12n
0394
(K12n
0394
)
A knot diagram
1
Linearized knot diagam
3 5 10 12 2 10 3 5 4 6 9 8
Solving Sequence
5,12 4,10
3 2 6 1 9 8 7 11
c
4
c
3
c
2
c
5
c
1
c
9
c
8
c
7
c
11
c
6
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
16
+ 50u
15
+ ··· + 23b − 101, −166u
16
− 487u
15
+ ··· + 69a + 216, u
17
+ 4u
16
+ ··· − 6u − 3i
I
u
2
= hu
2
+ b − u − 2, a − 2u + 2, u
3
− 2u
2
+ u + 1i
I
u
3
= hb + 1, −2u
4
a + 2u
4
+ 2u
2
a − u
3
+ a
2
− 2au − 3a + 2u + 3, u
5
− u
4
+ u
2
+ u − 1i
I
u
4
= hb + 1, −2u
4
a + 8u
4
+ 2u
2
a + 3u
3
+ a
2
+ 2au − 2u
2
− 3a − 8u + 11, u
5
+ u
4
− u
2
+ u + 1i
I
u
5
= hb − u − 1, a − u, u
2
− u + 1i
* 5 irreducible components of dim
C
= 0, with total 42 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
= h5u
16
+ 50u
15
+ · · · + 23b − 101, −166u
16
− 487u
15
+ · · · + 69a +
216, u
17
+ 4u
16
+ · · · − 6u − 3i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
10
=
2.40580u
16
+ 7.05797u
15
+ ··· − 7.44928u − 3.13043
−0.217391u
16
− 2.17391u
15
+ ··· + 2.34783u + 4.39130
a
3
=
1.53623u
16
+ 6.36232u
15
+ ··· − 7.05797u − 8.56522
1.39130u
16
+ 4.91304u
15
+ ··· − 5.82609u − 3.30435
a
2
=
0.144928u
16
+ 1.44928u
15
+ ··· − 1.23188u − 5.26087
1.39130u
16
+ 4.91304u
15
+ ··· − 5.82609u − 3.30435
a
6
=
1.89855u
16
+ 6.98551u
15
+ ··· − 9.63768u − 6.21739
0.304348u
16
+ 0.0434783u
15
+ ··· − 0.0869565u + 2.65217
a
1
=
−0.971014u
16
− 2.71014u
15
+ ··· + 2.75362u + 4.34783
0.782609u
16
+ 1.82609u
15
+ ··· − 1.65217u − 0.608696
a
9
=
1.01449u
16
+ 2.14493u
15
+ ··· − 1.62319u + 0.173913
−1.13043u
16
− 3.30435u
15
+ ··· + 2.60870u + 2.43478
a
8
=
−0.115942u
16
− 1.15942u
15
+ ··· + 0.985507u + 2.60870
−1.13043u
16
− 3.30435u
15
+ ··· + 2.60870u + 2.43478
a
7
=
−1.60870u
16
− 5.08696u
15
+ ··· + 9.17391u + 5.69565
1.82609u
16
+ 5.26087u
15
+ ··· − 5.52174u − 5.08696
a
11
=
−2.40580u
16
− 7.05797u
15
+ ··· + 9.44928u + 7.13043
0.652174u
16
+ 2.52174u
15
+ ··· − 3.04348u − 2.17391
(ii) Obstruction class = −1
(iii) Cusp Shapes =
117
23
u
16
+
365
23
u
15
+ ··· −
592
23
u −
459
23
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 16u
16
+ ··· + 10u − 1
c
2
, c
3
, c
5
c
9
u
17
+ 8u
15
+ ··· + 4u + 1
c
4
u
17
+ 4u
16
+ ··· − 6u − 3
c
6
, c
8
, c
10
u
17
+ u
16
+ ··· − 5u + 3
c
7
u
17
− u
16
+ ··· − 32u + 32
c
11
u
17
− 4u
16
+ ··· − 20u + 4
c
12
u
17
− u
16
+ ··· − 8u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 12y
16
+ ··· + 582y −1
c
2
, c
3
, c
5
c
9
y
17
+ 16y
16
+ ··· + 10y −1
c
4
y
17
− 4y
16
+ ··· + 30y −9
c
6
, c
8
, c
10
y
17
+ 9y
16
+ ··· − 77y −9
c
7
y
17
+ 49y
16
+ ··· + 512y −1024
c
11
y
17
+ 28y
15
+ ··· + 192y −16
c
12
y
17
− 13y
16
+ ··· + 16y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.646906 + 0.777899I
a = 0.092542 + 0.678674I
b = −0.777189 + 0.739752I
0.36478 + 1.63051I 1.33246 − 2.97241I
u = −0.646906 − 0.777899I
a = 0.092542 − 0.678674I
b = −0.777189 − 0.739752I
0.36478 − 1.63051I 1.33246 + 2.97241I
u = 0.784984 + 0.477130I
a = −1.94672 − 0.49177I
b = 0.452575 + 0.318517I
−11.20970 − 1.90455I −7.06546 + 3.61390I
u = 0.784984 − 0.477130I
a = −1.94672 + 0.49177I
b = 0.452575 − 0.318517I
−11.20970 + 1.90455I −7.06546 − 3.61390I
u = 0.026724 + 0.844372I
a = 0.015923 + 0.426626I
b = 0.443696 + 0.862498I
0.663995 + 1.197200I 5.46705 − 5.78482I
u = 0.026724 − 0.844372I
a = 0.015923 − 0.426626I
b = 0.443696 − 0.862498I
0.663995 − 1.197200I 5.46705 + 5.78482I
u = −0.773893 + 0.309967I
a = 0.41469 − 3.18002I
b = 1.333190 + 0.341589I
−12.05840 + 1.31476I −5.96182 − 5.42781I
u = −0.773893 − 0.309967I
a = 0.41469 + 3.18002I
b = 1.333190 − 0.341589I
−12.05840 − 1.31476I −5.96182 + 5.42781I
u = −0.843845 + 0.979007I
a = 0.448751 − 0.339775I
b = 1.69118 − 0.70021I
7.61133 − 5.51913I −0.22086 + 1.92858I
u = −0.843845 − 0.979007I
a = 0.448751 + 0.339775I
b = 1.69118 + 0.70021I
7.61133 + 5.51913I −0.22086 − 1.92858I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.657862
a = 2.09899
b = −1.11320
−2.54119 −9.83580
u = −1.029550 + 0.876363I
a = 0.93274 − 1.67101I
b = 1.75470 + 0.71072I
7.0039 + 12.3137I −1.13721 − 6.03542I
u = −1.029550 − 0.876363I
a = 0.93274 + 1.67101I
b = 1.75470 − 0.71072I
7.0039 − 12.3137I −1.13721 + 6.03542I
u = 1.244670 + 0.558531I
a = 0.23880 + 1.74740I
b = 1.68522 − 1.34789I
−3.20455 − 6.53546I −6.86200 + 8.35748I
u = 1.244670 − 0.558531I
a = 0.23880 − 1.74740I
b = 1.68522 + 1.34789I
−3.20455 + 6.53546I −6.86200 − 8.35748I
u = −1.091120 + 0.825988I
a = −0.746214 + 0.856671I
b = −1.026770 − 0.956290I
−1.06020 + 4.55876I −2.13426 − 7.08307I
u = −1.091120 − 0.825988I
a = −0.746214 − 0.856671I
b = −1.026770 + 0.956290I
−1.06020 − 4.55876I −2.13426 + 7.08307I
6
II. I
u
2
= hu
2
+ b − u − 2, a − 2u + 2, u
3
− 2u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
10
=
2u − 2
−u
2
+ u + 2
a
3
=
−1
u
2
− u
a
2
=
−u
2
+ u − 1
u
2
− u
a
6
=
u
2
− 2u + 1
u
a
1
=
−u
2
+ 2u − 1
1
a
9
=
−u
2
+ 3u − 2
−u + 1
a
8
=
−u
2
+ 2u − 1
−u + 1
a
7
=
−u
2
+ 2u − 1
−u + 1
a
11
=
−u
2
+ 4u − 4
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
2
− 6u + 3
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
3
− 2u
2
+ u + 1
c
2
, c
9
u
3
+ u + 1
c
3
, c
5
u
3
+ u − 1
c
6
u
3
− u
2
− 1
c
7
u
3
c
8
, c
10
u
3
+ u
2
+ 1
c
11
u
3
+ 3u
2
+ 4u + 3
c
12
(u + 1)
3
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
3
− 2y
2
+ 5y −1
c
2
, c
3
, c
5
c
9
y
3
+ 2y
2
+ y −1
c
6
, c
8
, c
10
y
3
− y
2
− 2y −1
c
7
y
3
c
11
y
3
− y
2
− 2y −9
c
12
(y −1)
3
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.23279 + 0.79255I
a = 0.46557 + 1.58510I
b = 2.34116 − 1.16154I
−2.26573 − 6.33267I 0.95302 + 6.96925I
u = 1.23279 − 0.79255I
a = 0.46557 − 1.58510I
b = 2.34116 + 1.16154I
−2.26573 + 6.33267I 0.95302 − 6.96925I
u = −0.465571
a = −2.93114
b = 1.31767
−2.04827 7.09400
10
III. I
u
3
= hb + 1, −2u
4
a + 2u
4
+ · · · − 3a + 3, u
5
− u
4
+ u
2
+ u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
10
=
a
−1
a
3
=
−u
4
− u
2
a + a − u
−u
2
a − u
2
+ 1
a
2
=
−u
4
+ u
2
+ a − u − 1
−u
2
a − u
2
+ 1
a
6
=
u
2
a
−u
4
a + u
2
a
1
=
−u
4
− u
3
− u
2
+ a − u
u
4
− u
2
a − u
3
− 3u
2
+ 2
a
9
=
−u
2
a + a + 1
u
4
a − u
2
− 1
a
8
=
u
4
a − u
2
a − u
2
+ a
u
4
a − u
2
− 1
a
7
=
−u
4
+ u
2
+ a − 1
−u
4
− 1
a
11
=
u
4
a + u
2
a + u
3
+ u
2
+ a − 1
−u
4
a − 2u
4
− u
3
+ u
2
+ u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
+ 4u
2
− 4u − 7
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 7u
9
+ ··· + 3u + 1
c
2
, c
3
, c
5
c
9
u
10
+ u
9
− 3u
8
− 2u
7
+ 10u
6
+ 7u
5
− 4u
4
+ u
3
+ 6u
2
+ 3u + 1
c
4
(u
5
− u
4
+ u
2
+ u − 1)
2
c
6
, c
8
, c
10
u
10
+ 3u
9
+ ··· + 102u + 21
c
7
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
2
c
11
u
10
− u
9
+ 8u
8
+ 6u
7
+ 19u
6
+ 54u
5
+ 22u
4
+ 51u
3
+ 47u
2
− 61u + 43
c
12
u
10
+ u
9
+ ··· + 87u + 43
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ 17y
9
+ ··· + 35y + 1
c
2
, c
3
, c
5
c
9
y
10
− 7y
9
+ ··· + 3y + 1
c
4
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
2
c
6
, c
8
, c
10
y
10
+ 21y
9
+ ··· + 852y + 441
c
7
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
2
c
11
y
10
+ 15y
9
+ ··· + 321y + 1849
c
12
y
10
− 25y
9
+ ··· + 3009y + 1849
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.758138 + 0.584034I
a = −0.221420 + 0.189697I
b = −1.00000
0.17487 + 2.21397I −0.11432 − 4.22289I
u = −0.758138 + 0.584034I
a = −0.22142 + 1.92175I
b = −1.00000
0.17487 + 2.21397I −0.11432 − 4.22289I
u = −0.758138 − 0.584034I
a = −0.221420 − 0.189697I
b = −1.00000
0.17487 − 2.21397I −0.11432 + 4.22289I
u = −0.758138 − 0.584034I
a = −0.22142 − 1.92175I
b = −1.00000
0.17487 − 2.21397I −0.11432 + 4.22289I
u = 0.935538 + 0.903908I
a = −0.479684 + 0.275456I
b = −1.00000
9.31336 − 3.33174I 0.91874 + 2.36228I
u = 0.935538 + 0.903908I
a = −0.47968 − 1.45659I
b = −1.00000
9.31336 − 3.33174I 0.91874 + 2.36228I
u = 0.935538 − 0.903908I
a = −0.479684 − 0.275456I
b = −1.00000
9.31336 + 3.33174I 0.91874 − 2.36228I
u = 0.935538 − 0.903908I
a = −0.47968 + 1.45659I
b = −1.00000
9.31336 + 3.33174I 0.91874 − 2.36228I
u = 0.645200
a = 1.90221 + 0.86603I
b = −1.00000
−2.52712 −8.60880
u = 0.645200
a = 1.90221 − 0.86603I
b = −1.00000
−2.52712 −8.60880
14
IV. I
u
4
= hb + 1, −2u
4
a + 8u
4
+ · · · − 3a + 11, u
5
+ u
4
− u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
10
=
a
−1
a
3
=
−3u
4
− u
2
a + 2u
2
+ a + 3u − 4
−u
2
a − u
2
+ 1
a
2
=
−3u
4
+ 3u
2
+ a + 3u − 5
−u
2
a − u
2
+ 1
a
6
=
u
2
a − 2a − 2
−u
4
a + u
2
+ 2
a
1
=
3u
4
+ u
3
− u
2
− a − 3u + 4
u
4
+ u
2
a + u
3
+ u
2
a
9
=
−u
2
a + a + 1
u
4
a − u
2
− 1
a
8
=
u
4
a − u
2
a − u
2
+ a
u
4
a − u
2
− 1
a
7
=
u
4
− u
2
− 3a + 1
u
4
+ 3
a
11
=
−u
4
a − u
2
a − u
3
− u
2
− a + 3
u
4
a + 2u
4
+ u
3
− u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
4
+ 4u
2
+ 4u − 7
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 13u
9
+ ··· − 59u + 9
c
2
, c
9
u
10
− u
9
+ 7u
8
− 6u
7
+ 18u
6
− 13u
5
+ 22u
4
− 13u
3
+ 14u
2
− 5u + 3
c
3
, c
5
u
10
+ u
9
+ 7u
8
+ 6u
7
+ 18u
6
+ 13u
5
+ 22u
4
+ 13u
3
+ 14u
2
+ 5u + 3
c
4
(u
5
+ u
4
− u
2
+ u + 1)
2
c
6
u
10
+ 3u
9
+ u
8
− 2u
7
+ 2u
6
+ 3u
5
− u
4
+ u
3
+ 2u
2
− 2u + 1
c
7
u
10
+ 19u
8
+ 112u
6
+ 161u
4
− 253u
2
+ 203
c
8
, c
10
u
10
− 3u
9
+ u
8
+ 2u
7
+ 2u
6
− 3u
5
− u
4
− u
3
+ 2u
2
+ 2u + 1
c
11
u
10
+ u
9
− 4u
8
+ 2u
7
+ 19u
6
+ 2u
5
− 24u
4
+ 5u
3
+ 41u
2
+ 21u + 7
c
12
u
10
− u
9
+ 4u
8
− u
7
+ 5u
6
− 2u
5
+ u
4
+ u
3
+ 5u
2
− 7u + 3
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
− 23y
9
+ ··· + 83y + 81
c
2
, c
3
, c
5
c
9
y
10
+ 13y
9
+ ··· + 59y + 9
c
4
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
2
c
6
, c
8
, c
10
y
10
− 7y
9
+ 17y
8
− 20y
7
+ 12y
6
+ 9y
5
− 3y
4
+ 11y
3
+ 6y
2
+ 1
c
7
(y
5
+ 19y
4
+ 112y
3
+ 161y
2
− 253y + 203)
2
c
11
y
10
− 9y
9
+ ··· + 133y + 49
c
12
y
10
+ 7y
9
+ ··· − 19y + 9
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758138 + 0.584034I
a = 1.022550 − 0.582879I
b = −1.00000
−9.69473 − 2.21397I −0.11432 + 4.22289I
u = 0.758138 + 0.584034I
a = −1.46539 − 1.52857I
b = −1.00000
−9.69473 − 2.21397I −0.11432 + 4.22289I
u = 0.758138 − 0.584034I
a = 1.022550 + 0.582879I
b = −1.00000
−9.69473 + 2.21397I −0.11432 − 4.22289I
u = 0.758138 − 0.584034I
a = −1.46539 + 1.52857I
b = −1.00000
−9.69473 + 2.21397I −0.11432 − 4.22289I
u = −0.935538 + 0.903908I
a = −0.575673 + 0.840559I
b = −1.00000
−0.55625 + 3.33174I 0.91874 − 2.36228I
u = −0.935538 + 0.903908I
a = −0.383695 + 0.340581I
b = −1.00000
−0.55625 + 3.33174I 0.91874 − 2.36228I
u = −0.935538 − 0.903908I
a = −0.575673 − 0.840559I
b = −1.00000
−0.55625 − 3.33174I 0.91874 + 2.36228I
u = −0.935538 − 0.903908I
a = −0.383695 − 0.340581I
b = −1.00000
−0.55625 − 3.33174I 0.91874 + 2.36228I
u = −0.645200
a = 1.90221 + 3.50588I
b = −1.00000
−12.3967 −8.60880
u = −0.645200
a = 1.90221 − 3.50588I
b = −1.00000
−12.3967 −8.60880
18
V. I
u
5
= hb − u − 1, a − u, u
2
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u + 1
a
10
=
u
u + 1
a
3
=
u
u
a
2
=
0
u
a
6
=
1
−u + 1
a
1
=
−1
u − 1
a
9
=
0
u
a
8
=
u
u
a
7
=
u
u
a
11
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
12
u
2
− u + 1
c
2
, c
8
, c
9
c
10
u
2
+ u + 1
c
7
, c
11
u
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
9
, c
10
c
12
y
2
+ y + 1
c
7
, c
11
y
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 1.50000 + 0.86603I
0 0
u = 0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 1.50000 − 0.86603I
0 0
22
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
3
− 2u
2
+ u + 1)(u
10
− 13u
9
+ ··· − 59u + 9)
· (u
10
− 7u
9
+ ··· + 3u + 1)(u
17
+ 16u
16
+ ··· + 10u − 1)
c
2
, c
9
(u
2
+ u + 1)(u
3
+ u + 1)
· (u
10
− u
9
+ 7u
8
− 6u
7
+ 18u
6
− 13u
5
+ 22u
4
− 13u
3
+ 14u
2
− 5u + 3)
· (u
10
+ u
9
− 3u
8
− 2u
7
+ 10u
6
+ 7u
5
− 4u
4
+ u
3
+ 6u
2
+ 3u + 1)
· (u
17
+ 8u
15
+ ··· + 4u + 1)
c
3
, c
5
(u
2
− u + 1)(u
3
+ u − 1)
· (u
10
+ u
9
− 3u
8
− 2u
7
+ 10u
6
+ 7u
5
− 4u
4
+ u
3
+ 6u
2
+ 3u + 1)
· (u
10
+ u
9
+ 7u
8
+ 6u
7
+ 18u
6
+ 13u
5
+ 22u
4
+ 13u
3
+ 14u
2
+ 5u + 3)
· (u
17
+ 8u
15
+ ··· + 4u + 1)
c
4
(u
2
− u + 1)(u
3
− 2u
2
+ u + 1)(u
5
− u
4
+ u
2
+ u − 1)
2
· ((u
5
+ u
4
− u
2
+ u + 1)
2
)(u
17
+ 4u
16
+ ··· − 6u − 3)
c
6
(u
2
− u + 1)(u
3
− u
2
− 1)
· (u
10
+ 3u
9
+ u
8
− 2u
7
+ 2u
6
+ 3u
5
− u
4
+ u
3
+ 2u
2
− 2u + 1)
· (u
10
+ 3u
9
+ ··· + 102u + 21)(u
17
+ u
16
+ ··· − 5u + 3)
c
7
u
5
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
2
· (u
10
+ 19u
8
+ 112u
6
+ 161u
4
− 253u
2
+ 203)
· (u
17
− u
16
+ ··· − 32u + 32)
c
8
, c
10
(u
2
+ u + 1)(u
3
+ u
2
+ 1)
· (u
10
− 3u
9
+ u
8
+ 2u
7
+ 2u
6
− 3u
5
− u
4
− u
3
+ 2u
2
+ 2u + 1)
· (u
10
+ 3u
9
+ ··· + 102u + 21)(u
17
+ u
16
+ ··· − 5u + 3)
c
11
u
2
(u
3
+ 3u
2
+ 4u + 3)
· (u
10
− u
9
+ 8u
8
+ 6u
7
+ 19u
6
+ 54u
5
+ 22u
4
+ 51u
3
+ 47u
2
− 61u + 43)
· (u
10
+ u
9
− 4u
8
+ 2u
7
+ 19u
6
+ 2u
5
− 24u
4
+ 5u
3
+ 41u
2
+ 21u + 7)
· (u
17
− 4u
16
+ ··· − 20u + 4)
c
12
(u + 1)
3
(u
2
− u + 1)
· (u
10
− u
9
+ 4u
8
− u
7
+ 5u
6
− 2u
5
+ u
4
+ u
3
+ 5u
2
− 7u + 3)
· (u
10
+ u
9
+ ··· + 87u + 43)(u
17
− u
16
+ ··· − 8u
2
+ 1)
23
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
3
− 2y
2
+ 5y −1)(y
10
− 23y
9
+ ··· + 83y + 81)
· (y
10
+ 17y
9
+ ··· + 35y + 1)(y
17
+ 12y
16
+ ··· + 582y −1)
c
2
, c
3
, c
5
c
9
(y
2
+ y + 1)(y
3
+ 2y
2
+ y −1)(y
10
− 7y
9
+ ··· + 3y + 1)
· (y
10
+ 13y
9
+ ··· + 59y + 9)(y
17
+ 16y
16
+ ··· + 10y −1)
c
4
(y
2
+ y + 1)(y
3
− 2y
2
+ 5y −1)(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
4
· (y
17
− 4y
16
+ ··· + 30y −9)
c
6
, c
8
, c
10
(y
2
+ y + 1)(y
3
− y
2
− 2y −1)
· (y
10
− 7y
9
+ 17y
8
− 20y
7
+ 12y
6
+ 9y
5
− 3y
4
+ 11y
3
+ 6y
2
+ 1)
· (y
10
+ 21y
9
+ ··· + 852y + 441)(y
17
+ 9y
16
+ ··· − 77y −9)
c
7
y
5
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
2
· (y
5
+ 19y
4
+ 112y
3
+ 161y
2
− 253y + 203)
2
· (y
17
+ 49y
16
+ ··· + 512y −1024)
c
11
y
2
(y
3
− y
2
− 2y −9)(y
10
− 9y
9
+ ··· + 133y + 49)
· (y
10
+ 15y
9
+ ··· + 321y + 1849)(y
17
+ 28y
15
+ ··· + 192y −16)
c
12
((y −1)
3
)(y
2
+ y + 1)(y
10
− 25y
9
+ ··· + 3009y + 1849)
· (y
10
+ 7y
9
+ ··· − 19y + 9)(y
17
− 13y
16
+ ··· + 16y −1)
24
