8u
6
+ 3u
5
− 7u
4
+ 3u
2
− 1
c
3
u
13
+ 2u
12
+ ··· + 9u + 3
c
4
, c
5
, c
9
u
13
+ 8u
11
+ ··· + 5u + 1
c
6
u
13
+ u
12
− 2u
11
− 3u
10
+ 4u
9
+ 6u
8
− 4u
7
− 8u
6
+ 3u
5
+ 7u
4
− 3u
2
+ 1
c
7
u
13
+ 5u
12
+ ··· + 6u + 1
c
8
u
13
− 3u
12
+ ··· − 3u + 1
c
10
u
13
+ 8u
11
+ ··· + 5u − 1
c
11
u
13
+ 3u
12
+ ··· − 3u − 1
c
12
u
13
+ 3u
12
+ ··· − 3u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
13
+ 11y
12
+ ··· − 10y −1
c
2
, c
6
y
13
− 5y
12
+ ··· + 6y −1
c
3
y
13
− 6y
12
+ ··· + 39y −9
c
4
, c
5
, c
9
c
10
y
13
+ 16y
12
+ ··· + 7y −1
c
8
, c
11
y
13
− 7y
12
+ ··· − 3y −1
c
12
y
13
+ 3y
12
+ ··· + 7y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.033900 + 0.364048I
a = 0.445935 − 0.499626I
b = −0.279166 + 0.678907I
−6.67636 + 0.41487I −4.61704 − 2.68258I
u = −1.033900 − 0.364048I
a = 0.445935 + 0.499626I
b = −0.279166 − 0.678907I
−6.67636 − 0.41487I −4.61704 + 2.68258I
u = 0.628298 + 0.593066I
a = 0.21176 + 2.10347I
b = −1.11445 + 1.44719I
−4.07671 + 1.23383I −1.69190 − 0.17539I
u = 0.628298 − 0.593066I
a = 0.21176 − 2.10347I
b = −1.11445 − 1.44719I
−4.07671 − 1.23383I −1.69190 + 0.17539I
u = 1.032670 + 0.557375I
a = −2.14778 + 0.03860I
b = −2.23946 − 1.15726I
−5.39322 − 5.84865I −3.49346 + 5.41334I
u = 1.032670 − 0.557375I
a = −2.14778 − 0.03860I
b = −2.23946 + 1.15726I
−5.39322 + 5.84865I −3.49346 − 5.41334I
u = 0.815001
a = 1.46736
b = 1.19590
0.406093 −5.99710
u = −0.899575 + 0.799634I
a = −0.180212 + 0.063376I
b = 0.111437 − 0.201115I
5.29164 + 3.00519I 11.80568 − 1.98854I
u = −0.899575 − 0.799634I
a = −0.180212 − 0.063376I
b = 0.111437 + 0.201115I
5.29164 − 3.00519I 11.80568 + 1.98854I
u = 0.917844 + 0.874021I
a = 0.756497 − 0.845675I
b = 1.43348 − 0.11500I
2.41795 − 3.23180I −1.51049 + 2.95825I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917844 − 0.874021I
a = 0.756497 + 0.845675I
b = 1.43348 + 0.11500I
2.41795 + 3.23180I −1.51049 − 2.95825I
u = −0.552837 + 0.348261I
a = 0.680116 − 1.051500I
b = −0.009797 + 0.818166I
−4.92582 + 2.64511I 0.50575 − 4.47671I
u = −0.552837 − 0.348261I
a = 0.680116 + 1.051500I
b = −0.009797 − 0.818166I
−4.92582 − 2.64511I 0.50575 + 4.47671I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
4
)(u
13
− 5u
12
+ ··· + 6u − 1)
· (u
21
+ 8u
20
+ ··· + 188u + 16)
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
4
· (u
13
− u
12
− 2u
11
+ 3u
10
+ 4u
9
− 6u
8
− 4u
7
+ 8u
6
+ 3u
5
− 7u
4
+ 3u
2
− 1)
· (u
21
− 6u
20
+ ··· + 26u − 4)
c
3
(u
13
+ 2u
12
+ ··· + 9u + 3)(u
21
− 2u
20
+ ··· + 5u − 1)
· (u
24
− 3u
23
+ ··· + 54u + 43)
c
4
, c
5
, c
9
(u
13
+ 8u
11
+ ··· + 5u + 1)(u
21
+ 13u
19
+ ··· + u − 1)
· (u
24
− u
23
+ ··· + 148u + 43)
c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
4
· (u
13
+ u
12
− 2u
11
− 3u
10
+ 4u
9
+ 6u
8
− 4u
7
− 8u
6
+ 3u
5
+ 7u
4
− 3u
2
+ 1)
· (u
21
− 6u
20
+ ··· + 26u − 4)
c
7
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
4
)(u
13
+ 5u
12
+ ··· + 6u + 1)
· (u
21
+ 8u
20
+ ··· + 188u + 16)
c
8
((u
2
+ u + 1)
12
)(u
13
− 3u
12
+ ··· − 3u + 1)
· (u
21
− 16u
20
+ ··· + 480u − 64)
c
10
(u
13
+ 8u
11
+ ··· + 5u − 1)(u
21
+ 13u
19
+ ··· + u − 1)
· (u
24
− u
23
+ ··· + 148u + 43)
c
11
((u
2
+ u + 1)
12
)(u
13
+ 3u
12
+ ··· − 3u − 1)
· (u
21
− 16u
20
+ ··· + 480u − 64)
c
12
(u
13
+ 3u
12
+ ··· − 3u − 1)(u
21
− 3u
20
+ ··· − 11u − 1)
· (u
24
+ 9u
23
+ ··· + 376u + 229)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
4
)(y
13
+ 11y
12
+ ··· − 10y −1)
· (y
21
+ 12y
20
+ ··· + 9072y −256)
c
2
, c
6
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
4
)(y
13
− 5y
12
+ ··· + 6y −1)
· (y
21
− 8y
20
+ ··· + 188y −16)
c
3
(y
13
− 6y
12
+ ··· + 39y −9)(y
21
− 36y
20
+ ··· + 47y −1)
· (y
24
− 33y
23
+ ··· − 52280y + 1849)
c
4
, c
5
, c
9
c
10
(y
13
+ 16y
12
+ ··· + 7y −1)(y
21
+ 26y
20
+ ··· − y −1)
· (y
24
+ 27y
23
+ ··· + 36576y + 1849)
c
8
, c
11
((y
2
+ y + 1)
12
)(y
13
− 7y
12
+ ··· − 3y −1)
· (y
21
− 6y
20
+ ··· − 7168y −4096)
c
12
(y
13
+ 3y
12
+ ··· + 7y −1)(y
21
+ 33y
20
+ ··· + 43y −1)
· (y
24
+ 27y
23
+ ··· + 65640y + 52441)
20
