12n
0629
(K12n
0629
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 3 11 2 5 6 1 4 6
Solving Sequence
3,7
2 8
1,11
6 5 9 4 10 12
c
2
c
7
c
1
c
6
c
5
c
8
c
4
c
10
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h979u
17
− 284u
16
+ ··· + 2700b − 1352, −3937u
17
− 1528u
16
+ ··· + 2700a − 754,
u
18
+ 8u
16
+ ··· − u + 2i
I
u
2
= hu
4
− u
3
+ b − u − 1, −u
4
+ a + u, u
5
− u
4
+ u
3
− 2u
2
+ u − 1i
I
u
3
= h44u
11
+ 41u
10
+ ··· + 211b + 343, 516u
11
+ 711u
10
+ ··· + 1055a + 1970,
u
12
+ u
11
+ 8u
10
+ 8u
9
+ 26u
8
+ 23u
7
+ 44u
6
+ 30u
5
+ 41u
4
+ 18u
3
+ 19u
2
+ 5u + 5i
I
u
4
= h−43712u
11
− 79401u
10
+ ··· + 207893b − 981135,
− 365996832u
11
− 669919369u
10
+ ··· + 1070441057a − 7841083848,
u
12
+ u
11
− 4u
10
− 2u
9
+ 16u
8
+ 3u
7
− 26u
6
+ 4u
5
+ 5u
4
− 10u
3
+ 3u
2
+ 29u − 19i
* 4 irreducible components of dim
C
= 0, with total 47 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
= h979u
17
− 284u
16
+ · · · + 2700b − 1352, −3937u
17
− 1528u
16
+ · · · +
2700a − 754, u
18
+ 8u
16
+ · · · − u + 2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
1.45815u
17
+ 0.565926u
16
+ ··· + 9.00519u + 0.279259
−0.362593u
17
+ 0.105185u
16
+ ··· − 1.51407u + 0.500741
a
6
=
0.813333u
17
+ 0.0700000u
16
+ ··· + 3.31000u − 1.44000
0.565926u
17
− 0.386296u
16
+ ··· + 1.73741u − 2.91630
a
5
=
0.247407u
17
+ 0.456296u
16
+ ··· + 1.57259u + 1.47630
0.565926u
17
− 0.386296u
16
+ ··· + 1.73741u − 2.91630
a
9
=
−0.312222u
17
+ 0.356667u
16
+ ··· − 3.17444u + 1.40889
0.396667u
17
+ 0.258889u
16
+ ··· + 5.39333u + 0.604444
a
4
=
−0.318519u
17
+ 0.842593u
16
+ ··· − 0.164815u + 4.39259
0.460741u
17
− 0.529259u
16
+ ··· + 1.59926u − 3.64148
a
10
=
1.64704u
17
+ 0.910370u
16
+ ··· + 10.6330u + 1.11259
−0.340370u
17
+ 0.155185u
16
+ ··· − 1.55296u − 0.0881481
a
12
=
0.615556u
17
+ 0.228889u
16
+ ··· + 4.93111u − 0.357778
1
6
u
17
+
53
180
u
16
+ ··· +
5
3
u +
64
45
(ii) Obstruction class = −1
(iii) Cusp Shapes =
157
27
u
17
+
70
27
u
16
+ ··· +
1184
27
u +
34
27
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 16u
17
+ ··· + 59u + 4
c
2
, c
4
, c
7
c
11
u
18
+ 8u
16
+ ··· + u + 2
c
3
u
18
− 5u
17
+ ··· − 27u + 9
c
5
, c
6
u
18
+ u
17
+ ··· − u + 1
c
8
u
18
− 3u
17
+ ··· − 25u + 125
c
9
u
18
− 5u
17
+ ··· − 125u + 46
c
10
u
18
− 2u
17
+ ··· + 4u + 1
c
12
u
18
+ u
17
+ ··· − 160u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 12y
17
+ ··· + 159y + 16
c
2
, c
4
, c
7
c
11
y
18
+ 16y
17
+ ··· + 59y + 4
c
3
y
18
− 5y
17
+ ··· − 117y + 81
c
5
, c
6
y
18
− 7y
17
+ ··· − 11y + 1
c
8
y
18
+ 11y
17
+ ··· + 194375y + 15625
c
9
y
18
+ 5y
17
+ ··· + 21911y + 2116
c
10
y
18
− 8y
17
+ ··· + 16y + 1
c
12
y
18
+ 55y
17
+ ··· + 10752y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215825 + 1.055720I
a = −0.734208 − 0.778679I
b = −1.64100 + 0.67983I
−2.40740 − 4.93155I −0.09123 + 5.12585I
u = −0.215825 − 1.055720I
a = −0.734208 + 0.778679I
b = −1.64100 − 0.67983I
−2.40740 + 4.93155I −0.09123 − 5.12585I
u = 0.478183 + 1.019630I
a = 0.317066 − 0.189944I
b = 1.32096 + 1.39042I
−2.57674 + 6.69706I −4.74227 − 7.81204I
u = 0.478183 − 1.019630I
a = 0.317066 + 0.189944I
b = 1.32096 − 1.39042I
−2.57674 − 6.69706I −4.74227 + 7.81204I
u = −0.190193 + 1.174750I
a = 1.023770 − 0.233990I
b = −0.071711 + 0.212167I
−10.20590 − 2.87633I −5.03342 + 3.27746I
u = −0.190193 − 1.174750I
a = 1.023770 + 0.233990I
b = −0.071711 − 0.212167I
−10.20590 + 2.87633I −5.03342 − 3.27746I
u = 0.306395 + 0.502489I
a = −1.54759 − 1.06420I
b = −1.43872 + 0.30168I
−5.29960 + 1.10158I −0.68390 − 6.02655I
u = 0.306395 − 0.502489I
a = −1.54759 + 1.06420I
b = −1.43872 − 0.30168I
−5.29960 − 1.10158I −0.68390 + 6.02655I
u = −0.361458 + 0.449248I
a = 0.610707 + 0.324621I
b = 0.276717 − 0.678638I
0.735931 − 0.874748I 7.31455 + 6.56056I
u = −0.361458 − 0.449248I
a = 0.610707 − 0.324621I
b = 0.276717 + 0.678638I
0.735931 + 0.874748I 7.31455 − 6.56056I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.106479 + 0.548573I
a = 0.36979 + 1.39973I
b = −0.823575 − 0.667813I
0.97688 − 1.19294I 6.66369 + 7.49944I
u = 0.106479 − 0.548573I
a = 0.36979 − 1.39973I
b = −0.823575 + 0.667813I
0.97688 + 1.19294I 6.66369 − 7.49944I
u = 1.06422 + 1.22609I
a = −1.204040 + 0.574237I
b = −1.67663 − 0.32270I
8.00245 + 5.89453I 4.19834 − 2.56372I
u = 1.06422 − 1.22609I
a = −1.204040 − 0.574237I
b = −1.67663 + 0.32270I
8.00245 − 5.89453I 4.19834 + 2.56372I
u = −0.07359 + 1.71354I
a = 0.542354 − 0.090003I
b = 0.794398 + 0.297779I
−13.22560 + 1.02068I −1.08623 − 7.18728I
u = −0.07359 − 1.71354I
a = 0.542354 + 0.090003I
b = 0.794398 − 0.297779I
−13.22560 − 1.02068I −1.08623 + 7.18728I
u = −1.11421 + 1.48248I
a = −1.127850 − 0.501165I
b = −1.74044 + 0.32902I
6.7281 − 12.7161I 2.96048 + 6.03348I
u = −1.11421 − 1.48248I
a = −1.127850 + 0.501165I
b = −1.74044 − 0.32902I
6.7281 + 12.7161I 2.96048 − 6.03348I
6
II. I
u
2
= hu
4
− u
3
+ b − u − 1, −u
4
+ a + u, u
5
− u
4
+ u
3
− 2u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
u
4
− u
−u
4
+ u
3
+ u + 1
a
6
=
−u
4
− u
2
+ u
−u
4
+ u
3
− u
2
+ u − 1
a
5
=
−u
3
+ 1
−u
4
+ u
3
− u
2
+ u − 1
a
9
=
u
4
− u
3
− u
−u
4
+ u
3
− u
2
+ 2u
a
4
=
u
4
− 2u
3
+ u
2
− u + 2
−u
4
+ 2u
3
− 2u
2
+ 3u − 2
a
10
=
2u
4
+ u
2
− u
u
3
+ u + 1
a
12
=
u
2
+ 1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
+ 2u
3
− 5u
2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
5
− u
4
− u
3
+ 4u
2
− 3u + 1
c
2
, c
4
u
5
− u
4
+ u
3
− 2u
2
+ u − 1
c
3
u
5
− 4u
4
+ 8u
3
− 9u
2
+ 6u − 1
c
5
, c
9
u
5
− 2u
4
− u
3
+ 2u
2
− 1
c
6
u
5
+ 2u
4
− u
3
− 2u
2
+ 1
c
7
, c
11
u
5
+ u
4
+ u
3
+ 2u
2
+ u + 1
c
8
u
5
− 2u
4
+ 2u
3
− 3u
2
+ 2u − 1
c
12
u
5
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
5
− 3y
4
+ 3y
3
− 8y
2
+ y −1
c
2
, c
4
, c
7
c
11
y
5
+ y
4
− y
3
− 4y
2
− 3y −1
c
3
y
5
+ 4y
3
+ 7y
2
+ 18y −1
c
5
, c
6
, c
9
y
5
− 6y
4
+ 9y
3
− 8y
2
+ 4y −1
c
8
y
5
− 4y
3
− 5y
2
− 2y −1
c
12
y
5
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428550 + 1.039280I
a = 0.438694 + 0.557752I
b = 1.87122 − 1.10766I
−1.91329 − 6.77491I 7.14260 + 9.74210I
u = −0.428550 − 1.039280I
a = 0.438694 − 0.557752I
b = 1.87122 + 1.10766I
−1.91329 + 6.77491I 7.14260 − 9.74210I
u = 0.276511 + 0.728237I
a = −0.232705 − 1.093810I
b = 0.813922 + 0.874646I
0.789751 − 0.607163I 1.60701 − 3.91429I
u = 0.276511 − 0.728237I
a = −0.232705 + 1.093810I
b = 0.813922 − 0.874646I
0.789751 + 0.607163I 1.60701 + 3.91429I
u = 1.30408
a = 1.58802
b = 1.62971
5.53695 7.50080
10
III. I
u
3
= h44u
11
+ 41u
10
+ · · · + 211b + 343, 516u
11
+ 711u
10
+ · · · + 1055a +
1970, u
12
+ u
11
+ · · · + 5u + 5i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
−0.489100u
11
− 0.673934u
10
+ ··· − 2.94692u − 1.86730
−0.208531u
11
− 0.194313u
10
+ ··· − 2.45024u − 1.62559
a
6
=
−0.0796209u
11
+ 0.0530806u
10
+ ··· − 7.73555u − 1.83886
−0.00473934u
11
+ 0.336493u
10
+ ··· − 1.80569u + 0.985782
a
5
=
−0.0748815u
11
− 0.283412u
10
+ ··· − 5.92986u − 2.82464
−0.00473934u
11
+ 0.336493u
10
+ ··· − 1.80569u + 0.985782
a
9
=
0.176303u
11
+ 0.882464u
10
+ ··· + 9.77156u + 3.92891
0.374408u
11
+ 0.417062u
10
+ ··· + 3.64929u + 2.12322
a
4
=
0.249289u
11
− 0.499526u
10
+ ··· − 9.22085u − 6.05213
0.199052u
11
− 0.132701u
10
+ ··· − 1.16114u − 1.40284
a
10
=
−0.863507u
11
− 1.09100u
10
+ ··· − 4.59621u − 3.99052
−0.0426540u
11
+ 0.0284360u
10
+ ··· + 0.748815u − 1.12796
a
12
=
0.367773u
11
+ 1.08815u
10
+ ··· + 5.92133u − 1.69668
−0.341232u
11
+ 0.227488u
10
+ ··· − 1.00948u − 1.02370
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
316
211
u
11
−
352
211
u
10
−
2504
211
u
9
−
2856
211
u
8
−
7676
211
u
7
−
8260
211
u
6
−
11672
211
u
5
−
10564
211
u
4
−
9416
211
u
3
−
6312
211
u
2
−
3080
211
u −
1581
211
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 15u
11
+ ··· − 165u + 25
c
2
, c
4
u
12
+ u
11
+ ··· + 5u + 5
c
3
(u
3
+ u
2
− 1)
4
c
5
u
12
+ u
11
+ ··· + 2u + 1
c
6
u
12
− u
11
+ ··· − 2u + 1
c
7
, c
11
u
12
− u
11
+ ··· − 5u + 5
c
8
u
12
− 3u
11
+ ··· − 54u + 121
c
9
u
12
− u
11
+ ··· + 965u + 475
c
10
u
12
− 3u
11
+ ··· + 6u + 1
c
12
u
12
+ 21u
10
+ 135u
8
+ 300u
6
− 65u
4
− 214u
2
+ 661
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 25y
11
+ ··· + 2325y + 625
c
2
, c
4
, c
7
c
11
y
12
+ 15y
11
+ ··· + 165y + 25
c
3
(y
3
− y
2
+ 2y −1)
4
c
5
, c
6
y
12
+ 9y
11
+ ··· + 2y + 1
c
8
y
12
− 19y
11
+ ··· + 15718y + 14641
c
9
y
12
+ 5y
11
+ ··· + 820575y + 225625
c
10
y
12
− 13y
11
+ ··· + 24y + 1
c
12
(y
6
+ 21y
5
+ 135y
4
+ 300y
3
− 65y
2
− 214y + 661)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.656577 + 0.856222I
a = −0.535394 − 0.579005I
b = −1.61803
−1.25270 + 2.82812I 4.50976 − 2.97945I
u = −0.656577 − 0.856222I
a = −0.535394 + 0.579005I
b = −1.61803
−1.25270 − 2.82812I 4.50976 + 2.97945I
u = −0.461010 + 0.702960I
a = −1.246290 + 0.566838I
b = −1.61803
−5.39028 −2.01951 + 0.I
u = −0.461010 − 0.702960I
a = −1.246290 − 0.566838I
b = −1.61803
−5.39028 −2.01951 + 0.I
u = 0.301588 + 0.677598I
a = 2.11023 + 0.98157I
b = 0.618034
−9.14838 + 2.82812I 4.50976 − 2.97945I
u = 0.301588 − 0.677598I
a = 2.11023 − 0.98157I
b = 0.618034
−9.14838 − 2.82812I 4.50976 + 2.97945I
u = 0.308571 + 1.258780I
a = −0.677986 + 0.401303I
b = −1.61803
−1.25270 + 2.82812I 4.50976 − 2.97945I
u = 0.308571 − 1.258780I
a = −0.677986 − 0.401303I
b = −1.61803
−1.25270 − 2.82812I 4.50976 + 2.97945I
u = −0.16866 + 1.48546I
a = −0.234496 + 0.241588I
b = 0.618034
−9.14838 − 2.82812I 4.50976 + 2.97945I
u = −0.16866 − 1.48546I
a = −0.234496 − 0.241588I
b = 0.618034
−9.14838 + 2.82812I 4.50976 − 2.97945I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17609 + 1.70638I
a = 0.583936 + 0.330427I
b = 0.618034
−13.2860 −2.01951 + 0.I
u = 0.17609 − 1.70638I
a = 0.583936 − 0.330427I
b = 0.618034
−13.2860 −2.01951 + 0.I
15
IV.
I
u
4
= h−4.37 × 10
4
u
11
− 7.94 × 10
4
u
10
+ · · · + 2.08 × 10
5
b − 9.81 × 10
5
, −3.66 ×
10
8
u
11
−6.70×10
8
u
10
+· · ·+1.07×10
9
a−7.84×10
9
, u
12
+u
11
+· · ·+29u−19i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
0.341912u
11
+ 0.625835u
10
+ ··· − 2.65709u + 7.32510
0.210262u
11
+ 0.381932u
10
+ ··· − 1.21740u + 4.71942
a
6
=
−0.467649u
11
− 0.798651u
10
+ ··· + 2.93801u − 11.4944
−0.219258u
11
− 0.339998u
10
+ ··· + 1.34725u − 5.50844
a
5
=
−0.248391u
11
− 0.458653u
10
+ ··· + 1.59076u − 5.98593
−0.219258u
11
− 0.339998u
10
+ ··· + 1.34725u − 5.50844
a
9
=
−0.141181u
11
− 0.201538u
10
+ ··· + 1.25160u − 3.49743
−0.0951718u
11
− 0.139896u
10
+ ··· + 0.138622u − 2.31389
a
4
=
0.164884u
11
+ 0.311952u
10
+ ··· − 1.05429u + 4.02767
0.112253u
11
+ 0.259321u
10
+ ··· − 1.21218u + 2.50135
a
10
=
0.353204u
11
+ 0.612703u
10
+ ··· − 3.01116u + 10.6267
0.158360u
11
+ 0.267974u
10
+ ··· − 1.10804u + 5.43443
a
12
=
0.511091u
11
+ 0.907271u
10
+ ··· − 2.97620u + 12.2196
0.299785u
11
+ 0.536124u
10
+ ··· − 1.58475u + 6.27294
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1261620
3314059
u
11
−
264928
473437
u
10
+ ··· +
1837608
3314059
u −
27359429
3314059
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 9u
11
+ ··· − 955u + 361
c
2
, c
4
, c
7
c
11
u
12
− u
11
+ ··· − 29u − 19
c
3
(u
3
+ u
2
− 1)
4
c
5
, c
6
u
12
+ u
11
+ ··· − 424u − 181
c
8
u
12
+ 3u
11
+ ··· + 1122u + 289
c
9
u
12
+ u
11
+ ··· − 33u − 19
c
10
u
12
− 3u
11
+ ··· + 30u + 101
c
12
(u
6
− u
5
+ 5u
4
− 2u
3
+ u
2
− 2u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
+ 23y
11
+ ··· − 623947y + 130321
c
2
, c
4
, c
7
c
11
y
12
− 9y
11
+ ··· − 955y + 361
c
3
(y
3
− y
2
+ 2y −1)
4
c
5
, c
6
y
12
− 27y
11
+ ··· + 27650y + 32761
c
8
y
12
+ 25y
11
+ ··· − 261834y + 83521
c
9
y
12
− 15y
11
+ ··· − 481y + 361
c
10
y
12
+ 11y
11
+ ··· + 12836y + 10201
c
12
(y
6
+ 9y
5
+ 23y
4
− 17y
2
− 6y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.176090 + 0.954853I
a = −0.511597 − 0.577155I
b = −0.618034
−3.41636 −2.01951 + 0.I
u = 0.176090 − 0.954853I
a = −0.511597 + 0.577155I
b = −0.618034
−3.41636 −2.01951 + 0.I
u = 1.042890 + 0.143496I
a = −0.246377 + 1.202250I
b = −0.618034
0.72122 − 2.82812I 4.50976 + 2.97945I
u = 1.042890 − 0.143496I
a = −0.246377 − 1.202250I
b = −0.618034
0.72122 + 2.82812I 4.50976 − 2.97945I
u = −0.909963 + 0.664361I
a = −0.088103 − 1.049580I
b = −0.618034
0.72122 − 2.82812I 4.50976 + 2.97945I
u = −0.909963 − 0.664361I
a = −0.088103 + 1.049580I
b = −0.618034
0.72122 + 2.82812I 4.50976 − 2.97945I
u = 0.766119
a = 2.36184
b = 1.61803
4.47932 −2.01950
u = −1.68814
a = 1.28048
b = 1.61803
4.47932 −2.01950
u = 1.30811 + 1.12304I
a = 1.218820 − 0.656524I
b = 1.61803
8.61690 + 2.82812I 4.50976 − 2.97945I
u = 1.30811 − 1.12304I
a = 1.218820 + 0.656524I
b = 1.61803
8.61690 − 2.82812I 4.50976 + 2.97945I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.65612 + 0.99196I
a = 1.174520 + 0.523632I
b = 1.61803
8.61690 + 2.82812I 4.50976 − 2.97945I
u = −1.65612 − 0.99196I
a = 1.174520 − 0.523632I
b = 1.61803
8.61690 − 2.82812I 4.50976 + 2.97945I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− u
4
− u
3
+ 4u
2
− 3u + 1)(u
12
− 15u
11
+ ··· − 165u + 25)
· (u
12
− 9u
11
+ ··· − 955u + 361)(u
18
+ 16u
17
+ ··· + 59u + 4)
c
2
, c
4
(u
5
− u
4
+ u
3
− 2u
2
+ u − 1)(u
12
− u
11
+ ··· − 29u − 19)
· (u
12
+ u
11
+ ··· + 5u + 5)(u
18
+ 8u
16
+ ··· + u + 2)
c
3
(u
3
+ u
2
− 1)
8
(u
5
− 4u
4
+ 8u
3
− 9u
2
+ 6u − 1)
· (u
18
− 5u
17
+ ··· − 27u + 9)
c
5
(u
5
− 2u
4
− u
3
+ 2u
2
− 1)(u
12
+ u
11
+ ··· − 424u − 181)
· (u
12
+ u
11
+ ··· + 2u + 1)(u
18
+ u
17
+ ··· − u + 1)
c
6
(u
5
+ 2u
4
− u
3
− 2u
2
+ 1)(u
12
− u
11
+ ··· − 2u + 1)
· (u
12
+ u
11
+ ··· − 424u − 181)(u
18
+ u
17
+ ··· − u + 1)
c
7
, c
11
(u
5
+ u
4
+ u
3
+ 2u
2
+ u + 1)(u
12
− u
11
+ ··· − 29u − 19)
· (u
12
− u
11
+ ··· − 5u + 5)(u
18
+ 8u
16
+ ··· + u + 2)
c
8
(u
5
− 2u
4
+ 2u
3
− 3u
2
+ 2u − 1)(u
12
− 3u
11
+ ··· − 54u + 121)
· (u
12
+ 3u
11
+ ··· + 1122u + 289)(u
18
− 3u
17
+ ··· − 25u + 125)
c
9
(u
5
− 2u
4
− u
3
+ 2u
2
− 1)(u
12
− u
11
+ ··· + 965u + 475)
· (u
12
+ u
11
+ ··· − 33u − 19)(u
18
− 5u
17
+ ··· − 125u + 46)
c
10
(u
5
− u
4
− u
3
+ 4u
2
− 3u + 1)(u
12
− 3u
11
+ ··· + 6u + 1)
· (u
12
− 3u
11
+ ··· + 30u + 101)(u
18
− 2u
17
+ ··· + 4u + 1)
c
12
u
5
(u
6
− u
5
+ 5u
4
− 2u
3
+ u
2
− 2u − 1)
2
· (u
12
+ 21u
10
+ 135u
8
+ 300u
6
− 65u
4
− 214u
2
+ 661)
· (u
18
+ u
17
+ ··· − 160u + 32)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 3y
4
+ 3y
3
− 8y
2
+ y −1)(y
12
− 25y
11
+ ··· + 2325y + 625)
· (y
12
+ 23y
11
+ ··· − 623947y + 130321)
· (y
18
+ 12y
17
+ ··· + 159y + 16)
c
2
, c
4
, c
7
c
11
(y
5
+ y
4
− y
3
− 4y
2
− 3y −1)(y
12
− 9y
11
+ ··· − 955y + 361)
· (y
12
+ 15y
11
+ ··· + 165y + 25)(y
18
+ 16y
17
+ ··· + 59y + 4)
c
3
(y
3
− y
2
+ 2y −1)
8
(y
5
+ 4y
3
+ 7y
2
+ 18y −1)
· (y
18
− 5y
17
+ ··· − 117y + 81)
c
5
, c
6
(y
5
− 6y
4
+ 9y
3
− 8y
2
+ 4y −1)(y
12
− 27y
11
+ ··· + 27650y + 32761)
· (y
12
+ 9y
11
+ ··· + 2y + 1)(y
18
− 7y
17
+ ··· − 11y + 1)
c
8
(y
5
− 4y
3
− 5y
2
− 2y −1)(y
12
− 19y
11
+ ··· + 15718y + 14641)
· (y
12
+ 25y
11
+ ··· − 261834y + 83521)
· (y
18
+ 11y
17
+ ··· + 194375y + 15625)
c
9
(y
5
− 6y
4
+ 9y
3
− 8y
2
+ 4y −1)(y
12
− 15y
11
+ ··· − 481y + 361)
· (y
12
+ 5y
11
+ ··· + 820575y + 225625)
· (y
18
+ 5y
17
+ ··· + 21911y + 2116)
c
10
(y
5
− 3y
4
+ 3y
3
− 8y
2
+ y −1)(y
12
− 13y
11
+ ··· + 24y + 1)
· (y
12
+ 11y
11
+ ··· + 12836y + 10201)(y
18
− 8y
17
+ ··· + 16y + 1)
c
12
y
5
(y
6
+ 9y
5
+ 23y
4
− 17y
2
− 6y + 1)
2
· (y
6
+ 21y
5
+ 135y
4
+ 300y
3
− 65y
2
− 214y + 661)
2
· (y
18
+ 55y
17
+ ··· + 10752y + 1024)
22
