12n
0767
(K12n
0767
)
A knot diagram
1
Linearized knot diagam
4 6 9 10 11 3 11 12 2 5 8 9
Solving Sequence
7,11
8 12
3,9
6 2 5 10 4 1
c
7
c
11
c
8
c
6
c
2
c
5
c
10
c
4
c
1
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.23603 × 10
37
u
44
+ 1.33966 × 10
38
u
43
+ ··· + 1.65382 × 10
39
b − 3.21123 × 10
39
,
− 6.36572 × 10
38
u
44
+ 8.22571 × 10
38
u
43
+ ··· + 3.30764 × 10
39
a + 1.07047 × 10
40
,
u
45
− 3u
44
+ ··· + 50u − 4i
I
u
2
= h−u
9
+ 5u
7
− 9u
5
+ u
4
+ 7u
3
− 3u
2
+ b − u + 2, 2u
9
− 12u
7
− u
6
+ 26u
5
+ 3u
4
− 23u
3
+ a + 5u − 4,
u
10
− 6u
8
+ 13u
6
− u
5
− 12u
4
+ 4u
3
+ 3u
2
− 4u + 1i
I
u
3
= hu
2
+ b + u − 1, a, u
3
+ u
2
− 2u − 1i
I
u
4
= ha
2
+ 2b + a + 1, a
4
+ a
2
− 4a + 1, u + 1i
I
u
5
= hb + 1, a, u + 1i
* 5 irreducible components of dim
C
= 0, with total 63 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−3.24 × 10
37
u
44
+ 1.34 × 10
38
u
43
+ · · · + 1.65 × 10
39
b − 3.21 ×
10
39
, −6.37 × 10
38
u
44
+ 8.23 × 10
38
u
43
+ · · · + 3.31 × 10
39
a + 1.07 ×
10
40
, u
45
− 3u
44
+ · · · + 50u − 4i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
12
=
u
−u
3
+ u
a
3
=
0.192455u
44
− 0.248689u
43
+ ··· − 8.80994u − 3.23636
0.0195670u
44
− 0.0810038u
43
+ ··· − 8.75930u + 1.94171
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−0.175770u
44
+ 0.507263u
43
+ ··· + 42.4168u − 8.30175
0.0965165u
44
− 0.317560u
43
+ ··· − 9.44223u + 2.32132
a
2
=
0.440671u
44
− 1.07384u
43
+ ··· − 43.5785u + 5.01696
0.266201u
44
− 0.416972u
43
+ ··· − 9.52908u − 0.181638
a
5
=
−0.175770u
44
+ 0.507263u
43
+ ··· + 42.4168u − 8.30175
0.157017u
44
− 0.419492u
43
+ ··· − 9.74149u + 2.40151
a
10
=
0.0526459u
44
− 0.238843u
43
+ ··· − 36.4630u + 5.97165
−0.213158u
44
+ 0.494391u
43
+ ··· + 7.97003u − 1.44277
a
4
=
0.111781u
44
− 0.130627u
43
+ ··· − 11.0582u − 1.93976
−0.246633u
44
+ 0.420180u
43
+ ··· + 1.66318u + 1.02808
a
1
=
u
3
− 2u
−u
5
+ 3u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.59706u
44
+ 5.33204u
43
+ ··· + 112.471u − 14.4760
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ u
44
+ ··· + 279u − 13
c
2
, c
6
u
45
− 4u
44
+ ··· + 2u + 1
c
3
u
45
− 2u
44
+ ··· + 413u − 43
c
4
, c
5
, c
10
u
45
− 27u
43
+ ··· + 104u + 1
c
7
, c
8
, c
11
c
12
u
45
+ 3u
44
+ ··· + 50u + 4
c
9
u
45
+ 2u
44
+ ··· + 113u − 29
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 35y
44
+ ··· + 35279y −169
c
2
, c
6
y
45
− 8y
44
+ ··· + 92y −1
c
3
y
45
+ 38y
44
+ ··· − 1603y −1849
c
4
, c
5
, c
10
y
45
− 54y
44
+ ··· + 10150y −1
c
7
, c
8
, c
11
c
12
y
45
− 37y
44
+ ··· + 812y −16
c
9
y
45
+ 4y
44
+ ··· − 1615y −841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.041408 + 1.014500I
a = −0.544128 + 0.813587I
b = −0.668184 + 0.559705I
−3.13407 − 4.15263I 3.01706 + 7.91785I
u = 0.041408 − 1.014500I
a = −0.544128 − 0.813587I
b = −0.668184 − 0.559705I
−3.13407 + 4.15263I 3.01706 − 7.91785I
u = −0.174430 + 1.008960I
a = 0.104541 − 1.265410I
b = 1.09285 − 1.10386I
−11.19940 + 0.59411I −0.389790 + 0.117454I
u = −0.174430 − 1.008960I
a = 0.104541 + 1.265410I
b = 1.09285 + 1.10386I
−11.19940 − 0.59411I −0.389790 − 0.117454I
u = 0.924387 + 0.268290I
a = 1.30873 − 1.48625I
b = −1.103840 − 0.669054I
−4.20645 + 4.64825I 2.38480 − 4.16816I
u = 0.924387 − 0.268290I
a = 1.30873 + 1.48625I
b = −1.103840 + 0.669054I
−4.20645 − 4.64825I 2.38480 + 4.16816I
u = −1.04388
a = 0.114632
b = −0.831047
1.64144 6.13540
u = 0.172930 + 1.107670I
a = 0.302565 + 1.166110I
b = 0.99663 + 1.10399I
−11.4488 + 8.5525I 0. − 5.01890I
u = 0.172930 − 1.107670I
a = 0.302565 − 1.166110I
b = 0.99663 − 1.10399I
−11.4488 − 8.5525I 0. + 5.01890I
u = 1.183020 + 0.194269I
a = −0.324146 + 0.894691I
b = 0.919413 + 0.825208I
4.00704 + 3.18534I 11.68963 − 6.13531I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.183020 − 0.194269I
a = −0.324146 − 0.894691I
b = 0.919413 − 0.825208I
4.00704 − 3.18534I 11.68963 + 6.13531I
u = 0.534356 + 0.586253I
a = −1.101580 + 0.538647I
b = −0.795649 + 0.846239I
−5.13534 − 1.11726I 0.73798 − 1.28105I
u = 0.534356 − 0.586253I
a = −1.101580 − 0.538647I
b = −0.795649 − 0.846239I
−5.13534 + 1.11726I 0.73798 + 1.28105I
u = 1.167650 + 0.322960I
a = −0.240809 + 0.733906I
b = −0.313834 + 0.831062I
−0.68736 + 4.21030I 4.00000 − 5.02071I
u = 1.167650 − 0.322960I
a = −0.240809 − 0.733906I
b = −0.313834 − 0.831062I
−0.68736 − 4.21030I 4.00000 + 5.02071I
u = 0.097797 + 0.779729I
a = 0.06028 − 1.52878I
b = −0.464144 − 0.749358I
−3.97386 − 0.23348I −1.018556 − 0.405241I
u = 0.097797 − 0.779729I
a = 0.06028 + 1.52878I
b = −0.464144 + 0.749358I
−3.97386 + 0.23348I −1.018556 + 0.405241I
u = 1.22285
a = −0.616977
b = 1.60763
6.34821 19.0110
u = −1.091580 + 0.620522I
a = 0.258135 − 0.780615I
b = 0.607158 − 0.350869I
1.16029 − 2.81472I 0. + 13.05919I
u = −1.091580 − 0.620522I
a = 0.258135 + 0.780615I
b = 0.607158 + 0.350869I
1.16029 + 2.81472I 0. − 13.05919I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.273640 + 0.133753I
a = −0.45180 + 1.46446I
b = −0.145492 + 0.099772I
−1.17659 + 4.15233I 0
u = 1.273640 − 0.133753I
a = −0.45180 − 1.46446I
b = −0.145492 − 0.099772I
−1.17659 − 4.15233I 0
u = −1.271760 + 0.215202I
a = 0.646150 + 1.192530I
b = −0.92299 + 1.17785I
−0.67716 − 6.28448I 0
u = −1.271760 − 0.215202I
a = 0.646150 − 1.192530I
b = −0.92299 − 1.17785I
−0.67716 + 6.28448I 0
u = −1.186450 + 0.545831I
a = 0.346861 + 0.155289I
b = 0.73612 + 1.35462I
−8.09139 − 6.07854I 0
u = −1.186450 − 0.545831I
a = 0.346861 − 0.155289I
b = 0.73612 − 1.35462I
−8.09139 + 6.07854I 0
u = −1.34838
a = 0.0600852
b = −0.938079
1.78156 0
u = −1.355850 + 0.355471I
a = 0.829889 + 0.927938I
b = −0.780033 + 0.657789I
0.61158 − 3.87330I 0
u = −1.355850 − 0.355471I
a = 0.829889 − 0.927938I
b = −0.780033 − 0.657789I
0.61158 + 3.87330I 0
u = 1.209790 + 0.720141I
a = 0.392103 − 0.127077I
b = 0.587982 − 1.074260I
−8.33246 − 2.24840I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.209790 − 0.720141I
a = 0.392103 + 0.127077I
b = 0.587982 + 1.074260I
−8.33246 + 2.24840I 0
u = 1.33029 + 0.50410I
a = 0.411973 − 1.081660I
b = −1.003550 − 0.717171I
0.92810 + 9.55627I 0
u = 1.33029 − 0.50410I
a = 0.411973 + 1.081660I
b = −1.003550 + 0.717171I
0.92810 − 9.55627I 0
u = −1.46627
a = −1.25063
b = 1.38819
8.29347 0
u = −1.44154 + 0.50693I
a = −0.735094 − 1.007510I
b = 1.26328 − 0.98250I
−6.3918 − 14.2928I 0
u = −1.44154 − 0.50693I
a = −0.735094 + 1.007510I
b = 1.26328 + 0.98250I
−6.3918 + 14.2928I 0
u = 1.45643 + 0.46943I
a = −0.956513 + 0.849625I
b = 1.31123 + 0.80369I
−6.04579 + 4.74034I 0
u = 1.45643 − 0.46943I
a = −0.956513 − 0.849625I
b = 1.31123 − 0.80369I
−6.04579 − 4.74034I 0
u = −0.134327 + 0.352329I
a = 1.36446 − 1.01479I
b = 0.455730 − 0.362630I
0.335623 − 1.031530I 5.27348 + 6.47148I
u = −0.134327 − 0.352329I
a = 1.36446 + 1.01479I
b = 0.455730 + 0.362630I
0.335623 + 1.031530I 5.27348 − 6.47148I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.63327
a = 0.749914
b = −0.994896
10.4857 0
u = 0.087790 + 0.304921I
a = −2.59328 − 3.84226I
b = −0.610911 − 0.807890I
−4.79980 + 4.02044I 0.46581 − 8.77034I
u = 0.087790 − 0.304921I
a = −2.59328 + 3.84226I
b = −0.610911 + 0.807890I
−4.79980 − 4.02044I 0.46581 + 8.77034I
u = −1.76260
a = −0.288186
b = 0.125896
3.04144 0
u = 0.117909
a = −4.42552
b = 1.31879
2.93768 −5.76770
9
II. I
u
2
= h−u
9
+ 5u
7
− 9u
5
+ u
4
+ 7u
3
− 3u
2
+ b − u + 2, 2u
9
− 12u
7
+ · · · +
a − 4, u
10
− 6u
8
+ · · · − 4u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
12
=
u
−u
3
+ u
a
3
=
−2u
9
+ 12u
7
+ u
6
− 26u
5
− 3u
4
+ 23u
3
− 5u + 4
u
9
− 5u
7
+ 9u
5
− u
4
− 7u
3
+ 3u
2
+ u − 2
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
2u
9
+ u
8
− 12u
7
− 6u
6
+ 26u
5
+ 11u
4
− 24u
3
− 4u
2
+ 7u − 5
−u
9
− u
8
+ 6u
7
+ 5u
6
− 13u
5
− 7u
4
+ 13u
3
+ u
2
− 6u + 4
a
2
=
u
9
+ u
8
− 5u
7
− 5u
6
+ 8u
5
+ 7u
4
− 5u
3
− u
2
+ u − 3
−2u
9
+ 11u
7
+ u
6
− 21u
5
− 2u
4
+ 16u
3
− 2u
2
− 3u + 3
a
5
=
2u
9
+ u
8
− 12u
7
− 6u
6
+ 26u
5
+ 11u
4
− 24u
3
− 4u
2
+ 7u − 5
−u
9
− u
8
+ 6u
7
+ 5u
6
− 14u
5
− 7u
4
+ 16u
3
+ u
2
− 8u + 5
a
10
=
−u
9
+ 6u
7
− 13u
5
+ u
4
+ 12u
3
− 5u
2
− 3u + 6
2u
9
+ u
8
− 11u
7
− 5u
6
+ 21u
5
+ 8u
4
− 17u
3
− 2u
2
+ 4u − 4
a
4
=
−2u
9
+ 12u
7
+ u
6
− 26u
5
− 3u
4
+ 24u
3
− 7u + 4
u
9
− u
8
− 5u
7
+ 5u
6
+ 8u
5
− 9u
4
− 3u
3
+ 7u
2
− 3u − 1
a
1
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
9
+ 4u
8
− 8u
7
− 16u
6
+ 11u
5
+ 17u
4
− 9u
3
+ u
2
+ 6u − 3
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 2u
9
− u
8
+ 9u
7
− 8u
6
− 9u
5
+ 18u
4
− 2u
3
− 10u
2
+ 4u + 1
c
2
u
10
− 2u
9
− 2u
8
+ 7u
7
− 3u
6
− 6u
5
+ 6u
4
+ u
3
− 2u
2
+ 1
c
3
u
10
− 2u
9
+ 4u
8
− 8u
7
+ 10u
6
− 12u
5
+ 9u
4
− 5u
3
+ u
2
+ 2u − 1
c
4
, c
5
u
10
− 5u
8
− u
7
+ 9u
6
+ 5u
5
− 6u
4
− 8u
3
+ u
2
+ 4u − 1
c
6
u
10
+ 2u
9
− 2u
8
− 7u
7
− 3u
6
+ 6u
5
+ 6u
4
− u
3
− 2u
2
+ 1
c
7
, c
8
u
10
− 6u
8
+ 13u
6
− u
5
− 12u
4
+ 4u
3
+ 3u
2
− 4u + 1
c
9
u
10
− 2u
9
− u
8
+ 5u
7
− 9u
6
+ 12u
5
− 10u
4
+ 8u
3
− 4u
2
+ 2u − 1
c
10
u
10
− 5u
8
+ u
7
+ 9u
6
− 5u
5
− 6u
4
+ 8u
3
+ u
2
− 4u − 1
c
11
, c
12
u
10
− 6u
8
+ 13u
6
+ u
5
− 12u
4
− 4u
3
+ 3u
2
+ 4u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
− 6y
9
+ ··· − 36y + 1
c
2
, c
6
y
10
− 8y
9
+ ··· − 4y + 1
c
3
y
10
+ 4y
9
+ 4y
8
− 14y
7
− 38y
6
− 30y
5
+ 5y
4
+ 21y
3
+ 3y
2
− 6y + 1
c
4
, c
5
, c
10
y
10
− 10y
9
+ ··· − 18y + 1
c
7
, c
8
, c
11
c
12
y
10
− 12y
9
+ ··· − 10y + 1
c
9
y
10
− 6y
9
+ 3y
8
+ 21y
7
+ 5y
6
− 30y
5
− 38y
4
− 14y
3
+ 4y
2
+ 4y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20478
a = −0.980273
b = 1.51324
5.82290 2.46150
u = −1.195710 + 0.441090I
a = −0.078451 − 0.972048I
b = 0.500388 − 0.335058I
1.23645 − 2.22223I 7.15723 − 0.57453I
u = −1.195710 − 0.441090I
a = −0.078451 + 0.972048I
b = 0.500388 + 0.335058I
1.23645 + 2.22223I 7.15723 + 0.57453I
u = 1.283760 + 0.213392I
a = 1.01246 − 1.42425I
b = −0.808287 − 0.797110I
−1.62689 + 5.63070I 2.15370 − 5.54722I
u = 1.283760 − 0.213392I
a = 1.01246 + 1.42425I
b = −0.808287 + 0.797110I
−1.62689 − 5.63070I 2.15370 + 5.54722I
u = 0.327169 + 0.496307I
a = −2.25689 + 0.68510I
b = −0.520471 + 0.577536I
−4.94627 − 3.16167I −1.44465 + 0.82842I
u = 0.327169 − 0.496307I
a = −2.25689 − 0.68510I
b = −0.520471 − 0.577536I
−4.94627 + 3.16167I −1.44465 − 0.82842I
u = −1.56924
a = 1.33343
b = −1.37777
7.07752 3.45960
u = 1.60443
a = −0.760124
b = 1.08548
10.7042 26.3010
u = 0.339155
a = 3.05273
b = −1.56421
0.228307 −0.954520
13
III. I
u
3
= hu
2
+ b + u − 1, a, u
3
+ u
2
− 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
12
=
u
u
2
− u − 1
a
3
=
0
−u
2
− u + 1
a
9
=
−u
2
+ 1
u
2
− u − 1
a
6
=
1
u + 2
a
2
=
u
2
+ u − 1
u
2
+ 2u
a
5
=
1
−u
2
+ u + 2
a
10
=
u
2u
2
+ u − 1
a
4
=
−u
2
+ 1
−2u
a
1
=
u
2
− 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
2
− 4u + 16
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ 2u
2
− u − 1
c
2
, c
10
, c
11
c
12
u
3
− u
2
− 2u + 1
c
3
, c
9
(u + 1)
3
c
4
, c
5
, c
6
c
7
, c
8
u
3
+ u
2
− 2u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− 6y
2
+ 5y −1
c
2
, c
4
, c
5
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
3
− 5y
2
+ 6y −1
c
3
, c
9
(y −1)
3
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24698
a = 0
b = −1.80194
3.28987 12.5670
u = −0.445042
a = 0
b = 1.24698
3.28987 17.9780
u = −1.80194
a = 0
b = −0.445042
3.28987 26.4550
17
IV. I
u
4
= ha
2
+ 2b + a + 1, a
4
+ a
2
− 4a + 1, u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
−1
a
8
=
1
−1
a
12
=
−1
0
a
3
=
a
−
1
2
a
2
−
1
2
a −
1
2
a
9
=
0
−1
a
6
=
−
1
2
a
3
−
1
2
a
2
−
1
2
a + 1
1
2
a
3
+
1
2
a
2
+
3
2
a
a
2
=
−
1
2
a
3
−
1
2
a
2
−
1
2
a + 1
a
3
+ a
2
+ 2a − 1
a
5
=
−
1
2
a
3
−
1
2
a
2
−
1
2
a + 1
a
3
+ a
2
+ 2a − 1
a
10
=
−
1
2
a
2
−
1
2
a −
1
2
a
3
+
3
2
a
2
+
5
2
a −
3
2
a
4
=
a
−
1
2
a
2
−
3
2
a −
1
2
a
1
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
− 2u
2
+ 1
c
2
, c
6
u
4
+ u
3
− 2u
2
+ 1
c
3
u
4
+ u
2
− 4u + 1
c
4
, c
5
, c
9
c
10
u
4
+ u
3
− 1
c
7
, c
8
, c
11
c
12
(u − 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
4
− 5y
3
+ 6y
2
− 4y + 1
c
3
y
4
+ 2y
3
+ 3y
2
− 14y + 1
c
4
, c
5
, c
9
c
10
y
4
− y
3
− 2y
2
+ 1
c
7
, c
8
, c
11
c
12
(y −1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.24938
b = −1.90517
1.64493 6.00000
u = −1.00000
a = −0.75943 + 1.54710I
b = 0.788105 + 0.401358I
1.64493 6.00000
u = −1.00000
a = −0.75943 − 1.54710I
b = 0.788105 − 0.401358I
1.64493 6.00000
u = −1.00000
a = 0.269472
b = −0.671044
1.64493 6.00000
21
V. I
u
5
= hb + 1, a, u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
−1
a
8
=
1
−1
a
12
=
−1
0
a
3
=
0
−1
a
9
=
0
−1
a
6
=
1
1
a
2
=
1
0
a
5
=
1
0
a
10
=
−1
−1
a
4
=
0
−1
a
1
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
7
, c
8
, c
9
c
10
, c
11
, c
12
u − 1
c
2
, c
6
u + 1
c
3
u
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y −1
c
3
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = −1.00000
1.64493 6.00000
25
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
3
+ 2u
2
− u − 1)(u
4
− u
3
− 2u
2
+ 1)
· (u
10
− 2u
9
− u
8
+ 9u
7
− 8u
6
− 9u
5
+ 18u
4
− 2u
3
− 10u
2
+ 4u + 1)
· (u
45
+ u
44
+ ··· + 279u − 13)
c
2
(u + 1)(u
3
− u
2
− 2u + 1)(u
4
+ u
3
− 2u
2
+ 1)
· (u
10
− 2u
9
− 2u
8
+ 7u
7
− 3u
6
− 6u
5
+ 6u
4
+ u
3
− 2u
2
+ 1)
· (u
45
− 4u
44
+ ··· + 2u + 1)
c
3
u(u + 1)
3
(u
4
+ u
2
− 4u + 1)
· (u
10
− 2u
9
+ 4u
8
− 8u
7
+ 10u
6
− 12u
5
+ 9u
4
− 5u
3
+ u
2
+ 2u − 1)
· (u
45
− 2u
44
+ ··· + 413u − 43)
c
4
, c
5
(u − 1)(u
3
+ u
2
− 2u − 1)(u
4
+ u
3
− 1)
· (u
10
− 5u
8
− u
7
+ 9u
6
+ 5u
5
− 6u
4
− 8u
3
+ u
2
+ 4u − 1)
· (u
45
− 27u
43
+ ··· + 104u + 1)
c
6
(u + 1)(u
3
+ u
2
− 2u − 1)(u
4
+ u
3
− 2u
2
+ 1)
· (u
10
+ 2u
9
− 2u
8
− 7u
7
− 3u
6
+ 6u
5
+ 6u
4
− u
3
− 2u
2
+ 1)
· (u
45
− 4u
44
+ ··· + 2u + 1)
c
7
, c
8
(u − 1)
5
(u
3
+ u
2
− 2u − 1)
· (u
10
− 6u
8
+ 13u
6
− u
5
− 12u
4
+ 4u
3
+ 3u
2
− 4u + 1)
· (u
45
+ 3u
44
+ ··· + 50u + 4)
c
9
(u − 1)(u + 1)
3
(u
4
+ u
3
− 1)
· (u
10
− 2u
9
− u
8
+ 5u
7
− 9u
6
+ 12u
5
− 10u
4
+ 8u
3
− 4u
2
+ 2u − 1)
· (u
45
+ 2u
44
+ ··· + 113u − 29)
c
10
(u − 1)(u
3
− u
2
− 2u + 1)(u
4
+ u
3
− 1)
· (u
10
− 5u
8
+ u
7
+ 9u
6
− 5u
5
− 6u
4
+ 8u
3
+ u
2
− 4u − 1)
· (u
45
− 27u
43
+ ··· + 104u + 1)
c
11
, c
12
(u − 1)
5
(u
3
− u
2
− 2u + 1)
· (u
10
− 6u
8
+ 13u
6
+ u
5
− 12u
4
− 4u
3
+ 3u
2
+ 4u + 1)
· (u
45
+ 3u
44
+ ··· + 50u + 4)
26
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
3
− 6y
2
+ 5y −1)(y
4
− 5y
3
+ 6y
2
− 4y + 1)
· (y
10
− 6y
9
+ ··· − 36y + 1)(y
45
− 35y
44
+ ··· + 35279y −169)
c
2
, c
6
(y −1)(y
3
− 5y
2
+ 6y −1)(y
4
− 5y
3
+ 6y
2
− 4y + 1)
· (y
10
− 8y
9
+ ··· − 4y + 1)(y
45
− 8y
44
+ ··· + 92y −1)
c
3
y(y −1)
3
(y
4
+ 2y
3
+ 3y
2
− 14y + 1)
· (y
10
+ 4y
9
+ 4y
8
− 14y
7
− 38y
6
− 30y
5
+ 5y
4
+ 21y
3
+ 3y
2
− 6y + 1)
· (y
45
+ 38y
44
+ ··· − 1603y −1849)
c
4
, c
5
, c
10
(y −1)(y
3
− 5y
2
+ 6y −1)(y
4
− y
3
− 2y
2
+ 1)(y
10
− 10y
9
+ ··· − 18y + 1)
· (y
45
− 54y
44
+ ··· + 10150y −1)
c
7
, c
8
, c
11
c
12
((y −1)
5
)(y
3
− 5y
2
+ 6y −1)(y
10
− 12y
9
+ ··· − 10y + 1)
· (y
45
− 37y
44
+ ··· + 812y −16)
c
9
(y −1)
4
(y
4
− y
3
− 2y
2
+ 1)
· (y
10
− 6y
9
+ 3y
8
+ 21y
7
+ 5y
6
− 30y
5
− 38y
4
− 14y
3
+ 4y
2
+ 4y + 1)
· (y
45
+ 4y
44
+ ··· − 1615y −841)
27
