12n
0610
(K12n
0610
)
A knot diagram
1
Linearized knot diagam
3 7 9 7 10 2 11 12 3 5 8 4
Solving Sequence
8,12 4,9
1 3 11 7 5 2 6 10
c
8
c
12
c
3
c
11
c
7
c
4
c
2
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h31u
18
+ 105u
17
+ ··· + 2b + 78, −23u
18
− 77u
17
+ ··· + 4a − 56, u
19
+ 5u
18
+ ··· − 2u + 4i
I
u
2
= h−u
10
− u
9
+ 5u
8
+ 5u
7
− 7u
6
− 7u
5
+ 2u
4
+ 2u
3
− 2u
2
+ b − 2u + 1,
2u
10
− 13u
8
− u
7
+ 29u
6
+ 6u
5
− 25u
4
− 11u
3
+ 9u
2
+ a + 6u − 5,
u
11
− 7u
9
− u
8
+ 17u
7
+ 6u
6
− 16u
5
− 11u
4
+ 5u
3
+ 6u
2
− 2u − 1i
I
u
3
= h22u
5
a
3
− 7u
5
a
2
+ ··· + 11a
3
− 12a
2
, 2u
5
a
3
− 2u
5
a
2
+ ··· − 9a + 31, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 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
= h31u
18
+ 105u
17
+ · · · + 2b + 78, −23u
18
− 77u
17
+ · · · + 4a −
56, u
19
+ 5u
18
+ · · · − 2u + 4i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
23
4
u
18
+
77
4
u
17
+ ··· −
73
4
u + 14
−
31
2
u
18
−
105
2
u
17
+ ··· +
89
2
u − 39
a
9
=
1
−u
2
a
1
=
−
5
2
u
18
− 8u
17
+ ··· + 7u −
11
2
11
2
u
18
+
35
2
u
17
+ ··· −
23
2
u + 12
a
3
=
21
4
u
18
+
71
4
u
17
+ ··· −
63
4
u + 13
−
27
2
u
18
−
93
2
u
17
+ ··· +
81
2
u − 35
a
11
=
−u
u
a
7
=
−u
2
+ 1
u
2
a
5
=
−
35
4
u
18
−
121
4
u
17
+ ··· +
97
4
u − 23
17
2
u
18
+
59
2
u
17
+ ··· −
47
2
u + 21
a
2
=
7
4
u
18
+
17
4
u
17
+ ··· −
9
4
u
2
+
11
4
u
−
9
2
u
18
−
25
2
u
17
+ ··· +
9
2
u − 7
a
6
=
17
2
u
18
+ 28u
17
+ ··· − 18u +
39
2
−
19
2
u
18
−
61
2
u
17
+ ··· +
39
2
u − 20
a
10
=
2u
18
+
15
2
u
17
+ ··· −
15
2
u +
13
2
−
5
2
u
18
−
19
2
u
17
+ ··· +
21
2
u − 8
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
18
+ 13u
17
−4u
16
−78u
15
−41u
14
+ 166u
13
+ 76u
12
−219u
11
+
32u
10
+ 271u
9
− 88u
8
− 117u
7
+ 158u
6
+ 35u
5
− 79u
4
+ 21u
3
+ 27u
2
− 14u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 14u
18
+ ··· + 5120u + 4096
c
2
, c
6
u
19
− 12u
18
+ ··· − 288u + 64
c
3
, c
5
, c
9
c
10
u
19
+ u
17
+ ··· − u − 1
c
4
, c
12
u
19
+ 4u
18
+ ··· − 5u + 1
c
7
, c
8
, c
11
u
19
− 5u
18
+ ··· − 2u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 30y
18
+ ··· − 175112192y −16777216
c
2
, c
6
y
19
− 14y
18
+ ··· + 5120y −4096
c
3
, c
5
, c
9
c
10
y
19
+ 2y
18
+ ··· − 5y −1
c
4
, c
12
y
19
+ 6y
18
+ ··· + 7y −1
c
7
, c
8
, c
11
y
19
− 21y
18
+ ··· − 20y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.657865 + 0.659754I
a = −1.83847 − 0.19703I
b = 0.840313 + 0.475404I
−6.26672 + 9.86714I −1.83864 − 7.22747I
u = 0.657865 − 0.659754I
a = −1.83847 + 0.19703I
b = 0.840313 − 0.475404I
−6.26672 − 9.86714I −1.83864 + 7.22747I
u = −0.731989 + 0.424524I
a = −0.236670 + 0.017802I
b = 0.014997 + 0.399746I
1.25043 − 1.39622I 3.01531 + 0.47414I
u = −0.731989 − 0.424524I
a = −0.236670 − 0.017802I
b = 0.014997 − 0.399746I
1.25043 + 1.39622I 3.01531 − 0.47414I
u = 0.343340 + 0.751449I
a = 0.82615 + 1.26298I
b = 0.042850 − 0.808910I
−7.21208 − 5.16693I −3.65094 + 2.70430I
u = 0.343340 − 0.751449I
a = 0.82615 − 1.26298I
b = 0.042850 + 0.808910I
−7.21208 + 5.16693I −3.65094 − 2.70430I
u = 0.681999 + 0.462895I
a = 1.52804 + 0.77389I
b = −0.565827 − 0.578592I
0.46687 + 4.27090I −1.13834 − 9.12104I
u = 0.681999 − 0.462895I
a = 1.52804 − 0.77389I
b = −0.565827 + 0.578592I
0.46687 − 4.27090I −1.13834 + 9.12104I
u = −1.354910 + 0.296926I
a = 0.145523 + 0.433113I
b = 0.213860 − 1.352780I
−1.85132 + 1.41251I −0.36067 − 3.57890I
u = −1.354910 − 0.296926I
a = 0.145523 − 0.433113I
b = 0.213860 + 1.352780I
−1.85132 − 1.41251I −0.36067 + 3.57890I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47733
a = 0.890647
b = −2.75655
4.17390 −0.157280
u = 0.186583 + 0.488198I
a = −1.295720 − 0.446937I
b = 0.229294 + 0.509039I
−0.957477 − 0.926186I −5.31698 + 3.03988I
u = 0.186583 − 0.488198I
a = −1.295720 + 0.446937I
b = 0.229294 − 0.509039I
−0.957477 + 0.926186I −5.31698 − 3.03988I
u = −1.58692 + 0.20962I
a = 1.074740 − 0.808456I
b = −3.13504 + 1.45007I
1.21163 − 13.10440I 1.22567 + 6.39706I
u = −1.58692 − 0.20962I
a = 1.074740 + 0.808456I
b = −3.13504 − 1.45007I
1.21163 + 13.10440I 1.22567 − 6.39706I
u = −1.60002 + 0.13490I
a = −0.946803 + 0.879127I
b = 2.76241 − 1.93610I
8.22021 − 6.49398I 0.71170 + 7.53180I
u = −1.60002 − 0.13490I
a = −0.946803 − 0.879127I
b = 2.76241 + 1.93610I
8.22021 + 6.49398I 0.71170 − 7.53180I
u = 1.64272 + 0.08524I
a = 0.047885 + 0.426520I
b = −0.024584 − 0.265877I
9.63124 + 3.23773I 4.43153 − 1.86824I
u = 1.64272 − 0.08524I
a = 0.047885 − 0.426520I
b = −0.024584 + 0.265877I
9.63124 − 3.23773I 4.43153 + 1.86824I
6
II.
I
u
2
= h−u
10
−u
9
+· · · +b+1, 2u
10
−13u
8
+· · · +a−5, u
11
−7u
9
+· · · −2u−1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
−2u
10
+ 13u
8
+ u
7
− 29u
6
− 6u
5
+ 25u
4
+ 11u
3
− 9u
2
− 6u + 5
u
10
+ u
9
− 5u
8
− 5u
7
+ 7u
6
+ 7u
5
− 2u
4
− 2u
3
+ 2u
2
+ 2u − 1
a
9
=
1
−u
2
a
1
=
3u
10
− 20u
8
− u
7
+ 46u
6
+ 8u
5
− 42u
4
− 18u
3
+ 18u
2
+ 12u − 9
−2u
10
− 2u
9
+ 11u
8
+ 11u
7
− 18u
6
− 20u
5
+ 6u
4
+ 13u
3
− 5u + 1
a
3
=
−2u
10
+ 13u
8
+ 2u
7
− 29u
6
− 10u
5
+ 24u
4
+ 15u
3
− 6u
2
− 6u + 4
u
10
− 5u
8
− u
7
+ 8u
6
+ 3u
5
− 5u
4
− 2u
3
+ 3u
2
+ 2u − 1
a
11
=
−u
u
a
7
=
−u
2
+ 1
u
2
a
5
=
−u
10
+ u
9
+ 7u
8
− 4u
7
− 18u
6
+ 2u
5
+ 19u
4
+ 6u
3
− 7u
2
− 3u + 4
−u
9
+ 5u
7
+ 2u
6
− 8u
5
− 7u
4
+ 4u
3
+ 6u
2
− 2
a
2
=
−u
10
+ 7u
8
+ u
7
− 17u
6
− 5u
5
+ 15u
4
+ 8u
3
− 3u
2
− 3u + 3
u
6
− u
5
− 3u
4
+ u
3
+ 2u
2
+ 2u − 1
a
6
=
−u
10
+ u
9
+ 8u
8
− 5u
7
− 23u
6
+ 5u
5
+ 28u
4
+ 6u
3
− 14u
2
− 7u + 6
−u
8
+ 5u
6
+ u
5
− 7u
4
− 3u
3
+ 2u
2
+ 2u − 2
a
10
=
u
10
− u
9
− 6u
8
+ 5u
7
+ 13u
6
− 7u
5
− 14u
4
+ 2u
3
+ 10u
2
− 4
−u
10
+ u
9
+ 6u
8
− 4u
7
− 13u
6
+ 2u
5
+ 13u
4
+ 5u
3
− 6u
2
− 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 5u
10
− 2u
9
− 38u
8
+ 6u
7
+ 97u
6
+ 11u
5
− 90u
4
− 43u
3
+ 21u
2
+ 19u − 10
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 11u
10
+ ··· + 7u − 1
c
2
u
11
− 3u
10
− u
9
+ 8u
8
− 11u
6
+ 5u
5
+ 6u
4
− 7u
3
− u
2
+ 3u − 1
c
3
, c
10
u
11
+ 4u
9
+ u
8
+ 4u
7
+ 3u
6
− u
5
+ 2u
4
− 2u
3
− u
2
− u − 1
c
4
, c
12
u
11
− 6u
9
− 9u
8
+ 2u
7
+ 21u
6
+ 35u
5
+ 22u
4
− 8u
3
− 19u
2
− 11u − 3
c
5
, c
9
u
11
+ 4u
9
− u
8
+ 4u
7
− 3u
6
− u
5
− 2u
4
− 2u
3
+ u
2
− u + 1
c
6
u
11
+ 3u
10
− u
9
− 8u
8
+ 11u
6
+ 5u
5
− 6u
4
− 7u
3
+ u
2
+ 3u + 1
c
7
, c
8
u
11
− 7u
9
− u
8
+ 17u
7
+ 6u
6
− 16u
5
− 11u
4
+ 5u
3
+ 6u
2
− 2u − 1
c
11
u
11
− 7u
9
+ u
8
+ 17u
7
− 6u
6
− 16u
5
+ 11u
4
+ 5u
3
− 6u
2
− 2u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− 23y
10
+ ··· − 13y −1
c
2
, c
6
y
11
− 11y
10
+ ··· + 7y −1
c
3
, c
5
, c
9
c
10
y
11
+ 8y
10
+ 24y
9
+ 29y
8
− 2y
7
− 39y
6
− 33y
5
+ 16y
3
+ 7y
2
− y −1
c
4
, c
12
y
11
− 12y
10
+ ··· + 7y −9
c
7
, c
8
, c
11
y
11
− 14y
10
+ ··· + 16y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.579371 + 0.652000I
a = −0.842460 − 0.562659I
b = 0.512370 + 0.070135I
1.84599 − 2.26752I 7.70963 + 6.53422I
u = −0.579371 − 0.652000I
a = −0.842460 + 0.562659I
b = 0.512370 − 0.070135I
1.84599 + 2.26752I 7.70963 − 6.53422I
u = −1.17071
a = 0.718847
b = −0.387689
−0.926107 2.28510
u = 0.548197 + 0.267302I
a = 0.773035 + 0.456348I
b = 0.051698 + 1.041650I
4.46954 + 0.96297I 1.50871 − 7.32884I
u = 0.548197 − 0.267302I
a = 0.773035 − 0.456348I
b = 0.051698 − 1.041650I
4.46954 − 0.96297I 1.50871 + 7.32884I
u = 1.52989
a = −1.75406
b = 5.06427
2.74678 −6.18970
u = −1.57622 + 0.07505I
a = −0.197276 + 0.748318I
b = 0.112310 − 0.460322I
11.80780 − 2.19766I 5.16669 + 2.50465I
u = −1.57622 − 0.07505I
a = −0.197276 − 0.748318I
b = 0.112310 + 0.460322I
11.80780 + 2.19766I 5.16669 − 2.50465I
u = 1.58380 + 0.17649I
a = 0.839023 + 0.333910I
b = −2.31428 − 0.45989I
9.15447 + 5.23820I 6.25661 − 4.80987I
u = 1.58380 − 0.17649I
a = 0.839023 − 0.333910I
b = −2.31428 + 0.45989I
9.15447 − 5.23820I 6.25661 + 4.80987I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.311994
a = 5.89057
b = −1.40079
−3.73847 −13.3790
11
III. I
u
3
= h22u
5
a
3
− 7u
5
a
2
+ · · · + 11a
3
− 12a
2
, 2u
5
a
3
− 2u
5
a
2
+ · · · − 9a +
31, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
a
−0.511628a
3
u
5
+ 0.162791a
2
u
5
+ ··· − 0.255814a
3
+ 0.279070a
2
a
9
=
1
−u
2
a
1
=
a
2
u
0.325581a
3
u
5
+ 0.837209a
2
u
5
+ ··· + 0.279070a − 1.53488
a
3
=
−0.511628a
3
u
5
+ 0.162791a
2
u
5
+ ··· + 0.279070a
2
+ a
0.674419a
3
u
5
− 0.465116a
2
u
5
+ ··· − 0.604651a + 0.325581
a
11
=
−u
u
a
7
=
−u
2
+ 1
u
2
a
5
=
−0.604651a
3
u
5
+ a
2
u
5
+ ··· − 0.0930233a − 0.488372
0.767442a
3
u
5
− 1.30233a
2
u
5
+ ··· + 0.488372a + 0.813953
a
2
=
−1.48837a
3
u
5
− 0.0930233a
2
u
5
+ ··· + 0.813953a + 0.0232558
2.23256a
3
u
5
+ 0.162791a
2
u
5
+ ··· − 1.11628a + 0.139535
a
6
=
1.95349a
3
u
5
+ 0.511628a
2
u
5
+ ··· + 0.372093a − 0.0465116
−2.79070a
3
u
5
− 0.418605a
2
u
5
+ ··· + 1.30233a − 1.16279
a
10
=
0.837209a
3
u
5
+ 0.418605a
2
u
5
+ ··· + 0.627907a − 1.95349
−0.720930a
3
u
5
− 0.488372a
2
u
5
+ ··· − 1.11628a + 0.139535
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 8u + 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ 3u + 1)
12
c
2
, c
6
(u
2
+ u − 1)
12
c
3
, c
5
, c
9
c
10
u
24
− u
23
+ ··· + 14u − 1
c
4
, c
12
u
24
+ 7u
23
+ ··· + 146u + 139
c
7
, c
8
, c
11
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 7y + 1)
12
c
2
, c
6
(y
2
− 3y + 1)
12
c
3
, c
5
, c
9
c
10
y
24
+ 7y
23
+ ··· − 92y + 1
c
4
, c
12
y
24
− 9y
23
+ ··· − 45780y + 19321
c
7
, c
8
, c
11
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493180 + 0.575288I
a = 0.657492 + 0.467942I
b = −0.520619 + 0.221185I
0.98760 − 1.97241I −3.42428 + 3.68478I
u = −0.493180 + 0.575288I
a = −1.132730 − 0.592761I
b = 0.463950 + 0.261122I
0.98760 − 1.97241I −3.42428 + 3.68478I
u = −0.493180 + 0.575288I
a = −0.877441 + 1.072190I
b = 0.49508 − 1.34709I
−6.90809 − 1.97241I −3.42428 + 3.68478I
u = −0.493180 + 0.575288I
a = 2.12164 − 0.74540I
b = −0.346720 + 0.084390I
−6.90809 − 1.97241I −3.42428 + 3.68478I
u = −0.493180 − 0.575288I
a = 0.657492 − 0.467942I
b = −0.520619 − 0.221185I
0.98760 + 1.97241I −3.42428 − 3.68478I
u = −0.493180 − 0.575288I
a = −1.132730 + 0.592761I
b = 0.463950 − 0.261122I
0.98760 + 1.97241I −3.42428 − 3.68478I
u = −0.493180 − 0.575288I
a = −0.877441 − 1.072190I
b = 0.49508 + 1.34709I
−6.90809 + 1.97241I −3.42428 − 3.68478I
u = −0.493180 − 0.575288I
a = 2.12164 + 0.74540I
b = −0.346720 − 0.084390I
−6.90809 + 1.97241I −3.42428 − 3.68478I
u = 0.483672
a = 1.38685 + 1.13721I
b = −0.452109 + 1.065290I
4.68669 5.41680
u = 0.483672
a = 1.38685 − 1.13721I
b = −0.452109 − 1.065290I
4.68669 5.41680
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.483672
a = −2.99214
b = 1.78193
−3.20899 5.41680
u = 0.483672
a = −4.26951
b = 0.585345
−3.20899 5.41680
u = 1.52087 + 0.16310I
a = 0.981577 + 0.385534I
b = −2.51558 − 0.17254I
7.64342 + 4.59213I 0.58114 − 3.20482I
u = 1.52087 + 0.16310I
a = −0.720483 + 0.010543I
b = 2.36775 − 0.07374I
7.64342 + 4.59213I 0.58114 − 3.20482I
u = 1.52087 + 0.16310I
a = −0.85700 − 1.31859I
b = 2.04763 + 2.23940I
−0.25226 + 4.59213I 0.58114 − 3.20482I
u = 1.52087 + 0.16310I
a = 0.173447 + 0.281644I
b = −1.66060 − 1.59461I
−0.25226 + 4.59213I 0.58114 − 3.20482I
u = 1.52087 − 0.16310I
a = 0.981577 − 0.385534I
b = −2.51558 + 0.17254I
7.64342 − 4.59213I 0.58114 + 3.20482I
u = 1.52087 − 0.16310I
a = −0.720483 − 0.010543I
b = 2.36775 + 0.07374I
7.64342 − 4.59213I 0.58114 + 3.20482I
u = 1.52087 − 0.16310I
a = −0.85700 + 1.31859I
b = 2.04763 − 2.23940I
−0.25226 − 4.59213I 0.58114 + 3.20482I
u = 1.52087 − 0.16310I
a = 0.173447 − 0.281644I
b = −1.66060 + 1.59461I
−0.25226 − 4.59213I 0.58114 + 3.20482I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53904
a = −0.554670 + 0.861910I
b = 1.58366 − 0.52245I
11.6079 4.26950
u = −1.53904
a = −0.554670 − 0.861910I
b = 1.58366 + 0.52245I
11.6079 4.26950
u = −1.53904
a = 1.11428
b = −3.94128
3.71224 4.26950
u = −1.53904
a = 1.79000
b = −4.35087
3.71224 4.26950
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ 3u + 1)
12
)(u
11
− 11u
10
+ ··· + 7u − 1)
· (u
19
+ 14u
18
+ ··· + 5120u + 4096)
c
2
(u
2
+ u − 1)
12
· (u
11
− 3u
10
− u
9
+ 8u
8
− 11u
6
+ 5u
5
+ 6u
4
− 7u
3
− u
2
+ 3u − 1)
· (u
19
− 12u
18
+ ··· − 288u + 64)
c
3
, c
10
(u
11
+ 4u
9
+ u
8
+ 4u
7
+ 3u
6
− u
5
+ 2u
4
− 2u
3
− u
2
− u − 1)
· (u
19
+ u
17
+ ··· − u − 1)(u
24
− u
23
+ ··· + 14u − 1)
c
4
, c
12
(u
11
− 6u
9
− 9u
8
+ 2u
7
+ 21u
6
+ 35u
5
+ 22u
4
− 8u
3
− 19u
2
− 11u − 3)
· (u
19
+ 4u
18
+ ··· − 5u + 1)(u
24
+ 7u
23
+ ··· + 146u + 139)
c
5
, c
9
(u
11
+ 4u
9
− u
8
+ 4u
7
− 3u
6
− u
5
− 2u
4
− 2u
3
+ u
2
− u + 1)
· (u
19
+ u
17
+ ··· − u − 1)(u
24
− u
23
+ ··· + 14u − 1)
c
6
(u
2
+ u − 1)
12
· (u
11
+ 3u
10
− u
9
− 8u
8
+ 11u
6
+ 5u
5
− 6u
4
− 7u
3
+ u
2
+ 3u + 1)
· (u
19
− 12u
18
+ ··· − 288u + 64)
c
7
, c
8
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
· (u
11
− 7u
9
− u
8
+ 17u
7
+ 6u
6
− 16u
5
− 11u
4
+ 5u
3
+ 6u
2
− 2u − 1)
· (u
19
− 5u
18
+ ··· − 2u − 4)
c
11
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
· (u
11
− 7u
9
+ u
8
+ 17u
7
− 6u
6
− 16u
5
+ 11u
4
+ 5u
3
− 6u
2
− 2u + 1)
· (u
19
− 5u
18
+ ··· − 2u − 4)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
− 7y + 1)
12
)(y
11
− 23y
10
+ ··· − 13y −1)
· (y
19
− 30y
18
+ ··· − 175112192y −16777216)
c
2
, c
6
((y
2
− 3y + 1)
12
)(y
11
− 11y
10
+ ··· + 7y −1)
· (y
19
− 14y
18
+ ··· + 5120y −4096)
c
3
, c
5
, c
9
c
10
(y
11
+ 8y
10
+ 24y
9
+ 29y
8
− 2y
7
− 39y
6
− 33y
5
+ 16y
3
+ 7y
2
− y −1)
· (y
19
+ 2y
18
+ ··· − 5y −1)(y
24
+ 7y
23
+ ··· − 92y + 1)
c
4
, c
12
(y
11
− 12y
10
+ ··· + 7y −9)(y
19
+ 6y
18
+ ··· + 7y −1)
· (y
24
− 9y
23
+ ··· − 45780y + 19321)
c
7
, c
8
, c
11
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
4
· (y
11
− 14y
10
+ ··· + 16y −1)(y
19
− 21y
18
+ ··· − 20y −16)
19
