12n
0643
(K12n
0643
)
A knot diagram
1
Linearized knot diagam
3 8 12 8 11 10 2 4 3 6 5 9
Solving Sequence
5,8
4
9,12
3 2 1 7 11 6 10
c
4
c
8
c
3
c
2
c
1
c
7
c
11
c
5
c
10
c
6
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−68009u
16
− 44301u
15
+ ··· + 147102b + 345073, a − 1, u
17
+ 9u
15
+ ··· + 2u + 1i
I
u
2
= h−2u
5
− 5u
4
+ 13u
2
+ 34b + 15u − 21, 59u
5
+ 122u
4
+ 187u
3
+ 135u
2
+ 34a + 25u + 628,
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 10u − 1i
I
u
3
= h−42u
10
− 15u
9
− 68u
8
− 63u
7
− 114u
6
− 63u
5
+ 35u
4
+ 150u
3
+ 89u
2
+ 23b + 116u + 25, a + 1,
u
11
+ 2u
9
+ u
8
+ 3u
7
+ u
6
− 3u
4
− u
3
− 4u
2
− 1i
I
u
4
= h−6u
11
− 5u
10
+ 48u
9
− 118u
8
+ 124u
7
− 211u
6
− 246u
5
− 51u
4
− 750u
3
+ 85u
2
+ 236b − 746u − 12,
65u
11
− 585u
10
+ ··· + 472a − 5416,
u
12
− 5u
11
+ 15u
10
− 32u
9
+ 58u
8
− 77u
7
+ 103u
6
− 93u
5
+ 100u
4
− 55u
3
+ 48u
2
− 12u + 8i
* 4 irreducible components of dim
C
= 0, with total 46 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−6.80 × 10
4
u
16
− 4.43 × 10
4
u
15
+ · · · + 1.47 × 10
5
b + 3.45 × 10
5
, a −
1, u
17
+ 9u
15
+ · · · + 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
9
=
u
u
3
+ u
a
12
=
1
0.462325u
16
+ 0.301158u
15
+ ··· − 5.67284u − 2.34581
a
3
=
−0.462325u
16
− 0.301158u
15
+ ··· + 5.67284u + 3.34581
−0.287392u
16
+ 0.502305u
15
+ ··· − 1.98646u − 0.919770
a
2
=
−0.462325u
16
− 0.301158u
15
+ ··· + 5.67284u + 3.34581
−0.279955u
16
+ 0.529707u
15
+ ··· − 3.05110u − 1.22093
a
1
=
−0.00743702u
16
− 0.0274028u
15
+ ··· + 1.06464u + 1.30116
0.190147u
16
+ 0.239167u
15
+ ··· − 4.54595u − 2.01725
a
7
=
−1.13202u
16
− 0.272111u
15
+ ··· + 8.20193u + 0.644696
0.0817596u
16
− 0.0818956u
15
+ ··· + 1.62497u + 0.308167
a
11
=
0.462325u
16
+ 0.301158u
15
+ ··· − 5.67284u − 1.34581
0.462325u
16
+ 0.301158u
15
+ ··· − 5.67284u − 2.34581
a
6
=
0.757155u
16
− 0.173743u
15
+ ··· − 4.75102u − 0.727196
0.294829u
16
− 0.474902u
15
+ ··· + 0.921816u + 0.618612
a
10
=
1.21378u
16
+ 0.190215u
15
+ ··· − 6.57697u − 0.336528
0.456629u
16
+ 0.363958u
15
+ ··· − 1.82594u + 0.390668
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
173298
24517
u
16
−
19700
24517
u
15
+ ··· +
1212498
24517
u −
66405
24517
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 25u
16
+ ··· − 5u + 1
c
2
, c
7
, c
12
u
17
+ u
16
+ ··· + u + 1
c
3
u
17
− 11u
16
+ ··· − 48u + 8
c
4
, c
8
u
17
+ 9u
15
+ ··· + 2u + 1
c
5
, c
6
, c
10
c
11
u
17
+ 7u
16
+ ··· + 72u + 8
c
9
u
17
− 20u
15
+ ··· + 194u + 259
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 65y
16
+ ··· + 87y −1
c
2
, c
7
, c
12
y
17
− 25y
16
+ ··· − 5y −1
c
3
y
17
+ 3y
16
+ ··· + 672y −64
c
4
, c
8
y
17
+ 18y
16
+ ··· + 20y −1
c
5
, c
6
, c
10
c
11
y
17
+ 19y
16
+ ··· + 288y −64
c
9
y
17
− 40y
16
+ ··· − 96526y −67081
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.273982 + 1.067890I
a = 1.00000
b = −0.476176 + 0.479879I
−0.94573 + 1.67377I −6.92989 − 3.16143I
u = 0.273982 − 1.067890I
a = 1.00000
b = −0.476176 − 0.479879I
−0.94573 − 1.67377I −6.92989 + 3.16143I
u = 0.124569 + 1.229950I
a = 1.00000
b = −0.37277 + 1.64716I
−5.40408 + 3.79366I −9.42026 − 1.67014I
u = 0.124569 − 1.229950I
a = 1.00000
b = −0.37277 − 1.64716I
−5.40408 − 3.79366I −9.42026 + 1.67014I
u = −0.747531 + 1.177200I
a = 1.00000
b = −0.11531 − 1.52558I
5.74347 − 3.70748I −0.330584 + 0.385083I
u = −0.747531 − 1.177200I
a = 1.00000
b = −0.11531 + 1.52558I
5.74347 + 3.70748I −0.330584 − 0.385083I
u = 0.18378 + 1.48034I
a = 1.00000
b = −0.958979 − 0.657777I
−12.88920 + 1.26003I −11.26337 − 0.06200I
u = 0.18378 − 1.48034I
a = 1.00000
b = −0.958979 + 0.657777I
−12.88920 − 1.26003I −11.26337 + 0.06200I
u = −0.435602 + 0.235065I
a = 1.00000
b = 0.02738 − 1.68451I
10.39050 − 1.51785I 0.08130 + 5.70683I
u = −0.435602 − 0.235065I
a = 1.00000
b = 0.02738 + 1.68451I
10.39050 + 1.51785I 0.08130 − 5.70683I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438102 + 0.020053I
a = 1.00000
b = −0.092822 + 0.789763I
1.61479 + 1.53966I −1.79490 − 4.96374I
u = 0.438102 − 0.020053I
a = 1.00000
b = −0.092822 − 0.789763I
1.61479 − 1.53966I −1.79490 + 4.96374I
u = −0.52463 + 1.57423I
a = 1.00000
b = −0.970536 − 0.552496I
−13.1856 − 7.5502I −11.07949 + 4.57676I
u = −0.52463 − 1.57423I
a = 1.00000
b = −0.970536 + 0.552496I
−13.1856 + 7.5502I −11.07949 − 4.57676I
u = −0.314233
a = 1.00000
b = −0.331071
−0.707107 −14.3070
u = 0.84444 + 1.52914I
a = 1.00000
b = −0.37526 + 1.57337I
−6.35474 + 12.51650I −8.10916 − 5.80852I
u = 0.84444 − 1.52914I
a = 1.00000
b = −0.37526 − 1.57337I
−6.35474 − 12.51650I −8.10916 + 5.80852I
6
II. I
u
2
= h−2u
5
− 5u
4
+ 13u
2
+ 34b + 15u − 21, 59u
5
+ 122u
4
+ · · · + 34a +
628, u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 10u − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
9
=
u
u
3
+ u
a
12
=
−1.73529u
5
− 3.58824u
4
+ ··· − 0.735294u − 18.4706
0.0588235u
5
+ 0.147059u
4
+ ··· − 0.441176u + 0.617647
a
3
=
1.47059u
5
+ 3.17647u
4
+ ··· + 0.470588u + 14.9412
0.0588235u
5
+ 0.147059u
4
+ ··· − 0.441176u − 0.382353
a
2
=
1.47059u
5
+ 3.17647u
4
+ ··· + 0.470588u + 14.9412
−0.0588235u
5
− 0.147059u
4
+ ··· + 0.441176u − 0.617647
a
1
=
−1.82353u
5
− 4.05882u
4
+ ··· − 0.823529u − 18.6471
0.323529u
5
+ 0.0588235u
4
+ ··· + 2.32353u + 0.147059
a
7
=
2.23529u
5
+ 4.58824u
4
+ ··· + 0.235294u + 22.4706
−0.117647u
5
− 0.294118u
4
+ ··· − 0.117647u − 0.735294
a
11
=
−1.67647u
5
− 3.44118u
4
+ ··· − 1.17647u − 17.8529
0.0588235u
5
+ 0.147059u
4
+ ··· − 0.441176u + 0.617647
a
6
=
−0.882353u
5
− 1.70588u
4
+ ··· + 0.117647u − 9.26471
0.176471u
5
+ 0.441176u
4
+ ··· − 0.323529u + 0.352941
a
10
=
−2.35294u
5
− 4.88235u
4
+ ··· − 0.352941u − 23.2059
0.117647u
5
+ 0.294118u
4
+ ··· + 0.117647u + 0.735294
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
16
17
u
5
−
40
17
u
4
− 4u
3
−
100
17
u
2
−
16
17
u −
338
17
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 6u
5
+ 5u
4
− 14u
3
+ 26u
2
+ 144u + 121
c
2
, c
7
, c
12
u
6
+ 2u
5
− u
4
+ 2u
2
− 10u − 11
c
3
(u
3
+ u
2
− 1)
2
c
4
, c
8
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 10u − 1
c
5
, c
6
, c
10
c
11
(u
3
− u
2
+ 2u − 1)
2
c
9
u
6
+ 5u
5
+ 4u
4
− 11u
3
− 14u
2
− 8
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 26y
5
+ 245y
4
− 1422y
3
+ 5918y
2
− 14444y + 14641
c
2
, c
7
, c
12
y
6
− 6y
5
+ 5y
4
+ 14y
3
+ 26y
2
− 144y + 121
c
3
(y
3
− y
2
+ 2y −1)
2
c
4
, c
8
y
6
+ 2y
5
+ y
4
− 46y
3
− 46y
2
− 100y + 1
c
5
, c
6
, c
10
c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
9
y
6
− 17y
5
+ 98y
4
− 249y
3
+ 132y
2
+ 224y + 64
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.714259 + 0.979949I
a = −1.55592 − 0.28013I
b = 0.215080 − 1.307140I
1.11345 + 5.65624I −6.98049 − 5.95889I
u = 0.714259 − 0.979949I
a = −1.55592 + 0.28013I
b = 0.215080 + 1.307140I
1.11345 − 5.65624I −6.98049 + 5.95889I
u = −1.85465
a = −0.0537944
b = 0.569840
−7.16171 −20.0390
u = 0.0997696
a = −18.5893
b = 0.569840
−7.16171 −20.0390
u = −0.83682 + 1.72481I
a = −0.622526 − 0.112080I
b = 0.215080 + 1.307140I
1.11345 − 5.65624I −6.98049 + 5.95889I
u = −0.83682 − 1.72481I
a = −0.622526 + 0.112080I
b = 0.215080 − 1.307140I
1.11345 + 5.65624I −6.98049 − 5.95889I
10
III. I
u
3
=
h−42u
10
−15u
9
+· · ·+ 23b + 25 , a + 1, u
11
+2u
9
+u
8
+3u
7
+u
6
−3u
4
−u
3
−4u
2
−1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
9
=
u
u
3
+ u
a
12
=
−1
1.82609u
10
+ 0.652174u
9
+ ··· − 5.04348u − 1.08696
a
3
=
1.82609u
10
+ 0.652174u
9
+ ··· − 5.04348u − 0.0869565
1.13043u
10
− 0.739130u
9
+ ··· − 2.21739u + 3.56522
a
2
=
1.82609u
10
+ 0.652174u
9
+ ··· − 5.04348u − 0.0869565
1.82609u
10
− 0.347826u
9
+ ··· − 4.04348u + 2.91304
a
1
=
0.695652u
10
+ 0.391304u
9
+ ··· − 1.82609u − 1.65217
2.30435u
10
+ 0.608696u
9
+ ··· − 6.17391u − 1.34783
a
7
=
1.65217u
10
− 0.695652u
9
+ ··· − 4.08696u + 1.82609
1.08696u
10
− 1.82609u
9
+ ··· − 0.478261u + 5.04348
a
11
=
1.82609u
10
+ 0.652174u
9
+ ··· − 5.04348u − 2.08696
1.82609u
10
+ 0.652174u
9
+ ··· − 5.04348u − 1.08696
a
6
=
−2.26087u
10
+ 0.478261u
9
+ ··· + 5.43478u − 2.13043
−0.434783u
10
+ 1.13043u
9
+ ··· + 0.391304u − 4.21739
a
10
=
−0.565217u
10
− 1.13043u
9
+ ··· + 3.60870u + 3.21739
−2.82609u
10
− 0.652174u
9
+ ··· + 9.04348u + 1.08696
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
31
23
u
10
+
7
23
u
9
−
48
23
u
8
+
11
23
u
7
−
71
23
u
6
+
34
23
u
5
+
91
23
u
4
+
137
23
u
3
−
17
23
u
2
+
21
23
u −
257
23
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 11u
10
+ ··· + 7u − 1
c
2
u
11
+ u
10
− 5u
9
− 5u
8
+ 9u
7
+ 8u
6
− 8u
5
− 7u
4
+ 4u
3
+ 3u
2
− u − 1
c
3
u
11
+ 4u
10
+ 10u
9
+ 16u
8
+ 16u
7
+ 7u
6
− 3u
5
− 5u
4
+ 2u
2
− 1
c
4
u
11
+ 2u
9
+ u
8
+ 3u
7
+ u
6
− 3u
4
− u
3
− 4u
2
− 1
c
5
, c
6
u
11
+ 8u
9
+ 23u
7
+ 28u
5
+ u
4
+ 12u
3
+ 3u
2
+ 1
c
7
, c
12
u
11
− u
10
− 5u
9
+ 5u
8
+ 9u
7
− 8u
6
− 8u
5
+ 7u
4
+ 4u
3
− 3u
2
− u + 1
c
8
u
11
+ 2u
9
− u
8
+ 3u
7
− u
6
+ 3u
4
− u
3
+ 4u
2
+ 1
c
9
u
11
− 5u
9
− 2u
8
+ 4u
7
+ 9u
6
+ 5u
5
− 2u
4
− 13u
3
+ 7u
2
+ 2u + 1
c
10
, c
11
u
11
+ 8u
9
+ 23u
7
+ 28u
5
− u
4
+ 12u
3
− 3u
2
− 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− 15y
10
+ ··· − 13y −1
c
2
, c
7
, c
12
y
11
− 11y
10
+ ··· + 7y −1
c
3
y
11
+ 4y
10
+ ··· + 4y −1
c
4
, c
8
y
11
+ 4y
10
+ ··· − 8y −1
c
5
, c
6
, c
10
c
11
y
11
+ 16y
10
+ ··· − 6y −1
c
9
y
11
− 10y
10
+ ··· − 10y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.02184
a = −1.00000
b = −0.445195
−6.47878 −5.43850
u = −0.960985 + 0.510912I
a = −1.00000
b = −0.233007 + 1.358440I
−1.89567 + 2.51034I −5.23089 − 0.60579I
u = −0.960985 − 0.510912I
a = −1.00000
b = −0.233007 − 1.358440I
−1.89567 − 2.51034I −5.23089 + 0.60579I
u = 0.062554 + 0.872739I
a = −1.00000
b = 0.166908 + 0.916041I
0.12106 + 1.89765I −8.02738 − 3.63931I
u = 0.062554 − 0.872739I
a = −1.00000
b = 0.166908 − 0.916041I
0.12106 − 1.89765I −8.02738 + 3.63931I
u = −0.448669 + 1.127200I
a = −1.00000
b = 0.193075 + 0.390923I
−1.65984 − 3.19570I −7.07775 + 5.40642I
u = −0.448669 − 1.127200I
a = −1.00000
b = 0.193075 − 0.390923I
−1.65984 + 3.19570I −7.07775 − 5.40642I
u = 0.065465 + 0.570358I
a = −1.00000
b = 0.02836 − 1.73242I
9.80306 − 1.15540I −10.75281 − 0.76912I
u = 0.065465 − 0.570358I
a = −1.00000
b = 0.02836 + 1.73242I
9.80306 + 1.15540I −10.75281 + 0.76912I
u = 0.77071 + 1.27691I
a = −1.00000
b = 0.06726 − 1.54442I
5.09546 + 4.16451I −9.19190 − 5.51053I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.77071 − 1.27691I
a = −1.00000
b = 0.06726 + 1.54442I
5.09546 − 4.16451I −9.19190 + 5.51053I
15
IV. I
u
4
= h−6u
11
− 5u
10
+ · · · + 236b − 12, 65u
11
− 585u
10
+ · · · + 472a −
5416, u
12
− 5u
11
+ · · · − 12u + 8i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
9
=
u
u
3
+ u
a
12
=
−0.137712u
11
+ 1.23941u
10
+ ··· − 19.0805u + 11.4746
0.0254237u
11
+ 0.0211864u
10
+ ··· + 3.16102u + 0.0508475
a
3
=
0.502119u
11
− 2.51907u
10
+ ··· + 13.3051u − 3.74576
−0.555085u
11
+ 2.74576u
10
+ ··· − 8.43220u + 0.389831
a
2
=
0.502119u
11
− 2.51907u
10
+ ··· + 13.3051u − 3.74576
−0.338983u
11
+ 1.80085u
10
+ ··· − 4.31356u + 0.322034
a
1
=
−0.252119u
11
+ 1.76907u
10
+ ··· − 15.5551u + 9.74576
0.0805085u
11
− 0.224576u
10
+ ··· + 7.09322u − 1.33898
a
7
=
−0.646186u
11
+ 3.56568u
10
+ ··· − 20.8008u + 7.95763
−0.00423729u
11
+ 0.0381356u
10
+ ··· + 2.38983u + 0.491525
a
11
=
−0.112288u
11
+ 1.26059u
10
+ ··· − 15.9195u + 11.5254
0.0254237u
11
+ 0.0211864u
10
+ ··· + 3.16102u + 0.0508475
a
6
=
1.18432u
11
− 5.65890u
10
+ ··· + 17.5424u + 4.11864
0.0296610u
11
− 0.0169492u
10
+ ··· + 0.771186u − 1.44068
a
10
=
0.641949u
11
− 3.52754u
10
+ ··· + 23.1907u − 7.46610
0.00423729u
11
− 0.0381356u
10
+ ··· − 2.38983u − 0.491525
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4
59
u
11
−
95
59
u
10
+
440
59
u
9
− 21u
8
+
2474
59
u
7
−
4068
59
u
6
+
4884
59
u
5
−
5807
59
u
4
+
4512
59
u
3
−
4344
59
u
2
+
1638
59
u −
1762
59
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 15u
11
+ ··· + 96u + 64
c
2
, c
7
, c
12
u
12
− 3u
11
+ ··· − 8u + 8
c
3
(u
3
+ u
2
− 1)
4
c
4
, c
8
u
12
− 5u
11
+ ··· − 12u + 8
c
5
, c
6
, c
10
c
11
(u
3
− u
2
+ 2u − 1)
4
c
9
u
12
− 6u
11
+ ··· + 18u + 59
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 15y
11
+ ··· − 18944y + 4096
c
2
, c
7
, c
12
y
12
− 15y
11
+ ··· − 96y + 64
c
3
(y
3
− y
2
+ 2y −1)
4
c
4
, c
8
y
12
+ 5y
11
+ ··· + 624y + 64
c
5
, c
6
, c
10
c
11
(y
3
+ 3y
2
+ 2y −1)
4
c
9
y
12
− 16y
11
+ ··· − 8820y + 3481
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.044973 + 0.916855I
a = −1.22501 − 0.79096I
b = 0.215080 + 1.307140I
1.11345 −6.98049 + 0.I
u = 0.044973 − 0.916855I
a = −1.22501 + 0.79096I
b = 0.215080 − 1.307140I
1.11345 −6.98049 + 0.I
u = −0.404600 + 1.033930I
a = −1.272350 + 0.353092I
b = 0.569840
−3.02413 − 2.82812I −13.50976 + 2.97945I
u = −0.404600 − 1.033930I
a = −1.272350 − 0.353092I
b = 0.569840
−3.02413 + 2.82812I −13.50976 − 2.97945I
u = 0.670107 + 1.158730I
a = −0.576131 − 0.371997I
b = 0.215080 − 1.307140I
1.11345 −6.98049 + 0.I
u = 0.670107 − 1.158730I
a = −0.576131 + 0.371997I
b = 0.215080 + 1.307140I
1.11345 −6.98049 + 0.I
u = 0.076727 + 0.622517I
a = 2.13780 − 2.88995I
b = 0.215080 + 1.307140I
−3.02413 − 2.82812I −13.50976 + 2.97945I
u = 0.076727 − 0.622517I
a = 2.13780 + 2.88995I
b = 0.215080 − 1.307140I
−3.02413 + 2.82812I −13.50976 − 2.97945I
u = 0.14972 + 1.45838I
a = −0.729747 + 0.202513I
b = 0.569840
−3.02413 + 2.82812I −13.50976 − 2.97945I
u = 0.14972 − 1.45838I
a = −0.729747 − 0.202513I
b = 0.569840
−3.02413 − 2.82812I −13.50976 + 2.97945I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.96307 + 1.10908I
a = 0.165439 + 0.223646I
b = 0.215080 + 1.307140I
−3.02413 − 2.82812I −13.50976 + 2.97945I
u = 1.96307 − 1.10908I
a = 0.165439 − 0.223646I
b = 0.215080 − 1.307140I
−3.02413 + 2.82812I −13.50976 − 2.97945I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 6u
5
+ 5u
4
− 14u
3
+ 26u
2
+ 144u + 121)
· (u
11
− 11u
10
+ ··· + 7u − 1)(u
12
+ 15u
11
+ ··· + 96u + 64)
· (u
17
+ 25u
16
+ ··· − 5u + 1)
c
2
(u
6
+ 2u
5
− u
4
+ 2u
2
− 10u − 11)
· (u
11
+ u
10
− 5u
9
− 5u
8
+ 9u
7
+ 8u
6
− 8u
5
− 7u
4
+ 4u
3
+ 3u
2
− u − 1)
· (u
12
− 3u
11
+ ··· − 8u + 8)(u
17
+ u
16
+ ··· + u + 1)
c
3
(u
3
+ u
2
− 1)
6
· (u
11
+ 4u
10
+ 10u
9
+ 16u
8
+ 16u
7
+ 7u
6
− 3u
5
− 5u
4
+ 2u
2
− 1)
· (u
17
− 11u
16
+ ··· − 48u + 8)
c
4
(u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 10u − 1)
· (u
11
+ 2u
9
+ u
8
+ 3u
7
+ u
6
− 3u
4
− u
3
− 4u
2
− 1)
· (u
12
− 5u
11
+ ··· − 12u + 8)(u
17
+ 9u
15
+ ··· + 2u + 1)
c
5
, c
6
(u
3
− u
2
+ 2u − 1)
6
(u
11
+ 8u
9
+ 23u
7
+ 28u
5
+ u
4
+ 12u
3
+ 3u
2
+ 1)
· (u
17
+ 7u
16
+ ··· + 72u + 8)
c
7
, c
12
(u
6
+ 2u
5
− u
4
+ 2u
2
− 10u − 11)
· (u
11
− u
10
− 5u
9
+ 5u
8
+ 9u
7
− 8u
6
− 8u
5
+ 7u
4
+ 4u
3
− 3u
2
− u + 1)
· (u
12
− 3u
11
+ ··· − 8u + 8)(u
17
+ u
16
+ ··· + u + 1)
c
8
(u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 10u − 1)
· (u
11
+ 2u
9
− u
8
+ 3u
7
− u
6
+ 3u
4
− u
3
+ 4u
2
+ 1)
· (u
12
− 5u
11
+ ··· − 12u + 8)(u
17
+ 9u
15
+ ··· + 2u + 1)
c
9
(u
6
+ 5u
5
+ 4u
4
− 11u
3
− 14u
2
− 8)
· (u
11
− 5u
9
− 2u
8
+ 4u
7
+ 9u
6
+ 5u
5
− 2u
4
− 13u
3
+ 7u
2
+ 2u + 1)
· (u
12
− 6u
11
+ ··· + 18u + 59)(u
17
− 20u
15
+ ··· + 194u + 259)
c
10
, c
11
(u
3
− u
2
+ 2u − 1)
6
(u
11
+ 8u
9
+ 23u
7
+ 28u
5
− u
4
+ 12u
3
− 3u
2
− 1)
· (u
17
+ 7u
16
+ ··· + 72u + 8)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 26y
5
+ 245y
4
− 1422y
3
+ 5918y
2
− 14444y + 14641)
· (y
11
− 15y
10
+ ··· − 13y −1)(y
12
− 15y
11
+ ··· − 18944y + 4096)
· (y
17
− 65y
16
+ ··· + 87y −1)
c
2
, c
7
, c
12
(y
6
− 6y
5
+ 5y
4
+ 14y
3
+ 26y
2
− 144y + 121)
· (y
11
− 11y
10
+ ··· + 7y −1)(y
12
− 15y
11
+ ··· − 96y + 64)
· (y
17
− 25y
16
+ ··· − 5y −1)
c
3
((y
3
− y
2
+ 2y −1)
6
)(y
11
+ 4y
10
+ ··· + 4y −1)
· (y
17
+ 3y
16
+ ··· + 672y −64)
c
4
, c
8
(y
6
+ 2y
5
+ ··· − 100y + 1)(y
11
+ 4y
10
+ ··· − 8y −1)
· (y
12
+ 5y
11
+ ··· + 624y + 64)(y
17
+ 18y
16
+ ··· + 20y −1)
c
5
, c
6
, c
10
c
11
((y
3
+ 3y
2
+ 2y −1)
6
)(y
11
+ 16y
10
+ ··· − 6y −1)
· (y
17
+ 19y
16
+ ··· + 288y −64)
c
9
(y
6
− 17y
5
+ 98y
4
− 249y
3
+ 132y
2
+ 224y + 64)
· (y
11
− 10y
10
+ ··· − 10y −1)(y
12
− 16y
11
+ ··· − 8820y + 3481)
· (y
17
− 40y
16
+ ··· − 96526y −67081)
22
