12n
0443
(K12n
0443
)
A knot diagram
1
Linearized knot diagam
3 6 12 11 2 4 12 11 3 6 8 10
Solving Sequence
3,12 4,8
7 6 2 1 5 11 9 10
c
3
c
7
c
6
c
2
c
1
c
5
c
11
c
8
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 64645u
14
− 65427u
13
+ ··· + 135557a + 338831,
u
15
+ 10u
13
+ 3u
12
+ 43u
11
+ 24u
10
+ 99u
9
+ 76u
8
+ 124u
7
+ 108u
6
+ 79u
5
+ 56u
4
+ 21u
3
+ u
2
− 1i
I
u
2
= hb + u, −8u
8
+ 3u
7
− 25u
6
+ 25u
5
− 9u
4
+ 26u
3
+ 23u
2
+ a − 34u − 19,
u
9
+ 3u
7
− 2u
6
− 3u
4
− 4u
3
+ 3u
2
+ 4u + 1i
I
u
3
= h80577u
11
− 475411u
10
+ ··· + 2674873b − 7542897,
1788526u
11
− 120225u
10
+ ··· + 29423603a + 69597502,
u
12
− 2u
11
+ 4u
10
− 9u
9
+ 8u
8
− 14u
7
+ 17u
6
− 10u
5
+ 40u
4
− u
3
+ 45u
2
− 5u + 11i
I
u
4
= hb − u − 1, a, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 38 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
=
hb−u, 64645u
14
−65427u
13
+· · ·+135557a+338831, u
15
+10u
13
+· · ·+u
2
−1i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
8
=
−0.476884u
14
+ 0.482653u
13
+ ··· + 1.81451u − 2.49955
u
a
7
=
−0.476884u
14
+ 0.482653u
13
+ ··· + 1.81451u − 2.49955
0.00639583u
14
− 0.283881u
13
+ ··· + 0.523116u + 0.482653
a
6
=
−0.476884u
14
+ 0.482653u
13
+ ··· + 2.81451u − 2.49955
0.00639583u
14
− 0.283881u
13
+ ··· + 0.523116u + 0.482653
a
2
=
−0.0111245u
14
+ 0.0185605u
13
+ ··· − 0.528095u + 2.36120
0.205168u
14
− 0.302522u
13
+ ··· − 0.493778u + 0.0121646
a
1
=
0.194044u
14
− 0.283962u
13
+ ··· − 1.02187u + 2.37336
0.205168u
14
− 0.302522u
13
+ ··· − 0.493778u + 0.0121646
a
5
=
−0.879586u
14
− 0.206208u
13
+ ··· + 4.63070u − 0.816210
−0.198691u
14
+ 0.0715566u
13
+ ··· + 0.126183u + 0.282840
a
11
=
0.897106u
14
− 0.0962326u
13
+ ··· − 5.57949u − 2.06234
−0.00639583u
14
+ 0.283881u
13
+ ··· + 1.47688u − 0.482653
a
9
=
0.475313u
14
− 0.416371u
13
+ ··· − 7.11258u + 0.678549
0.0187228u
14
+ 0.0271177u
13
+ ··· + 0.579778u − 0.386420
a
10
=
0.494036u
14
− 0.389253u
13
+ ··· − 6.53280u + 0.292128
0.0187228u
14
+ 0.0271177u
13
+ ··· + 0.579778u − 0.386420
(ii) Obstruction class = −1
(iii) Cusp Shapes =
335739
135557
u
14
−
152409
135557
u
13
+ ··· +
281645
135557
u +
754781
135557
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 20u
14
+ ··· + 849u + 16
c
2
, c
5
u
15
+ 8u
14
+ ··· + 23u − 4
c
3
, c
6
u
15
+ 10u
13
+ ··· + u
2
− 1
c
4
, c
9
u
15
+ 13u
13
+ ··· + u − 1
c
7
, c
8
, c
11
u
15
+ 6u
14
+ ··· − 5u − 2
c
10
, c
12
u
15
− u
14
+ ··· − 11u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 44y
14
+ ··· + 606753y −256
c
2
, c
5
y
15
− 20y
14
+ ··· + 849y −16
c
3
, c
6
y
15
+ 20y
14
+ ··· + 2y −1
c
4
, c
9
y
15
+ 26y
14
+ ··· − 3y −1
c
7
, c
8
, c
11
y
15
+ 10y
14
+ ··· − 39y −4
c
10
, c
12
y
15
+ 19y
14
+ ··· + 95y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.045427 + 1.039060I
a = 1.54244 − 0.28684I
b = 0.045427 + 1.039060I
−11.28150 + 1.93400I −1.23160 − 1.02985I
u = 0.045427 − 1.039060I
a = 1.54244 + 0.28684I
b = 0.045427 − 1.039060I
−11.28150 − 1.93400I −1.23160 + 1.02985I
u = −0.608111 + 0.211954I
a = 0.250704 − 0.629982I
b = −0.608111 + 0.211954I
−1.45492 + 0.35788I −5.52968 − 1.62247I
u = −0.608111 − 0.211954I
a = 0.250704 + 0.629982I
b = −0.608111 − 0.211954I
−1.45492 − 0.35788I −5.52968 + 1.62247I
u = 0.06518 + 1.45860I
a = −0.406098 − 0.405536I
b = 0.06518 + 1.45860I
3.63562 + 1.34338I 2.60619 − 3.21341I
u = 0.06518 − 1.45860I
a = −0.406098 + 0.405536I
b = 0.06518 − 1.45860I
3.63562 − 1.34338I 2.60619 + 3.21341I
u = −0.094803 + 0.399698I
a = −3.16771 + 0.99078I
b = −0.094803 + 0.399698I
−3.74744 + 2.10465I 5.87690 − 3.70353I
u = −0.094803 − 0.399698I
a = −3.16771 − 0.99078I
b = −0.094803 − 0.399698I
−3.74744 − 2.10465I 5.87690 + 3.70353I
u = 0.23646 + 1.59594I
a = 0.306052 − 0.769874I
b = 0.23646 + 1.59594I
−4.76135 − 4.08820I 0.76517 + 2.11409I
u = 0.23646 − 1.59594I
a = 0.306052 + 0.769874I
b = 0.23646 − 1.59594I
−4.76135 + 4.08820I 0.76517 − 2.11409I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.47405 + 1.56562I
a = 0.532315 − 0.431362I
b = −0.47405 + 1.56562I
2.30289 + 5.28134I −1.29339 − 3.24953I
u = −0.47405 − 1.56562I
a = 0.532315 + 0.431362I
b = −0.47405 − 1.56562I
2.30289 − 5.28134I −1.29339 + 3.24953I
u = 0.273398
a = −2.01535
b = 0.273398
0.899032 11.1030
u = 0.69320 + 1.66542I
a = −0.550040 − 0.669032I
b = 0.69320 + 1.66542I
−8.17186 − 11.29110I −0.74494 + 5.10967I
u = 0.69320 − 1.66542I
a = −0.550040 + 0.669032I
b = 0.69320 − 1.66542I
−8.17186 + 11.29110I −0.74494 − 5.10967I
6
II.
I
u
2
= hb+u, −8u
8
+3u
7
+· · ·+a−19, u
9
+3u
7
−2u
6
−3u
4
−4u
3
+3u
2
+4u+1i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
8
=
8u
8
− 3u
7
+ 25u
6
− 25u
5
+ 9u
4
− 26u
3
− 23u
2
+ 34u + 19
−u
a
7
=
8u
8
− 3u
7
+ 25u
6
− 25u
5
+ 9u
4
− 26u
3
− 23u
2
+ 34u + 19
u
8
+ 3u
6
− 2u
5
− 2u
3
− 4u
2
+ 3u + 3
a
6
=
8u
8
− 3u
7
+ 25u
6
− 25u
5
+ 9u
4
− 26u
3
− 23u
2
+ 33u + 19
u
8
+ 3u
6
− 2u
5
− 3u
3
− 4u
2
+ 3u + 3
a
2
=
−11u
8
+ 5u
7
− 35u
6
+ 38u
5
− 16u
4
+ 40u
3
+ 27u
2
− 47u − 23
−2u
8
+ u
7
− 6u
6
+ 7u
5
− 2u
4
+ 6u
3
+ 5u
2
− 10u − 6
a
1
=
−13u
8
+ 6u
7
− 41u
6
+ 45u
5
− 18u
4
+ 46u
3
+ 32u
2
− 57u − 29
−2u
8
+ u
7
− 6u
6
+ 7u
5
− 2u
4
+ 6u
3
+ 5u
2
− 10u − 6
a
5
=
−4u
8
+ 3u
7
− 14u
6
+ 18u
5
− 13u
4
+ 19u
3
+ 2u
2
− 16u − 3
−3u
8
+ u
7
− 10u
6
+ 9u
5
− 5u
4
+ 11u
3
+ 9u
2
− 10u − 5
a
11
=
14u
8
− 8u
7
+ 46u
6
− 54u
5
+ 29u
4
− 57u
3
− 25u
2
+ 58u + 24
u
8
+ 3u
6
− 2u
5
− 2u
3
− 4u
2
+ 5u + 3
a
9
=
4u
8
− 3u
7
+ 14u
6
− 18u
5
+ 13u
4
− 20u
3
− 2u
2
+ 14u + 4
3u
8
− 2u
7
+ 10u
6
− 13u
5
+ 7u
4
− 14u
3
− 4u
2
+ 13u + 5
a
10
=
7u
8
− 5u
7
+ 24u
6
− 31u
5
+ 20u
4
− 34u
3
− 6u
2
+ 27u + 9
3u
8
− 2u
7
+ 10u
6
− 13u
5
+ 7u
4
− 14u
3
− 4u
2
+ 13u + 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 37u
8
−21u
7
+ 123u
6
−143u
5
+ 80u
4
−154u
3
−65u
2
+ 148u + 61
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 11u
8
+ ··· + 105u − 25
c
2
u
9
+ 5u
8
+ 7u
7
− 3u
6
− 14u
5
− 4u
4
+ 13u
3
+ 8u
2
− 5u − 5
c
3
, c
6
u
9
+ 3u
7
− 2u
6
− 3u
4
− 4u
3
+ 3u
2
+ 4u + 1
c
4
, c
9
u
9
+ 4u
7
− 4u
5
+ 7u
4
+ 3u
3
− 4u
2
+ u + 1
c
5
u
9
− 5u
8
+ 7u
7
+ 3u
6
− 14u
5
+ 4u
4
+ 13u
3
− 8u
2
− 5u + 5
c
7
, c
8
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 20u
5
+ 22u
4
+ 23u
3
+ 17u
2
+ 11u + 3
c
10
, c
12
u
9
+ u
8
+ 5u
7
+ 6u
6
+ 8u
5
− u
3
− 3u
2
− u − 1
c
11
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 20u
5
− 22u
4
+ 23u
3
− 17u
2
+ 11u − 3
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− 19y
8
+ ··· − 675y −625
c
2
, c
5
y
9
− 11y
8
+ ··· + 105y −25
c
3
, c
6
y
9
+ 6y
8
+ 9y
7
− 12y
6
− 28y
5
+ 27y
4
+ 38y
3
− 35y
2
+ 10y −1
c
4
, c
9
y
9
+ 8y
8
+ 8y
7
− 26y
6
+ 42y
5
− 65y
4
+ 57y
3
− 24y
2
+ 9y −1
c
7
, c
8
, c
11
y
9
+ 7y
8
+ 26y
7
+ 65y
6
+ 116y
5
+ 152y
4
+ 143y
3
+ 85y
2
+ 19y −9
c
10
, c
12
y
9
+ 9y
8
+ 29y
7
+ 42y
6
+ 58y
5
+ 12y
4
− 3y
3
− 7y
2
− 5y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.060910 + 0.248265I
a = 0.603246 + 0.904793I
b = −1.060910 − 0.248265I
−14.5038 + 1.7038I −5.12137 − 0.30387I
u = 1.060910 − 0.248265I
a = 0.603246 − 0.904793I
b = −1.060910 + 0.248265I
−14.5038 − 1.7038I −5.12137 + 0.30387I
u = −0.513365 + 0.121815I
a = −0.35477 + 2.45080I
b = 0.513365 − 0.121815I
−4.37176 + 2.01399I −7.44425 − 1.80958I
u = −0.513365 − 0.121815I
a = −0.35477 − 2.45080I
b = 0.513365 + 0.121815I
−4.37176 − 2.01399I −7.44425 + 1.80958I
u = 0.12963 + 1.46755I
a = 0.724641 + 0.570324I
b = −0.12963 − 1.46755I
3.37793 − 0.60932I 0.678183 + 0.313757I
u = 0.12963 − 1.46755I
a = 0.724641 − 0.570324I
b = −0.12963 + 1.46755I
3.37793 + 0.60932I 0.678183 − 0.313757I
u = −0.524571
a = 0.862725
b = 0.524571
−0.323696 2.44920
u = −0.41489 + 1.57652I
a = −0.404481 + 0.632682I
b = 0.41489 − 1.57652I
4.14493 + 5.44292I 3.66282 − 5.29674I
u = −0.41489 − 1.57652I
a = −0.404481 − 0.632682I
b = 0.41489 + 1.57652I
4.14493 − 5.44292I 3.66282 + 5.29674I
10
III.
I
u
3
= h8.06 × 10
4
u
11
− 4.75 × 10
5
u
10
+ · · · + 2.67 × 10
6
b − 7.54 × 10
6
, 1.79 ×
10
6
u
11
−1.20×10
5
u
10
+· · ·+2.94×10
7
a+6.96×10
7
, u
12
−2u
11
+· · ·−5u+11i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
8
=
−0.0607854u
11
+ 0.00408601u
10
+ ··· − 2.36373u − 2.36536
−0.0301237u
11
+ 0.177732u
10
+ ··· − 1.72718u + 2.81991
a
7
=
−0.0607854u
11
+ 0.00408601u
10
+ ··· − 2.36373u − 2.36536
−0.0213565u
11
+ 0.254975u
10
+ ··· − 1.64596u + 4.11224
a
6
=
−0.0909091u
11
+ 0.181818u
10
+ ··· − 4.09091u + 0.454545
−0.0301237u
11
+ 0.177732u
10
+ ··· − 0.727180u + 2.81991
a
2
=
0.256355u
11
− 0.482587u
10
+ ··· + 7.74069u + 0.445403
−0.00489332u
11
− 0.0509161u
10
+ ··· − 0.643385u − 4.28738
a
1
=
0.251462u
11
− 0.533503u
10
+ ··· + 7.09731u − 3.84198
−0.00489332u
11
− 0.0509161u
10
+ ··· − 0.643385u − 4.28738
a
5
=
0.268729u
11
− 0.424867u
10
+ ··· + 9.92533u + 0.682260
0.0431217u
11
− 0.254037u
10
+ ··· − 1.36716u − 6.19453
a
11
=
−0.0475752u
11
+ 0.137019u
10
+ ··· − 1.83773u + 2.65443
0.108361u
11
− 0.141105u
10
+ ··· + 5.20146u − 0.289069
a
9
=
0.107514u
11
− 0.277645u
10
+ ··· + 3.09999u − 2.88464
−0.159615u
11
+ 0.245201u
10
+ ··· − 5.43439u − 0.607579
a
10
=
−0.0521010u
11
− 0.0324441u
10
+ ··· − 2.33440u − 3.49222
−0.159615u
11
+ 0.245201u
10
+ ··· − 5.43439u − 0.607579
(ii) Obstruction class = −1
(iii) Cusp Shapes =
364002
2674873
u
11
−
239807
2674873
u
10
+ ··· +
14456768
2674873
u +
4628741
2674873
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 10u
5
+ 37u
4
+ 63u
3
+ 50u
2
+ 8u + 1)
2
c
2
, c
5
(u
6
− 2u
5
− 3u
4
+ 5u
3
+ 4u
2
− 4u + 1)
2
c
3
, c
6
u
12
− 2u
11
+ ··· − 5u + 11
c
4
, c
9
u
12
+ 10u
10
+ ··· + 21u + 85
c
7
, c
8
, c
11
(u
6
− u
5
+ 2u
4
− u
3
+ 3u
2
− u + 2)
2
c
10
, c
12
u
12
+ 3u
11
+ ··· + 34u + 97
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 26y
5
+ 209y
4
− 427y
3
+ 1566y
2
+ 36y + 1)
2
c
2
, c
5
(y
6
− 10y
5
+ 37y
4
− 63y
3
+ 50y
2
− 8y + 1)
2
c
3
, c
6
y
12
+ 4y
11
+ ··· + 965y + 121
c
4
, c
9
y
12
+ 20y
11
+ ··· + 4489y + 7225
c
7
, c
8
, c
11
(y
6
+ 3y
5
+ 8y
4
+ 13y
3
+ 15y
2
+ 11y + 4)
2
c
10
, c
12
y
12
+ 13y
11
+ ··· + 6410y + 9409
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.954376 + 0.767237I
a = −0.347916 + 0.700187I
b = −0.288553 − 1.211850I
−1.32320 + 0.88172I −1.96296 − 1.82677I
u = −0.954376 − 0.767237I
a = −0.347916 − 0.700187I
b = −0.288553 + 1.211850I
−1.32320 − 0.88172I −1.96296 + 1.82677I
u = −0.288553 + 1.211850I
a = 0.768435 − 0.013672I
b = −0.954376 − 0.767237I
−1.32320 − 0.88172I −1.96296 + 1.82677I
u = −0.288553 − 1.211850I
a = 0.768435 + 0.013672I
b = −0.954376 + 0.767237I
−1.32320 + 0.88172I −1.96296 − 1.82677I
u = 0.507879 + 1.312290I
a = 0.416941 + 0.844475I
b = −0.16044 − 1.50723I
3.57385 − 3.35669I 1.80671 + 2.26936I
u = 0.507879 − 1.312290I
a = 0.416941 − 0.844475I
b = −0.16044 + 1.50723I
3.57385 + 3.35669I 1.80671 − 2.26936I
u = 0.102054 + 0.545648I
a = −1.46225 − 1.37604I
b = 1.79344 − 0.39470I
−12.94270 − 2.40920I 0.65626 + 2.92591I
u = 0.102054 − 0.545648I
a = −1.46225 + 1.37604I
b = 1.79344 + 0.39470I
−12.94270 + 2.40920I 0.65626 − 2.92591I
u = −0.16044 + 1.50723I
a = −0.577713 + 0.656253I
b = 0.507879 − 1.312290I
3.57385 + 3.35669I 1.80671 − 2.26936I
u = −0.16044 − 1.50723I
a = −0.577713 − 0.656253I
b = 0.507879 + 1.312290I
3.57385 − 3.35669I 1.80671 + 2.26936I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.79344 + 0.39470I
a = 0.429775 + 0.428603I
b = 0.102054 − 0.545648I
−12.94270 + 2.40920I 0.65626 − 2.92591I
u = 1.79344 − 0.39470I
a = 0.429775 − 0.428603I
b = 0.102054 + 0.545648I
−12.94270 − 2.40920I 0.65626 + 2.92591I
15
IV. I
u
4
= hb − u − 1, a, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
−u − 1
a
8
=
0
u + 1
a
7
=
0
u + 1
a
6
=
u + 1
1
a
2
=
−u
−1
a
1
=
−u − 1
−1
a
5
=
1
0
a
11
=
0
u
a
9
=
0
u + 1
a
10
=
u + 1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
c
12
(u − 1)
2
c
3
, c
4
, c
6
c
9
u
2
+ u + 1
c
5
(u + 1)
2
c
7
, c
8
, c
11
u
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
, c
12
(y −1)
2
c
3
, c
4
, c
6
c
9
y
2
+ y + 1
c
7
, c
8
, c
11
y
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
0 3.00000
u = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
0 3.00000
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u
6
+ 10u
5
+ 37u
4
+ 63u
3
+ 50u
2
+ 8u + 1)
2
· (u
9
− 11u
8
+ ··· + 105u − 25)(u
15
+ 20u
14
+ ··· + 849u + 16)
c
2
(u − 1)
2
(u
6
− 2u
5
− 3u
4
+ 5u
3
+ 4u
2
− 4u + 1)
2
· (u
9
+ 5u
8
+ 7u
7
− 3u
6
− 14u
5
− 4u
4
+ 13u
3
+ 8u
2
− 5u − 5)
· (u
15
+ 8u
14
+ ··· + 23u − 4)
c
3
, c
6
(u
2
+ u + 1)(u
9
+ 3u
7
− 2u
6
− 3u
4
− 4u
3
+ 3u
2
+ 4u + 1)
· (u
12
− 2u
11
+ ··· − 5u + 11)(u
15
+ 10u
13
+ ··· + u
2
− 1)
c
4
, c
9
(u
2
+ u + 1)(u
9
+ 4u
7
− 4u
5
+ 7u
4
+ 3u
3
− 4u
2
+ u + 1)
· (u
12
+ 10u
10
+ ··· + 21u + 85)(u
15
+ 13u
13
+ ··· + u − 1)
c
5
(u + 1)
2
(u
6
− 2u
5
− 3u
4
+ 5u
3
+ 4u
2
− 4u + 1)
2
· (u
9
− 5u
8
+ 7u
7
+ 3u
6
− 14u
5
+ 4u
4
+ 13u
3
− 8u
2
− 5u + 5)
· (u
15
+ 8u
14
+ ··· + 23u − 4)
c
7
, c
8
u
2
(u
6
− u
5
+ 2u
4
− u
3
+ 3u
2
− u + 2)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 20u
5
+ 22u
4
+ 23u
3
+ 17u
2
+ 11u + 3)
· (u
15
+ 6u
14
+ ··· − 5u − 2)
c
10
, c
12
(u − 1)
2
(u
9
+ u
8
+ 5u
7
+ 6u
6
+ 8u
5
− u
3
− 3u
2
− u − 1)
· (u
12
+ 3u
11
+ ··· + 34u + 97)(u
15
− u
14
+ ··· − 11u − 1)
c
11
u
2
(u
6
− u
5
+ 2u
4
− u
3
+ 3u
2
− u + 2)
2
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 20u
5
− 22u
4
+ 23u
3
− 17u
2
+ 11u − 3)
· (u
15
+ 6u
14
+ ··· − 5u − 2)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
(y
6
− 26y
5
+ 209y
4
− 427y
3
+ 1566y
2
+ 36y + 1)
2
· (y
9
− 19y
8
+ ··· − 675y −625)(y
15
− 44y
14
+ ··· + 606753y −256)
c
2
, c
5
(y −1)
2
(y
6
− 10y
5
+ 37y
4
− 63y
3
+ 50y
2
− 8y + 1)
2
· (y
9
− 11y
8
+ ··· + 105y −25)(y
15
− 20y
14
+ ··· + 849y −16)
c
3
, c
6
(y
2
+ y + 1)
· (y
9
+ 6y
8
+ 9y
7
− 12y
6
− 28y
5
+ 27y
4
+ 38y
3
− 35y
2
+ 10y −1)
· (y
12
+ 4y
11
+ ··· + 965y + 121)(y
15
+ 20y
14
+ ··· + 2y −1)
c
4
, c
9
(y
2
+ y + 1)
· (y
9
+ 8y
8
+ 8y
7
− 26y
6
+ 42y
5
− 65y
4
+ 57y
3
− 24y
2
+ 9y −1)
· (y
12
+ 20y
11
+ ··· + 4489y + 7225)(y
15
+ 26y
14
+ ··· − 3y −1)
c
7
, c
8
, c
11
y
2
(y
6
+ 3y
5
+ 8y
4
+ 13y
3
+ 15y
2
+ 11y + 4)
2
· (y
9
+ 7y
8
+ 26y
7
+ 65y
6
+ 116y
5
+ 152y
4
+ 143y
3
+ 85y
2
+ 19y −9)
· (y
15
+ 10y
14
+ ··· − 39y −4)
c
10
, c
12
((y −1)
2
)(y
9
+ 9y
8
+ ··· − 5y −1)
· (y
12
+ 13y
11
+ ··· + 6410y + 9409)(y
15
+ 19y
14
+ ··· + 95y −1)
21
