11a
268
(K11a
268
)
1
Arc Sequences
9 8 1 10 2 3 11 6 4 5 7
Solving Sequence
7,11
8
1,3
4 2 6 9 5 10
c
7
c
11
c
3
c
2
c
6
c
8
c
5
c
10
c
1
, c
4
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
20
+ 4u
18
+ ··· 3u 1, 63903312u
19
+ 453578u
18
+ ··· + 55899125a 323065377,
3983906234u
19
1854796104u
18
+ ··· + 1196241275b 8030147964i
I
u
2
= hu
89
+ u
88
+ ··· + 84u 2543,
8.36409 × 10
387
u
88
1.04032 × 10
388
u
87
+ ··· + 9.38838 × 10
389
b + 3.56566 × 10
390
,
4.36623 × 10
391
u
88
5.85109 × 10
391
u
87
+ ··· + 2.38746 × 10
393
a 3.96726 × 10
394
i
There are 2 irreducible components with 109 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
20
+ 4u
18
+ · · · 3u 1, 6.39 × 10
7
u
19
+ 4.54 × 10
5
u
18
+ · · · + 5.59 ×
10
7
a 3.23 ×10
8
, 3.98×10
9
u
19
1.85× 10
9
u
18
+· · ·+ 1.20 ×10
9
b 8.03 ×10
9
i
(i) Arc colorings
a
7
=
0
u
a
11
=
1.14319u
19
0.00811422u
18
+ ··· + 1.80940u + 5.77944
3.33035u
19
+ 1.55052u
18
+ ··· + 6.81571u + 6.71282
a
8
=
4.77944u
19
1.14319u
18
+ ··· 4.35297u 12.5289
4.68504u
19
2.46863u
18
+ ··· 8.70082u 9.00452
a
1
=
1.14319u
19
0.00811422u
18
+ ··· + 1.80940u + 5.77944
3.72297u
19
+ 1.90690u
18
+ ··· + 7.98324u + 6.72093
a
3
=
1
0
a
4
=
7.86133u
19
+ 4.69316u
18
+ ··· + 17.4122u + 13.5333
4.50777u
19
2.47019u
18
+ ··· 10.1925u 7.53582
a
2
=
11.5325u
19
5.90676u
18
+ ··· 24.1972u 23.2035
5.95275u
19
2.99175u
18
+ ··· 12.0233u 12.2620
a
6
=
u
u
a
9
=
6.08507u
19
2.11917u
18
+ ··· 8.42369u 13.8543
5.99068u
19
3.44461u
18
+ ··· 12.7715u 10.3300
a
5
=
9.69672u
19
+ 4.72549u
18
+ ··· + 18.7934u + 19.2966
4.89080u
19
+ 2.52801u
18
+ ··· + 9.94731u + 9.69685
a
10
=
5.88258u
19
3.13836u
18
+ ··· 10.8875u 9.18916
0.498050u
19
+ 0.220098u
18
+ ··· + 2.91851u + 1.05551
a
10
=
5.88258u
19
3.13836u
18
+ ··· 10.8875u 9.18916
0.498050u
19
+ 0.220098u
18
+ ··· + 2.91851u + 1.05551
(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 = 0.920204 0.446036I
a = 0.010899 1.235491I
b = 0.56082 2.26819I
5.23739 5.55861I 8.63842 + 8.06052I
u = 0.920204 + 0.446036I
a = 0.010899 + 1.235491I
b = 0.56082 + 2.26819I
5.23739 + 5.55861I 8.63842 8.06052I
u = 0.732984 0.987021I
a = 0.728571 0.864853I
b = 0.16357 1.45959I
9.99863 6.70009I 6.33266 + 4.76825I
u = 0.732984 + 0.987021I
a = 0.728571 + 0.864853I
b = 0.16357 + 1.45959I
9.99863 + 6.70009I 6.33266 4.76825I
u = 0.572386 0.096735I
a = 1.58699 1.54169I
b = 0.573417 0.162255I
5.62801 + 1.51138I 5.02190 9.76370I
u = 0.572386 + 0.096735I
a = 1.58699 + 1.54169I
b = 0.573417 + 0.162255I
5.62801 1.51138I 5.02190 + 9.76370I
u = 0.485579
a = 2.62617
b = 0.759645
1.31038 6.20021
u = 0.300055 0.812653I
a = 0.671829 + 0.120599I
b = 1.137435 0.548250I
2.20697 2.35727I 0.75955 + 2.29179I
u = 0.300055 + 0.812653I
a = 0.671829 0.120599I
b = 1.137435 + 0.548250I
2.20697 + 2.35727I 0.75955 2.29179I
u = 0.19540 1.74306I
a = 0.429584 + 0.034906I
b = 1.37623 + 0.62846I
0.16874 + 2.77142I 2.49688 6.12151I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.19540 + 1.74306I
a = 0.429584 0.034906I
b = 1.37623 0.62846I
0.16874 2.77142I 2.49688 + 6.12151I
u = 0.274254 1.252554I
a = 0.531825 0.073625I
b = 0.203408 + 0.314069I
0.41433 + 2.93710I 8.44025 5.37355I
u = 0.274254 + 1.252554I
a = 0.531825 + 0.073625I
b = 0.203408 0.314069I
0.41433 2.93710I 8.44025 + 5.37355I
u = 0.483546
a = 2.68251
b = 0.293804
2.35090 37.5794
u = 0.558207 0.814180I
a = 0.628287 0.218750I
b = 1.20875 1.95898I
5.94321 6.14570I 10.52858 + 8.02706I
u = 0.558207 + 0.814180I
a = 0.628287 + 0.218750I
b = 1.20875 + 1.95898I
5.94321 + 6.14570I 10.52858 8.02706I
u = 0.869606 0.821260I
a = 0.500306 + 1.006153I
b = 0.379049 + 1.157254I
2.62899 + 3.66788I 5.57286 1.70794I
u = 0.869606 + 0.821260I
a = 0.500306 1.006153I
b = 0.379049 1.157254I
2.62899 3.66788I 5.57286 + 1.70794I
u = 1.019979 0.686033I
a = 0.263086 + 0.998099I
b = 0.59421 + 1.97897I
2.35880 + 5.00950I 4.53218 5.02781I
u = 1.019979 + 0.686033I
a = 0.263086 0.998099I
b = 0.59421 1.97897I
2.35880 5.00950I 4.53218 + 5.02781I
4
II. I
u
2
= hu
89
+ u
88
+ · · · + 84u 2543, 8.36 × 10
387
u
88
1.04 ×
10
388
u
87
+ · · · + 9.39 × 10
389
b + 3.57 × 10
390
, 4.37 × 10
391
u
88
5.85 ×
10
391
u
87
+ · · · + 2.39 × 10
393
a 3.97 × 10
394
i
(i) Arc colorings
a
7
=
0
u
a
11
=
0.0182882u
88
+ 0.0245075u
87
+ ··· + 142.169u + 16.6170
0.00890898u
88
+ 0.0110809u
87
+ ··· + 66.2207u 3.79795
a
8
=
0.0148129u
88
0.0230845u
87
+ ··· 69.1163u 7.62590
0.00107982u
88
+ 0.000450313u
87
+ ··· 8.81296u 5.27923
a
1
=
0.0182882u
88
+ 0.0245075u
87
+ ··· + 142.169u + 16.6170
0.00250776u
88
+ 0.00175897u
87
+ ··· + 20.2363u 19.6138
a
3
=
1
0
a
4
=
0.00619567u
88
+ 0.0140839u
87
+ ··· + 33.7286u + 28.6817
0.00564619u
88
0.00250203u
87
+ ··· 53.0921u + 8.63113
a
2
=
0.00948500u
88
+ 0.00242833u
87
+ ··· + 89.5960u 77.0361
0.00888330u
88
+ 0.00717275u
87
+ ··· + 58.1536u 27.7455
a
6
=
u
u
a
9
=
0.00726070u
88
0.0105483u
87
+ ··· 29.3431u + 11.8081
0.00863198u
88
+ 0.0129865u
87
+ ··· + 30.9602u + 14.1548
a
5
=
0.00230112u
88
0.00641861u
87
+ ··· + 82.8821u 85.2664
0.00155642u
88
+ 0.000642548u
87
+ ··· + 9.80660u 25.5485
a
10
=
0.00472895u
88
+ 0.00149100u
87
+ ··· 93.6545u + 68.4368
0.00583296u
88
+ 0.00647773u
87
+ ··· 3.60709u 16.4222
a
10
=
0.00472895u
88
+ 0.00149100u
87
+ ··· 93.6545u + 68.4368
0.00583296u
88
+ 0.00647773u
87
+ ··· 3.60709u 16.4222
(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 = 1.46438 0.92926I
a = 0.207807 + 0.773312I
b = 0.76875 + 2.07688I
4.63913 7.16183I 6.35797 + 5.29478I
u = 1.46438 + 0.92926I
a = 0.207807 0.773312I
b = 0.76875 2.07688I
4.63913 + 7.16183I 6.35797 5.29478I
u = 1.44730 0.78897I
a = 0.077106 0.706634I
b = 0.36643 2.22004I
3.75095 4.98969I 9.19267 + 8.65960I
u = 1.44730 + 0.78897I
a = 0.077106 + 0.706634I
b = 0.36643 + 2.22004I
3.75095 + 4.98969I 9.19267 8.65960I
u = 1.40808 0.97394I
a = 0.160031 + 0.872871I
b = 0.60195 + 2.18010I
10.6453 17.3382I 6.68042 + 8.68737I
u = 1.40808 + 0.97394I
a = 0.160031 0.872871I
b = 0.60195 2.18010I
10.6453 + 17.3382I 6.68042 8.68737I
u = 1.191082 0.080568I
a = 0.364776 0.891341I
b = 0.52660 1.36846I
3.66544 1.93275I 9.84934 + 1.25490I
u = 1.191082 + 0.080568I
a = 0.364776 + 0.891341I
b = 0.52660 + 1.36846I
3.66544 + 1.93275I 9.84934 1.25490I
u = 1.130118 0.483941I
a = 0.077722 1.317829I
b = 0.46589 1.94609I
7.35822 7.24063I 5.48519 + 8.01234I
u = 1.130118 + 0.483941I
a = 0.077722 + 1.317829I
b = 0.46589 + 1.94609I
7.35822 + 7.24063I 5.48519 8.01234I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.117053 0.384555I
a = 0.277854 0.956410I
b = 0.39551 1.90482I
4.26488 4.97917I 1.90496 + 6.21325I
u = 1.117053 + 0.384555I
a = 0.277854 + 0.956410I
b = 0.39551 + 1.90482I
4.26488 + 4.97917I 1.90496 6.21325I
u = 1.044917 0.622691I
a = 0.955676 + 0.447482I
b = 0.032877 0.173826I
6.62392 10.71347I 5.42331 + 7.09113I
u = 1.044917 + 0.622691I
a = 0.955676 0.447482I
b = 0.032877 + 0.173826I
6.62392 + 10.71347I 5.42331 7.09113I
u = 1.031155 0.909995I
a = 0.466224 + 0.661728I
b = 0.89714 + 1.37568I
1.75568 2.78654I 3.96265 + 0.80830I
u = 1.031155 + 0.909995I
a = 0.466224 0.661728I
b = 0.89714 1.37568I
1.75568 + 2.78654I 3.96265 0.80830I
u = 1.030796 0.166941I
a = 0.07087 + 1.58171I
b = 0.29845 + 1.40586I
12.68786 + 4.35097I 10.38679 2.99509I
u = 1.030796 + 0.166941I
a = 0.07087 1.58171I
b = 0.29845 1.40586I
12.68786 4.35097I 10.38679 + 2.99509I
u = 1.017063 0.460738I
a = 0.365313 0.892723I
b = 0.74922 1.60297I
4.07004 0.47327I 8.11473 + 0.01216I
u = 1.017063 + 0.460738I
a = 0.365313 + 0.892723I
b = 0.74922 + 1.60297I
4.07004 + 0.47327I 8.11473 0.01216I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.800692 0.560525I
a = 0.516941 0.177447I
b = 0.423534 + 0.016157I
1.23216 1.17836I 4.88311 + 4.54684I
u = 0.800692 + 0.560525I
a = 0.516941 + 0.177447I
b = 0.423534 0.016157I
1.23216 + 1.17836I 4.88311 4.54684I
u = 0.782757
a = 1.95040
b = 0.449560
2.00885 7.27944
u = 0.775482 0.702564I
a = 0.070862 + 0.335267I
b = 1.40250 + 1.31661I
5.46219 + 5.61812I 2.79757 0.10435I
u = 0.775482 + 0.702564I
a = 0.070862 0.335267I
b = 1.40250 1.31661I
5.46219 5.61812I 2.79757 + 0.10435I
u = 0.70775 2.08057I
a = 0.521011 0.063733I
b = 1.226700 0.645730I
7.96934 + 7.75557I 5.83315 9.04917I
u = 0.70775 + 2.08057I
a = 0.521011 + 0.063733I
b = 1.226700 + 0.645730I
7.96934 7.75557I 5.83315 + 9.04917I
u = 0.695662 0.461228I
a = 0.66342 1.53474I
b = 0.92728 1.80614I
11.08239 7.06191I 14.3070 + 7.3501I
u = 0.695662 + 0.461228I
a = 0.66342 + 1.53474I
b = 0.92728 + 1.80614I
11.08239 + 7.06191I 14.3070 7.3501I
u = 0.692230 0.691299I
a = 0.67232 + 1.47767I
b = 0.326730 + 0.897497I
2.70633 4.15001I 9.2225 + 18.2393I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.692230 + 0.691299I
a = 0.67232 1.47767I
b = 0.326730 0.897497I
2.70633 + 4.15001I 9.2225 18.2393I
u = 0.659896 0.535201I
a = 0.513333 1.119510I
b = 0.91838 2.22628I
0.59074 5.03975I 0.37180 + 8.73151I
u = 0.659896 + 0.535201I
a = 0.513333 + 1.119510I
b = 0.91838 + 2.22628I
0.59074 + 5.03975I 0.37180 8.73151I
u = 0.619681 0.601987I
a = 0.409203 + 0.887975I
b = 0.274977 0.196294I
0.06582 2.81820I 0.23839 + 4.97032I
u = 0.619681 + 0.601987I
a = 0.409203 0.887975I
b = 0.274977 + 0.196294I
0.06582 + 2.81820I 0.23839 4.97032I
u = 0.596379
a = 1.14585
b = 0.571104
2.43815 4.51530
u = 0.531325 0.593484I
a = 1.34480 0.49436I
b = 0.346204 + 0.166649I
2.70373 + 0.98079I 1.75261 1.15561I
u = 0.531325 + 0.593484I
a = 1.34480 + 0.49436I
b = 0.346204 0.166649I
2.70373 0.98079I 1.75261 + 1.15561I
u = 0.477386 0.066075I
a = 1.29452 + 1.82122I
b = 0.06476 + 1.52905I
4.69329 + 4.27856I 4.35092 2.98387I
u = 0.477386 + 0.066075I
a = 1.29452 1.82122I
b = 0.06476 1.52905I
4.69329 4.27856I 4.35092 + 2.98387I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.352124 1.046439I
a = 0.555372 + 0.041707I
b = 0.324147 0.362843I
0.84180 2.66745I 5.74905 1.98095I
u = 0.352124 + 1.046439I
a = 0.555372 0.041707I
b = 0.324147 + 0.362843I
0.84180 + 2.66745I 5.74905 + 1.98095I
u = 0.288716 1.130940I
a = 0.154476 0.263099I
b = 0.516252 0.223314I
1.14260 3.25401I 3.95954 + 7.62313I
u = 0.288716 + 1.130940I
a = 0.154476 + 0.263099I
b = 0.516252 + 0.223314I
1.14260 + 3.25401I 3.95954 7.62313I
u = 0.111187 1.159689I
a = 0.862300 0.123013I
b = 0.379329 + 0.405946I
3.50317 + 2.78548I 6.25542 3.26156I
u = 0.111187 + 1.159689I
a = 0.862300 + 0.123013I
b = 0.379329 0.405946I
3.50317 2.78548I 6.25542 + 3.26156I
u = 0.155945 0.596885I
a = 0.30434 + 1.38663I
b = 0.339862 0.017109I
2.36715 + 0.35769I 7.82388 + 1.85714I
u = 0.155945 + 0.596885I
a = 0.30434 1.38663I
b = 0.339862 + 0.017109I
2.36715 0.35769I 7.82388 1.85714I
u = 0.19737 2.33544I
a = 0.420958 0.001789I
b = 1.55666 + 0.17870I
0.50502 3.23925I 3.97067 + 7.51565I
u = 0.19737 + 2.33544I
a = 0.420958 + 0.001789I
b = 1.55666 0.17870I
0.50502 + 3.23925I 3.97067 7.51565I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.410749 0.471628I
a = 1.284800 0.422379I
b = 0.145829 0.802914I
0.12055 1.56154I 0.20818 + 3.43481I
u = 0.410749 + 0.471628I
a = 1.284800 + 0.422379I
b = 0.145829 + 0.802914I
0.12055 + 1.56154I 0.20818 3.43481I
u = 0.418317
a = 2.98267
b = 0.375680
2.46420 33.6241
u = 0.560076 1.171314I
a = 0.671054 + 0.204537I
b = 0.223167 + 0.438075I
4.51518 + 3.24714I 5.57266 2.73443I
u = 0.560076 + 1.171314I
a = 0.671054 0.204537I
b = 0.223167 0.438075I
4.51518 3.24714I 5.57266 + 2.73443I
u = 0.571797 0.795448I
a = 0.491871 + 0.914291I
b = 0.61211 + 2.51423I
5.19564 + 7.48572I 6.12867 11.33536I
u = 0.571797 + 0.795448I
a = 0.491871 0.914291I
b = 0.61211 2.51423I
5.19564 7.48572I 6.12867 + 11.33536I
u = 0.627270 0.234640I
a = 0.61649 + 1.48107I
b = 1.18175 + 1.63408I
3.66917 + 2.24819I 7.46389 2.06250I
u = 0.627270 + 0.234640I
a = 0.61649 1.48107I
b = 1.18175 1.63408I
3.66917 2.24819I 7.46389 + 2.06250I
u = 0.641469 0.112408I
a = 1.97692 1.26672I
b = 0.185757 0.080789I
5.83989 1.30562I 24.9817 6.5610I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.641469 + 0.112408I
a = 1.97692 + 1.26672I
b = 0.185757 + 0.080789I
5.83989 + 1.30562I 24.9817 + 6.5610I
u = 0.686607 0.222863I
a = 0.08998 1.96347I
b = 0.455844 0.912488I
4.57148 1.94462I 8.58806 + 6.86868I
u = 0.686607 + 0.222863I
a = 0.08998 + 1.96347I
b = 0.455844 + 0.912488I
4.57148 + 1.94462I 8.58806 6.86868I
u = 0.793130 0.382921I
a = 0.35631 + 1.37664I
b = 0.76428 + 1.72513I
4.75803 + 4.24642I 9.99593 7.14193I
u = 0.793130 + 0.382921I
a = 0.35631 1.37664I
b = 0.76428 1.72513I
4.75803 4.24642I 9.99593 + 7.14193I
u = 0.911465 0.659115I
a = 0.799511 0.508697I
b = 0.061580 + 0.226853I
0.03232 + 7.23979I 1.36389 8.17769I
u = 0.911465 + 0.659115I
a = 0.799511 + 0.508697I
b = 0.061580 0.226853I
0.03232 7.23979I 1.36389 + 8.17769I
u = 0.920623 0.747247I
a = 0.318526 1.299100I
b = 0.336502 1.236948I
9.42451 + 9.01167I 6.58514 8.56377I
u = 0.920623 + 0.747247I
a = 0.318526 + 1.299100I
b = 0.336502 + 1.236948I
9.42451 9.01167I 6.58514 + 8.56377I
u = 0.960722 0.879130I
a = 0.321524 0.430056I
b = 1.08054 1.31714I
0.09907 1.94759I 1.047268 0.082305I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.960722 + 0.879130I
a = 0.321524 + 0.430056I
b = 1.08054 + 1.31714I
0.09907 + 1.94759I 1.047268 + 0.082305I
u = 0.993481 0.278310I
a = 0.534357 0.344154I
b = 0.240491 1.078669I
0.11272 1.93319I 1.42858 + 4.41047I
u = 0.993481 + 0.278310I
a = 0.534357 + 0.344154I
b = 0.240491 + 1.078669I
0.11272 + 1.93319I 1.42858 4.41047I
u = 1.001690 0.662057I
a = 0.632037 + 0.764776I
b = 0.70987 + 1.46300I
9.69819 3.33662I 10.59340 + 0.52034I
u = 1.001690 + 0.662057I
a = 0.632037 0.764776I
b = 0.70987 1.46300I
9.69819 + 3.33662I 10.59340 0.52034I
u = 1.021099 0.309250I
a = 0.048306 + 0.537800I
b = 1.15077 + 1.18839I
7.02333 + 2.79209I 10.65282 2.82685I
u = 1.021099 + 0.309250I
a = 0.048306 0.537800I
b = 1.15077 1.18839I
7.02333 2.79209I 10.65282 + 2.82685I
u = 1.052984 0.528704I
a = 0.095098 + 1.191944I
b = 0.51330 + 2.00122I
1.83963 + 5.67513I 1.83097 12.32614I
u = 1.052984 + 0.528704I
a = 0.095098 1.191944I
b = 0.51330 2.00122I
1.83963 5.67513I 1.83097 + 12.32614I
u = 1.069566 0.571323I
a = 0.394259 + 0.448579I
b = 0.572637 + 0.680698I
7.15487 + 2.90968I 8.77339 3.39857I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.069566 + 0.571323I
a = 0.394259 0.448579I
b = 0.572637 0.680698I
7.15487 2.90968I 8.77339 + 3.39857I
u = 1.42757 0.93579I
a = 0.163394 0.826934I
b = 0.67887 2.16422I
4.02189 + 12.94079I 4.13091 8.89362I
u = 1.42757 + 0.93579I
a = 0.163394 + 0.826934I
b = 0.67887 + 2.16422I
4.02189 12.94079I 4.13091 + 8.89362I
u = 1.44148 0.01984I
a = 0.459074 0.847240I
b = 0.41883 1.37506I
9.62472 2.50943I 10.21690 + 0.66180I
u = 1.44148 + 0.01984I
a = 0.459074 + 0.847240I
b = 0.41883 + 1.37506I
9.62472 + 2.50943I 10.21690 0.66180I
u = 1.44678 1.39596I
a = 0.288982 + 0.584891I
b = 0.55149 + 2.16776I
11.29010 + 6.82846I 14.0322 6.3990I
u = 1.44678 + 1.39596I
a = 0.288982 0.584891I
b = 0.55149 2.16776I
11.29010 6.82846I 14.0322 + 6.3990I
u = 1.46023 0.90075I
a = 0.315537 0.794116I
b = 0.70152 1.86561I
12.93759 + 3.41499I 10.10191 3.00232I
u = 1.46023 + 0.90075I
a = 0.315537 + 0.794116I
b = 0.70152 + 1.86561I
12.93759 3.41499I 10.10191 + 3.00232I
14
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
20
+ u
19
+ ··· u 1)(u
89
+ 4u
88
+ ··· 121118u + 30299)
c
2
(u
20
u
18
+ ··· u 1)(u
89
+ u
88
+ ··· + 74u + 3)
c
3
(u
20
+ 7u
19
+ ··· + 26u
2
1)(u
89
+ 6u
88
+ ··· + 9173u 3187)
c
4
(u
20
u
19
+ ··· + 2u + 1)(u
89
45u
87
+ ··· 29u 1)
c
5
(u
20
+ 3u
19
+ ··· u 1)(u
89
+ 5u
87
+ ··· 1510u 191)
c
6
(u
20
+ 4u
18
+ ··· + 3u 1)(u
89
+ u
88
+ ··· + 84u 2543)
c
7
(u
20
2u
19
+ ··· + u 1)(u
89
+ u
88
+ ··· + 48u 59)
c
8
(u
20
3u
19
+ ··· 3u
2
+ 1)(u
89
+ 8u
88
+ ··· + 21u + 1)
c
9
(u
20
+ u
19
+ ··· 2u + 1)(u
89
45u
87
+ ··· 29u 1)
c
10
(u
20
+ u
19
+ ··· 2u + 1)(u
89
45u
87
+ ··· 29u 1)
c
11
(u
20
+ 2u
19
+ ··· u 1)(u
89
+ u
88
+ ··· + 48u 59)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
20
9y
19
+ ··· + y + 1)
(y
89
+ 22y
88
+ ··· 31326433005y 918029401)
c
2
(y
20
2y
19
+ ··· + y + 1)(y
89
7y
88
+ ··· + 1222y 9)
c
3
(y
20
3y
19
+ ··· 52y + 1)
(y
89
40y
88
+ ··· + 740124139y 10156969)
c
4
(y
20
21y
19
+ ··· 28y + 1)(y
89
90y
88
+ ··· + 123y 1)
c
5
(y
20
+ 3y
19
+ ··· + 11y + 1)(y
89
+ 10y
88
+ ··· 1020380y 36481)
c
6
(y
20
+ 8y
19
+ ··· 11y + 1)
(y
89
17y
88
+ ··· + 242227806y 6466849)
c
7
, c
11
(y
20
+ 10y
19
+ ··· + 19y + 1)(y
89
+ 57y
88
+ ··· 106492y 3481)
c
8
(y
20
+ y
19
+ ··· 6y + 1)(y
89
+ 12y
88
+ ··· + 29y 1)
c
9
(y
20
21y
19
+ ··· 28y + 1)(y
89
90y
88
+ ··· + 123y 1)
c
10
(y
20
21y
19
+ ··· 28y + 1)(y
89
90y
88
+ ··· + 123y 1)
16