12n
0383
(K12n
0383
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 12 5 1 5 9 7 9
Solving Sequence
2,6
3 1
5,9
10 4 8 7 12 11
c
2
c
1
c
5
c
9
c
4
c
8
c
7
c
12
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4u
23
+ 14u
22
+ ··· + b + 7, −5u
24
+ 13u
23
+ ··· + 2a + 6, u
25
− 5u
24
+ ··· + 4u − 2i
I
u
2
= hu
15
− 5u
13
− 3u
12
+ 11u
11
+ 10u
10
− 11u
9
− 18u
8
+ 3u
7
+ 17u
6
+ 8u
5
− 9u
4
− 10u
3
− 2u
2
+ b + 5u + 3,
u
15
− 6u
13
− 4u
12
+ 13u
11
+ 14u
10
− 12u
9
− 24u
8
− u
7
+ 22u
6
+ 14u
5
− 10u
4
− 16u
3
− 3u
2
+ 2a + 6u + 5,
u
16
+ 2u
15
+ ··· + 3u + 2i
I
u
3
= h−u
7
a − 2u
7
+ u
5
a − u
6
+ u
4
a + 2u
5
− 2u
3
a + 2u
4
− u
2
a − 3u
3
− u
2
+ b + a + u + 3,
− 2u
7
a − u
6
a − 3u
7
+ 2u
5
a − 2u
6
+ 3u
4
a + 4u
5
− 2u
3
a + 5u
4
− 2u
2
a − 5u
3
+ a
2
− 5u
2
+ 3a + 3u + 6,
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 57 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−4u
23
+14u
22
+· · ·+b+7, −5u
24
+13u
23
+· · ·+2a+6, u
25
−5u
24
+· · ·+4u−2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
9
=
5
2
u
24
−
13
2
u
23
+ ··· −
7
2
u − 3
4u
23
− 14u
22
+ ··· + 3u − 7
a
10
=
7
2
u
24
−
23
2
u
23
+ ··· −
13
2
u + 1
u
24
− u
23
+ ··· + 5u
2
− 3
a
4
=
−
5
2
u
24
+
21
2
u
23
+ ··· +
13
2
u − 3
−2u
24
+ 10u
23
+ ··· + 7u − 5
a
8
=
3
2
u
24
−
17
2
u
23
+ ··· −
13
2
u + 6
−6u
24
+ 24u
23
+ ··· + 13u − 7
a
7
=
5
2
u
24
−
11
2
u
23
+ ··· −
3
2
u − 4
−5u
24
+ 27u
23
+ ··· + 18u − 17
a
12
=
−
3
2
u
24
+
7
2
u
23
+ ··· +
1
2
u + 3
−2u
24
+ 5u
23
+ ··· + 2u + 1
a
11
=
−3u
24
+ 6u
23
+ ··· + 2u + 6
2u
24
− 16u
23
+ ··· − 11u + 14
(ii) Obstruction class = −1
(iii) Cusp Shapes = −15u
24
+ 60u
23
− 42u
22
− 200u
21
+ 425u
20
+ 33u
19
− 1003u
18
+
891u
17
+ 934u
16
−2122u
15
+ 393u
14
+ 2207u
13
−1874u
12
−878u
11
+ 2018u
10
−425u
9
−
1106u
8
+ 819u
7
+ 40u
6
− 235u
5
+ 74u
4
− 34u
3
+ 12u
2
+ 32u − 28
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
+ 11u
24
+ ··· + 12u + 4
c
2
, c
5
u
25
+ 5u
24
+ ··· + 4u + 2
c
3
, c
4
, c
9
u
25
+ 19u
23
+ ··· + u + 1
c
6
, c
11
u
25
− 18u
24
+ ··· − 1792u + 256
c
7
u
25
− u
24
+ ··· + 3881u + 1993
c
8
, c
12
u
25
+ u
24
+ ··· + 18u + 1
c
10
u
25
− 38u
24
+ ··· − 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
+ 9y
24
+ ··· + 232y −16
c
2
, c
5
y
25
− 11y
24
+ ··· + 12y −4
c
3
, c
4
, c
9
y
25
+ 38y
24
+ ··· − 7y −1
c
6
, c
11
y
25
+ 8y
24
+ ··· + 393216y −65536
c
7
y
25
+ 59y
24
+ ··· + 49162391y −3972049
c
8
, c
12
y
25
+ 33y
24
+ ··· + 88y −1
c
10
y
25
− 122y
24
+ ··· + 73y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.825841 + 0.556794I
a = −0.402690 − 0.517828I
b = −0.906052 − 0.019110I
1.50077 + 2.23684I −2.22810 − 4.30531I
u = −0.825841 − 0.556794I
a = −0.402690 + 0.517828I
b = −0.906052 + 0.019110I
1.50077 − 2.23684I −2.22810 + 4.30531I
u = 0.816024 + 0.629187I
a = 0.710669 + 1.151560I
b = 1.101890 + 0.658711I
1.87514 + 0.07553I −5.11439 + 0.60620I
u = 0.816024 − 0.629187I
a = 0.710669 − 1.151560I
b = 1.101890 − 0.658711I
1.87514 − 0.07553I −5.11439 − 0.60620I
u = 0.479269 + 0.953467I
a = 1.46509 + 0.67711I
b = −0.248526 + 0.073771I
16.3921 − 2.3241I −0.96077 + 1.78819I
u = 0.479269 − 0.953467I
a = 1.46509 − 0.67711I
b = −0.248526 − 0.073771I
16.3921 + 2.3241I −0.96077 − 1.78819I
u = 0.533110 + 0.937237I
a = −1.23338 − 1.32849I
b = 0.216650 − 0.151554I
16.7595 + 7.3794I −1.22017 − 2.27864I
u = 0.533110 − 0.937237I
a = −1.23338 + 1.32849I
b = 0.216650 + 0.151554I
16.7595 − 7.3794I −1.22017 + 2.27864I
u = 0.884641 + 0.632548I
a = −1.15580 − 0.83468I
b = −1.61829 − 0.44614I
1.66131 − 5.01873I −5.13335 + 4.42111I
u = 0.884641 − 0.632548I
a = −1.15580 + 0.83468I
b = −1.61829 + 0.44614I
1.66131 + 5.01873I −5.13335 − 4.42111I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.130790 + 0.397647I
a = −0.250090 + 0.145886I
b = −0.517131 + 0.760870I
−3.90858 − 2.14605I −13.03933 − 1.76915I
u = 1.130790 − 0.397647I
a = −0.250090 − 0.145886I
b = −0.517131 − 0.760870I
−3.90858 + 2.14605I −13.03933 + 1.76915I
u = −1.106540 + 0.514773I
a = 0.501024 + 0.175726I
b = 0.976709 − 0.360023I
−3.10459 + 5.50284I −10.38958 − 5.97916I
u = −1.106540 − 0.514773I
a = 0.501024 − 0.175726I
b = 0.976709 + 0.360023I
−3.10459 − 5.50284I −10.38958 + 5.97916I
u = 0.751304
a = −0.162564
b = 0.399340
−0.992382 −10.4670
u = −1.287770 + 0.035273I
a = −0.330208 + 1.190730I
b = −0.61690 + 2.67578I
9.80615 + 5.07733I −5.58280 − 2.54938I
u = −1.287770 − 0.035273I
a = −0.330208 − 1.190730I
b = −0.61690 − 2.67578I
9.80615 − 5.07733I −5.58280 + 2.54938I
u = −0.656789 + 0.222334I
a = 0.64095 + 1.30667I
b = 0.991318 + 0.792825I
−0.79508 − 1.66969I −0.88932 + 1.84897I
u = −0.656789 − 0.222334I
a = 0.64095 − 1.30667I
b = 0.991318 − 0.792825I
−0.79508 + 1.66969I −0.88932 − 1.84897I
u = 1.122380 + 0.708240I
a = 1.22419 + 0.85781I
b = 2.25460 + 1.97923I
14.9497 − 13.4134I −3.26715 + 6.49403I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.122380 − 0.708240I
a = 1.22419 − 0.85781I
b = 2.25460 − 1.97923I
14.9497 + 13.4134I −3.26715 − 6.49403I
u = 1.155240 + 0.691095I
a = −0.673625 − 0.975766I
b = −1.24536 − 2.26158I
14.3146 − 3.6962I −2.96996 + 2.38083I
u = 1.155240 − 0.691095I
a = −0.673625 + 0.975766I
b = −1.24536 + 2.26158I
14.3146 + 3.6962I −2.96996 − 2.38083I
u = −0.120160 + 0.530735I
a = −0.414841 + 0.873103I
b = 0.411425 + 0.199437I
−0.69000 − 1.30270I −6.47181 + 4.99859I
u = −0.120160 − 0.530735I
a = −0.414841 − 0.873103I
b = 0.411425 − 0.199437I
−0.69000 + 1.30270I −6.47181 − 4.99859I
7
II.
I
u
2
= hu
15
−5u
13
+· · ·+b+3, u
15
−6u
13
+· · ·+2a+5, u
16
+2u
15
+· · ·+3u+2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
9
=
−
1
2
u
15
+ 3u
13
+ ··· − 3u −
5
2
−u
15
+ 5u
13
+ ··· − 5u − 3
a
10
=
1
2
u
15
+ u
14
+ ··· − u −
1
2
u
14
+ 2u
13
+ ··· − 3u − 1
a
4
=
3
2
u
15
+ 2u
14
+ ··· + 2u +
7
2
−u
15
− u
14
+ ··· − u − 3
a
8
=
1
2
u
15
+ u
14
+ ··· − 2u −
3
2
u
14
+ u
13
+ ··· − 2u − 1
a
7
=
−
3
2
u
15
− u
14
+ ··· − 4u −
7
2
−2u
15
− u
14
+ ··· − 4u − 3
a
12
=
3
2
u
15
+ 2u
14
+ ··· + u +
5
2
2u
15
+ 2u
14
+ ··· + u + 1
a
11
=
3u
15
+ 4u
14
+ ··· + 2u + 5
4u
15
+ 4u
14
+ ··· + 4u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
15
− 4u
14
+ 8u
13
+ 15u
12
− 12u
11
− 29u
10
+ 5u
9
+ 35u
8
+
7u
7
− 27u
6
− 22u
5
+ 10u
4
+ 16u
3
+ 3u
2
− 11u − 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 8u
15
+ ··· − 17u + 4
c
2
u
16
+ 2u
15
+ ··· + 3u + 2
c
3
, c
9
u
16
+ 9u
14
+ ··· − 4u + 1
c
4
u
16
+ 9u
14
+ ··· + 4u + 1
c
5
u
16
− 2u
15
+ ··· − 3u + 2
c
6
u
16
− u
15
+ ··· − u + 1
c
7
u
16
+ u
15
+ ··· − u
2
+ 1
c
8
u
16
+ u
15
+ ··· + u + 1
c
10
u
16
− 18u
15
+ ··· + 4u + 1
c
11
u
16
+ u
15
+ ··· + u + 1
c
12
u
16
− u
15
+ ··· − u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 4y
15
+ ··· − 17y + 16
c
2
, c
5
y
16
− 8y
15
+ ··· − 17y + 4
c
3
, c
4
, c
9
y
16
+ 18y
15
+ ··· − 4y + 1
c
6
, c
11
y
16
+ 9y
15
+ ··· + 5y + 1
c
7
y
16
+ 15y
15
+ ··· − 2y + 1
c
8
, c
12
y
16
+ 5y
15
+ ··· + 9y + 1
c
10
y
16
− 38y
15
+ ··· − 60y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.656997 + 0.743635I
a = −0.775458 + 1.141130I
b = −0.435041 + 0.316889I
3.25303 − 1.48953I −2.71099 + 1.52251I
u = −0.656997 − 0.743635I
a = −0.775458 − 1.141130I
b = −0.435041 − 0.316889I
3.25303 + 1.48953I −2.71099 − 1.52251I
u = −0.874191 + 0.334550I
a = −0.878721 − 0.189370I
b = −0.20139 − 1.91357I
5.81030 + 1.43838I −3.56257 − 4.86268I
u = −0.874191 − 0.334550I
a = −0.878721 + 0.189370I
b = −0.20139 + 1.91357I
5.81030 − 1.43838I −3.56257 + 4.86268I
u = 0.864296 + 0.625602I
a = 0.975538 − 0.892188I
b = 1.96131 + 0.43343I
7.59435 − 2.44938I −5.19072 + 2.76813I
u = 0.864296 − 0.625602I
a = 0.975538 + 0.892188I
b = 1.96131 − 0.43343I
7.59435 + 2.44938I −5.19072 − 2.76813I
u = 0.901146 + 0.140958I
a = −0.503170 + 1.005270I
b = −0.93293 + 1.12841I
−1.44134 + 1.66902I −13.69558 − 2.63152I
u = 0.901146 − 0.140958I
a = −0.503170 − 1.005270I
b = −0.93293 − 1.12841I
−1.44134 − 1.66902I −13.69558 + 2.63152I
u = −0.218755 + 0.798974I
a = 0.953181 − 0.233826I
b = −0.138155 + 0.327234I
0.924346 − 0.806526I −1.176197 + 0.589571I
u = −0.218755 − 0.798974I
a = 0.953181 + 0.233826I
b = −0.138155 − 0.327234I
0.924346 + 0.806526I −1.176197 − 0.589571I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002050 + 0.665576I
a = 1.051270 − 0.691243I
b = 1.76255 − 0.90512I
2.21180 + 6.86626I −5.48184 − 7.08918I
u = −1.002050 − 0.665576I
a = 1.051270 + 0.691243I
b = 1.76255 + 0.90512I
2.21180 − 6.86626I −5.48184 + 7.08918I
u = 1.165520 + 0.342736I
a = −0.333649 − 0.493333I
b = −0.168076 − 1.173650I
−3.25196 − 2.70217I −4.91112 + 4.04086I
u = 1.165520 − 0.342736I
a = −0.333649 + 0.493333I
b = −0.168076 + 1.173650I
−3.25196 + 2.70217I −4.91112 − 4.04086I
u = −1.178970 + 0.529446I
a = −0.238992 + 0.463717I
b = −0.84826 + 1.13723I
−1.94104 + 5.74574I −3.77099 − 5.59852I
u = −1.178970 − 0.529446I
a = −0.238992 − 0.463717I
b = −0.84826 − 1.13723I
−1.94104 − 5.74574I −3.77099 + 5.59852I
12
III. I
u
3
= h−u
7
a − 2u
7
+ · · · + a + 3, −2u
7
a − 3u
7
+ · · · + 3a + 6, u
8
+ u
7
−
u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
9
=
a
u
7
a + 2u
7
+ ··· − a − 3
a
10
=
−u
7
a − u
7
+ u
5
a − u
6
+ u
5
− 2u
3
a + 2u
4
− u
3
+ au − u
2
+ 2a + 1
u
7
− u
4
a − u
5
+ u
2
a + 2u
3
+ au − u − 2
a
4
=
−u
7
a − 4u
7
+ ··· + 2a + 7
−u
7
a + u
5
a + u
6
+ u
4
a + 2u
5
− 2u
3
a − 3u
3
− u
2
+ a + u + 1
a
8
=
−u
6
− u
3
a + u
4
+ u
3
+ au + a − 1
u
7
a + 2u
7
− 2u
5
a − u
4
a − 2u
5
+ 2u
3
a + u
2
a + 4u
3
− a − 2u − 3
a
7
=
u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ 2u
2
− 2
u
7
a + 3u
7
+ ··· − 2a − 4
a
12
=
u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ 2u
2
− 2
u
7
a + 3u
7
+ ··· − 2a − 4
a
11
=
2u
7
+ 2u
6
− 2u
5
− 4u
4
+ 2u
3
+ 4u
2
− 4
2u
7
a + 6u
7
+ ··· − 4a − 8
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
7
− 8u
5
− 4u
4
+ 8u
3
+ 4u
2
− 4u − 6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
2
c
2
, c
5
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
2
c
3
, c
4
, c
9
u
16
+ u
15
+ ··· + 344u + 313
c
6
, c
11
(u + 1)
16
c
7
u
16
− u
15
+ ··· − 400u + 617
c
8
, c
12
u
16
− 9u
15
+ ··· + 62u + 23
c
10
u
16
− 27u
15
+ ··· − 600312u + 97969
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
2
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
2
c
3
, c
4
, c
9
y
16
+ 27y
15
+ ··· + 600312y + 97969
c
6
, c
11
(y −1)
16
c
7
y
16
+ 39y
15
+ ··· + 950600y + 380689
c
8
, c
12
y
16
+ 7y
15
+ ··· + 3424y + 529
c
10
y
16
− 53y
15
+ ··· − 13866765616y + 9597924961
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570868 + 0.730671I
a = 0.748660 − 1.136300I
b = 0.218417 + 0.534766I
5.53908 − 1.13123I 0.584775 + 0.510791I
u = −0.570868 + 0.730671I
a = −1.73857 + 0.97979I
b = −0.653022 + 0.489982I
5.53908 − 1.13123I 0.584775 + 0.510791I
u = −0.570868 − 0.730671I
a = 0.748660 + 1.136300I
b = 0.218417 − 0.534766I
5.53908 + 1.13123I 0.584775 − 0.510791I
u = −0.570868 − 0.730671I
a = −1.73857 − 0.97979I
b = −0.653022 − 0.489982I
5.53908 + 1.13123I 0.584775 − 0.510791I
u = 0.855237 + 0.665892I
a = −0.019462 + 0.209322I
b = −1.39721 − 1.40003I
8.73915 − 2.57849I 3.72292 + 3.56796I
u = 0.855237 + 0.665892I
a = 1.78204 − 1.77063I
b = 2.65743 − 0.64416I
8.73915 − 2.57849I 3.72292 + 3.56796I
u = 0.855237 − 0.665892I
a = −0.019462 − 0.209322I
b = −1.39721 + 1.40003I
8.73915 + 2.57849I 3.72292 − 3.56796I
u = 0.855237 − 0.665892I
a = 1.78204 + 1.77063I
b = 2.65743 + 0.64416I
8.73915 + 2.57849I 3.72292 − 3.56796I
u = 1.09818
a = 0.054797 + 1.006860I
b = 0.67901 + 1.74126I
0.0770056 −5.86400
u = 1.09818
a = 0.054797 − 1.006860I
b = 0.67901 − 1.74126I
0.0770056 −5.86400
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031810 + 0.655470I
a = −0.842370 + 0.591433I
b = −2.18592 + 0.93071I
4.20006 + 6.44354I −1.42845 − 5.29417I
u = −1.031810 + 0.655470I
a = 0.99429 − 1.31993I
b = 1.27643 − 2.02437I
4.20006 + 6.44354I −1.42845 − 5.29417I
u = −1.031810 − 0.655470I
a = −0.842370 − 0.591433I
b = −2.18592 − 0.93071I
4.20006 − 6.44354I −1.42845 + 5.29417I
u = −1.031810 − 0.655470I
a = 0.99429 + 1.31993I
b = 1.27643 + 2.02437I
4.20006 − 6.44354I −1.42845 + 5.29417I
u = −0.603304
a = −1.47939 + 1.27008I
b = −1.09513 − 1.46928I
5.73470 −3.89450
u = −0.603304
a = −1.47939 − 1.27008I
b = −1.09513 + 1.46928I
5.73470 −3.89450
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
2
· (u
16
− 8u
15
+ ··· − 17u + 4)(u
25
+ 11u
24
+ ··· + 12u + 4)
c
2
((u
8
− u
7
+ ··· + 2u − 1)
2
)(u
16
+ 2u
15
+ ··· + 3u + 2)
· (u
25
+ 5u
24
+ ··· + 4u + 2)
c
3
, c
9
(u
16
+ 9u
14
+ ··· − 4u + 1)(u
16
+ u
15
+ ··· + 344u + 313)
· (u
25
+ 19u
23
+ ··· + u + 1)
c
4
(u
16
+ 9u
14
+ ··· + 4u + 1)(u
16
+ u
15
+ ··· + 344u + 313)
· (u
25
+ 19u
23
+ ··· + u + 1)
c
5
((u
8
− u
7
+ ··· + 2u − 1)
2
)(u
16
− 2u
15
+ ··· − 3u + 2)
· (u
25
+ 5u
24
+ ··· + 4u + 2)
c
6
((u + 1)
16
)(u
16
− u
15
+ ··· − u + 1)(u
25
− 18u
24
+ ··· − 1792u + 256)
c
7
(u
16
− u
15
+ ··· − 400u + 617)(u
16
+ u
15
+ ··· − u
2
+ 1)
· (u
25
− u
24
+ ··· + 3881u + 1993)
c
8
(u
16
− 9u
15
+ ··· + 62u + 23)(u
16
+ u
15
+ ··· + u + 1)
· (u
25
+ u
24
+ ··· + 18u + 1)
c
10
(u
16
− 27u
15
+ ··· − 600312u + 97969)(u
16
− 18u
15
+ ··· + 4u + 1)
· (u
25
− 38u
24
+ ··· − 7u + 1)
c
11
((u + 1)
16
)(u
16
+ u
15
+ ··· + u + 1)(u
25
− 18u
24
+ ··· − 1792u + 256)
c
12
(u
16
− 9u
15
+ ··· + 62u + 23)(u
16
− u
15
+ ··· − u + 1)
· (u
25
+ u
24
+ ··· + 18u + 1)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
2
· (y
16
+ 4y
15
+ ··· − 17y + 16)(y
25
+ 9y
24
+ ··· + 232y −16)
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
2
· (y
16
− 8y
15
+ ··· − 17y + 4)(y
25
− 11y
24
+ ··· + 12y −4)
c
3
, c
4
, c
9
(y
16
+ 18y
15
+ ··· − 4y + 1)(y
16
+ 27y
15
+ ··· + 600312y + 97969)
· (y
25
+ 38y
24
+ ··· − 7y −1)
c
6
, c
11
((y −1)
16
)(y
16
+ 9y
15
+ ··· + 5y + 1)
· (y
25
+ 8y
24
+ ··· + 393216y −65536)
c
7
(y
16
+ 15y
15
+ ··· − 2y + 1)(y
16
+ 39y
15
+ ··· + 950600y + 380689)
· (y
25
+ 59y
24
+ ··· + 49162391y −3972049)
c
8
, c
12
(y
16
+ 5y
15
+ ··· + 9y + 1)(y
16
+ 7y
15
+ ··· + 3424y + 529)
· (y
25
+ 33y
24
+ ··· + 88y −1)
c
10
(y
16
− 53y
15
+ ··· − 13866765616y + 9597924961)
· (y
16
− 38y
15
+ ··· − 60y + 1)(y
25
− 122y
24
+ ··· + 73y −1)
19
