12a
0523
(K12a
0523
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 12 2 6 11 5 1 4 10
Solving Sequence
4,9 5,12
6 10 1 11 8 3 7 2
c
4
c
5
c
9
c
12
c
11
c
8
c
3
c
7
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.53596 × 10
293
u
104
+ 7.87917 × 10
293
u
103
+ ··· + 2.51893 × 10
295
b + 4.10389 × 10
293
,
5.19190 × 10
296
u
104
− 1.30156 × 10
297
u
103
+ ··· + 7.80867 × 10
296
a + 2.98862 × 10
296
,
u
105
− 2u
104
+ ··· + 3u
2
+ 1i
I
u
2
= hb, a + 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 106 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−6.54 × 10
293
u
104
+ 7.88 × 10
293
u
103
+ · · · + 2.52 × 10
295
b + 4.10 ×
10
293
, 5.19 × 10
296
u
104
− 1.30 × 10
297
u
103
+ · · · + 7.81 × 10
296
a + 2.99 ×
10
296
, u
105
− 2u
104
+ · · · + 3u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
12
=
−0.664889u
104
+ 1.66681u
103
+ ··· + 1.49798u − 0.382731
0.0259474u
104
− 0.0312799u
103
+ ··· + 2.02082u − 0.0162922
a
6
=
−4.30965u
104
+ 4.08364u
103
+ ··· + 3.79930u + 8.10925
0.0507263u
104
− 0.0723374u
103
+ ··· − 0.0688675u − 0.0910713
a
10
=
u
−u
3
+ u
a
1
=
−0.675206u
104
+ 1.69171u
103
+ ··· + 0.487482u − 0.370705
−u
3
+ u
a
11
=
−0.638941u
104
+ 1.63553u
103
+ ··· + 3.51880u − 0.399023
0.0259474u
104
− 0.0312799u
103
+ ··· + 2.02082u − 0.0162922
a
8
=
5.02213u
104
− 5.76629u
103
+ ··· − 14.5025u − 3.74387
−0.0685443u
104
+ 0.0806585u
103
+ ··· − 0.927508u + 0.0754778
a
3
=
1.84791u
104
− 1.44973u
103
+ ··· − 1.12604u − 1.51565
−0.104549u
104
+ 0.0699046u
103
+ ··· + 0.0417599u + 0.0704983
a
7
=
5.89546u
104
− 6.94305u
103
+ ··· − 11.8346u − 4.93404
−0.278081u
104
+ 0.312953u
103
+ ··· − 0.771699u + 0.279228
a
2
=
1.53539u
104
− 0.555872u
103
+ ··· − 2.03889u − 2.74853
−0.0668628u
104
+ 0.0559341u
103
+ ··· + 0.951702u + 0.0225999
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.59047u
104
− 1.27532u
103
+ ··· + 8.64459u − 8.12545
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
105
+ 34u
104
+ ··· − 6u + 1
c
2
, c
6
u
105
− 2u
104
+ ··· + 2u − 1
c
3
u
105
+ 4u
104
+ ··· − 317390u − 19141
c
4
, c
9
u
105
− 2u
104
+ ··· + 3u
2
+ 1
c
5
31(31u
105
+ 196u
104
+ ··· + 3.96866 × 10
7
u + 4806371)
c
8
31(31u
105
− 196u
104
+ ··· − 554872u − 22063)
c
10
, c
12
u
105
+ 3u
104
+ ··· + 1098u − 81
c
11
u
105
+ 3u
104
+ ··· + 1440u + 279
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
105
+ 74y
104
+ ··· + 18y −1
c
2
, c
6
y
105
− 34y
104
+ ··· − 6y −1
c
3
y
105
− 22y
104
+ ··· + 16340336002y −366377881
c
4
, c
9
y
105
− 78y
104
+ ··· − 6y −1
c
5
961
· (961y
105
+ 107098y
104
+ ··· − 351460639183822y −23101202189641)
c
8
961(961y
105
+ 31830y
104
+ ··· + 2.58328 × 10
10
y −4.86776 × 10
8
)
c
10
, c
12
y
105
− 75y
104
+ ··· + 599886y −6561
c
11
y
105
+ 9y
104
+ ··· − 4365162y −77841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.001250 + 0.088635I
a = −2.64914 + 5.35272I
b = −0.038011 − 0.343487I
4.00760 − 5.28754I 0
u = −1.001250 − 0.088635I
a = −2.64914 − 5.35272I
b = −0.038011 + 0.343487I
4.00760 + 5.28754I 0
u = 1.037460 + 0.104080I
a = 1.02767 + 3.93015I
b = −0.075087 − 0.439132I
4.74875 + 0.03581I 0
u = 1.037460 − 0.104080I
a = 1.02767 − 3.93015I
b = −0.075087 + 0.439132I
4.74875 − 0.03581I 0
u = 1.047450 + 0.159162I
a = 1.32246 + 0.67047I
b = −0.040020 − 0.427091I
3.59853 − 0.03988I 0
u = 1.047450 − 0.159162I
a = 1.32246 − 0.67047I
b = −0.040020 + 0.427091I
3.59853 + 0.03988I 0
u = 1.029210 + 0.252615I
a = 0.504533 + 1.067150I
b = 0.348579 − 0.558726I
1.77503 + 1.08366I 0
u = 1.029210 − 0.252615I
a = 0.504533 − 1.067150I
b = 0.348579 + 0.558726I
1.77503 − 1.08366I 0
u = −1.066080 + 0.143000I
a = −1.39931 + 0.46826I
b = 0.123128 − 0.376700I
2.65966 + 5.47007I 0
u = −1.066080 − 0.143000I
a = −1.39931 − 0.46826I
b = 0.123128 + 0.376700I
2.65966 − 5.47007I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.183896 + 1.081830I
a = −0.119743 + 0.157510I
b = −0.891981 − 0.657983I
−3.14658 − 6.82487I 0
u = −0.183896 − 1.081830I
a = −0.119743 − 0.157510I
b = −0.891981 + 0.657983I
−3.14658 + 6.82487I 0
u = −0.138219 + 1.094920I
a = −0.147917 + 0.115663I
b = −0.905202 − 0.860589I
2.52804 − 12.97190I 0
u = −0.138219 − 1.094920I
a = −0.147917 − 0.115663I
b = −0.905202 + 0.860589I
2.52804 + 12.97190I 0
u = 0.143059 + 1.107000I
a = 0.133437 + 0.111080I
b = 0.843222 − 0.849587I
3.64054 + 7.10836I 0
u = 0.143059 − 1.107000I
a = 0.133437 − 0.111080I
b = 0.843222 + 0.849587I
3.64054 − 7.10836I 0
u = −0.351677 + 1.075110I
a = −0.023335 + 0.193334I
b = −0.702928 − 0.316022I
−1.404440 − 0.105905I 0
u = −0.351677 − 1.075110I
a = −0.023335 − 0.193334I
b = −0.702928 + 0.316022I
−1.404440 + 0.105905I 0
u = 1.14082
a = −1.00687
b = −0.761997
3.91618 0
u = −1.080450 + 0.395669I
a = 0.151530 + 1.044050I
b = −0.877507 − 0.498572I
0.58128 − 4.51844I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.080450 − 0.395669I
a = 0.151530 − 1.044050I
b = −0.877507 + 0.498572I
0.58128 + 4.51844I 0
u = 0.216903 + 1.144560I
a = 0.071825 + 0.135759I
b = 0.677532 − 0.614095I
1.14640 + 4.18416I 0
u = 0.216903 − 1.144560I
a = 0.071825 − 0.135759I
b = 0.677532 + 0.614095I
1.14640 − 4.18416I 0
u = −0.604422 + 0.510373I
a = 0.001363 + 0.303028I
b = −0.557423 + 0.021591I
−1.294600 + 0.266261I −9.33366 + 0.I
u = −0.604422 − 0.510373I
a = 0.001363 − 0.303028I
b = −0.557423 − 0.021591I
−1.294600 − 0.266261I −9.33366 + 0.I
u = 1.21149
a = 0.364379
b = −1.43398
3.79413 0
u = 0.186143 + 0.758490I
a = −0.041179 + 0.402886I
b = 1.023650 + 0.274246I
−2.75964 + 3.82456I −7.69394 − 5.15963I
u = 0.186143 − 0.758490I
a = −0.041179 − 0.402886I
b = 1.023650 − 0.274246I
−2.75964 − 3.82456I −7.69394 + 5.15963I
u = −1.175660 + 0.322718I
a = 0.13151 + 1.62525I
b = −0.95555 − 1.17209I
1.64381 − 4.37178I 0
u = −1.175660 − 0.322718I
a = 0.13151 − 1.62525I
b = −0.95555 + 1.17209I
1.64381 + 4.37178I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.199780 + 0.219409I
a = 0.34279 + 1.87081I
b = 0.09902 − 1.60939I
5.55471 − 0.56979I 0
u = 1.199780 − 0.219409I
a = 0.34279 − 1.87081I
b = 0.09902 + 1.60939I
5.55471 + 0.56979I 0
u = 1.162080 + 0.371487I
a = −0.31585 + 1.40380I
b = 1.14678 − 0.84513I
0.238755 + 0.320365I 0
u = 1.162080 − 0.371487I
a = −0.31585 − 1.40380I
b = 1.14678 + 0.84513I
0.238755 − 0.320365I 0
u = −1.197630 + 0.242815I
a = −0.24103 + 1.86816I
b = −0.33800 − 1.59119I
5.86921 − 4.87500I 0
u = −1.197630 − 0.242815I
a = −0.24103 − 1.86816I
b = −0.33800 + 1.59119I
5.86921 + 4.87500I 0
u = −1.222500 + 0.093211I
a = −0.618978 + 1.252910I
b = 1.22271 − 1.10340I
5.71349 − 1.89041I 0
u = −1.222500 − 0.093211I
a = −0.618978 − 1.252910I
b = 1.22271 + 1.10340I
5.71349 + 1.89041I 0
u = 1.227930 + 0.136503I
a = 0.65931 + 1.63245I
b = −0.89616 − 1.54631I
2.52130 + 3.67820I 0
u = 1.227930 − 0.136503I
a = 0.65931 − 1.63245I
b = −0.89616 + 1.54631I
2.52130 − 3.67820I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.202250 + 0.346653I
a = −0.34406 + 1.69024I
b = 1.26890 − 1.21120I
−2.45776 + 6.16809I 0
u = 1.202250 − 0.346653I
a = −0.34406 − 1.69024I
b = 1.26890 + 1.21120I
−2.45776 − 6.16809I 0
u = −1.255710 + 0.057159I
a = −1.016010 + 0.818544I
b = 1.87080 − 0.87723I
9.02776 − 1.33183I 0
u = −1.255710 − 0.057159I
a = −1.016010 − 0.818544I
b = 1.87080 + 0.87723I
9.02776 + 1.33183I 0
u = 1.258390 + 0.046924I
a = 1.058200 + 0.680510I
b = −1.96530 − 0.73898I
8.40796 − 4.25540I 0
u = 1.258390 − 0.046924I
a = 1.058200 − 0.680510I
b = −1.96530 + 0.73898I
8.40796 + 4.25540I 0
u = −1.217260 + 0.325928I
a = 0.27210 + 1.85122I
b = −1.21658 − 1.46883I
3.61544 − 6.31212I 0
u = −1.217260 − 0.325928I
a = 0.27210 − 1.85122I
b = −1.21658 + 1.46883I
3.61544 + 6.31212I 0
u = −1.255260 + 0.117370I
a = −0.92722 + 1.52083I
b = 1.35471 − 1.65467I
8.36985 − 3.15222I 0
u = −1.255260 − 0.117370I
a = −0.92722 − 1.52083I
b = 1.35471 + 1.65467I
8.36985 + 3.15222I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.257520 + 0.125339I
a = 0.92754 + 1.60282I
b = −1.28893 − 1.76611I
7.54940 + 8.78410I 0
u = 1.257520 − 0.125339I
a = 0.92754 − 1.60282I
b = −1.28893 + 1.76611I
7.54940 − 8.78410I 0
u = 1.222260 + 0.332374I
a = −0.33002 + 1.86212I
b = 1.30750 − 1.46504I
2.59147 + 11.95360I 0
u = 1.222260 − 0.332374I
a = −0.33002 − 1.86212I
b = 1.30750 + 1.46504I
2.59147 − 11.95360I 0
u = 0.110022 + 0.709216I
a = −0.132806 + 0.485406I
b = 1.023330 + 0.544364I
−5.80400 − 2.26364I −10.97921 + 2.02009I
u = 0.110022 − 0.709216I
a = −0.132806 − 0.485406I
b = 1.023330 − 0.544364I
−5.80400 + 2.26364I −10.97921 − 2.02009I
u = 0.029234 + 1.290430I
a = 0.0082975 + 0.0595641I
b = 0.073881 − 0.793429I
7.30962 + 3.06464I 0
u = 0.029234 − 1.290430I
a = 0.0082975 − 0.0595641I
b = 0.073881 + 0.793429I
7.30962 − 3.06464I 0
u = 0.058274 + 0.684355I
a = −0.225911 + 0.552452I
b = 0.988094 + 0.748338I
−0.96466 − 8.18446I −5.29812 + 6.41381I
u = 0.058274 − 0.684355I
a = −0.225911 − 0.552452I
b = 0.988094 − 0.748338I
−0.96466 + 8.18446I −5.29812 − 6.41381I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198391 + 0.656872I
a = 0.128951 + 0.351468I
b = −0.807130 + 0.376578I
−1.37508 + 0.69491I −5.30659 − 1.43743I
u = −0.198391 − 0.656872I
a = 0.128951 − 0.351468I
b = −0.807130 − 0.376578I
−1.37508 − 0.69491I −5.30659 + 1.43743I
u = −0.066609 + 0.664501I
a = 0.251170 + 0.510908I
b = −0.910547 + 0.727872I
0.10737 + 2.61763I −3.53159 − 1.71174I
u = −0.066609 − 0.664501I
a = 0.251170 − 0.510908I
b = −0.910547 − 0.727872I
0.10737 − 2.61763I −3.53159 + 1.71174I
u = 1.40362 + 0.48950I
a = 0.00883 − 1.60449I
b = −1.16869 + 1.20887I
7.3598 + 18.5471I 0
u = 1.40362 − 0.48950I
a = 0.00883 + 1.60449I
b = −1.16869 − 1.20887I
7.3598 − 18.5471I 0
u = −1.40671 + 0.49098I
a = 0.01328 − 1.57139I
b = 1.12578 + 1.21228I
8.4984 − 12.7188I 0
u = −1.40671 − 0.49098I
a = 0.01328 + 1.57139I
b = 1.12578 − 1.21228I
8.4984 + 12.7188I 0
u = 1.41075 + 0.48080I
a = 0.08806 − 1.51090I
b = −1.12260 + 1.08649I
1.82215 + 12.33280I 0
u = 1.41075 − 0.48080I
a = 0.08806 + 1.51090I
b = −1.12260 − 1.08649I
1.82215 − 12.33280I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42223 + 0.48655I
a = −0.018088 − 1.406970I
b = 0.99133 + 1.09509I
6.23656 − 9.84835I 0
u = −1.42223 − 0.48655I
a = −0.018088 + 1.406970I
b = 0.99133 − 1.09509I
6.23656 + 9.84835I 0
u = 1.43045 + 0.47266I
a = 0.129535 − 1.323860I
b = −0.977552 + 0.952506I
3.94876 + 5.59214I 0
u = 1.43045 − 0.47266I
a = 0.129535 + 1.323860I
b = −0.977552 − 0.952506I
3.94876 − 5.59214I 0
u = −1.43719 + 0.51844I
a = 0.246826 − 1.221380I
b = 0.669947 + 1.223210I
12.1930 − 9.2857I 0
u = −1.43719 − 0.51844I
a = 0.246826 + 1.221380I
b = 0.669947 − 1.223210I
12.1930 + 9.2857I 0
u = 1.44374 + 0.52482I
a = −0.270248 − 1.146870I
b = −0.588875 + 1.196410I
12.12610 + 3.28595I 0
u = 1.44374 − 0.52482I
a = −0.270248 + 1.146870I
b = −0.588875 − 1.196410I
12.12610 − 3.28595I 0
u = 0.045808 + 0.458306I
a = 0.818270 − 0.034288I
b = −0.155246 + 0.850670I
2.32263 + 2.17537I −1.25483 − 4.43451I
u = 0.045808 − 0.458306I
a = 0.818270 + 0.034288I
b = −0.155246 − 0.850670I
2.32263 − 2.17537I −1.25483 + 4.43451I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.095860 + 0.444326I
a = −1.149790 − 0.090487I
b = 0.012329 + 0.925237I
1.86071 + 3.04955I −2.34350 − 1.80734I
u = −0.095860 − 0.444326I
a = −1.149790 + 0.090487I
b = 0.012329 − 0.925237I
1.86071 − 3.04955I −2.34350 + 1.80734I
u = −0.256720 + 0.364302I
a = −2.57277 − 0.09048I
b = −0.566482 + 0.850730I
3.11999 − 7.09682I −1.22727 + 6.68806I
u = −0.256720 − 0.364302I
a = −2.57277 + 0.09048I
b = −0.566482 − 0.850730I
3.11999 + 7.09682I −1.22727 − 6.68806I
u = 0.259161 + 0.341076I
a = 2.70653 − 0.22007I
b = 0.575046 + 0.774355I
3.95977 + 1.57224I 0.72765 − 1.22976I
u = 0.259161 − 0.341076I
a = 2.70653 + 0.22007I
b = 0.575046 − 0.774355I
3.95977 − 1.57224I 0.72765 + 1.22976I
u = −0.185439 + 0.373872I
a = −2.03610 − 0.36458I
b = −0.333036 + 0.850412I
−1.55602 − 1.86353I −7.04309 + 3.50475I
u = −0.185439 − 0.373872I
a = −2.03610 + 0.36458I
b = −0.333036 − 0.850412I
−1.55602 + 1.86353I −7.04309 − 3.50475I
u = −0.384548 + 0.144143I
a = −4.17541 − 0.15190I
b = −0.771056 + 0.219016I
3.79007 + 4.86557I −3.91765 − 5.78099I
u = −0.384548 − 0.144143I
a = −4.17541 + 0.15190I
b = −0.771056 − 0.219016I
3.79007 − 4.86557I −3.91765 + 5.78099I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54081 + 0.44876I
a = −0.198025 − 0.762752I
b = 0.581214 + 0.586799I
3.16248 − 7.87070I 0
u = −1.54081 − 0.44876I
a = −0.198025 + 0.762752I
b = 0.581214 − 0.586799I
3.16248 + 7.87070I 0
u = 0.352843 + 0.170127I
a = 4.04123 − 0.28066I
b = 0.730822 + 0.288597I
4.48313 + 0.58245I −1.56702 + 0.71193I
u = 0.352843 − 0.170127I
a = 4.04123 + 0.28066I
b = 0.730822 − 0.288597I
4.48313 − 0.58245I −1.56702 − 0.71193I
u = −1.45640 + 0.72941I
a = 0.412409 − 0.298435I
b = −0.225627 + 0.675899I
6.15662 + 6.42755I 0
u = −1.45640 − 0.72941I
a = 0.412409 + 0.298435I
b = −0.225627 − 0.675899I
6.15662 − 6.42755I 0
u = 1.55729 + 0.52982I
a = −0.030593 − 0.671169I
b = −0.367899 + 0.684184I
5.35803 + 3.08361I 0
u = 1.55729 − 0.52982I
a = −0.030593 + 0.671169I
b = −0.367899 − 0.684184I
5.35803 − 3.08361I 0
u = 1.49683 + 0.69386I
a = −0.355902 − 0.391949I
b = 0.100044 + 0.709134I
7.37741 − 0.45511I 0
u = 1.49683 − 0.69386I
a = −0.355902 + 0.391949I
b = 0.100044 − 0.709134I
7.37741 + 0.45511I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.347632
a = −4.59360
b = −0.664125
−0.447801 −12.5780
u = 0.170027 + 0.238840I
a = 2.84527 − 1.60576I
b = 0.343400 + 0.495146I
1.76251 + 0.66899I 4.46975 + 0.53128I
u = 0.170027 − 0.238840I
a = 2.84527 + 1.60576I
b = 0.343400 − 0.495146I
1.76251 − 0.66899I 4.46975 − 0.53128I
u = −1.75988 + 0.61452I
a = −0.006746 − 0.326907I
b = 0.171742 + 0.388574I
0.283122 − 0.464056I 0
u = −1.75988 − 0.61452I
a = −0.006746 + 0.326907I
b = 0.171742 − 0.388574I
0.283122 + 0.464056I 0
15
II. I
u
2
= hb, a + 1, u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
−1
a
5
=
1
−1
a
12
=
−1
0
a
6
=
2
−1
a
10
=
−1
0
a
1
=
−1
0
a
11
=
−1
0
a
8
=
1
−1
a
3
=
2
−1
a
7
=
−1
0
a
2
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
u + 1
c
8
u − 1
c
10
, c
11
, c
12
u
17
(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
7
, c
8
, c
9
y −1
c
10
, c
11
, c
12
y
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−1.64493 −6.00000
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u + 1)(u
105
+ 34u
104
+ ··· − 6u + 1)
c
2
, c
6
(u + 1)(u
105
− 2u
104
+ ··· + 2u − 1)
c
3
(u + 1)(u
105
+ 4u
104
+ ··· − 317390u − 19141)
c
4
, c
9
(u + 1)(u
105
− 2u
104
+ ··· + 3u
2
+ 1)
c
5
31(u + 1)(31u
105
+ 196u
104
+ ··· + 3.96866 × 10
7
u + 4806371)
c
8
31(u − 1)(31u
105
− 196u
104
+ ··· − 554872u − 22063)
c
10
, c
12
u(u
105
+ 3u
104
+ ··· + 1098u − 81)
c
11
u(u
105
+ 3u
104
+ ··· + 1440u + 279)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y −1)(y
105
+ 74y
104
+ ··· + 18y −1)
c
2
, c
6
(y −1)(y
105
− 34y
104
+ ··· − 6y −1)
c
3
(y −1)(y
105
− 22y
104
+ ··· + 1.63403 × 10
10
y −3.66378 × 10
8
)
c
4
, c
9
(y −1)(y
105
− 78y
104
+ ··· − 6y −1)
c
5
961(y −1)
· (961y
105
+ 107098y
104
+ ··· − 351460639183822y −23101202189641)
c
8
961(y −1)
· (961y
105
+ 31830y
104
+ ··· + 25832765582y −486775969)
c
10
, c
12
y(y
105
− 75y
104
+ ··· + 599886y −6561)
c
11
y(y
105
+ 9y
104
+ ··· − 4365162y −77841)
21
