12n
0520
(K12n
0520
)
A knot diagram
1
Linearized knot diagam
3 5 12 8 2 4 10 6 3 4 6 10
Solving Sequence
4,6 7,11
12 3 10 8 1 2 5 9
c
6
c
11
c
3
c
10
c
7
c
12
c
1
c
5
c
9
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.00773 × 10
215
u
54
+ 3.95891 × 10
215
u
53
+ ··· + 5.25110 × 10
219
b − 1.48407 × 10
220
,
− 1.77810 × 10
217
u
54
− 8.41460 × 10
217
u
53
+ ··· + 1.78060 × 10
221
a + 4.35856 × 10
221
,
u
55
+ 3u
54
+ ··· + 4862u − 6341i
I
u
2
= h9.41498 × 10
23
u
19
+ 2.05689 × 10
24
u
18
+ ··· + 9.99999 × 10
23
b − 4.03582 × 10
24
,
3.23988 × 10
25
u
19
+ 7.09015 × 10
25
u
18
+ ··· + 9.99999 × 10
23
a − 1.70850 × 10
26
, u
20
+ 2u
19
+ ··· − 14u + 1i
* 2 irreducible components of dim
C
= 0, with total 75 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−1.01 × 10
215
u
54
+ 3.96 × 10
215
u
53
+ · · · + 5.25 × 10
219
b − 1.48 ×
10
220
, −1.78 × 10
217
u
54
− 8.41 × 10
217
u
53
+ · · · + 1.78 × 10
221
a + 4.36 ×
10
221
, u
55
+ 3u
54
+ · · · + 4862u − 6341i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
11
=
0.0000998597u
54
+ 0.000472571u
53
+ ··· − 1.70493u − 2.44781
0.0000191908u
54
− 0.0000753920u
53
+ ··· + 2.51058u + 2.82621
a
12
=
0.000119051u
54
+ 0.000397179u
53
+ ··· + 0.805651u + 0.378407
0.0000191908u
54
− 0.0000753920u
53
+ ··· + 2.51058u + 2.82621
a
3
=
0.000439453u
54
+ 0.00130155u
53
+ ··· − 9.12833u + 2.22261
5.39110 × 10
−6
u
54
− 0.0000762385u
53
+ ··· + 0.556271u + 2.93121
a
10
=
0.0000998597u
54
+ 0.000472571u
53
+ ··· − 1.70493u − 2.44781
0.0000160377u
54
− 0.0000345076u
53
+ ··· + 2.71846u + 1.72927
a
8
=
−0.0000108886u
54
− 0.0000519635u
53
+ ··· − 1.50476u + 0.832419
−0.000450416u
54
− 0.00135705u
53
+ ··· + 13.8133u − 1.51385
a
1
=
8.14406 × 10
−8
u
54
− 0.000279970u
53
+ ··· + 6.32497u + 7.75382
−0.000125932u
54
− 0.000589665u
53
+ ··· + 3.03504u + 3.45260
a
2
=
−0.0000620439u
54
− 0.000144711u
53
+ ··· + 3.04412u + 0.737987
0.000267626u
54
+ 0.000799507u
53
+ ··· − 8.68003u + 0.274355
a
5
=
0.000100081u
54
+ 0.000476708u
53
+ ··· − 2.36634u − 2.92983
0.000135989u
54
+ 0.000606267u
53
+ ··· − 0.718613u − 4.76962
a
9
=
−0.000461305u
54
− 0.00140901u
53
+ ··· + 12.3085u − 0.681429
−0.000450416u
54
− 0.00135705u
53
+ ··· + 13.8133u − 1.51385
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00197309u
54
− 0.00651879u
53
+ ··· + 43.1168u + 3.92550
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
+ 34u
54
+ ··· + 261u − 169
c
2
, c
5
u
55
+ 17u
53
+ ··· − u − 13
c
3
u
55
− 4u
54
+ ··· − 29u − 1
c
4
u
55
− 3u
54
+ ··· − 160u − 29
c
6
u
55
+ 3u
54
+ ··· + 4862u − 6341
c
7
, c
11
u
55
+ u
54
+ ··· + 1301u − 319
c
8
u
55
+ 9u
54
+ ··· − 23423u − 2897
c
9
u
55
− 2u
54
+ ··· − 8637u − 2059
c
10
u
55
+ 2u
54
+ ··· + 31739u − 6187
c
12
u
55
+ 4u
54
+ ··· + 5373u − 431
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
− 18y
54
+ ··· + 2763333y −28561
c
2
, c
5
y
55
+ 34y
54
+ ··· + 261y −169
c
3
y
55
− 6y
54
+ ··· + 581y −1
c
4
y
55
− 5y
54
+ ··· − 35184y −841
c
6
y
55
+ 73y
54
+ ··· − 1088711858y −40208281
c
7
, c
11
y
55
+ 63y
54
+ ··· − 2658559y −101761
c
8
y
55
+ 35y
54
+ ··· − 164702969y −8392609
c
9
y
55
+ 62y
54
+ ··· − 51063001y −4239481
c
10
y
55
− 68y
54
+ ··· + 631132651y −38278969
c
12
y
55
+ 50y
54
+ ··· + 5965789y −185761
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.458700 + 0.836212I
a = 0.47157 + 1.49663I
b = 0.305132 − 0.747908I
0.11183 + 1.55303I 1.95072 − 2.89152I
u = 0.458700 − 0.836212I
a = 0.47157 − 1.49663I
b = 0.305132 + 0.747908I
0.11183 − 1.55303I 1.95072 + 2.89152I
u = 0.913175 + 0.260802I
a = −0.223977 − 0.423038I
b = −0.550856 − 0.738530I
3.80751 − 0.71144I 10.81195 − 1.56897I
u = 0.913175 − 0.260802I
a = −0.223977 + 0.423038I
b = −0.550856 + 0.738530I
3.80751 + 0.71144I 10.81195 + 1.56897I
u = −1.113670 + 0.091899I
a = −0.65683 + 1.51641I
b = 0.111069 − 0.811383I
−5.06254 + 5.92628I 0. − 4.32930I
u = −1.113670 − 0.091899I
a = −0.65683 − 1.51641I
b = 0.111069 + 0.811383I
−5.06254 − 5.92628I 0. + 4.32930I
u = 0.797854 + 0.338507I
a = 1.240170 + 0.296206I
b = −0.473741 + 0.512242I
0.29315 − 1.97385I 5.19969 + 3.03837I
u = 0.797854 − 0.338507I
a = 1.240170 − 0.296206I
b = −0.473741 − 0.512242I
0.29315 + 1.97385I 5.19969 − 3.03837I
u = −0.591324 + 0.479194I
a = −0.793327 + 0.649542I
b = −0.407085 + 0.865255I
3.30919 − 4.09772I 10.16062 + 6.84746I
u = −0.591324 − 0.479194I
a = −0.793327 − 0.649542I
b = −0.407085 − 0.865255I
3.30919 + 4.09772I 10.16062 − 6.84746I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.708799 + 0.253071I
a = 0.831284 + 0.009450I
b = −0.209759 + 0.509237I
−1.81477 − 2.14360I 1.18374 + 4.80550I
u = −0.708799 − 0.253071I
a = 0.831284 − 0.009450I
b = −0.209759 − 0.509237I
−1.81477 + 2.14360I 1.18374 − 4.80550I
u = 0.138897 + 0.673640I
a = 0.011792 − 0.623544I
b = 0.910818 − 0.785919I
−7.26057 + 1.21645I 0.427980 + 0.554142I
u = 0.138897 − 0.673640I
a = 0.011792 + 0.623544I
b = 0.910818 + 0.785919I
−7.26057 − 1.21645I 0.427980 − 0.554142I
u = −0.409118 + 0.518801I
a = 1.81243 − 0.36306I
b = −0.368450 − 0.362485I
0.707490 + 1.043870I 2.63060 + 1.21674I
u = −0.409118 − 0.518801I
a = 1.81243 + 0.36306I
b = −0.368450 + 0.362485I
0.707490 − 1.043870I 2.63060 − 1.21674I
u = −0.467933 + 1.326800I
a = 0.355998 + 0.883423I
b = −0.520534 − 1.220730I
−2.57844 + 3.79796I 0
u = −0.467933 − 1.326800I
a = 0.355998 − 0.883423I
b = −0.520534 + 1.220730I
−2.57844 − 3.79796I 0
u = −0.177490 + 0.564262I
a = 0.264895 + 0.985043I
b = 1.079970 + 0.527227I
−2.81057 + 3.19886I 4.08250 − 3.76051I
u = −0.177490 − 0.564262I
a = 0.264895 − 0.985043I
b = 1.079970 − 0.527227I
−2.81057 − 3.19886I 4.08250 + 3.76051I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.122496 + 0.504032I
a = 0.083451 − 1.312890I
b = 1.280030 − 0.596135I
−6.14972 − 8.50203I 1.50480 + 6.85692I
u = 0.122496 − 0.504032I
a = 0.083451 + 1.312890I
b = 1.280030 + 0.596135I
−6.14972 + 8.50203I 1.50480 − 6.85692I
u = −0.038547 + 0.511598I
a = 1.50581 + 0.77163I
b = 0.185020 − 0.254061I
0.38570 + 1.60336I 2.33296 − 4.99216I
u = −0.038547 − 0.511598I
a = 1.50581 − 0.77163I
b = 0.185020 + 0.254061I
0.38570 − 1.60336I 2.33296 + 4.99216I
u = 0.454497
a = 0.867401
b = −0.487142
0.882935 11.1550
u = −0.35658 + 1.53590I
a = −0.006681 − 1.169070I
b = −0.22183 + 1.78303I
−7.14735 − 6.72459I 0
u = −0.35658 − 1.53590I
a = −0.006681 + 1.169070I
b = −0.22183 − 1.78303I
−7.14735 + 6.72459I 0
u = 1.32120 + 0.87148I
a = 0.072899 − 0.543533I
b = −0.362960 + 0.792328I
−0.103767 + 0.867284I 0
u = 1.32120 − 0.87148I
a = 0.072899 + 0.543533I
b = −0.362960 − 0.792328I
−0.103767 − 0.867284I 0
u = 0.150297 + 0.353433I
a = 1.088790 − 0.154193I
b = −1.184760 + 0.246323I
1.04688 − 1.12802I −3.55524 − 3.81322I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.150297 − 0.353433I
a = 1.088790 + 0.154193I
b = −1.184760 − 0.246323I
1.04688 + 1.12802I −3.55524 + 3.81322I
u = 0.19519 + 1.66111I
a = 0.124385 + 1.042830I
b = −0.23067 − 1.60897I
−4.50056 + 3.53769I 0
u = 0.19519 − 1.66111I
a = 0.124385 − 1.042830I
b = −0.23067 + 1.60897I
−4.50056 − 3.53769I 0
u = −0.17081 + 1.69824I
a = 0.260758 − 1.042020I
b = 0.445170 + 1.129250I
−1.68388 + 4.70781I 0
u = −0.17081 − 1.69824I
a = 0.260758 + 1.042020I
b = 0.445170 − 1.129250I
−1.68388 − 4.70781I 0
u = −0.37546 + 1.72257I
a = −0.042439 − 0.816658I
b = −0.01000 + 1.66318I
−6.17568 − 1.37212I 0
u = −0.37546 − 1.72257I
a = −0.042439 + 0.816658I
b = −0.01000 − 1.66318I
−6.17568 + 1.37212I 0
u = −0.47575 + 1.78827I
a = −0.437619 − 0.836026I
b = −0.01817 + 1.74737I
−10.05530 − 0.59545I 0
u = −0.47575 − 1.78827I
a = −0.437619 + 0.836026I
b = −0.01817 − 1.74737I
−10.05530 + 0.59545I 0
u = 0.50496 + 1.78171I
a = −0.451915 + 0.949040I
b = 0.01078 − 1.76502I
−14.8051 + 5.1933I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50496 − 1.78171I
a = −0.451915 − 0.949040I
b = 0.01078 + 1.76502I
−14.8051 − 5.1933I 0
u = 0.47150 + 1.79275I
a = −0.520806 + 0.790076I
b = −0.02767 − 1.71161I
−13.3198 − 4.9860I 0
u = 0.47150 − 1.79275I
a = −0.520806 − 0.790076I
b = −0.02767 + 1.71161I
−13.3198 + 4.9860I 0
u = 0.48338 + 1.81853I
a = 0.197047 + 0.819227I
b = −0.06259 − 1.51621I
−6.21422 + 3.83703I 0
u = 0.48338 − 1.81853I
a = 0.197047 − 0.819227I
b = −0.06259 + 1.51621I
−6.21422 − 3.83703I 0
u = −1.78497 + 0.62407I
a = −0.272598 + 0.574120I
b = −0.141685 − 0.657394I
−4.48898 − 5.80054I 0
u = −1.78497 − 0.62407I
a = −0.272598 − 0.574120I
b = −0.141685 + 0.657394I
−4.48898 + 5.80054I 0
u = 0.40813 + 2.08970I
a = 0.007416 − 0.968701I
b = 0.45117 + 1.67641I
−9.89971 + 9.10784I 0
u = 0.40813 − 2.08970I
a = 0.007416 + 0.968701I
b = 0.45117 − 1.67641I
−9.89971 − 9.10784I 0
u = −0.21276 + 2.13416I
a = 0.217139 − 0.984595I
b = −0.08489 + 1.49140I
−8.29738 − 3.26193I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21276 − 2.13416I
a = 0.217139 + 0.984595I
b = −0.08489 − 1.49140I
−8.29738 + 3.26193I 0
u = −0.47216 + 2.09522I
a = −0.031964 + 0.982080I
b = 0.44713 − 1.72011I
−13.6692 − 14.9575I 0
u = −0.47216 − 2.09522I
a = −0.031964 − 0.982080I
b = 0.44713 + 1.72011I
−13.6692 + 14.9575I 0
u = −0.33765 + 2.15781I
a = 0.049776 + 1.003920I
b = 0.39293 − 1.63470I
−14.8380 − 3.7469I 0
u = −0.33765 − 2.15781I
a = 0.049776 − 1.003920I
b = 0.39293 + 1.63470I
−14.8380 + 3.7469I 0
10
II. I
u
2
=
h9.41×10
23
u
19
+2.06×10
24
u
18
+· · ·+1.00×10
24
b−4.04×10
24
, 3.24×10
25
u
19
+
7.09 × 10
25
u
18
+ · · · + 1.00 × 10
24
a − 1.71 × 10
26
, u
20
+ 2u
19
+ · · · − 14u + 1i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
11
=
−32.3988u
19
− 70.9016u
18
+ ··· − 1491.77u + 170.850
−0.941499u
19
− 2.05689u
18
+ ··· − 43.9860u + 4.03582
a
12
=
−33.3403u
19
− 72.9585u
18
+ ··· − 1535.76u + 174.886
−0.941499u
19
− 2.05689u
18
+ ··· − 43.9860u + 4.03582
a
3
=
−16.8236u
19
− 36.8452u
18
+ ··· − 771.199u + 85.2522
5.36412u
19
+ 11.7183u
18
+ ··· + 248.289u − 28.2108
a
10
=
−32.3988u
19
− 70.9016u
18
+ ··· − 1491.77u + 170.850
0.168831u
19
+ 0.351278u
18
+ ··· + 9.07021u − 2.06811
a
8
=
−26.5155u
19
− 58.0667u
18
+ ··· − 1216.85u + 140.767
−0.753809u
19
− 1.66202u
18
+ ··· − 33.7724u + 2.85889
a
1
=
−13.0882u
19
− 28.5954u
18
+ ··· − 607.666u + 65.7562
4.56802u
19
+ 9.98468u
18
+ ··· + 210.998u − 23.7432
a
2
=
−13.1542u
19
− 28.7857u
18
+ ··· − 606.496u + 64.0210
7.11259u
19
+ 15.5565u
18
+ ··· + 326.928u − 36.6149
a
5
=
−32.6380u
19
− 71.5392u
18
+ ··· − 1489.53u + 168.175
3.97446u
19
+ 8.71120u
18
+ ··· + 182.668u − 21.0322
a
9
=
−27.2693u
19
− 59.7288u
18
+ ··· − 1250.62u + 143.626
−0.753809u
19
− 1.66202u
18
+ ··· − 33.7724u + 2.85889
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
62641622421330731218172603
999998536254646311244669
u
19
−
137124516846403670777326513
999998536254646311244669
u
18
+
··· −
2878152757722006579821255122
999998536254646311244669
u +
338046622815474243224796674
999998536254646311244669
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
20
− 11u
19
+ ··· − 13u + 1
c
2
u
20
+ 3u
19
+ ··· + 3u + 1
c
3
u
20
+ 3u
19
+ ··· + u + 1
c
4
u
20
− 2u
19
+ ··· − 7u
2
+ 1
c
5
u
20
− 3u
19
+ ··· − 3u + 1
c
6
u
20
+ 2u
19
+ ··· − 14u + 1
c
7
u
20
+ 4u
19
+ ··· + 5u + 1
c
8
u
20
+ 2u
18
+ ··· + u + 1
c
9
u
20
− u
19
+ ··· + 11u + 1
c
10
u
20
+ u
19
+ ··· − 103u + 73
c
11
u
20
− 4u
19
+ ··· − 5u + 1
c
12
u
20
− 3u
19
+ ··· − u + 1
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 3y
19
+ ··· − 11y + 1
c
2
, c
5
y
20
+ 11y
19
+ ··· + 13y + 1
c
3
y
20
+ 11y
19
+ ··· + 9y + 1
c
4
y
20
− 16y
19
+ ··· − 14y + 1
c
6
y
20
+ 10y
19
+ ··· − 64y + 1
c
7
, c
11
y
20
+ 16y
19
+ ··· + 9y + 1
c
8
y
20
+ 4y
19
+ ··· − 25y + 1
c
9
y
20
+ 11y
19
+ ··· − 21y + 1
c
10
y
20
− 7y
19
+ ··· + 8663y + 5329
c
12
y
20
+ 11y
19
+ ··· + 13y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.940992 + 0.620229I
a = 0.773568 + 0.165278I
b = 0.231111 + 0.786500I
3.34471 − 1.65498I 6.43907 + 4.20509I
u = 0.940992 − 0.620229I
a = 0.773568 − 0.165278I
b = 0.231111 − 0.786500I
3.34471 + 1.65498I 6.43907 − 4.20509I
u = −0.842075 + 0.871841I
a = 0.793322 + 0.085027I
b = 0.226922 − 1.109400I
2.16792 − 3.50657I 3.05923 + 2.59992I
u = −0.842075 − 0.871841I
a = 0.793322 − 0.085027I
b = 0.226922 + 1.109400I
2.16792 + 3.50657I 3.05923 − 2.59992I
u = −0.402447 + 0.588078I
a = 1.56479 + 0.11995I
b = −0.468313 − 1.079950I
−0.64497 + 2.98534I 3.61521 − 5.29378I
u = −0.402447 − 0.588078I
a = 1.56479 − 0.11995I
b = −0.468313 + 1.079950I
−0.64497 − 2.98534I 3.61521 + 5.29378I
u = 1.134020 + 0.818765I
a = 0.079337 − 1.103920I
b = −0.220466 + 0.561392I
0.85761 + 1.50900I 14.5318 − 3.4126I
u = 1.134020 − 0.818765I
a = 0.079337 + 1.103920I
b = −0.220466 − 0.561392I
0.85761 − 1.50900I 14.5318 + 3.4126I
u = 0.339290 + 0.111161I
a = 1.95398 + 1.57017I
b = −0.748209 + 0.283121I
1.42125 − 1.38443I 14.3541 + 3.8433I
u = 0.339290 − 0.111161I
a = 1.95398 − 1.57017I
b = −0.748209 − 0.283121I
1.42125 + 1.38443I 14.3541 − 3.8433I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.57084 + 1.62511I
a = 0.163422 − 1.039380I
b = 0.07015 + 1.53272I
−7.72375 − 4.56543I −0.60389 + 5.70350I
u = −0.57084 − 1.62511I
a = 0.163422 + 1.039380I
b = 0.07015 − 1.53272I
−7.72375 + 4.56543I −0.60389 − 5.70350I
u = −1.74775 + 0.15837I
a = −0.006275 − 0.902457I
b = 0.323711 + 0.686202I
−3.96953 + 6.70083I 6.00000 − 9.43611I
u = −1.74775 − 0.15837I
a = −0.006275 + 0.902457I
b = 0.323711 − 0.686202I
−3.96953 − 6.70083I 6.00000 + 9.43611I
u = 0.193733 + 0.009969I
a = 2.07668 − 3.17071I
b = −0.874447 − 0.085240I
1.40571 + 1.37087I 13.2500 − 6.0434I
u = 0.193733 − 0.009969I
a = 2.07668 + 3.17071I
b = −0.874447 + 0.085240I
1.40571 − 1.37087I 13.2500 + 6.0434I
u = 0.24584 + 1.80696I
a = 0.179807 + 0.867154I
b = −0.12456 − 1.62181I
−5.72982 + 2.73889I 4.19668 − 0.49415I
u = 0.24584 − 1.80696I
a = 0.179807 − 0.867154I
b = −0.12456 + 1.62181I
−5.72982 − 2.73889I 4.19668 + 0.49415I
u = −0.29077 + 1.90159I
a = −0.078632 + 0.972344I
b = −0.415898 − 1.061560I
−0.99873 + 4.79549I 12.00812 − 6.11844I
u = −0.29077 − 1.90159I
a = −0.078632 − 0.972344I
b = −0.415898 + 1.061560I
−0.99873 − 4.79549I 12.00812 + 6.11844I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 11u
19
+ ··· − 13u + 1)(u
55
+ 34u
54
+ ··· + 261u − 169)
c
2
(u
20
+ 3u
19
+ ··· + 3u + 1)(u
55
+ 17u
53
+ ··· − u − 13)
c
3
(u
20
+ 3u
19
+ ··· + u + 1)(u
55
− 4u
54
+ ··· − 29u − 1)
c
4
(u
20
− 2u
19
+ ··· − 7u
2
+ 1)(u
55
− 3u
54
+ ··· − 160u − 29)
c
5
(u
20
− 3u
19
+ ··· − 3u + 1)(u
55
+ 17u
53
+ ··· − u − 13)
c
6
(u
20
+ 2u
19
+ ··· − 14u + 1)(u
55
+ 3u
54
+ ··· + 4862u − 6341)
c
7
(u
20
+ 4u
19
+ ··· + 5u + 1)(u
55
+ u
54
+ ··· + 1301u − 319)
c
8
(u
20
+ 2u
18
+ ··· + u + 1)(u
55
+ 9u
54
+ ··· − 23423u − 2897)
c
9
(u
20
− u
19
+ ··· + 11u + 1)(u
55
− 2u
54
+ ··· − 8637u − 2059)
c
10
(u
20
+ u
19
+ ··· − 103u + 73)(u
55
+ 2u
54
+ ··· + 31739u − 6187)
c
11
(u
20
− 4u
19
+ ··· − 5u + 1)(u
55
+ u
54
+ ··· + 1301u − 319)
c
12
(u
20
− 3u
19
+ ··· − u + 1)(u
55
+ 4u
54
+ ··· + 5373u − 431)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 3y
19
+ ··· − 11y + 1)(y
55
− 18y
54
+ ··· + 2763333y −28561)
c
2
, c
5
(y
20
+ 11y
19
+ ··· + 13y + 1)(y
55
+ 34y
54
+ ··· + 261y −169)
c
3
(y
20
+ 11y
19
+ ··· + 9y + 1)(y
55
− 6y
54
+ ··· + 581y −1)
c
4
(y
20
− 16y
19
+ ··· − 14y + 1)(y
55
− 5y
54
+ ··· − 35184y −841)
c
6
(y
20
+ 10y
19
+ ··· − 64y + 1)
· (y
55
+ 73y
54
+ ··· − 1088711858y −40208281)
c
7
, c
11
(y
20
+ 16y
19
+ ··· + 9y + 1)(y
55
+ 63y
54
+ ··· − 2658559y −101761)
c
8
(y
20
+ 4y
19
+ ··· − 25y + 1)
· (y
55
+ 35y
54
+ ··· − 164702969y −8392609)
c
9
(y
20
+ 11y
19
+ ··· − 21y + 1)
· (y
55
+ 62y
54
+ ··· − 51063001y −4239481)
c
10
(y
20
− 7y
19
+ ··· + 8663y + 5329)
· (y
55
− 68y
54
+ ··· + 631132651y −38278969)
c
12
(y
20
+ 11y
19
+ ··· + 13y + 1)
· (y
55
+ 50y
54
+ ··· + 5965789y −185761)
19
