12n
0203
(K12n
0203
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 4 12 5 8 6 10
Solving Sequence
3,5
2 1
4,10
9 6 12 8 7 11
c
2
c
1
c
4
c
9
c
5
c
12
c
8
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−51478029223711u
17
− 94965699826026u
16
+ ··· + 9603901893745904b − 98088892223296,
− 2.34490 × 10
14
u
17
− 5.69398 × 10
14
u
16
+ ··· + 9.60390 × 10
15
a − 3.43754 × 10
16
,
u
18
+ 5u
17
+ ··· − 108u + 16i
I
u
2
= h−u
11
− 4u
10
− 3u
9
+ 5u
8
+ 7u
7
− 2u
6
− 4u
5
+ u
4
+ 2u
3
+ u
2
+ b + u,
− u
11
− 4u
10
− 2u
9
+ 9u
8
+ 11u
7
− 3u
6
− 8u
5
− 2u
4
− 2u
3
− u
2
+ a + 2u + 1,
u
12
+ 5u
11
+ 7u
10
− 3u
9
− 17u
8
− 13u
7
+ 4u
6
+ 12u
5
+ 8u
4
+ 2u
3
− 2u
2
− 2u − 1i
I
u
3
= ha
2
+ 2b − a + 2, a
3
+ 2a + 1, u − 1i
I
u
4
= h−14a
3
u + 5a
3
− 10a
2
u + 8a
2
+ 27au + 31b − 3a + 12u + 9,
a
4
+ a
3
+ 6a
2
u + 14a
2
+ 6au + 14a + 30u + 73, u
2
+ 2u − 1i
I
u
5
= h−a
3
+ b − 2a + 1, a
4
− a
3
+ 2a
2
− 2a + 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 45 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−5.15 × 10
13
u
17
− 9.50 × 10
13
u
16
+ · · · + 9.60 × 10
15
b − 9.81 ×
10
13
, −2.34 × 10
14
u
17
− 5.69 × 10
14
u
16
+ · · · + 9.60 × 10
15
a − 3.44 ×
10
16
, u
18
+ 5u
17
+ · · · − 108u + 16i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
0.0244161u
17
+ 0.0592882u
16
+ ··· − 2.08611u + 3.57931
0.00536012u
17
+ 0.00988824u
16
+ ··· − 2.52686u + 0.0102134
a
9
=
0.0244161u
17
+ 0.0592882u
16
+ ··· − 2.08611u + 3.57931
−0.0722239u
17
− 0.275667u
16
+ ··· + 4.64539u − 0.994467
a
6
=
−0.00210596u
17
− 0.0126160u
16
+ ··· + 1.37231u − 1.55076
−0.0194628u
17
− 0.0641489u
16
+ ··· + 1.60320u + 0.0763384
a
12
=
0.00368464u
17
+ 0.0157751u
16
+ ··· − 1.75467u + 2.18995
−0.0138662u
17
− 0.0634618u
16
+ ··· − 0.358806u − 0.0322530
a
8
=
−0.0979771u
17
− 0.396405u
16
+ ··· + 9.53653u + 1.24502
0.0102874u
17
+ 0.0611624u
16
+ ··· − 2.32701u − 0.0719485
a
7
=
−0.0882516u
17
− 0.373557u
16
+ ··· + 10.5756u + 1.08043
−0.0373820u
17
− 0.114869u
16
+ ··· + 1.65191u − 0.649024
a
11
=
−0.126113u
17
− 0.483663u
16
+ ··· + 11.1577u + 1.06434
0.0672052u
17
+ 0.236972u
16
+ ··· − 8.81033u + 0.956875
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
7248898902357663
38415607574983616
u
17
−
19550123270823501
19207803787491808
u
16
+···−
53749314921709817
9603901893745904
u−
32406067335746281
2400975473436476
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 19u
17
+ ··· + 15984u + 256
c
2
, c
4
u
18
− 5u
17
+ ··· + 108u + 16
c
3
, c
7
u
18
− 9u
16
+ ··· − 160u − 128
c
5
, c
6
, c
9
c
11
u
18
+ 4u
16
+ ··· + u − 1
c
8
u
18
+ 9u
17
+ ··· + 28u + 4
c
10
, c
12
u
18
− 4u
17
+ ··· − 13u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 13y
17
+ ··· − 211267328y + 65536
c
2
, c
4
y
18
− 19y
17
+ ··· − 15984y + 256
c
3
, c
7
y
18
− 18y
17
+ ··· − 257024y + 16384
c
5
, c
6
, c
9
c
11
y
18
+ 8y
17
+ ··· − 13y + 1
c
8
y
18
+ 3y
17
+ ··· + 88y + 16
c
10
, c
12
y
18
− 12y
17
+ ··· − 27y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498072 + 0.803560I
a = 0.804411 − 0.072881I
b = 0.601639 + 0.155591I
3.85179 + 0.21064I −8.48737 − 0.11416I
u = −0.498072 − 0.803560I
a = 0.804411 + 0.072881I
b = 0.601639 − 0.155591I
3.85179 − 0.21064I −8.48737 + 0.11416I
u = 0.854940
a = −0.328563
b = −2.47470
−2.86169 −58.1310
u = 0.731104 + 0.323621I
a = 0.210674 − 0.558567I
b = −0.567133 + 0.114177I
−0.825090 − 0.258812I −11.03204 − 0.79258I
u = 0.731104 − 0.323621I
a = 0.210674 + 0.558567I
b = −0.567133 − 0.114177I
−0.825090 + 0.258812I −11.03204 + 0.79258I
u = −1.067010 + 0.610706I
a = −0.142436 + 0.567488I
b = −0.526588 + 0.193604I
2.12814 + 5.07138I −8.91832 − 8.83616I
u = −1.067010 − 0.610706I
a = −0.142436 − 0.567488I
b = −0.526588 − 0.193604I
2.12814 − 5.07138I −8.91832 + 8.83616I
u = −1.236400 + 0.168858I
a = 0.057682 + 1.280350I
b = 0.079988 + 0.291227I
7.38910 − 4.84420I −12.25477 − 0.83439I
u = −1.236400 − 0.168858I
a = 0.057682 − 1.280350I
b = 0.079988 − 0.291227I
7.38910 + 4.84420I −12.25477 + 0.83439I
u = 1.41842 + 0.74975I
a = −0.720025 + 0.318355I
b = −1.45615 + 0.15501I
−3.70938 + 0.73390I −13.05363 − 1.20335I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41842 − 0.74975I
a = −0.720025 − 0.318355I
b = −1.45615 − 0.15501I
−3.70938 − 0.73390I −13.05363 + 1.20335I
u = 1.22478 + 1.30063I
a = 0.896477 − 0.274017I
b = 1.44915 − 0.14091I
−2.93065 − 5.27680I −11.38955 + 3.92982I
u = 1.22478 − 1.30063I
a = 0.896477 + 0.274017I
b = 1.44915 + 0.14091I
−2.93065 + 5.27680I −11.38955 − 3.92982I
u = −1.73766 + 0.57784I
a = 0.621844 − 0.638194I
b = 1.94004 − 0.09952I
−12.9639 + 5.8348I −10.78539 − 2.21152I
u = −1.73766 − 0.57784I
a = 0.621844 + 0.638194I
b = 1.94004 + 0.09952I
−12.9639 − 5.8348I −10.78539 + 2.21152I
u = 0.132712
a = 3.15830
b = −0.353393
−0.661114 −14.7530
u = −1.82899 + 0.67910I
a = −0.768496 + 0.689009I
b = −2.10690 + 0.22733I
−11.7403 + 13.7046I −10.51182 − 5.40024I
u = −1.82899 − 0.67910I
a = −0.768496 − 0.689009I
b = −2.10690 − 0.22733I
−11.7403 − 13.7046I −10.51182 + 5.40024I
6
II.
I
u
2
= h−u
11
−4u
10
+· · ·+b+u, −u
11
−4u
10
+· · ·+a+1, u
12
+5u
11
+· · ·−2u−1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
u
11
+ 4u
10
+ 2u
9
− 9u
8
− 11u
7
+ 3u
6
+ 8u
5
+ 2u
4
+ 2u
3
+ u
2
− 2u − 1
u
11
+ 4u
10
+ 3u
9
− 5u
8
− 7u
7
+ 2u
6
+ 4u
5
− u
4
− 2u
3
− u
2
− u
a
9
=
u
11
+ 4u
10
+ 2u
9
− 9u
8
− 11u
7
+ 3u
6
+ 8u
5
+ 2u
4
+ 2u
3
+ u
2
− 2u − 1
u
11
+ 3u
10
− 4u
8
+ 2u
7
+ 8u
6
− 2u
5
− 8u
4
− 4u
3
+ 1
a
6
=
u
11
+ 5u
10
+ ··· − 4u − 3
u
10
+ 4u
9
+ 2u
8
− 9u
7
− 12u
6
+ 7u
4
+ 4u
3
+ 2u
2
− u − 1
a
12
=
−u
11
− 5u
10
+ ··· + 3u + 3
−u
11
− 5u
10
− 8u
9
− 2u
8
+ 9u
7
+ 11u
6
+ 5u
5
− u
4
− 4u
3
− 5u
2
− u
a
8
=
−2u
11
− 8u
10
− 6u
9
+ 12u
8
+ 22u
7
+ 3u
6
− 14u
5
− 10u
4
− u
3
+ 2u + 1
u
8
+ 3u
7
− 5u
5
− 3u
4
+ 2u
3
+ u
2
+ u
a
7
=
−2u
11
− 8u
10
− 5u
9
+ 15u
8
+ 22u
7
− 2u
6
− 17u
5
− 8u
4
+ u
2
+ 2u + 1
−u
11
− 3u
10
+ u
9
+ 9u
8
+ 6u
7
− 7u
6
− 9u
5
− 2u
4
+ 3u
3
+ 2u
2
+ u
a
11
=
u
11
+ 4u
10
+ 2u
9
− 9u
8
− 11u
7
+ 3u
6
+ 8u
5
+ 2u
4
+ 2u
3
− 2u
u
11
+ 4u
10
+ 3u
9
− 5u
8
− 7u
7
+ 2u
6
+ 4u
5
− u
3
− 2u
2
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
11
+ 3u
10
+ 2u
9
−7u
7
−16u
6
−15u
5
+ 5u
4
+ 10u
3
+ 10u
2
+ 5u −2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 11u
11
+ ··· − 4u
2
+ 1
c
2
u
12
+ 5u
11
+ ··· − 2u − 1
c
3
u
12
+ 4u
11
+ ··· − 2u − 1
c
4
u
12
− 5u
11
+ ··· + 2u − 1
c
5
, c
11
u
12
+ 4u
10
+ ··· − 7u + 1
c
6
, c
9
u
12
+ 4u
10
+ ··· + 7u + 1
c
7
u
12
− 4u
11
+ ··· + 2u − 1
c
8
u
12
+ 3u
11
+ 5u
10
+ 2u
9
− u
8
− 4u
7
+ 3u
6
+ 3u
4
− 6u
3
− 2u
2
− 4u + 1
c
10
, c
12
u
12
+ 4u
11
− 2u
10
+ 6u
9
+ 3u
8
+ 3u
6
+ 4u
5
− u
4
− 2u
3
+ 5u
2
− 3u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 31y
11
+ ··· − 8y + 1
c
2
, c
4
y
12
− 11y
11
+ ··· − 4y
2
+ 1
c
3
, c
7
y
12
− 6y
11
+ ··· + 4y + 1
c
5
, c
6
, c
9
c
11
y
12
+ 8y
11
+ ··· − 69y + 1
c
8
y
12
+ y
11
+ ··· − 20y + 1
c
10
, c
12
y
12
− 20y
11
+ ··· + y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.057460 + 0.095971I
a = −0.406859 − 1.196210I
b = −3.90485 + 1.89018I
3.16210 − 2.20591I −7.78632 − 10.61857I
u = 1.057460 − 0.095971I
a = −0.406859 + 1.196210I
b = −3.90485 − 1.89018I
3.16210 + 2.20591I −7.78632 + 10.61857I
u = −1.069100 + 0.511997I
a = −0.555353 + 0.877193I
b = −0.927124 − 0.102377I
4.24653 + 6.29114I −8.72473 − 7.60786I
u = −1.069100 − 0.511997I
a = −0.555353 − 0.877193I
b = −0.927124 + 0.102377I
4.24653 − 6.29114I −8.72473 + 7.60786I
u = 0.716863
a = −0.162026
b = −1.91362
−2.72064 6.26870
u = −0.462027 + 0.528026I
a = 1.05312 − 1.37955I
b = 0.804945 − 0.512875I
6.06972 − 2.00606I −4.60411 + 0.72202I
u = −0.462027 − 0.528026I
a = 1.05312 + 1.37955I
b = 0.804945 + 0.512875I
6.06972 + 2.00606I −4.60411 − 0.72202I
u = −1.154720 + 0.677187I
a = −0.051735 − 0.619586I
b = −0.108869 − 0.166947I
2.03383 + 4.28434I −10.27189 + 0.84720I
u = −1.154720 − 0.677187I
a = −0.051735 + 0.619586I
b = −0.108869 + 0.166947I
2.03383 − 4.28434I −10.27189 − 0.84720I
u = −0.034452 + 0.645190I
a = −1.85887 − 0.62285I
b = −0.388161 + 0.546694I
5.19852 + 1.22317I −3.65798 − 0.64482I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.034452 − 0.645190I
a = −1.85887 + 0.62285I
b = −0.388161 − 0.546694I
5.19852 − 1.22317I −3.65798 + 0.64482I
u = −2.39117
a = 0.801439
b = 1.96174
−15.6717 −10.1790
11
III. I
u
3
= ha
2
+ 2b − a + 2, a
3
+ 2a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
4
=
1
0
a
10
=
a
−
1
2
a
2
+
1
2
a − 1
a
9
=
a
−
1
2
a
2
−
1
2
a − 1
a
6
=
−a
2
1
2
a
2
+
1
2
a
12
=
−a
2
−
1
2
a
2
−
3
2
a
8
=
a
2
− a − 1
0
a
7
=
a
2
− a − 1
0
a
11
=
−a
2
− 2a − 1
−
1
2
a
2
+
1
2
a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
15
4
a
2
+
15
2
a −
31
4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
u
3
+ 2u − 1
c
8
u
3
− 3u
2
+ 5u − 2
c
9
, c
10
, c
11
c
12
u
3
+ 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
c
8
y
3
+ y
2
+ 13y −4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.22670 + 1.46771I
b = 0.164742 + 0.401127I
7.79580 − 5.13794I 1.83568 + 8.51237I
u = 1.00000
a = 0.22670 − 1.46771I
b = 0.164742 − 0.401127I
7.79580 + 5.13794I 1.83568 − 8.51237I
u = 1.00000
a = −0.453398
b = −1.32948
−2.43213 −11.9210
15
IV.
I
u
4
= h−14a
3
u − 10a
2
u + · · · − 3a + 9, 6a
2
u + 6au + · · · + 14a + 73, u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
2u − 1
a
1
=
2u
2u − 1
a
4
=
u
−4u + 2
a
10
=
a
0.451613a
3
u + 0.322581a
2
u + ··· + 0.0967742a − 0.290323
a
9
=
a
0.451613a
3
u + 0.322581a
2
u + ··· − 0.903226a − 0.290323
a
6
=
−a
2
u
−0.161290a
3
u + 3.74194a
2
u + ··· + 0.322581a + 1.03226
a
12
=
−0.322581a
3
u − 0.516129a
2
u + ··· + 0.645161a + 2.06452
0.774194a
3
u + 1.83871a
2
u + ··· − 0.548387a + 0.645161
a
8
=
−1
−u + 1
a
7
=
3u − 2
−15u + 7
a
11
=
−0.451613a
3
u − 0.322581a
2
u + ··· − 0.0967742a + 0.290323
1.96774a
3
u + 1.54839a
2
u + ··· + 3.06452a − 0.193548
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
56
31
a
3
u +
20
31
a
3
−
40
31
a
2
u +
32
31
a
2
−
16
31
au −
12
31
a +
48
31
u −
212
31
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ 6u + 1)
4
c
2
, c
4
(u
2
− 2u − 1)
4
c
3
, c
7
(u
2
− 4u + 2)
4
c
5
, c
6
, c
9
c
11
u
8
+ 2u
7
− u
6
+ 14u
4
− 18u
3
+ 56u
2
− 40u + 49
c
8
(u
2
− u + 1)
4
c
10
, c
12
u
8
+ 2u
7
− 35u
6
− 16u
5
+ 570u
4
− 1118u
3
+ 1720u
2
− 1316u + 409
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 34y + 1)
4
c
2
, c
4
(y
2
− 6y + 1)
4
c
3
, c
7
(y
2
− 12y + 4)
4
c
5
, c
6
, c
9
c
11
y
8
− 6y
7
+ ··· + 3888y + 2401
c
8
(y
2
+ y + 1)
4
c
10
, c
12
y
8
− 74y
7
+ ··· − 324896y + 167281
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.414214
a = −1.07609 + 2.49104I
b = 0.945731 − 0.165796I
4.11234 + 2.02988I −10.00000 − 3.46410I
u = 0.414214
a = −1.07609 − 2.49104I
b = 0.945731 + 0.165796I
4.11234 − 2.02988I −10.00000 + 3.46410I
u = 0.414214
a = 0.57609 + 3.35706I
b = 0.26138 − 2.25657I
4.11234 − 2.02988I −10.00000 + 3.46410I
u = 0.414214
a = 0.57609 − 3.35706I
b = 0.26138 + 2.25657I
4.11234 + 2.02988I −10.00000 − 3.46410I
u = −2.41421
a = −1.037090 + 0.476159I
b = −2.00374 + 0.28352I
−15.6269 − 2.0299I −10.00000 + 3.46410I
u = −2.41421
a = −1.037090 − 0.476159I
b = −2.00374 − 0.28352I
−15.6269 + 2.0299I −10.00000 − 3.46410I
u = −2.41421
a = 0.537085 + 0.389866I
b = 1.79664 + 0.07519I
−15.6269 − 2.0299I −10.00000 + 3.46410I
u = −2.41421
a = 0.537085 − 0.389866I
b = 1.79664 − 0.07519I
−15.6269 + 2.0299I −10.00000 − 3.46410I
19
V. I
u
5
= h−a
3
+ b − 2a + 1, a
4
− a
3
+ 2a
2
− 2a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
4
=
1
0
a
10
=
a
a
3
+ 2a − 1
a
9
=
a
a
3
+ a − 1
a
6
=
−a
2
−a
3
+ a
2
− a + 2
a
12
=
−a
2
−a
3
− a
a
8
=
1
0
a
7
=
1
0
a
11
=
−a
3
− a + 1
a
3
+ 2a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
3
+ 4a − 12
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
8
(u
2
+ u + 1)
2
c
9
, c
10
, c
11
c
12
u
4
− u
3
+ 2u
2
− 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
8
(y
2
+ y + 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.621744 + 0.440597I
b = 0.121744 + 1.306620I
1.64493 − 2.02988I −10.00000 + 3.46410I
u = 1.00000
a = 0.621744 − 0.440597I
b = 0.121744 − 1.306620I
1.64493 + 2.02988I −10.00000 − 3.46410I
u = 1.00000
a = −0.121744 + 1.306620I
b = −0.621744 + 0.440597I
1.64493 + 2.02988I −10.00000 − 3.46410I
u = 1.00000
a = −0.121744 − 1.306620I
b = −0.621744 − 0.440597I
1.64493 − 2.02988I −10.00000 + 3.46410I
23
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
7
)(u
2
+ 6u + 1)
4
(u
12
− 11u
11
+ ··· − 4u
2
+ 1)
· (u
18
+ 19u
17
+ ··· + 15984u + 256)
c
2
((u − 1)
7
)(u
2
− 2u − 1)
4
(u
12
+ 5u
11
+ ··· − 2u − 1)
· (u
18
− 5u
17
+ ··· + 108u + 16)
c
3
u
7
(u
2
− 4u + 2)
4
(u
12
+ 4u
11
+ ··· − 2u − 1)
· (u
18
− 9u
16
+ ··· − 160u − 128)
c
4
((u + 1)
7
)(u
2
− 2u − 1)
4
(u
12
− 5u
11
+ ··· + 2u − 1)
· (u
18
− 5u
17
+ ··· + 108u + 16)
c
5
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
8
+ 2u
7
− u
6
+ 14u
4
− 18u
3
+ 56u
2
− 40u + 49)
· (u
12
+ 4u
10
+ ··· − 7u + 1)(u
18
+ 4u
16
+ ··· + u − 1)
c
6
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
8
+ 2u
7
− u
6
+ 14u
4
− 18u
3
+ 56u
2
− 40u + 49)
· (u
12
+ 4u
10
+ ··· + 7u + 1)(u
18
+ 4u
16
+ ··· + u − 1)
c
7
u
7
(u
2
− 4u + 2)
4
(u
12
− 4u
11
+ ··· + 2u − 1)
· (u
18
− 9u
16
+ ··· − 160u − 128)
c
8
(u
2
− u + 1)
4
(u
2
+ u + 1)
2
(u
3
− 3u
2
+ 5u − 2)
· (u
12
+ 3u
11
+ 5u
10
+ 2u
9
− u
8
− 4u
7
+ 3u
6
+ 3u
4
− 6u
3
− 2u
2
− 4u + 1)
· (u
18
+ 9u
17
+ ··· + 28u + 4)
c
9
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
8
+ 2u
7
− u
6
+ 14u
4
− 18u
3
+ 56u
2
− 40u + 49)
· (u
12
+ 4u
10
+ ··· + 7u + 1)(u
18
+ 4u
16
+ ··· + u − 1)
c
10
, c
12
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
8
+ 2u
7
− 35u
6
− 16u
5
+ 570u
4
− 1118u
3
+ 1720u
2
− 1316u + 409)
· (u
12
+ 4u
11
− 2u
10
+ 6u
9
+ 3u
8
+ 3u
6
+ 4u
5
− u
4
− 2u
3
+ 5u
2
− 3u + 1)
· (u
18
− 4u
17
+ ··· − 13u + 1)
c
11
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
8
+ 2u
7
− u
6
+ 14u
4
− 18u
3
+ 56u
2
− 40u + 49)
· (u
12
+ 4u
10
+ ··· − 7u + 1)(u
18
+ 4u
16
+ ··· + u − 1)
24
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
7
)(y
2
− 34y + 1)
4
(y
12
− 31y
11
+ ··· − 8y + 1)
· (y
18
+ 13y
17
+ ··· − 211267328y + 65536)
c
2
, c
4
((y −1)
7
)(y
2
− 6y + 1)
4
(y
12
− 11y
11
+ ··· − 4y
2
+ 1)
· (y
18
− 19y
17
+ ··· − 15984y + 256)
c
3
, c
7
y
7
(y
2
− 12y + 4)
4
(y
12
− 6y
11
+ ··· + 4y + 1)
· (y
18
− 18y
17
+ ··· − 257024y + 16384)
c
5
, c
6
, c
9
c
11
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
8
− 6y
7
+ ··· + 3888y + 2401)
· (y
12
+ 8y
11
+ ··· − 69y + 1)(y
18
+ 8y
17
+ ··· − 13y + 1)
c
8
((y
2
+ y + 1)
6
)(y
3
+ y
2
+ 13y −4)(y
12
+ y
11
+ ··· − 20y + 1)
· (y
18
+ 3y
17
+ ··· + 88y + 16)
c
10
, c
12
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
8
− 74y
7
+ ··· − 324896y + 167281)(y
12
− 20y
11
+ ··· + y + 1)
· (y
18
− 12y
17
+ ··· − 27y + 1)
25
