12n
0531
(K12n
0531
)
A knot diagram
1
Linearized knot diagam
3 6 11 8 2 9 5 12 6 1 4 9
Solving Sequence
2,6 3,9
7 10 1 11 5 8 4 12
c
2
c
6
c
9
c
1
c
10
c
5
c
7
c
4
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.98168 × 10
59
u
66
− 1.61635 × 10
59
u
65
+ ··· + 8.56121 × 10
58
b + 6.93366 × 10
59
,
− 3.91666 × 10
57
u
66
− 2.46674 × 10
59
u
65
+ ··· + 8.56121 × 10
58
a + 7.09288 × 10
59
, u
67
− u
66
+ ··· − u − 1i
I
u
2
= h2u
18
− 2u
17
+ ··· + b − 1, 3u
18
− u
17
+ ··· + a + 1, u
19
− 5u
17
+ ··· + u − 1i
* 2 irreducible components of dim
C
= 0, with total 86 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
= h3.98×10
59
u
66
−1.62×10
59
u
65
+· · ·+8.56×10
58
b+6.93×10
59
, −3.92×
10
57
u
66
−2.47×10
59
u
65
+· · ·+8.56×10
58
a+7.09×10
59
, u
67
−u
66
+· · ·−u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
0.0457489u
66
+ 2.88130u
65
+ ··· − 27.2442u − 8.28490
−4.65084u
66
+ 1.88799u
65
+ ··· − 26.3094u − 8.09892
a
7
=
−11.1496u
66
+ 2.79842u
65
+ ··· − 32.9791u − 16.1327
−5.95825u
66
− 0.0553272u
65
+ ··· − 0.0564103u − 4.23853
a
10
=
0.0457489u
66
+ 2.88130u
65
+ ··· − 27.2442u − 8.28490
−0.178100u
66
+ 1.80249u
65
+ ··· − 23.3366u − 5.17187
a
1
=
−u
2
+ 1
−u
4
a
11
=
−2.13841u
66
+ 4.49817u
65
+ ··· − 47.2572u − 13.4375
−3.31213u
66
+ 2.20785u
65
+ ··· − 30.1781u − 8.48270
a
5
=
u
u
a
8
=
−11.5127u
66
+ 4.27285u
65
+ ··· − 40.5082u − 18.4704
−6.32132u
66
+ 1.41910u
65
+ ··· − 7.58545u − 6.57617
a
4
=
4.82960u
66
− 5.95359u
65
+ ··· + 62.5953u + 18.9033
6.29424u
66
− 4.13193u
65
+ ··· + 48.8147u + 13.7851
a
12
=
0.918229u
66
+ 1.37577u
65
+ ··· − 14.7930u − 2.94334
−0.625938u
66
+ 2.40274u
65
+ ··· − 25.0155u − 4.68849
(ii) Obstruction class = −1
(iii) Cusp Shapes = −60.9077u
66
+ 29.1274u
65
+ ··· − 300.156u − 103.773
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
67
+ 37u
66
+ ··· + 7u + 1
c
2
, c
5
u
67
+ u
66
+ ··· − u + 1
c
3
, c
11
u
67
− 2u
66
+ ··· − 89u + 29
c
4
, c
7
u
67
− 3u
66
+ ··· + 1479u + 1799
c
6
, c
9
u
67
− 10u
66
+ ··· − 14957u + 583
c
8
, c
12
u
67
− 3u
66
+ ··· + 1963u + 409
c
10
u
67
+ 6u
66
+ ··· + 958404u − 46939
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
67
− 5y
66
+ ··· + 59y −1
c
2
, c
5
y
67
− 37y
66
+ ··· + 7y −1
c
3
, c
11
y
67
− 66y
66
+ ··· + 7283y −841
c
4
, c
7
y
67
+ 35y
66
+ ··· − 114931057y −3236401
c
6
, c
9
y
67
− 50y
66
+ ··· − 1103445y −339889
c
8
, c
12
y
67
− 43y
66
+ ··· + 32507091y −167281
c
10
y
67
+ 22y
66
+ ··· + 83085423428y −2203269721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.252718 + 0.954803I
a = −0.26765 − 1.61765I
b = 0.0508940 − 0.0605544I
5.44022 + 9.83317I 3.49519 − 5.08650I
u = 0.252718 − 0.954803I
a = −0.26765 + 1.61765I
b = 0.0508940 + 0.0605544I
5.44022 − 9.83317I 3.49519 + 5.08650I
u = −0.992189 + 0.285907I
a = 0.299845 − 0.936902I
b = 0.110971 − 0.511676I
−0.72386 + 3.39798I 0
u = −0.992189 − 0.285907I
a = 0.299845 + 0.936902I
b = 0.110971 + 0.511676I
−0.72386 − 3.39798I 0
u = 1.003700 + 0.377660I
a = −0.36326 − 2.02909I
b = −0.22611 − 1.95101I
6.90463 − 5.17042I 0
u = 1.003700 − 0.377660I
a = −0.36326 + 2.02909I
b = −0.22611 + 1.95101I
6.90463 + 5.17042I 0
u = −0.407354 + 0.830734I
a = 0.62622 + 1.45214I
b = 0.0808578 − 0.0470274I
1.53350 − 1.63271I 4.18307 + 1.16614I
u = −0.407354 − 0.830734I
a = 0.62622 − 1.45214I
b = 0.0808578 + 0.0470274I
1.53350 + 1.63271I 4.18307 − 1.16614I
u = −0.999539 + 0.414079I
a = −0.68465 + 1.36026I
b = −1.62369 + 0.88630I
7.15973 + 0.55296I 0
u = −0.999539 − 0.414079I
a = −0.68465 − 1.36026I
b = −1.62369 − 0.88630I
7.15973 − 0.55296I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.123677 + 0.896241I
a = 0.46772 − 1.45771I
b = 0.188411 + 0.059427I
−0.54114 − 5.20408I 0.74353 + 5.07775I
u = −0.123677 − 0.896241I
a = 0.46772 + 1.45771I
b = 0.188411 − 0.059427I
−0.54114 + 5.20408I 0.74353 − 5.07775I
u = 0.058282 + 0.894932I
a = 0.22934 + 1.41748I
b = −0.420848 + 0.236426I
1.96860 + 2.63316I 3.47626 − 2.77896I
u = 0.058282 − 0.894932I
a = 0.22934 − 1.41748I
b = −0.420848 − 0.236426I
1.96860 − 2.63316I 3.47626 + 2.77896I
u = 0.888129 + 0.007732I
a = −0.216716 + 0.589577I
b = 0.397274 − 0.090049I
−1.42025 + 0.09498I −5.88538 + 0.49320I
u = 0.888129 − 0.007732I
a = −0.216716 − 0.589577I
b = 0.397274 + 0.090049I
−1.42025 − 0.09498I −5.88538 − 0.49320I
u = 0.818749 + 0.312512I
a = 0.261521 + 0.302439I
b = −0.94854 − 1.42046I
2.49844 − 1.45815I 5.05080 + 4.52220I
u = 0.818749 − 0.312512I
a = 0.261521 − 0.302439I
b = −0.94854 + 1.42046I
2.49844 + 1.45815I 5.05080 − 4.52220I
u = −0.826794 + 0.261915I
a = −1.15533 − 0.90370I
b = −1.65362 + 0.22840I
2.29966 + 1.29505I 7.24915 − 5.10541I
u = −0.826794 − 0.261915I
a = −1.15533 + 0.90370I
b = −1.65362 − 0.22840I
2.29966 − 1.29505I 7.24915 + 5.10541I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.062370 + 0.439025I
a = −0.1189350 + 0.0634968I
b = 0.08475 − 1.49717I
6.23019 + 6.25320I 0
u = −1.062370 − 0.439025I
a = −0.1189350 − 0.0634968I
b = 0.08475 + 1.49717I
6.23019 − 6.25320I 0
u = 1.078930 + 0.400055I
a = 0.966889 − 0.461546I
b = 1.50362 + 0.72539I
5.90798 − 0.58176I 0
u = 1.078930 − 0.400055I
a = 0.966889 + 0.461546I
b = 1.50362 − 0.72539I
5.90798 + 0.58176I 0
u = 1.139110 + 0.269989I
a = −1.336930 − 0.044286I
b = −2.77376 + 0.09507I
−3.24471 − 0.99304I 0
u = 1.139110 − 0.269989I
a = −1.336930 + 0.044286I
b = −2.77376 − 0.09507I
−3.24471 + 0.99304I 0
u = −0.870317 + 0.790370I
a = −0.382693 − 0.266135I
b = −0.207034 − 0.348229I
4.48838 + 2.95750I 0
u = −0.870317 − 0.790370I
a = −0.382693 + 0.266135I
b = −0.207034 + 0.348229I
4.48838 − 2.95750I 0
u = 0.790678 + 0.880867I
a = 0.506555 − 0.282964I
b = −0.109676 + 0.105383I
9.15754 − 5.60614I 0
u = 0.790678 − 0.880867I
a = 0.506555 + 0.282964I
b = −0.109676 − 0.105383I
9.15754 + 5.60614I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.126398 + 0.792019I
a = −0.34046 + 1.55116I
b = 0.141669 + 0.103536I
−2.45188 − 0.35885I −3.63602 + 0.23516I
u = 0.126398 − 0.792019I
a = −0.34046 − 1.55116I
b = 0.141669 − 0.103536I
−2.45188 + 0.35885I −3.63602 − 0.23516I
u = 0.962593 + 0.817723I
a = 0.208169 − 0.306861I
b = 0.616506 − 0.727645I
8.63874 − 0.64633I 0
u = 0.962593 − 0.817723I
a = 0.208169 + 0.306861I
b = 0.616506 + 0.727645I
8.63874 + 0.64633I 0
u = 1.196810 + 0.425223I
a = 0.992583 + 0.428060I
b = 2.34581 + 0.17564I
−2.51573 − 3.88919I 0
u = 1.196810 − 0.425223I
a = 0.992583 − 0.428060I
b = 2.34581 − 0.17564I
−2.51573 + 3.88919I 0
u = −0.095962 + 0.718089I
a = −0.870727 − 1.075470I
b = −0.514432 + 0.209197I
1.107230 − 0.185144I 4.79017 − 0.71844I
u = −0.095962 − 0.718089I
a = −0.870727 + 1.075470I
b = −0.514432 − 0.209197I
1.107230 + 0.185144I 4.79017 + 0.71844I
u = −1.222550 + 0.406422I
a = 1.373620 + 0.083582I
b = 2.55563 + 0.01499I
−6.39757 + 4.49155I 0
u = −1.222550 − 0.406422I
a = 1.373620 − 0.083582I
b = 2.55563 − 0.01499I
−6.39757 − 4.49155I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.190060 + 0.501845I
a = −0.803790 − 0.598061I
b = −1.74421 − 0.52832I
−1.97091 + 4.80612I 0
u = −1.190060 − 0.501845I
a = −0.803790 + 0.598061I
b = −1.74421 + 0.52832I
−1.97091 − 4.80612I 0
u = −1.150470 + 0.612288I
a = 1.177240 + 0.454917I
b = 2.37784 + 0.80163I
−0.72397 + 7.05260I 0
u = −1.150470 − 0.612288I
a = 1.177240 − 0.454917I
b = 2.37784 − 0.80163I
−0.72397 − 7.05260I 0
u = 1.205080 + 0.518507I
a = −1.148840 + 0.185650I
b = −2.18745 + 0.58972I
−5.59025 − 4.50406I 0
u = 1.205080 − 0.518507I
a = −1.148840 − 0.185650I
b = −2.18745 − 0.58972I
−5.59025 + 4.50406I 0
u = 1.264300 + 0.382115I
a = 1.009520 − 0.475156I
b = 2.03470 − 0.67673I
−4.90333 + 0.82967I 0
u = 1.264300 − 0.382115I
a = 1.009520 + 0.475156I
b = 2.03470 + 0.67673I
−4.90333 − 0.82967I 0
u = −1.265610 + 0.421354I
a = 0.943794 − 0.070930I
b = 1.70252 + 0.53403I
−2.14236 + 1.98560I 0
u = −1.265610 − 0.421354I
a = 0.943794 + 0.070930I
b = 1.70252 − 0.53403I
−2.14236 − 1.98560I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.308880 + 0.267985I
a = −1.123170 − 0.336397I
b = −2.17522 − 0.78717I
0.18085 − 5.77518I 0
u = −1.308880 − 0.267985I
a = −1.123170 + 0.336397I
b = −2.17522 + 0.78717I
0.18085 + 5.77518I 0
u = 1.245830 + 0.493179I
a = −1.43974 + 0.17283I
b = −2.43608 − 0.13299I
−1.63829 − 7.60166I 0
u = 1.245830 − 0.493179I
a = −1.43974 − 0.17283I
b = −2.43608 + 0.13299I
−1.63829 + 7.60166I 0
u = −1.235560 + 0.521982I
a = −1.234460 + 0.179282I
b = −2.59326 + 0.12435I
−3.91456 + 10.33250I 0
u = −1.235560 − 0.521982I
a = −1.234460 − 0.179282I
b = −2.59326 − 0.12435I
−3.91456 − 10.33250I 0
u = 1.225640 + 0.591919I
a = 1.41828 + 0.02698I
b = 2.74705 + 0.09456I
2.4570 − 15.4421I 0
u = 1.225640 − 0.591919I
a = 1.41828 − 0.02698I
b = 2.74705 − 0.09456I
2.4570 + 15.4421I 0
u = 0.596336 + 0.122603I
a = 2.26885 + 1.87775I
b = 2.01780 + 0.76808I
8.49281 + 2.29820I 6.25286 − 4.10564I
u = 0.596336 − 0.122603I
a = 2.26885 − 1.87775I
b = 2.01780 − 0.76808I
8.49281 − 2.29820I 6.25286 + 4.10564I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.592523
a = −0.956423
b = 0.295328
−1.13446 −10.7330
u = −0.497958 + 0.215908I
a = 0.68502 − 2.08646I
b = 1.76295 − 0.08326I
8.74993 + 2.73352I 4.86441 − 2.29828I
u = −0.497958 − 0.215908I
a = 0.68502 + 2.08646I
b = 1.76295 + 0.08326I
8.74993 − 2.73352I 4.86441 + 2.29828I
u = −0.291880 + 0.442830I
a = −0.880180 − 0.165991I
b = −0.525541 + 0.323507I
1.258410 − 0.412792I 6.74896 + 1.13109I
u = −0.291880 − 0.442830I
a = −0.880180 + 0.165991I
b = −0.525541 − 0.323507I
1.258410 + 0.412792I 6.74896 − 1.13109I
u = −0.108371 + 0.359754I
a = −2.08944 − 0.74875I
b = 1.272570 − 0.328628I
8.55502 − 2.64869I 5.98628 + 2.06746I
u = −0.108371 − 0.359754I
a = −2.08944 + 0.74875I
b = 1.272570 + 0.328628I
8.55502 + 2.64869I 5.98628 − 2.06746I
11
II.
I
u
2
= h2u
18
−2u
17
+· · ·+b −1, 3u
18
−u
17
+· · ·+a +1, u
19
−5u
17
+· · ·+u −1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−3u
18
+ u
17
+ ··· − 4u − 1
−2u
18
+ 2u
17
+ ··· − 5u
2
+ 1
a
7
=
3u
18
− 3u
17
+ ··· + 4u − 4
5u
18
− 3u
17
+ ··· + 10u − 3
a
10
=
−3u
18
+ u
17
+ ··· − 4u − 1
−4u
18
+ 3u
17
+ ··· − 4u + 2
a
1
=
−u
2
+ 1
−u
4
a
11
=
−3u
18
+ u
17
+ ··· − u − 2
−3u
18
+ 3u
17
+ ··· − u + 1
a
5
=
u
u
a
8
=
3u
18
− 3u
17
+ ··· + 2u − 4
5u
18
− 3u
17
+ ··· + 8u − 3
a
4
=
u
18
− 6u
16
+ ··· − 2u
2
+ 8u
−2u
18
+ u
17
+ ··· + 2u − 1
a
12
=
2u
18
− 4u
17
+ ··· + 3u − 3
3u
18
− 4u
17
+ ··· + 4u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
18
+ 3u
17
− 33u
16
− 14u
15
+ 87u
14
+ 36u
13
− 144u
12
− 65u
11
+
165u
10
+ 92u
9
− 115u
8
− 96u
7
+ 35u
6
+ 79u
5
+ 21u
4
− 48u
3
− 25u
2
+ 11u + 8
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
19
− 10u
18
+ ··· + 11u − 1
c
2
u
19
− 5u
17
+ ··· + u − 1
c
3
u
19
+ u
18
+ ··· + u − 1
c
4
u
19
− 2u
18
+ ··· − u − 1
c
5
u
19
− 5u
17
+ ··· + u + 1
c
6
u
19
− 3u
18
+ ··· − 7u − 1
c
7
u
19
+ 2u
18
+ ··· − u + 1
c
8
u
19
− 4u
18
+ ··· + u + 1
c
9
u
19
+ 3u
18
+ ··· − 7u + 1
c
10
u
19
− u
18
+ ··· + 236u + 43
c
11
u
19
− u
18
+ ··· + u + 1
c
12
u
19
+ 4u
18
+ ··· + u − 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 6y
18
+ ··· + 27y −1
c
2
, c
5
y
19
− 10y
18
+ ··· + 11y −1
c
3
, c
11
y
19
− 23y
18
+ ··· − 13y −1
c
4
, c
7
y
19
+ 10y
18
+ ··· + 3y −1
c
6
, c
9
y
19
− 3y
18
+ ··· + 35y −1
c
8
, c
12
y
19
− 16y
18
+ ··· − 5y −1
c
10
y
19
− 3y
18
+ ··· + 26284y −1849
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.978751 + 0.307404I
a = −0.08895 − 1.68231I
b = 0.094662 − 0.624680I
7.28503 + 4.10785I 2.95414 − 2.86490I
u = −0.978751 − 0.307404I
a = −0.08895 + 1.68231I
b = 0.094662 + 0.624680I
7.28503 − 4.10785I 2.95414 + 2.86490I
u = 0.904209 + 0.228834I
a = 0.786990 − 0.518544I
b = 1.44158 + 0.87989I
1.67334 − 1.02006I −5.81141 − 0.72669I
u = 0.904209 − 0.228834I
a = 0.786990 + 0.518544I
b = 1.44158 − 0.87989I
1.67334 + 1.02006I −5.81141 + 0.72669I
u = 0.818844 + 0.700124I
a = −0.333710 − 0.781860I
b = −0.51330 − 1.32368I
10.34880 − 4.45139I 6.18516 + 3.57443I
u = 0.818844 − 0.700124I
a = −0.333710 + 0.781860I
b = −0.51330 + 1.32368I
10.34880 + 4.45139I 6.18516 − 3.57443I
u = −0.880057 + 0.723725I
a = −0.183448 − 0.085198I
b = 0.138934 − 0.604807I
4.90128 + 2.76357I 8.38876 + 0.35727I
u = −0.880057 − 0.723725I
a = −0.183448 + 0.085198I
b = 0.138934 + 0.604807I
4.90128 − 2.76357I 8.38876 − 0.35727I
u = −0.787321 + 0.274997I
a = −1.42135 + 0.91420I
b = −2.37267 + 1.42356I
8.01888 − 1.56355I 1.27949 − 2.89433I
u = −0.787321 − 0.274997I
a = −1.42135 − 0.91420I
b = −2.37267 − 1.42356I
8.01888 + 1.56355I 1.27949 + 2.89433I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.940062 + 0.692222I
a = 0.550056 + 0.651231I
b = 0.133210 + 0.249610I
9.96906 − 0.91166I 6.80985 + 1.74521I
u = 0.940062 − 0.692222I
a = 0.550056 − 0.651231I
b = 0.133210 − 0.249610I
9.96906 + 0.91166I 6.80985 − 1.74521I
u = −0.233447 + 0.755562I
a = 0.49290 + 1.41879I
b = 0.316972 − 0.038293I
−0.214249 − 0.827859I −0.372742 + 0.698304I
u = −0.233447 − 0.755562I
a = 0.49290 − 1.41879I
b = 0.316972 + 0.038293I
−0.214249 + 0.827859I −0.372742 − 0.698304I
u = 1.193260 + 0.407397I
a = −1.117000 − 0.146511I
b = −2.25532 + 0.23263I
−4.05195 − 2.93073I −3.39124 + 2.59909I
u = 1.193260 − 0.407397I
a = −1.117000 + 0.146511I
b = −2.25532 − 0.23263I
−4.05195 + 2.93073I −3.39124 − 2.59909I
u = −1.199490 + 0.536666I
a = 1.122270 + 0.371800I
b = 2.14595 + 0.39527I
−3.09315 + 5.79872I −2.42694 − 4.74421I
u = −1.199490 − 0.536666I
a = 1.122270 − 0.371800I
b = 2.14595 − 0.39527I
−3.09315 − 5.79872I −2.42694 + 4.74421I
u = 0.445385
a = −1.61551
b = 0.739953
−0.586933 5.76990
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
19
− 10u
18
+ ··· + 11u − 1)(u
67
+ 37u
66
+ ··· + 7u + 1)
c
2
(u
19
− 5u
17
+ ··· + u − 1)(u
67
+ u
66
+ ··· − u + 1)
c
3
(u
19
+ u
18
+ ··· + u − 1)(u
67
− 2u
66
+ ··· − 89u + 29)
c
4
(u
19
− 2u
18
+ ··· − u − 1)(u
67
− 3u
66
+ ··· + 1479u + 1799)
c
5
(u
19
− 5u
17
+ ··· + u + 1)(u
67
+ u
66
+ ··· − u + 1)
c
6
(u
19
− 3u
18
+ ··· − 7u − 1)(u
67
− 10u
66
+ ··· − 14957u + 583)
c
7
(u
19
+ 2u
18
+ ··· − u + 1)(u
67
− 3u
66
+ ··· + 1479u + 1799)
c
8
(u
19
− 4u
18
+ ··· + u + 1)(u
67
− 3u
66
+ ··· + 1963u + 409)
c
9
(u
19
+ 3u
18
+ ··· − 7u + 1)(u
67
− 10u
66
+ ··· − 14957u + 583)
c
10
(u
19
− u
18
+ ··· + 236u + 43)(u
67
+ 6u
66
+ ··· + 958404u − 46939)
c
11
(u
19
− u
18
+ ··· + u + 1)(u
67
− 2u
66
+ ··· − 89u + 29)
c
12
(u
19
+ 4u
18
+ ··· + u − 1)(u
67
− 3u
66
+ ··· + 1963u + 409)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
19
+ 6y
18
+ ··· + 27y −1)(y
67
− 5y
66
+ ··· + 59y −1)
c
2
, c
5
(y
19
− 10y
18
+ ··· + 11y −1)(y
67
− 37y
66
+ ··· + 7y −1)
c
3
, c
11
(y
19
− 23y
18
+ ··· − 13y −1)(y
67
− 66y
66
+ ··· + 7283y −841)
c
4
, c
7
(y
19
+ 10y
18
+ ··· + 3y −1)
· (y
67
+ 35y
66
+ ··· − 114931057y −3236401)
c
6
, c
9
(y
19
− 3y
18
+ ··· + 35y −1)(y
67
− 50y
66
+ ··· − 1103445y −339889)
c
8
, c
12
(y
19
− 16y
18
+ ··· − 5y −1)
· (y
67
− 43y
66
+ ··· + 32507091y −167281)
c
10
(y
19
− 3y
18
+ ··· + 26284y −1849)
· (y
67
+ 22y
66
+ ··· + 83085423428y −2203269721)
20
