11a
209
(K11a
209
)
1
Arc Sequences
7 1 11 8 10 2 5 3 6 4 9
Solving Sequence
2,6 7,9
10 1 3 5 8 4 11
c
6
c
9
c
1
c
2
c
5
c
8
c
4
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
16
+ 4u
14
+ u
13
+ 10u
12
+ 5u
11
+ 16u
10
+ 10u
9
+ 20u
8
+ 13u
7
+ 19u
6
+ 10u
5
+ 13u
4
+ 5u
3
+ 5u
2
+ u + 1,
u
15
u
14
+ 4u
13
2u
12
+ 8u
11
u
10
+ 9u
9
+ 2u
8
+ 9u
7
+ 2u
6
+ 7u
5
+ 4u
3
u
2
+ b u,
2u
15
6u
13
2u
12
13u
11
8u
10
16u
9
11u
8
17u
7
11u
6
12u
5
3u
4
4u
3
+ a + u + 1i
I
u
2
= hu
86
u
85
+ ··· 22u + 23,
1.32674 × 10
125
u
85
1.02318 × 10
127
u
84
+ ··· + 9.00015 × 10
126
b 2.03979 × 10
128
,
6.05580 × 10
127
u
85
2.05639 × 10
128
u
84
+ ··· + 2.07003 × 10
128
a 4.37071 × 10
129
i
There are 2 irreducible components with 102 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I.
I
u
1
= hu
16
+4u
14
+· · ·+u+1, u
15
u
14
+· · ·+bu, 2u
15
6u
13
+· · ·+a+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
9
=
2u
15
+ 6u
13
+ ··· u 1
u
15
+ u
14
+ ··· + u
2
+ u
a
10
=
2u
15
+ 6u
13
+ ··· u 1
u
15
+ u
14
+ ··· + 4u
2
+ 3u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
5
=
u
15
+ u
14
+ ··· u
2
u
2u
15
+ u
14
+ ··· + 5u
2
+ 4u
a
8
=
2u
15
+ 6u
13
+ ··· + 4u
3
1
u
14
u
13
+ ··· + u
2
+ u
a
4
=
u
15
+ u
14
+ ··· + u + 1
u
15
+ 3u
13
+ ··· u + 1
a
11
=
u
14
+ 4u
12
+ ··· + u + 1
u
13
+ 3u
11
+ 7u
9
+ 2u
8
+ 8u
7
+ 3u
6
+ 8u
5
+ 5u
4
+ 7u
3
+ 2u
2
+ 4u + 1
a
11
=
u
14
+ 4u
12
+ ··· + u + 1
u
13
+ 3u
11
+ 7u
9
+ 2u
8
+ 8u
7
+ 3u
6
+ 8u
5
+ 5u
4
+ 7u
3
+ 2u
2
+ 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.798443 0.511463I
a = 0.687622 0.449925I
b = 0.0754944 0.0449931I
0.31683 + 4.82313I 2.45674 4.45720I
u = 0.798443 + 0.511463I
a = 0.687622 + 0.449925I
b = 0.0754944 + 0.0449931I
0.31683 4.82313I 2.45674 + 4.45720I
u = 0.487072 1.055755I
a = 0.895444 0.250233I
b = 2.11216 + 1.37671I
2.30232 + 7.54648I 2.14299 11.74045I
u = 0.487072 + 1.055755I
a = 0.895444 + 0.250233I
b = 2.11216 1.37671I
2.30232 7.54648I 2.14299 + 11.74045I
u = 0.394909 0.626627I
a = 0.260086 + 1.131737I
b = 1.70714 0.82845I
0.74107 3.74159I 1.01930 + 5.15973I
u = 0.394909 + 0.626627I
a = 0.260086 1.131737I
b = 1.70714 + 0.82845I
0.74107 + 3.74159I 1.01930 5.15973I
u = 0.327557 1.160532I
a = 0.758844 0.482723I
b = 0.603018 0.536416I
2.86838 0.11828I 0.88069 + 2.46501I
u = 0.327557 + 1.160532I
a = 0.758844 + 0.482723I
b = 0.603018 + 0.536416I
2.86838 + 0.11828I 0.88069 2.46501I
u = 0.158611 0.649341I
a = 1.024088 + 0.822932I
b = 0.109047 1.330879I
0.080629 + 0.400598I 1.246602 0.185548I
u = 0.158611 + 0.649341I
a = 1.024088 0.822932I
b = 0.109047 + 1.330879I
0.080629 0.400598I 1.246602 + 0.185548I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.343340 0.903837I
a = 1.85187 0.82712I
b = 0.42790 1.45789I
7.14694 1.43565I 10.40664 2.32978I
u = 0.343340 + 0.903837I
a = 1.85187 + 0.82712I
b = 0.42790 + 1.45789I
7.14694 + 1.43565I 10.40664 + 2.32978I
u = 0.738361 0.873406I
a = 0.382558 0.264297I
b = 0.68692 1.40866I
3.66939 2.80776I 10.64447 + 1.16069I
u = 0.738361 + 0.873406I
a = 0.382558 + 0.264297I
b = 0.68692 + 1.40866I
3.66939 + 2.80776I 10.64447 1.16069I
u = 0.767670 1.139482I
a = 0.919408 + 0.421777I
b = 0.727530 + 1.090208I
4.16761 3.51464I 0.94360 6.61638I
u = 0.767670 + 1.139482I
a = 0.919408 0.421777I
b = 0.727530 1.090208I
4.16761 + 3.51464I 0.94360 + 6.61638I
4
II. I
u
2
= hu
86
u
85
+ · · · 22u + 23, 1.33 × 10
125
u
85
1.02 × 10
127
u
84
+
· · · + 9.00 × 10
126
b 2.04 × 10
128
, 6.06 × 10
127
u
85
2.06 × 10
128
u
84
+ · · · +
2.07 × 10
128
a 4.37 × 10
129
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
9
=
0.292546u
85
+ 0.993410u
84
+ ··· 18.0143u + 21.1142
0.0147413u
85
+ 1.13685u
84
+ ··· 4.40116u + 22.6639
a
10
=
0.292546u
85
+ 0.993410u
84
+ ··· 18.0143u + 21.1142
0.579944u
85
+ 1.60016u
84
+ ··· 26.5487u + 38.7838
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
5
=
0.996362u
85
0.556078u
84
+ ··· + 21.3009u 5.99237
0.663745u
85
0.00723873u
84
+ ··· + 7.00036u + 4.13110
a
8
=
0.264840u
85
+ 1.12529u
84
+ ··· 16.9671u + 25.9190
0.456493u
85
+ 1.52328u
84
+ ··· 22.7491u + 38.8186
a
4
=
0.560715u
85
+ 0.0245877u
84
+ ··· + 12.8360u + 5.72573
0.169524u
85
+ 1.07154u
84
+ ··· 3.61732u + 26.0738
a
11
=
0.375034u
85
+ 0.462020u
84
+ ··· 1.79049u + 8.18760
0.757832u
85
+ 0.415727u
84
+ ··· 11.4070u 3.49545
a
11
=
0.375034u
85
+ 0.462020u
84
+ ··· 1.79049u + 8.18760
0.757832u
85
+ 0.415727u
84
+ ··· 11.4070u 3.49545
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.131388 0.532631I
a = 0.498636 + 0.593499I
b = 0.062797 + 0.669766I
0.23931 + 5.38129I 5.23507 11.04207I
u = 1.131388 + 0.532631I
a = 0.498636 0.593499I
b = 0.062797 0.669766I
0.23931 5.38129I 5.23507 + 11.04207I
u = 1.002180 0.442960I
a = 0.018620 1.146422I
b = 0.716745 0.377330I
3.53168 4.85270I 5.12139 + 5.71774I
u = 1.002180 + 0.442960I
a = 0.018620 + 1.146422I
b = 0.716745 + 0.377330I
3.53168 + 4.85270I 5.12139 5.71774I
u = 0.819335 0.516743I
a = 0.372153 + 1.178266I
b = 1.188660 + 0.548684I
4.27251 4.47107I 2.26941 + 3.51066I
u = 0.819335 + 0.516743I
a = 0.372153 1.178266I
b = 1.188660 0.548684I
4.27251 + 4.47107I 2.26941 3.51066I
u = 0.727983 0.866986I
a = 0.020505 0.619882I
b = 1.221908 0.589002I
1.80523 + 3.66895I 2.19284 2.56041I
u = 0.727983 + 0.866986I
a = 0.020505 + 0.619882I
b = 1.221908 + 0.589002I
1.80523 3.66895I 2.19284 + 2.56041I
u = 0.718222 0.590569I
a = 1.249985 0.562960I
b = 1.65554 + 0.41721I
2.36607 4.79257I 3.90958 + 3.18934I
u = 0.718222 + 0.590569I
a = 1.249985 + 0.562960I
b = 1.65554 0.41721I
2.36607 + 4.79257I 3.90958 3.18934I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.689193 1.161247I
a = 1.044386 0.140269I
b = 1.49167 1.40057I
1.32319 + 10.94465I 1.81845 8.17889I
u = 0.689193 + 1.161247I
a = 1.044386 + 0.140269I
b = 1.49167 + 1.40057I
1.32319 10.94465I 1.81845 + 8.17889I
u = 0.678602 0.851107I
a = 0.791605 + 0.197168I
b = 0.64522 1.36352I
1.82473 + 1.72939I 2.71054 1.92962I
u = 0.678602 + 0.851107I
a = 0.791605 0.197168I
b = 0.64522 + 1.36352I
1.82473 1.72939I 2.71054 + 1.92962I
u = 0.657555 1.085688I
a = 1.000584 + 0.203202I
b = 1.28522 + 2.08107I
5.97898 + 10.01161I 3.79331 7.88036I
u = 0.657555 + 1.085688I
a = 1.000584 0.203202I
b = 1.28522 2.08107I
5.97898 10.01161I 3.79331 + 7.88036I
u = 0.624334 1.022789I
a = 0.505599 + 1.130925I
b = 1.59264 0.38837I
1.06511 + 9.94951I 0.88140 8.66029I
u = 0.624334 + 1.022789I
a = 0.505599 1.130925I
b = 1.59264 + 0.38837I
1.06511 9.94951I 0.88140 + 8.66029I
u = 0.62384 1.28071I
a = 0.572499 + 0.283387I
b = 0.707325 + 0.955234I
3.04048 + 1.33044I 4.66494 3.15821I
u = 0.62384 + 1.28071I
a = 0.572499 0.283387I
b = 0.707325 0.955234I
3.04048 1.33044I 4.66494 + 3.15821I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.591175 0.049975I
a = 0.99593 + 1.97716I
b = 0.843680 + 0.750866I
1.62551 3.43865I 0.96501 + 2.90877I
u = 0.591175 + 0.049975I
a = 0.99593 1.97716I
b = 0.843680 0.750866I
1.62551 + 3.43865I 0.96501 2.90877I
u = 0.519186 0.913358I
a = 1.148425 + 0.395293I
b = 1.82570 + 0.54472I
0.55328 + 3.31179I 1.84860 3.21939I
u = 0.519186 + 0.913358I
a = 1.148425 0.395293I
b = 1.82570 0.54472I
0.55328 3.31179I 1.84860 + 3.21939I
u = 0.498753 0.796047I
a = 0.759540 + 1.075985I
b = 0.088049 0.522283I
0.958565 + 0.837035I 2.77789 3.94919I
u = 0.498753 + 0.796047I
a = 0.759540 1.075985I
b = 0.088049 + 0.522283I
0.958565 0.837035I 2.77789 + 3.94919I
u = 0.472137 0.915188I
a = 0.073116 0.647076I
b = 0.935321 + 0.271721I
0.27091 + 2.38443I 1.53972 3.23411I
u = 0.472137 + 0.915188I
a = 0.073116 + 0.647076I
b = 0.935321 0.271721I
0.27091 2.38443I 1.53972 + 3.23411I
u = 0.471061 1.075989I
a = 1.356937 0.333237I
b = 1.72209 + 1.50012I
4.20557 + 7.31255I 5.58228 7.90023I
u = 0.471061 + 1.075989I
a = 1.356937 + 0.333237I
b = 1.72209 1.50012I
4.20557 7.31255I 5.58228 + 7.90023I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.435411 0.874421I
a = 0.895985 0.175253I
b = 1.21433 1.77989I
0.020421 + 1.232539I 1.27365 4.00526I
u = 0.435411 + 0.874421I
a = 0.895985 + 0.175253I
b = 1.21433 + 1.77989I
0.020421 1.232539I 1.27365 + 4.00526I
u = 0.385965 0.524461I
a = 0.642396 + 0.188243I
b = 0.227992 0.911270I
0.610346 + 1.128090I 4.76161 5.52253I
u = 0.385965 + 0.524461I
a = 0.642396 0.188243I
b = 0.227992 + 0.911270I
0.610346 1.128090I 4.76161 + 5.52253I
u = 0.356735 1.106464I
a = 1.053418 0.804677I
b = 0.057719 0.923731I
4.90859 0.03496I 5.71054 0.11712I
u = 0.356735 + 1.106464I
a = 1.053418 + 0.804677I
b = 0.057719 + 0.923731I
4.90859 + 0.03496I 5.71054 + 0.11712I
u = 0.155910 0.854062I
a = 0.401305 + 1.354893I
b = 1.161303 0.326518I
2.07684 4.50458I 4.60378 + 5.16323I
u = 0.155910 + 0.854062I
a = 0.401305 1.354893I
b = 1.161303 + 0.326518I
2.07684 + 4.50458I 4.60378 5.16323I
u = 0.145997 0.558877I
a = 1.150773 + 0.536193I
b = 0.496295 0.738764I
0.40918 + 1.48015I 2.24000 5.97587I
u = 0.145997 + 0.558877I
a = 1.150773 0.536193I
b = 0.496295 + 0.738764I
0.40918 1.48015I 2.24000 + 5.97587I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.037161 1.155376I
a = 1.225153 0.184518I
b = 0.940579 + 0.366199I
10.06355 2.70380I 8.34957 + 1.45800I
u = 0.037161 + 1.155376I
a = 1.225153 + 0.184518I
b = 0.940579 0.366199I
10.06355 + 2.70380I 8.34957 1.45800I
u = 0.006838 1.320154I
a = 0.980503 + 0.275176I
b = 0.750103 + 0.059805I
7.52252 + 8.52696I 5.04909 6.29979I
u = 0.006838 + 1.320154I
a = 0.980503 0.275176I
b = 0.750103 0.059805I
7.52252 8.52696I 5.04909 + 6.29979I
u = 0.178929 1.357481I
a = 0.824468 0.018298I
b = 0.879594 + 0.082029I
4.10884 1.64866I 8.35074 + 2.45290I
u = 0.178929 + 1.357481I
a = 0.824468 + 0.018298I
b = 0.879594 0.082029I
4.10884 + 1.64866I 8.35074 2.45290I
u = 0.254148 0.997671I
a = 0.429547 0.769207I
b = 0.0682742 0.0044667I
3.68445 0.23182I 5.95735 + 0.67749I
u = 0.254148 + 0.997671I
a = 0.429547 + 0.769207I
b = 0.0682742 + 0.0044667I
3.68445 + 0.23182I 5.95735 0.67749I
u = 0.301901 1.060787I
a = 0.760436 0.530608I
b = 0.580835 0.113981I
3.68916 0.50545I 8.20073 + 1.94431I
u = 0.301901 + 1.060787I
a = 0.760436 + 0.530608I
b = 0.580835 + 0.113981I
3.68916 + 0.50545I 8.20073 1.94431I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.363945 0.853778I
a = 0.722531 0.375984I
b = 2.05914 1.53941I
1.69428 + 3.12126I 4.34505 2.19109I
u = 0.363945 + 0.853778I
a = 0.722531 + 0.375984I
b = 2.05914 + 1.53941I
1.69428 3.12126I 4.34505 + 2.19109I
u = 0.440608 0.882453I
a = 1.82146 + 1.07326I
b = 0.521225 + 1.300261I
6.69565 1.80753I 1.04366 + 6.05610I
u = 0.440608 + 0.882453I
a = 1.82146 1.07326I
b = 0.521225 1.300261I
6.69565 + 1.80753I 1.04366 6.05610I
u = 0.458991 1.014051I
a = 0.047169 0.302150I
b = 1.25185 + 1.10715I
2.49113 6.25666I 3.92489 + 5.91134I
u = 0.458991 + 1.014051I
a = 0.047169 + 0.302150I
b = 1.25185 1.10715I
2.49113 + 6.25666I 3.92489 5.91134I
u = 0.535541 0.976845I
a = 1.41823 0.27490I
b = 0.86851 1.86578I
5.79066 2.94337I 4.87395 + 1.85803I
u = 0.535541 + 0.976845I
a = 1.41823 + 0.27490I
b = 0.86851 + 1.86578I
5.79066 + 2.94337I 4.87395 1.85803I
u = 0.536132 1.087661I
a = 0.814105 0.294363I
b = 1.73737 + 1.24802I
2.10386 6.56947I 0.38859 + 4.46923I
u = 0.536132 + 1.087661I
a = 0.814105 + 0.294363I
b = 1.73737 1.24802I
2.10386 + 6.56947I 0.38859 4.46923I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.566298 0.952248I
a = 1.072700 + 0.143690I
b = 2.33483 + 1.21169I
0.23044 7.80201I 1.42340 + 9.65097I
u = 0.566298 + 0.952248I
a = 1.072700 0.143690I
b = 2.33483 1.21169I
0.23044 + 7.80201I 1.42340 9.65097I
u = 0.573481 1.085075I
a = 0.901214 0.013522I
b = 1.56289 + 1.49684I
1.93850 6.65557I 1.27101 + 5.90795I
u = 0.573481 + 1.085075I
a = 0.901214 + 0.013522I
b = 1.56289 1.49684I
1.93850 + 6.65557I 1.27101 5.90795I
u = 0.574135 0.697745I
a = 0.422149 + 1.198451I
b = 1.045570 0.655590I
0.55800 + 3.23439I 4.18992 2.82083I
u = 0.574135 + 0.697745I
a = 0.422149 1.198451I
b = 1.045570 + 0.655590I
0.55800 3.23439I 4.18992 + 2.82083I
u = 0.613434 0.381423I
a = 0.049157 + 1.289514I
b = 0.963316 0.013594I
0.03093 + 1.91449I 1.42093 2.93716I
u = 0.613434 + 0.381423I
a = 0.049157 1.289514I
b = 0.963316 + 0.013594I
0.03093 1.91449I 1.42093 + 2.93716I
u = 0.624780 0.343324I
a = 0.418470 + 1.095134I
b = 1.049706 0.179115I
0.00762 + 1.99264I 2.82106 2.47705I
u = 0.624780 + 0.343324I
a = 0.418470 1.095134I
b = 1.049706 + 0.179115I
0.00762 1.99264I 2.82106 + 2.47705I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.651807 0.489532I
a = 0.71657 1.35842I
b = 0.434562 1.119463I
4.44910 1.59822I 3.44505 + 3.04430I
u = 0.651807 + 0.489532I
a = 0.71657 + 1.35842I
b = 0.434562 + 1.119463I
4.44910 + 1.59822I 3.44505 3.04430I
u = 0.682783 1.148320I
a = 1.167957 0.083174I
b = 1.61905 1.73921I
2.8205 17.3023I 1.21964 + 9.69117I
u = 0.682783 + 1.148320I
a = 1.167957 + 0.083174I
b = 1.61905 + 1.73921I
2.8205 + 17.3023I 1.21964 9.69117I
u = 0.683162 0.995349I
a = 0.384415 + 0.738533I
b = 1.031978 0.400071I
5.03331 5.32903I 6.26908 + 4.72833I
u = 0.683162 + 0.995349I
a = 0.384415 0.738533I
b = 1.031978 + 0.400071I
5.03331 + 5.32903I 6.26908 4.72833I
u = 0.784201 0.874304I
a = 0.551454 0.407916I
b = 0.58870 1.54759I
3.13190 2.94290I 4.18516 + 4.22737I
u = 0.784201 + 0.874304I
a = 0.551454 + 0.407916I
b = 0.58870 + 1.54759I
3.13190 + 2.94290I 4.18516 4.22737I
u = 0.788393 0.093088I
a = 0.317731 0.855254I
b = 0.166840 + 0.225277I
0.40272 2.72268I 2.86940 + 3.16788I
u = 0.788393 + 0.093088I
a = 0.317731 + 0.855254I
b = 0.166840 0.225277I
0.40272 + 2.72268I 2.86940 3.16788I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.799498 0.671496I
a = 0.837503 0.287153I
b = 1.185539 + 0.346531I
6.03113 0.23797I 8.11472 + 1.20090I
u = 0.799498 + 0.671496I
a = 0.837503 + 0.287153I
b = 1.185539 0.346531I
6.03113 + 0.23797I 8.11472 1.20090I
u = 0.87956 1.15875I
a = 0.794501 0.484740I
b = 0.594142 1.050080I
4.20851 3.78318I 6.2924 + 21.9623I
u = 0.87956 + 1.15875I
a = 0.794501 + 0.484740I
b = 0.594142 + 1.050080I
4.20851 + 3.78318I 6.2924 21.9623I
u = 0.957226 0.470426I
a = 0.022295 1.347106I
b = 1.100437 0.560290I
0.73034 + 11.32341I 0.94970 6.25020I
u = 0.957226 + 0.470426I
a = 0.022295 + 1.347106I
b = 1.100437 + 0.560290I
0.73034 11.32341I 0.94970 + 6.25020I
14
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
16
+ 4u
14
+ ··· + u + 1)(u
86
+ u
85
+ ··· + 22u + 23)
c
2
(u
16
+ 8u
15
+ ··· + 9u + 1)(u
86
+ 37u
85
+ ··· + 8624u + 529)
c
3
(u
16
+ 8u
14
+ ··· + u + 2)(u
86
+ 5u
85
+ ··· + 228u + 34)
c
4
(u
16
2u
15
+ ··· + 8u
2
+ 1)(u
86
+ 3u
85
+ ··· + 3u + 1)
c
5
(u
16
+ 8u
14
+ ··· + 2u + 1)(u
86
+ u
85
+ ··· 977u + 253)
c
6
(u
16
+ 4u
14
+ ··· u + 1)(u
86
+ u
85
+ ··· + 22u + 23)
c
7
(u
16
+ 2u
15
+ ··· + 8u
2
+ 1)(u
86
+ 3u
85
+ ··· + 3u + 1)
c
8
(u
16
+ 3u
14
+ ··· 4u + 1)(u
86
+ u
85
+ ··· 5u + 1)
c
9
(u
16
+ 8u
14
+ ··· 2u + 1)(u
86
+ u
85
+ ··· 977u + 253)
c
10
(u
16
+ 8u
14
+ ··· u + 2)(u
86
+ 5u
85
+ ··· + 228u + 34)
c
11
(u
16
+ 6u
15
+ ··· + 5u
3
+ 1)(u
86
+ 3u
85
+ ··· + 453u + 83)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
16
+ 8y
15
+ ··· + 9y + 1)(y
86
+ 37y
85
+ ··· + 8624y + 529)
c
2
(y
16
+ 8y
15
+ ··· + y + 1)(y
86
+ 33y
85
+ ··· + 1800508y + 279841)
c
3
(y
16
+ 16y
15
+ ··· + 39y + 4)(y
86
+ 61y
85
+ ··· + 39068y + 1156)
c
4
(y
16
+ 14y
15
+ ··· + 16y + 1)(y
86
+ 51y
85
+ ··· + 79y + 1)
c
5
(y
16
+ 16y
15
+ ··· + 14y + 1)(y
86
+ 57y
85
+ ··· + 492125y + 64009)
c
7
(y
16
+ 14y
15
+ ··· + 16y + 1)(y
86
+ 51y
85
+ ··· + 79y + 1)
c
8
(y
16
+ 6y
15
+ ··· 2y + 1)(y
86
+ 7y
85
+ ··· + 89y + 1)
c
9
(y
16
+ 16y
15
+ ··· + 14y + 1)(y
86
+ 57y
85
+ ··· + 492125y + 64009)
c
10
(y
16
+ 16y
15
+ ··· + 39y + 4)(y
86
+ 61y
85
+ ··· + 39068y + 1156)
c
11
(y
16
4y
15
+ ··· + 30y
2
+ 1)(y
86
15y
85
+ ··· 330041y + 6889)
16