12n
0264
(K12n
0264
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 12 11 4 7 5 9 6
Solving Sequence
3,9
4
8,12
11 7 10 6 1 5 2
c
3
c
8
c
11
c
7
c
9
c
6
c
12
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.93403 × 10
149
u
37
− 1.74178 × 10
149
u
36
+ ··· + 2.21546 × 10
152
b + 1.76661 × 10
154
,
7.93734 × 10
149
u
37
− 3.29411 × 10
149
u
36
+ ··· + 4.43092 × 10
152
a + 3.55362 × 10
154
,
u
38
− u
37
+ ··· + 86016u − 25088i
I
u
2
= h8082115793u
16
+ 864266486u
15
+ ··· + 5782655035b − 29654101499,
682951511u
16
− 479427583u
15
+ ··· + 5782655035a − 12663191293, u
17
+ 6u
15
+ ··· − 3u + 1i
I
v
1
= ha, −579074v
8
+ 1101995v
7
+ ··· + 5353327b + 7952402,
v
9
− v
8
− 8v
7
+ v
6
+ 33v
5
+ 23v
4
− 14v
3
− 2v
2
+ 3v −7i
* 3 irreducible components of dim
C
= 0, with total 64 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
= h3.93 × 10
149
u
37
− 1.74 × 10
149
u
36
+ · · · + 2.22 × 10
152
b + 1.77 ×
10
154
, 7.94 × 10
149
u
37
− 3.29 × 10
149
u
36
+ · · · + 4.43 × 10
152
a + 3.55 ×
10
154
, u
38
− u
37
+ · · · + 86016u − 25088i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
12
=
−0.00179135u
37
+ 0.000743437u
36
+ ··· + 147.911u − 80.2006
−0.00177572u
37
+ 0.000786192u
36
+ ··· + 151.635u − 79.7401
a
11
=
−0.00179135u
37
+ 0.000743437u
36
+ ··· + 147.911u − 80.2006
−0.00247624u
37
+ 0.00101022u
36
+ ··· + 196.831u − 106.030
a
7
=
−0.00108938u
37
+ 0.000479390u
36
+ ··· + 86.4568u − 38.9386
−0.00129295u
37
+ 0.000455453u
36
+ ··· + 89.7492u − 44.1198
a
10
=
−0.00134130u
37
+ 0.000498496u
36
+ ··· + 100.346u − 57.3777
−0.00207949u
37
+ 0.000840213u
36
+ ··· + 166.563u − 92.5692
a
6
=
−0.00126938u
37
+ 0.000412248u
36
+ ··· + 85.1965u − 49.2329
−0.00261068u
37
+ 0.000910744u
36
+ ··· + 185.542u − 106.611
a
1
=
−0.000219442u
37
+ 0.000183073u
36
+ ··· + 30.0161u − 10.6041
−0.000132258u
37
+ 0.000107784u
36
+ ··· + 18.7525u − 7.96288
a
5
=
0.0000871841u
37
− 0.0000752884u
36
+ ··· − 11.2636u + 2.64124
−0.000143931u
37
+ 0.000121946u
36
+ ··· + 19.9165u − 7.66444
a
2
=
−0.0000871841u
37
+ 0.0000752884u
36
+ ··· + 11.2636u − 2.64124
−0.000132258u
37
+ 0.000107784u
36
+ ··· + 18.7525u − 7.96288
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00823228u
37
− 0.00319378u
36
+ ··· − 645.161u + 373.502
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 46u
36
+ ··· + 6958u + 2401
c
2
, c
4
u
38
− 16u
37
+ ··· + 378u − 49
c
3
, c
8
u
38
− u
37
+ ··· + 86016u − 25088
c
5
, c
10
u
38
− 2u
37
+ ··· − 3904u − 5873
c
6
, c
12
u
38
− 3u
37
+ ··· − 446u + 44
c
7
u
38
+ u
37
+ ··· + 40881797u + 3617129
c
9
u
38
+ 4u
37
+ ··· − 114u − 17
c
11
u
38
+ u
37
+ ··· + 79046u − 14009
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 92y
37
+ ··· + 262856678y + 5764801
c
2
, c
4
y
38
+ 46y
36
+ ··· − 6958y + 2401
c
3
, c
8
y
38
+ 69y
37
+ ··· + 3750756352y + 629407744
c
5
, c
10
y
38
− 12y
37
+ ··· − 781291844y + 34492129
c
6
, c
12
y
38
+ 35y
37
+ ··· − 111884y + 1936
c
7
y
38
− 107y
37
+ ··· − 346184004395873y + 13083622202641
c
9
y
38
− 6y
37
+ ··· − 8270y + 289
c
11
y
38
− 69y
37
+ ··· − 9544952050y + 196252081
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.542649 + 0.614305I
a = 0.515994 + 1.233570I
b = −0.104502 + 0.163985I
1.68943 + 7.69679I −0.16453 − 13.04445I
u = −0.542649 − 0.614305I
a = 0.515994 − 1.233570I
b = −0.104502 − 0.163985I
1.68943 − 7.69679I −0.16453 + 13.04445I
u = 0.072090 + 0.744709I
a = 0.81163 − 1.20274I
b = 0.230747 + 0.056669I
3.31755 + 0.54950I 6.15791 + 2.31967I
u = 0.072090 − 0.744709I
a = 0.81163 + 1.20274I
b = 0.230747 − 0.056669I
3.31755 − 0.54950I 6.15791 − 2.31967I
u = −0.554003 + 0.499646I
a = 0.259417 + 1.163440I
b = 0.126830 + 0.775649I
−1.38624 + 1.33481I −2.97345 − 3.66862I
u = −0.554003 − 0.499646I
a = 0.259417 − 1.163440I
b = 0.126830 − 0.775649I
−1.38624 − 1.33481I −2.97345 + 3.66862I
u = 0.434969 + 0.601443I
a = 1.185780 − 0.546611I
b = 0.144861 + 0.163719I
1.48961 + 0.57943I 5.02569 − 0.39325I
u = 0.434969 − 0.601443I
a = 1.185780 + 0.546611I
b = 0.144861 − 0.163719I
1.48961 − 0.57943I 5.02569 + 0.39325I
u = 0.606671 + 0.412287I
a = −1.202140 + 0.417819I
b = −1.72769 − 0.34007I
−4.47346 + 0.84284I −11.66035 − 0.97344I
u = 0.606671 − 0.412287I
a = −1.202140 − 0.417819I
b = −1.72769 + 0.34007I
−4.47346 − 0.84284I −11.66035 + 0.97344I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.185752 + 1.318190I
a = 0.519872 + 0.356267I
b = −0.524833 + 0.069232I
−2.12322 − 4.24125I −4.26882 + 3.51292I
u = 0.185752 − 1.318190I
a = 0.519872 − 0.356267I
b = −0.524833 − 0.069232I
−2.12322 + 4.24125I −4.26882 − 3.51292I
u = 0.626028 + 0.000453I
a = 0.99835 + 1.48871I
b = 1.84598 + 1.42085I
0.61462 + 3.26287I −1.84851 − 7.14359I
u = 0.626028 − 0.000453I
a = 0.99835 − 1.48871I
b = 1.84598 − 1.42085I
0.61462 − 3.26287I −1.84851 + 7.14359I
u = 0.220678 + 0.522522I
a = −0.299614 − 0.840555I
b = −2.25916 − 0.15809I
−0.41969 − 2.46857I 5.02234 + 6.21524I
u = 0.220678 − 0.522522I
a = −0.299614 + 0.840555I
b = −2.25916 + 0.15809I
−0.41969 + 2.46857I 5.02234 − 6.21524I
u = 0.134435 + 0.540176I
a = 1.65614 + 0.96243I
b = 0.467042 + 0.770777I
0.34862 + 2.64648I 0.38453 − 4.62015I
u = 0.134435 − 0.540176I
a = 1.65614 − 0.96243I
b = 0.467042 − 0.770777I
0.34862 − 2.64648I 0.38453 + 4.62015I
u = −0.487313
a = −0.299932
b = −0.879403
−1.21395 −9.56810
u = −1.68632 + 0.08026I
a = 0.014317 + 0.422528I
b = −0.16420 + 1.88746I
1.94242 + 0.25898I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.68632 − 0.08026I
a = 0.014317 − 0.422528I
b = −0.16420 − 1.88746I
1.94242 − 0.25898I 0
u = 1.86202
a = −0.669370
b = 1.04021
−6.81012 0
u = −0.78573 + 1.74324I
a = −1.105090 − 0.592834I
b = −0.214357 − 0.763758I
6.33444 − 4.25779I 0
u = −0.78573 − 1.74324I
a = −1.105090 + 0.592834I
b = −0.214357 + 0.763758I
6.33444 + 4.25779I 0
u = 0.36940 + 1.96319I
a = −0.015181 − 1.352630I
b = 0.05084 − 2.20969I
10.56750 − 4.02468I 0
u = 0.36940 − 1.96319I
a = −0.015181 + 1.352630I
b = 0.05084 + 2.20969I
10.56750 + 4.02468I 0
u = 1.13922 + 2.02195I
a = −0.145900 + 0.974160I
b = −0.03782 + 2.28437I
17.0081 − 15.1515I 0
u = 1.13922 − 2.02195I
a = −0.145900 − 0.974160I
b = −0.03782 − 2.28437I
17.0081 + 15.1515I 0
u = −1.07898 + 2.08221I
a = −0.003796 − 0.816704I
b = −0.37487 − 1.96325I
16.6139 + 6.3485I 0
u = −1.07898 − 2.08221I
a = −0.003796 + 0.816704I
b = −0.37487 + 1.96325I
16.6139 − 6.3485I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.95530 + 1.96183I
a = −0.665322 + 0.086310I
b = 0.704808 + 0.014037I
8.32107 − 2.64989I 0
u = 1.95530 − 1.96183I
a = −0.665322 − 0.086310I
b = 0.704808 − 0.014037I
8.32107 + 2.64989I 0
u = −0.18789 + 2.88116I
a = −0.176028 − 0.917819I
b = 0.20196 − 2.09465I
18.1843 + 3.4592I 0
u = −0.18789 − 2.88116I
a = −0.176028 + 0.917819I
b = 0.20196 + 2.09465I
18.1843 − 3.4592I 0
u = −0.89301 + 2.76858I
a = 0.023279 + 0.734216I
b = 0.04287 + 2.25868I
12.09730 + 5.36685I 0
u = −0.89301 − 2.76858I
a = 0.023279 − 0.734216I
b = 0.04287 − 2.25868I
12.09730 − 5.36685I 0
u = −0.20333 + 3.10034I
a = 0.041511 + 0.844710I
b = −0.13176 + 2.19457I
19.1617 + 5.3151I 0
u = −0.20333 − 3.10034I
a = 0.041511 − 0.844710I
b = −0.13176 − 2.19457I
19.1617 − 5.3151I 0
8
II.
I
u
2
= h8.08 × 10
9
u
16
+ 8.64 × 10
8
u
15
+ · · · + 5.78 × 10
9
b − 2.97 × 10
10
, 6.83 ×
10
8
u
16
−4.79×10
8
u
15
+· · ·+5.78×10
9
a−1.27×10
10
, u
17
+6u
15
+· · ·−3u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
12
=
−0.118103u
16
+ 0.0829079u
15
+ ··· − 0.587774u + 2.18986
−1.39765u
16
− 0.149458u
15
+ ··· − 5.69145u + 5.12811
a
11
=
−0.118103u
16
+ 0.0829079u
15
+ ··· − 0.587774u + 2.18986
−1.29814u
16
− 0.108155u
15
+ ··· − 5.32462u + 5.04520
a
7
=
−0.446141u
16
+ 0.123421u
15
+ ··· − 0.579812u + 2.45214
−1.49333u
16
− 0.286083u
15
+ ··· − 6.76385u + 4.74588
a
10
=
0.165246u
16
+ 0.188150u
15
+ ··· + 0.228629u + 2.06644
−0.948386u
16
+ 0.0348973u
15
+ ··· − 3.47584u + 4.81654
a
6
=
0.833403u
16
+ 0.355787u
15
+ ··· + 4.52387u − 0.486115
0.998649u
16
+ 0.543937u
15
+ ··· + 4.75250u + 1.58032
a
1
=
0.0889186u
16
− 0.141079u
15
+ ··· + 0.611062u − 0.716020
0.114263u
16
− 0.0409080u
15
+ ··· + 0.312606u − 1.08969
a
5
=
−0.0253442u
16
− 0.100171u
15
+ ··· + 0.298457u + 0.373667
−0.118103u
16
+ 0.0829079u
15
+ ··· − 0.587774u + 1.18986
a
2
=
−0.0253442u
16
− 0.100171u
15
+ ··· + 0.298457u + 0.373667
0.114263u
16
− 0.0409080u
15
+ ··· + 0.312606u − 1.08969
(ii) Obstruction class = 1
(iii) Cusp Shapes =
45091796106
5782655035
u
16
+
12435236787
5782655035
u
15
+ ··· +
43331514147
1156531007
u −
96632179643
5782655035
9
(iv) u-Polynomials at the component
10
Crossings u-Polynomials at each crossing
c
1
u
17
− 8u
16
+ ··· + 3u − 1
c
2
u
17
+ 6u
16
+ ··· + u + 1
c
3
u
17
+ 6u
15
+ ··· − 3u + 1
c
4
u
17
− 6u
16
+ ··· + u − 1
c
5
u
17
+ 6u
15
+ ··· + 3u − 1
c
6
u
17
+ 3u
16
+ ··· + 6u
2
+ 1
c
7
u
17
+ 3u
16
+ ··· + 6u + 1
c
8
u
17
+ 6u
15
+ ··· − 3u − 1
c
9
u
17
− 6u
16
+ ··· + 3u − 1
c
10
u
17
+ 6u
15
+ ··· + 3u + 1
c
11
u
17
− 5u
16
+ ··· + 5u − 1
c
12
u
17
− 3u
16
+ ··· − 6u
2
− 1
11
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 8y
16
+ ··· − 25y − 1
c
2
, c
4
y
17
− 8y
16
+ ··· + 3y − 1
c
3
, c
8
y
17
+ 12y
16
+ ··· + 3y − 1
c
5
, c
10
y
17
+ 12y
16
+ ··· − 3y − 1
c
6
, c
12
y
17
+ 3y
16
+ ··· − 12y − 1
c
7
y
17
− 19y
16
+ ··· − 2y − 1
c
9
y
17
+ 2y
16
+ ··· + 19y − 1
c
11
y
17
− 17y
16
+ ··· + 7y − 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.123817 + 0.916477I
a = 0.468487 − 0.527233I
b = 0.848975 + 0.187757I
2.61790 + 2.40485I 3.33881 − 2.22795I
u = −0.123817 − 0.916477I
a = 0.468487 + 0.527233I
b = 0.848975 − 0.187757I
2.61790 − 2.40485I 3.33881 + 2.22795I
u = 0.519605 + 0.973810I
a = −0.045901 − 0.497479I
b = −0.642933 − 0.280867I
1.04490 − 6.61108I −1.52634 + 5.44334I
u = 0.519605 − 0.973810I
a = −0.045901 + 0.497479I
b = −0.642933 + 0.280867I
1.04490 + 6.61108I −1.52634 − 5.44334I
u = 0.718697 + 0.273065I
a = 1.301770 + 0.430364I
b = −0.061570 + 1.362440I
1.14952 + 2.21103I 2.23770 − 3.38646I
u = 0.718697 − 0.273065I
a = 1.301770 − 0.430364I
b = −0.061570 − 1.362440I
1.14952 − 2.21103I 2.23770 + 3.38646I
u = −0.535223 + 1.162140I
a = −0.064866 + 0.614609I
b = 0.405304 + 0.608509I
−1.12324 + 5.07181I −0.31929 − 6.91281I
u = −0.535223 − 1.162140I
a = −0.064866 − 0.614609I
b = 0.405304 − 0.608509I
−1.12324 − 5.07181I −0.31929 + 6.91281I
u = 0.259361 + 1.266310I
a = 0.449036 + 0.835046I
b = −0.176709 + 1.029420I
0.516364 + 0.300871I 0.207427 − 0.470649I
u = 0.259361 − 1.266310I
a = 0.449036 − 0.835046I
b = −0.176709 − 1.029420I
0.516364 − 0.300871I 0.207427 + 0.470649I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.642620 + 0.176331I
a = 1.82999 + 0.22284I
b = 2.02895 − 0.99762I
−3.99885 − 0.50220I −2.39894 − 6.28246I
u = −0.642620 − 0.176331I
a = 1.82999 − 0.22284I
b = 2.02895 + 0.99762I
−3.99885 + 0.50220I −2.39894 + 6.28246I
u = 0.314004 + 0.270023I
a = 1.99812 − 0.08558I
b = 3.08746 − 2.37905I
−0.26934 + 3.00568I −3.5088 + 14.7647I
u = 0.314004 − 0.270023I
a = 1.99812 + 0.08558I
b = 3.08746 + 2.37905I
−0.26934 − 3.00568I −3.5088 − 14.7647I
u = −1.73212
a = −0.671734
b = 0.989401
−6.94010 −36.0810
u = 0.35606 + 2.09120I
a = −0.100766 − 1.164660I
b = 0.01582 − 2.10159I
10.11250 − 4.21829I −4.98986 + 4.99941I
u = 0.35606 − 2.09120I
a = −0.100766 + 1.164660I
b = 0.01582 + 2.10159I
10.11250 + 4.21829I −4.98986 − 4.99941I
15
III. I
v
1
= ha, −5.79 × 10
5
v
8
+ 1.10 × 10
6
v
7
+ · · · + 5.35 × 10
6
b + 7.95 ×
10
6
, v
9
− v
8
+ · · · + 3v − 7i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
8
=
v
0
a
12
=
0
0.108171v
8
− 0.205852v
7
+ ··· + 0.000774472v − 1.48551
a
11
=
−0.102023v
8
+ 0.224509v
7
+ ··· − 1.05024v + 0.683770
0.108171v
8
− 0.205852v
7
+ ··· + 0.000774472v − 1.48551
a
7
=
−0.159020v
8
+ 0.294157v
7
+ ··· − 0.0933167v + 0.754991
0.109964v
8
− 0.217820v
7
+ ··· + 1.73167v − 1.00939
a
10
=
−0.0944713v
8
+ 0.166302v
7
+ ··· + 0.644723v + 0.337094
−0.0798487v
8
+ 0.139548v
7
+ ··· − 0.391226v − 0.126428
a
6
=
−0.159020v
8
+ 0.294157v
7
+ ··· − 0.0933167v + 0.754991
0.0798487v
8
− 0.139548v
7
+ ··· + 0.391226v + 0.126428
a
1
=
0.163153v
8
− 0.314762v
7
+ ··· + 0.866612v − 1.49020
−1
a
5
=
−0.163153v
8
+ 0.314762v
7
+ ··· − 0.866612v + 1.49020
1
a
2
=
0.163153v
8
− 0.314762v
7
+ ··· + 0.866612v − 0.490203
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
41627955
37473289
v
8
−
61862036
37473289
v
7
−
282471299
37473289
v
6
+
146298199
37473289
v
5
+
1154392026
37473289
v
4
+
495537892
37473289
v
3
−
23961352
5353327
v
2
+
145490692
37473289
v −
344731995
37473289
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
6
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
7
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
9
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
10
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
11
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
9
c
3
, c
8
y
9
c
5
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1
c
6
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1
c
7
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
c
9
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.094310 + 0.114265I
a = 0
b = −0.650520 − 0.534295I
−3.42837 + 2.09337I −6.52230 − 4.24226I
v = −1.094310 − 0.114265I
a = 0
b = −0.650520 + 0.534295I
−3.42837 − 2.09337I −6.52230 + 4.24226I
v = 0.703774
a = 0
b = −1.17358
−0.446489 3.16660
v = 0.187998 + 0.564097I
a = 0
b = −1.104930 − 0.619057I
−1.02799 + 2.45442I −8.21790 − 4.39771I
v = 0.187998 − 0.564097I
a = 0
b = −1.104930 + 0.619057I
−1.02799 − 2.45442I −8.21790 + 4.39771I
v = −1.51733 + 0.93950I
a = 0
b = 0.443756 + 0.532821I
2.72642 + 1.33617I 0.84367 − 3.27176I
v = −1.51733 − 0.93950I
a = 0
b = 0.443756 − 0.532821I
2.72642 − 1.33617I 0.84367 + 3.27176I
v = 2.57175 + 0.82630I
a = 0
b = 0.469909 + 0.043588I
1.95319 + 7.08493I 3.61934 − 1.74309I
v = 2.57175 − 0.82630I
a = 0
b = 0.469909 − 0.043588I
1.95319 − 7.08493I 3.61934 + 1.74309I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
17
− 8u
16
+ ··· + 3u − 1)(u
38
+ 46u
36
+ ··· + 6958u + 2401)
c
2
((u − 1)
9
)(u
17
+ 6u
16
+ ··· + u + 1)(u
38
− 16u
37
+ ··· + 378u − 49)
c
3
u
9
(u
17
+ 6u
15
+ ··· − 3u + 1)(u
38
− u
37
+ ··· + 86016u − 25088)
c
4
((u + 1)
9
)(u
17
− 6u
16
+ ··· + u − 1)(u
38
− 16u
37
+ ··· + 378u − 49)
c
5
(u
9
− u
8
+ ··· + u + 1)(u
17
+ 6u
15
+ ··· + 3u − 1)
· (u
38
− 2u
37
+ ··· − 3904u − 5873)
c
6
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
17
+ 3u
16
+ ··· + 6u
2
+ 1)(u
38
− 3u
37
+ ··· − 446u + 44)
c
7
(u
9
− u
8
+ ··· − u + 1)(u
17
+ 3u
16
+ ··· + 6u + 1)
· (u
38
+ u
37
+ ··· + 40881797u + 3617129)
c
8
u
9
(u
17
+ 6u
15
+ ··· − 3u − 1)(u
38
− u
37
+ ··· + 86016u − 25088)
c
9
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
17
− 6u
16
+ ··· + 3u − 1)(u
38
+ 4u
37
+ ··· − 114u − 17)
c
10
(u
9
+ u
8
+ ··· + u − 1)(u
17
+ 6u
15
+ ··· + 3u + 1)
· (u
38
− 2u
37
+ ··· − 3904u − 5873)
c
11
(u
9
+ u
8
+ ··· − u − 1)(u
17
− 5u
16
+ ··· + 5u − 1)
· (u
38
+ u
37
+ ··· + 79046u − 14009)
c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
17
− 3u
16
+ ··· − 6u
2
− 1)(u
38
− 3u
37
+ ··· − 446u + 44)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
17
+ 8y
16
+ ··· − 25y − 1)
· (y
38
+ 92y
37
+ ··· + 262856678y + 5764801)
c
2
, c
4
((y − 1)
9
)(y
17
− 8y
16
+ ··· + 3y − 1)(y
38
+ 46y
36
+ ··· − 6958y + 2401)
c
3
, c
8
y
9
(y
17
+ 12y
16
+ ··· + 3y − 1)
· (y
38
+ 69y
37
+ ··· + 3750756352y + 629407744)
c
5
, c
10
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
17
+ 12y
16
+ ··· − 3y − 1)
· (y
38
− 12y
37
+ ··· − 781291844y + 34492129)
c
6
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
17
+ 3y
16
+ ··· − 12y − 1)(y
38
+ 35y
37
+ ··· − 111884y + 1936)
c
7
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
17
− 19y
16
+ ··· − 2y − 1)
· (y
38
− 107y
37
+ ··· − 346184004395873y + 13083622202641)
c
9
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
17
+ 2y
16
+ ··· + 19y − 1)(y
38
− 6y
37
+ ··· − 8270y + 289)
c
11
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
17
− 17y
16
+ ··· + 7y − 1)
· (y
38
− 69y
37
+ ··· − 9544952050y + 196252081)
21
