12n
0144
(K12n
0144
)
A knot diagram
1
Linearized knot diagam
3 4 11 2 10 3 12 4 6 9 7 8
Solving Sequence
7,11
12
4,8
9 1 3 2 5 6 10
c
11
c
7
c
8
c
12
c
3
c
2
c
4
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h7.34372 × 10
20
u
43
+ 1.60104 × 10
21
u
42
+ ··· + 6.28525 × 10
21
b + 5.02483 × 10
21
,
1.42649 × 10
20
u
43
+ 6.11830 × 10
20
u
42
+ ··· + 3.14262 × 10
21
a − 1.33924 × 10
20
, u
44
+ 4u
43
+ ··· + 32u + 16i
I
u
2
= h4b + 2a − u + 2, 2a
2
− 2au + 7, u
2
− 2i
I
u
3
= hau + 7b + 4a + u + 4, 2a
2
+ au − 3u + 7, u
2
− 2i
I
u
4
= h3a
4
− 4a
3
+ 24a
2
+ 2b − 25a + 8, a
5
− 2a
4
+ 9a
3
− 14a
2
+ 9a − 2, u − 1i
I
v
1
= ha, b − v −1, v
2
+ v + 1i
I
v
2
= ha, b
2
− b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 61 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
=
h7.34×10
20
u
43
+1.60×10
21
u
42
+· · ·+6.29×10
21
b+5.02×10
21
, 1.43×10
20
u
43
+
6.12 × 10
20
u
42
+ · · · + 3.14 × 10
21
a − 1.34 × 10
20
, u
44
+ 4u
43
+ · · · + 32u + 16i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
4
=
−0.0453917u
43
− 0.194688u
42
+ ··· − 0.0781355u + 0.0426155
−0.116841u
43
− 0.254730u
42
+ ··· − 2.09430u − 0.799464
a
8
=
u
−u
3
+ u
a
9
=
0.191388u
43
+ 0.550760u
42
+ ··· + 3.38008u + 3.58656
−0.0541941u
43
− 0.188082u
42
+ ··· − 0.273250u − 1.13238
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
−0.162232u
43
− 0.449417u
42
+ ··· − 2.17243u − 0.756849
−0.116841u
43
− 0.254730u
42
+ ··· − 2.09430u − 0.799464
a
2
=
−0.459894u
43
− 1.20645u
42
+ ··· − 7.93846u − 3.69776
0.319896u
43
+ 0.993797u
42
+ ··· + 4.40818u + 5.01424
a
5
=
0.873473u
43
+ 2.49705u
42
+ ··· + 13.0049u + 12.6274
u
4
− 2u
2
a
6
=
−0.776380u
43
− 2.07570u
42
+ ··· − 12.3449u − 8.51440
0.297158u
43
+ 0.926397u
42
+ ··· + 6.35873u + 4.85216
a
10
=
−0.335109u
43
− 1.04952u
42
+ ··· − 6.89963u − 4.51774
−0.185846u
43
− 0.499407u
42
+ ··· − 2.65438u − 1.59651
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1752784223058518261005
785655665183033765648
u
43
+
2500993104539143938499
392827832591516882824
u
42
+ ··· +
1124081559828742593975
49103479073939610353
u +
1641699334520185355340
49103479073939610353
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 51u
43
+ ··· − 38168u + 2401
c
2
, c
4
u
44
− 11u
43
+ ··· − 796u + 49
c
3
u
44
+ 3u
43
+ ··· − 4u + 7
c
5
, c
9
u
44
− 3u
43
+ ··· − 14u + 7
c
6
u
44
+ 2u
43
+ ··· − 7517u + 13159
c
7
, c
11
, c
12
u
44
+ 4u
43
+ ··· + 32u + 16
c
8
u
44
− 2u
43
+ ··· − 23256067u + 7050439
c
10
u
44
+ 27u
43
+ ··· + 476u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
− 109y
43
+ ··· − 778696200y + 5764801
c
2
, c
4
y
44
+ 51y
43
+ ··· − 38168y + 2401
c
3
y
44
+ 11y
43
+ ··· + 796y + 49
c
5
, c
9
y
44
+ 27y
43
+ ··· + 476y + 49
c
6
y
44
+ 26y
43
+ ··· + 5158564319y + 173159281
c
7
, c
11
, c
12
y
44
− 36y
43
+ ··· + 1024y + 256
c
8
y
44
− 50y
43
+ ··· − 570620658530165y + 49708690092721
c
10
y
44
− 13y
43
+ ··· + 67816y + 2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053172 + 0.977197I
a = −0.726530 − 0.386151I
b = −0.881310 + 0.926174I
−7.21788 + 3.26048I 2.64523 − 2.48280I
u = 0.053172 − 0.977197I
a = −0.726530 + 0.386151I
b = −0.881310 − 0.926174I
−7.21788 − 3.26048I 2.64523 + 2.48280I
u = −0.969991 + 0.414842I
a = 0.607490 + 0.368276I
b = −0.799478 + 0.075673I
−1.73925 − 3.53680I 0.98095 + 4.14861I
u = −0.969991 − 0.414842I
a = 0.607490 − 0.368276I
b = −0.799478 − 0.075673I
−1.73925 + 3.53680I 0.98095 − 4.14861I
u = −0.174827 + 1.043030I
a = −0.718830 + 0.754972I
b = −0.888329 − 1.005910I
−11.08430 − 8.59782I 0.28005 + 5.55448I
u = −0.174827 − 1.043030I
a = −0.718830 − 0.754972I
b = −0.888329 + 1.005910I
−11.08430 + 8.59782I 0.28005 − 5.55448I
u = 0.074358 + 1.061190I
a = −0.353302 + 0.278439I
b = −0.957730 − 0.874395I
−11.51210 + 1.82027I −0.464174 − 0.761806I
u = 0.074358 − 1.061190I
a = −0.353302 − 0.278439I
b = −0.957730 + 0.874395I
−11.51210 − 1.82027I −0.464174 + 0.761806I
u = −1.060920 + 0.195318I
a = 0.943353 − 0.723894I
b = 0.729269 + 0.856189I
1.66107 − 5.45145I 5.86619 + 6.59616I
u = −1.060920 − 0.195318I
a = 0.943353 + 0.723894I
b = 0.729269 − 0.856189I
1.66107 + 5.45145I 5.86619 − 6.59616I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.396864 + 0.675816I
a = 0.320038 − 0.485056I
b = 0.767519 + 0.420310I
−3.41945 − 0.63164I −2.08485 + 2.40121I
u = −0.396864 − 0.675816I
a = 0.320038 + 0.485056I
b = 0.767519 − 0.420310I
−3.41945 + 0.63164I −2.08485 − 2.40121I
u = 1.209100 + 0.327502I
a = −0.52561 − 2.57152I
b = −0.313533 + 1.159410I
1.94616 + 7.53567I 4.00000 − 7.30881I
u = 1.209100 − 0.327502I
a = −0.52561 + 2.57152I
b = −0.313533 − 1.159410I
1.94616 − 7.53567I 4.00000 + 7.30881I
u = −1.244840 + 0.163819I
a = −0.40678 + 2.39610I
b = −0.306940 − 1.055000I
4.81580 − 3.31538I 11.03880 + 4.12292I
u = −1.244840 − 0.163819I
a = −0.40678 − 2.39610I
b = −0.306940 + 1.055000I
4.81580 + 3.31538I 11.03880 − 4.12292I
u = −1.193050 + 0.633879I
a = −0.488351 + 0.504147I
b = 0.926853 − 0.905761I
−7.99420 + 2.74053I 0
u = −1.193050 − 0.633879I
a = −0.488351 − 0.504147I
b = 0.926853 + 0.905761I
−7.99420 − 2.74053I 0
u = 1.277500 + 0.501120I
a = −0.535158 − 0.270801I
b = 0.908252 + 0.813085I
−3.43084 + 1.99299I 0
u = 1.277500 − 0.501120I
a = −0.535158 + 0.270801I
b = 0.908252 − 0.813085I
−3.43084 − 1.99299I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.155102 + 0.599275I
a = 0.352478 − 1.113320I
b = 0.478851 + 1.053130I
−1.29319 − 4.02132I −0.30638 + 3.65044I
u = 0.155102 − 0.599275I
a = 0.352478 + 1.113320I
b = 0.478851 − 1.053130I
−1.29319 + 4.02132I −0.30638 − 3.65044I
u = −1.405870 + 0.102387I
a = −0.89393 + 1.77081I
b = −0.149374 − 0.798948I
6.37799 − 2.69804I 0
u = −1.405870 − 0.102387I
a = −0.89393 − 1.77081I
b = −0.149374 + 0.798948I
6.37799 + 2.69804I 0
u = 1.286440 + 0.585860I
a = 0.43019 + 1.54824I
b = 0.898558 − 0.969867I
−7.79148 + 3.97595I 0
u = 1.286440 − 0.585860I
a = 0.43019 − 1.54824I
b = 0.898558 + 0.969867I
−7.79148 − 3.97595I 0
u = 1.41894 + 0.07907I
a = −1.13538 − 1.16362I
b = −0.065725 + 0.584352I
5.49142 − 1.80694I 0
u = 1.41894 − 0.07907I
a = −1.13538 + 1.16362I
b = −0.065725 − 0.584352I
5.49142 + 1.80694I 0
u = −1.35375 + 0.46551I
a = 0.66647 − 1.74497I
b = 0.826223 + 1.007890I
−2.81404 − 8.41153I 0
u = −1.35375 − 0.46551I
a = 0.66647 + 1.74497I
b = 0.826223 − 1.007890I
−2.81404 + 8.41153I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44498 + 0.10365I
a = 0.25589 − 1.83310I
b = −0.582379 + 0.972015I
4.02565 + 1.74679I 0
u = −1.44498 − 0.10365I
a = 0.25589 + 1.83310I
b = −0.582379 − 0.972015I
4.02565 − 1.74679I 0
u = −1.38764 + 0.51587I
a = −0.717568 + 0.258839I
b = 0.967178 − 0.764646I
−6.94944 − 7.42595I 0
u = −1.38764 − 0.51587I
a = −0.717568 − 0.258839I
b = 0.967178 + 0.764646I
−6.94944 + 7.42595I 0
u = −0.353533 + 0.362697I
a = 1.81787 + 0.90961I
b = −0.443035 + 0.586833I
−0.20174 + 3.16277I 3.03176 + 0.27471I
u = −0.353533 − 0.362697I
a = 1.81787 − 0.90961I
b = −0.443035 − 0.586833I
−0.20174 − 3.16277I 3.03176 − 0.27471I
u = 0.344360 + 0.354929I
a = 1.54824 + 0.67408I
b = −0.072149 − 0.658876I
0.836056 + 1.038800I 7.69659 − 5.53666I
u = 0.344360 − 0.354929I
a = 1.54824 − 0.67408I
b = −0.072149 + 0.658876I
0.836056 − 1.038800I 7.69659 + 5.53666I
u = 1.43633 + 0.46857I
a = 0.58445 + 1.94710I
b = 0.824013 − 1.059570I
−6.0040 + 14.0033I 0
u = 1.43633 − 0.46857I
a = 0.58445 − 1.94710I
b = 0.824013 + 1.059570I
−6.0040 − 14.0033I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50906 + 0.09274I
a = 0.209822 − 1.305860I
b = −0.677586 + 0.683171I
3.07707 + 3.14518I 0
u = 1.50906 − 0.09274I
a = 0.209822 + 1.305860I
b = −0.677586 − 0.683171I
3.07707 − 3.14518I 0
u = 0.221879 + 0.395714I
a = 0.765153 + 0.917828I
b = 0.310852 − 0.803316I
0.452406 + 1.318670I 4.68386 − 5.79682I
u = 0.221879 − 0.395714I
a = 0.765153 − 0.917828I
b = 0.310852 + 0.803316I
0.452406 − 1.318670I 4.68386 + 5.79682I
9
II. I
u
2
= h4b + 2a − u + 2, 2a
2
− 2au + 7, u
2
− 2i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−2
a
4
=
a
−
1
2
a +
1
4
u −
1
2
a
8
=
u
−u
a
9
=
−
1
2
au +
3
2
a −
3
4
u
−
1
2
a +
1
4
u −
1
2
a
1
=
−1
0
a
3
=
1
2
a +
1
4
u −
1
2
−
1
2
a +
1
4
u −
1
2
a
2
=
1
4
au +
1
4
u −
9
4
−
1
2
a +
1
4
u +
1
2
a
5
=
1
0
a
6
=
1
2
au − a +
1
2
u +
1
2
1
2
a −
1
4
u +
1
2
a
10
=
−
1
4
au +
1
2
a +
1
2
u −
5
4
−
1
2
a +
1
4
u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a − 2u + 8
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
(u
2
− u + 1)
2
c
2
, c
9
, c
10
(u
2
+ u + 1)
2
c
6
u
4
+ 4u
3
+ 8u
2
+ 8u + 7
c
7
, c
11
, c
12
(u
2
− 2)
2
c
8
u
4
− 4u
3
+ 8u
2
− 8u + 7
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
c
10
(y
2
+ y + 1)
2
c
6
, c
8
y
4
+ 14y
2
+ 48y + 49
c
7
, c
11
, c
12
(y −2)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 0.70711 + 1.73205I
b = −0.500000 − 0.866025I
4.93480 − 4.05977I 8.00000 + 6.92820I
u = 1.41421
a = 0.70711 − 1.73205I
b = −0.500000 + 0.866025I
4.93480 + 4.05977I 8.00000 − 6.92820I
u = −1.41421
a = −0.70711 + 1.73205I
b = −0.500000 − 0.866025I
4.93480 − 4.05977I 8.00000 + 6.92820I
u = −1.41421
a = −0.70711 − 1.73205I
b = −0.500000 + 0.866025I
4.93480 + 4.05977I 8.00000 − 6.92820I
13
III. I
u
3
= hau + 7b + 4a + u + 4, 2a
2
+ au − 3u + 7, u
2
− 2i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−2
a
4
=
a
−
1
7
au −
4
7
a −
1
7
u −
4
7
a
8
=
u
−u
a
9
=
−
3
7
au −
5
7
a −
13
14
u +
16
7
1
7
au +
4
7
a +
1
7
u −
3
7
a
1
=
−1
0
a
3
=
−
1
7
au +
3
7
a −
1
7
u −
4
7
−
1
7
au −
4
7
a −
1
7
u −
4
7
a
2
=
−
2
7
au −
1
7
a +
3
14
u −
15
7
−
1
7
au −
4
7
a −
1
7
u +
3
7
a
5
=
1
0
a
6
=
2
7
au +
1
7
a +
11
14
u −
13
7
−
1
7
au −
4
7
a −
1
7
u +
3
7
a
10
=
−
1
7
au −
11
7
a −
8
7
u +
10
7
1
7
au +
4
7
a +
1
7
u +
4
7
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
(u
2
− u + 1)
2
c
2
, c
9
, c
10
(u
2
+ u + 1)
2
c
6
u
4
− 2u
3
+ 5u
2
− 10u + 7
c
7
, c
11
, c
12
(u
2
− 2)
2
c
8
u
4
+ 2u
3
+ 5u
2
+ 10u + 7
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
c
10
(y
2
+ y + 1)
2
c
6
, c
8
y
4
+ 6y
3
− y
2
− 30y + 49
c
7
, c
11
, c
12
(y −2)
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.353553 + 1.119680I
b = −0.500000 − 0.866025I
4.93480 8.00000
u = 1.41421
a = −0.353553 − 1.119680I
b = −0.500000 + 0.866025I
4.93480 8.00000
u = −1.41421
a = 0.35355 + 2.34442I
b = −0.500000 − 0.866025I
4.93480 8.00000
u = −1.41421
a = 0.35355 − 2.34442I
b = −0.500000 + 0.866025I
4.93480 8.00000
17
IV.
I
u
4
= h3a
4
− 4a
3
+ 24a
2
+ 2b − 25a + 8, a
5
− 2a
4
+ 9a
3
− 14a
2
+ 9a − 2, u − 1i
(i) Arc colorings
a
7
=
0
1
a
11
=
1
0
a
12
=
1
−1
a
4
=
a
−
3
2
a
4
+ 2a
3
− 12a
2
+
25
2
a − 4
a
8
=
1
0
a
9
=
−a
4
+
3
2
a
3
−
17
2
a
2
+
19
2
a − 2
−
1
2
a
3
+
1
2
a
2
−
7
2
a + 2
a
1
=
0
−1
a
3
=
−
3
2
a
4
+ 2a
3
− 12a
2
+
27
2
a − 4
−
3
2
a
4
+ 2a
3
− 12a
2
+
25
2
a − 4
a
2
=
−2a
4
+
5
2
a
3
−
31
2
a
2
+
31
2
a − 4
−a
4
+ a
3
− 8a
2
+ 6a − 2
a
5
=
a
4
− 2a
3
+ 8a
2
− 13a + 5
−1
a
6
=
2a
4
−
5
2
a
3
+
31
2
a
2
−
31
2
a + 4
a
4
− a
3
+ 8a
2
− 6a + 2
a
10
=
a
3
− a
2
+ 6a − 2
−
3
2
a
4
+ 2a
3
− 12a
2
+
27
2
a − 4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
+ 2u
4
+ 3u
3
+ 6u
2
+ 5u − 1
c
2
, c
4
u
5
− 2u
4
+ 3u
3
− 2u
2
+ u + 1
c
3
, c
5
, c
8
c
9
u
5
+ u
3
+ u − 1
c
6
u
5
− 2u
4
+ 3u
3
− 6u
2
+ 5u + 1
c
7
, c
11
, c
12
(u − 1)
5
c
10
u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
5
+ 2y
4
− 5y
3
− 2y
2
+ 37y −1
c
2
, c
4
, c
10
y
5
+ 2y
4
+ 3y
3
+ 6y
2
+ 5y −1
c
3
, c
5
, c
8
c
9
y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y −1
c
7
, c
11
, c
12
(y −1)
5
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.669275 + 0.346167I
b = 0.707729 − 0.841955I
1.64493 6.00000
u = 1.00000
a = 0.669275 − 0.346167I
b = 0.707729 + 0.841955I
1.64493 6.00000
u = 1.00000
a = 0.472355
b = −0.636883
1.64493 6.00000
u = 1.00000
a = 0.09455 + 2.72921I
b = −0.389287 − 1.070680I
1.64493 6.00000
u = 1.00000
a = 0.09455 − 2.72921I
b = −0.389287 + 1.070680I
1.64493 6.00000
21
V. I
v
1
= ha, b − v − 1, v
2
+ v + 1i
(i) Arc colorings
a
7
=
v
0
a
11
=
1
0
a
12
=
1
0
a
4
=
0
v + 1
a
8
=
v
0
a
9
=
v
−v − 1
a
1
=
1
0
a
3
=
v + 1
v + 1
a
2
=
v + 1
v
a
5
=
−1
0
a
6
=
−1
−v − 1
a
10
=
0
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8v + 10
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
9
u
2
− u + 1
c
2
, c
3
, c
5
c
10
u
2
+ u + 1
c
6
, c
8
(u + 1)
2
c
7
, c
11
, c
12
u
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
c
10
y
2
+ y + 1
c
6
, c
8
(y − 1)
2
c
7
, c
11
, c
12
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
− 4.05977I 6.00000 + 6.92820I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
4.05977I 6.00000 − 6.92820I
25
VI. I
v
2
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
1
0
a
12
=
1
0
a
4
=
0
b
a
8
=
1
0
a
9
=
1
b − 1
a
1
=
1
0
a
3
=
b
b
a
2
=
b
b − 1
a
5
=
−1
0
a
6
=
b
b − 1
a
10
=
−b + 2
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
8
, c
9
u
2
− u + 1
c
2
, c
3
, c
5
c
10
u
2
+ u + 1
c
7
, c
11
, c
12
u
2
27
(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
y
2
+ y + 1
c
7
, c
11
, c
12
y
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
0 0
v = 1.00000
a = 0
b = 0.500000 − 0.866025I
0 0
29
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
6
(u
5
+ 2u
4
+ 3u
3
+ 6u
2
+ 5u − 1)
· (u
44
+ 51u
43
+ ··· − 38168u + 2401)
c
2
(u
2
+ u + 1)
6
(u
5
− 2u
4
+ 3u
3
− 2u
2
+ u + 1)
· (u
44
− 11u
43
+ ··· − 796u + 49)
c
3
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
5
+ u
3
+ u − 1)(u
44
+ 3u
43
+ ··· − 4u + 7)
c
4
(u
2
− u + 1)
6
(u
5
− 2u
4
+ 3u
3
− 2u
2
+ u + 1)
· (u
44
− 11u
43
+ ··· − 796u + 49)
c
5
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
5
+ u
3
+ u − 1)(u
44
− 3u
43
+ ··· − 14u + 7)
c
6
((u + 1)
2
)(u
2
− u + 1)(u
4
− 2u
3
+ ··· − 10u + 7)(u
4
+ 4u
3
+ ··· + 8u + 7)
· (u
5
− 2u
4
+ 3u
3
− 6u
2
+ 5u + 1)(u
44
+ 2u
43
+ ··· − 7517u + 13159)
c
7
, c
11
, c
12
u
4
(u − 1)
5
(u
2
− 2)
4
(u
44
+ 4u
43
+ ··· + 32u + 16)
c
8
((u + 1)
2
)(u
2
− u + 1)(u
4
− 4u
3
+ ··· − 8u + 7)(u
4
+ 2u
3
+ ··· + 10u + 7)
· (u
5
+ u
3
+ u − 1)(u
44
− 2u
43
+ ··· − 2.32561 × 10
7
u + 7050439)
c
9
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
5
+ u
3
+ u − 1)(u
44
− 3u
43
+ ··· − 14u + 7)
c
10
(u
2
+ u + 1)
6
(u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1)
· (u
44
+ 27u
43
+ ··· + 476u + 49)
30
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
6
(y
5
+ 2y
4
− 5y
3
− 2y
2
+ 37y − 1)
· (y
44
− 109y
43
+ ··· − 778696200y + 5764801)
c
2
, c
4
(y
2
+ y + 1)
6
(y
5
+ 2y
4
+ 3y
3
+ 6y
2
+ 5y − 1)
· (y
44
+ 51y
43
+ ··· − 38168y + 2401)
c
3
(y
2
+ y + 1)
6
(y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y − 1)
· (y
44
+ 11y
43
+ ··· + 796y + 49)
c
5
, c
9
(y
2
+ y + 1)
6
(y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y − 1)
· (y
44
+ 27y
43
+ ··· + 476y + 49)
c
6
((y − 1)
2
)(y
2
+ y + 1)(y
4
+ 14y
2
+ 48y + 49)(y
4
+ 6y
3
+ ··· − 30y + 49)
· (y
5
+ 2y
4
− 5y
3
− 2y
2
+ 37y − 1)
· (y
44
+ 26y
43
+ ··· + 5158564319y + 173159281)
c
7
, c
11
, c
12
y
4
(y − 2)
8
(y − 1)
5
(y
44
− 36y
43
+ ··· + 1024y + 256)
c
8
((y − 1)
2
)(y
2
+ y + 1)(y
4
+ 14y
2
+ 48y + 49)(y
4
+ 6y
3
+ ··· − 30y + 49)
· (y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y − 1)
· (y
44
− 50y
43
+ ··· − 570620658530165y + 49708690092721)
c
10
(y
2
+ y + 1)
6
(y
5
+ 2y
4
+ 3y
3
+ 6y
2
+ 5y − 1)
· (y
44
− 13y
43
+ ··· + 67816y + 2401)
31
