11a
255
(K11a
255
)
1
Arc Sequences
10 8 1 2 9 3 11 5 6 4 7
Solving Sequence
1,4 3,7
6 11 8 10 2 5 9
c
3
c
6
c
11
c
7
c
10
c
1
c
4
c
9
c
2
, c
5
, c
8
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
17
9u
16
+ ··· + 12u 1, 519u
16
2386u
15
+ ··· + 393a 3191,
1763u
16
14729u
15
+ ··· + 393b + 5411i
I
u
2
= hu
88
2u
87
+ ··· 1392u + 133,
1.46858 × 10
390
u
87
4.20199 × 10
390
u
86
+ ··· + 1.51443 × 10
390
b + 2.30629 × 10
392
,
2.52158 × 10
392
u
87
7.20387 × 10
392
u
86
+ ··· + 2.01420 × 10
392
a + 3.86964 × 10
394
i
There are 2 irreducible components with 105 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
17
9u
16
+ · · · + 12u 1, 519u
16
2386u
15
+ · · · + 393a
3191, 1763u
16
14729u
15
+ · · · + 393b + 5411i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
7
=
1.32061u
16
+ 6.07125u
15
+ ··· 74.9109u + 8.11959
4.48601u
16
+ 37.4784u
15
+ ··· + 111.598u 13.7684
a
6
=
2.55725u
16
25.6794u
15
+ ··· 113.099u + 11.0382
0.608142u
16
+ 5.72774u
15
+ ··· + 73.4097u 10.8499
a
11
=
30.7405u
16
259.053u
15
+ ··· 502.150u + 48.4936
18.6107u
16
159.247u
15
+ ··· 383.392u + 41.7405
a
8
=
11.6768u
16
94.7430u
15
+ ··· 53.2621u 0.770992
2.39440u
16
12.7913u
15
+ ··· + 262.094u 40.6260
a
10
=
30.7405u
16
259.053u
15
+ ··· 502.150u + 48.4936
10.3613u
16
87.3766u
15
+ ··· 202.804u + 24.1298
a
2
=
u
16
+ 9u
15
+ ··· + 63u 11
13.7684u
16
+ 119.430u
15
+ ··· + 468.954u 63.6234
a
5
=
u
16
9u
15
+ ··· 62u + 10
9.28244u
16
81.9517u
15
+ ··· 366.356u + 49.8550
a
9
=
18.5140u
16
155.855u
15
+ ··· 302.402u + 29.8982
20.2316u
16
171.903u
15
+ ··· 426.046u + 50.0433
a
9
=
18.5140u
16
155.855u
15
+ ··· 302.402u + 29.8982
20.2316u
16
171.903u
15
+ ··· 426.046u + 50.0433
(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 = 0.668036 1.073056I
a = 1.13817 + 1.30384I
b = 0.018927 + 0.733970I
6.49554 + 5.64721I 4.24800 5.28734I
u = 0.668036 + 1.073056I
a = 1.13817 1.30384I
b = 0.018927 0.733970I
6.49554 5.64721I 4.24800 + 5.28734I
u = 0.057733 0.951073I
a = 1.143602 0.306899I
b = 0.101023 0.636506I
0.39343 + 3.18951I 2.48922 8.07163I
u = 0.057733 + 0.951073I
a = 1.143602 + 0.306899I
b = 0.101023 + 0.636506I
0.39343 3.18951I 2.48922 + 8.07163I
u = 0.239180
a = 0.122363
b = 1.86405
9.97638 80.3957
u = 0.337728 0.912764I
a = 0.874909 0.725167I
b = 0.343513 1.276775I
3.66769 + 6.66143I 4.22453 5.17747I
u = 0.337728 + 0.912764I
a = 0.874909 + 0.725167I
b = 0.343513 + 1.276775I
3.66769 6.66143I 4.22453 + 5.17747I
u = 0.493177 0.381587I
a = 0.291371 0.316362I
b = 0.932738 + 0.190257I
1.024425 + 0.934539I 3.42338 2.45300I
u = 0.493177 + 0.381587I
a = 0.291371 + 0.316362I
b = 0.932738 0.190257I
1.024425 0.934539I 3.42338 + 2.45300I
u = 0.643995 0.214476I
a = 1.10414 + 2.89971I
b = 0.185967 + 1.393160I
3.91587 + 3.42072I 20.1307 16.0266I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.643995 + 0.214476I
a = 1.10414 2.89971I
b = 0.185967 1.393160I
3.91587 3.42072I 20.1307 + 16.0266I
u = 0.806233 1.133430I
a = 0.141983 + 0.575675I
b = 0.287573 + 0.472967I
2.31141 + 2.16263I 6.33291 1.14130I
u = 0.806233 + 1.133430I
a = 0.141983 0.575675I
b = 0.287573 0.472967I
2.31141 2.16263I 6.33291 + 1.14130I
u = 1.18357 0.87091I
a = 0.447814 + 1.259982I
b = 0.396650 + 1.232914I
3.35478 + 5.00709I 1.93752 5.36803I
u = 1.18357 + 0.87091I
a = 0.447814 1.259982I
b = 0.396650 1.232914I
3.35478 5.00709I 1.93752 + 5.36803I
u = 1.64147 1.17117I
a = 0.310302 1.117939I
b = 0.370147 1.163037I
0.09550 + 5.07949I 3.41161 6.03160I
u = 1.64147 + 1.17117I
a = 0.310302 + 1.117939I
b = 0.370147 + 1.163037I
0.09550 5.07949I 3.41161 + 6.03160I
4
II. I
u
2
= hu
88
2u
87
+ · · · 1392u + 133, 1.47 × 10
390
u
87
4.20 ×
10
390
u
86
+ · · · + 1.51 × 10
390
b + 2.31 × 10
392
, 2.52 × 10
392
u
87
7.20 ×
10
392
u
86
+ · · · + 2.01 × 10
392
a + 3.87 × 10
394
i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
7
=
1.25190u
87
+ 3.57655u
86
+ ··· + 2252.01u 192.118
0.969724u
87
+ 2.77463u
86
+ ··· + 1745.52u 152.287
a
6
=
1.05500u
87
+ 3.01877u
86
+ ··· + 1883.79u 160.522
0.772815u
87
+ 2.21685u
86
+ ··· + 1377.30u 120.692
a
11
=
0.228606u
87
+ 0.661130u
86
+ ··· + 408.990u 37.5366
1.30383u
87
+ 3.71059u
86
+ ··· + 2357.42u 198.540
a
8
=
0.0904264u
87
0.237916u
86
+ ··· 255.903u + 27.1285
0.192090u
87
0.559370u
86
+ ··· 266.292u + 13.6245
a
10
=
0.228606u
87
+ 0.661130u
86
+ ··· + 408.990u 37.5366
1.12561u
87
+ 3.20022u
86
+ ··· + 2043.16u 171.419
a
2
=
1.32235u
87
+ 3.74890u
86
+ ··· + 2380.69u 196.322
2.21196u
87
+ 6.33383u
86
+ ··· + 4055.74u 362.550
a
5
=
0.809937u
87
+ 2.30255u
86
+ ··· + 1451.57u 118.286
1.70838u
87
+ 4.91195u
86
+ ··· + 3055.44u 273.571
a
9
=
1.43951u
87
+ 4.12506u
86
+ ··· + 2586.00u 227.371
2.01854u
87
+ 5.77408u
86
+ ··· + 3591.32u 301.522
a
9
=
1.43951u
87
+ 4.12506u
86
+ ··· + 2586.00u 227.371
2.01854u
87
+ 5.77408u
86
+ ··· + 3591.32u 301.522
(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 = 1.35036 1.05778I
a = 0.458331 1.277195I
b = 0.59896 1.30787I
3.7463 17.3074I 4.74718 + 8.94667I
u = 1.35036 + 1.05778I
a = 0.458331 + 1.277195I
b = 0.59896 + 1.30787I
3.7463 + 17.3074I 4.74718 8.94667I
u = 1.31555 0.90486I
a = 0.42688 + 1.34847I
b = 0.59458 + 1.30691I
2.63728 13.13357I 1.48177 + 9.15573I
u = 1.31555 + 0.90486I
a = 0.42688 1.34847I
b = 0.59458 1.30691I
2.63728 + 13.13357I 1.48177 9.15573I
u = 1.31280 0.86921I
a = 0.106149 1.398778I
b = 0.168784 0.607951I
7.10229 + 5.03178I 11.17379 + 0.23568I
u = 1.31280 + 0.86921I
a = 0.106149 + 1.398778I
b = 0.168784 + 0.607951I
7.10229 5.03178I 11.17379 0.23568I
u = 1.22378 0.74371I
a = 0.296461 0.947446I
b = 0.507340 0.954770I
5.06894 1.03566I 9.19102 0.41125I
u = 1.22378 + 0.74371I
a = 0.296461 + 0.947446I
b = 0.507340 + 0.954770I
5.06894 + 1.03566I 9.19102 + 0.41125I
u = 1.174466 0.741807I
a = 0.42742 1.48323I
b = 0.58598 1.31107I
1.90928 7.75289I 3.09462 + 5.99910I
u = 1.174466 + 0.741807I
a = 0.42742 + 1.48323I
b = 0.58598 + 1.31107I
1.90928 + 7.75289I 3.09462 5.99910I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.084366 0.043630I
a = 0.062783 + 1.218163I
b = 0.489726 + 0.278597I
6.71196 5.09265I 8.85774 + 4.27356I
u = 1.084366 + 0.043630I
a = 0.062783 1.218163I
b = 0.489726 0.278597I
6.71196 + 5.09265I 8.85774 4.27356I
u = 0.955824 0.815141I
a = 0.0595934 + 0.1191830I
b = 1.122268 + 0.163021I
7.34238 11.23935I 7.36525 + 7.13269I
u = 0.955824 + 0.815141I
a = 0.0595934 0.1191830I
b = 1.122268 0.163021I
7.34238 + 11.23935I 7.36525 7.13269I
u = 0.887412 0.681602I
a = 0.155436 0.123733I
b = 1.123069 0.172402I
0.94916 7.07982I 4.04073 + 7.98473I
u = 0.887412 + 0.681602I
a = 0.155436 + 0.123733I
b = 1.123069 + 0.172402I
0.94916 + 7.07982I 4.04073 7.98473I
u = 0.851830 0.627147I
a = 0.12177 + 1.49762I
b = 0.244342 + 0.574128I
1.08733 + 1.99106I 6.09235 1.36477I
u = 0.851830 + 0.627147I
a = 0.12177 1.49762I
b = 0.244342 0.574128I
1.08733 1.99106I 6.09235 + 1.36477I
u = 0.846541 0.044566I
a = 0.18852 1.42850I
b = 0.408841 0.538029I
0.94922 1.67367I 6.07995 + 4.98191I
u = 0.846541 + 0.044566I
a = 0.18852 + 1.42850I
b = 0.408841 + 0.538029I
0.94922 + 1.67367I 6.07995 4.98191I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.843757 0.020441I
a = 0.52552 + 1.34772I
b = 0.26940 + 1.50948I
1.55133 5.83848I 0.09771 + 5.45598I
u = 0.843757 + 0.020441I
a = 0.52552 1.34772I
b = 0.26940 1.50948I
1.55133 + 5.83848I 0.09771 5.45598I
u = 0.807419 0.101376I
a = 0.68138 + 1.60569I
b = 0.25185 + 1.41547I
4.87171 + 1.98745I 3.66665 4.32136I
u = 0.807419 + 0.101376I
a = 0.68138 1.60569I
b = 0.25185 1.41547I
4.87171 1.98745I 3.66665 + 4.32136I
u = 0.799827 0.745621I
a = 0.71049 + 1.63240I
b = 0.550727 + 1.273456I
6.15553 4.54274I 8.44861 + 4.45149I
u = 0.799827 + 0.745621I
a = 0.71049 1.63240I
b = 0.550727 1.273456I
6.15553 + 4.54274I 8.44861 4.45149I
u = 0.75500 2.08003I
a = 0.049536 + 0.692418I
b = 0.280728 + 0.984283I
5.87411 + 7.49299I 7.53247 9.19945I
u = 0.75500 + 2.08003I
a = 0.049536 0.692418I
b = 0.280728 0.984283I
5.87411 7.49299I 7.53247 + 9.19945I
u = 0.740373 0.199504I
a = 0.76534 2.31374I
b = 0.264183 1.381403I
4.10019 3.25868I 4.16235 7.85474I
u = 0.740373 + 0.199504I
a = 0.76534 + 2.31374I
b = 0.264183 + 1.381403I
4.10019 + 3.25868I 4.16235 + 7.85474I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.698286 0.534605I
a = 0.324307 + 0.014317I
b = 1.145901 + 0.160272I
1.75411 1.70043I 7.59443 + 6.08619I
u = 0.698286 + 0.534605I
a = 0.324307 0.014317I
b = 1.145901 0.160272I
1.75411 + 1.70043I 7.59443 6.08619I
u = 0.651197 0.220970I
a = 1.69945 2.70481I
b = 0.193292 1.310604I
4.12384 3.33457I 15.8193 + 4.0101I
u = 0.651197 + 0.220970I
a = 1.69945 + 2.70481I
b = 0.193292 + 1.310604I
4.12384 + 3.33457I 15.8193 4.0101I
u = 0.614408 0.531789I
a = 2.38039 + 0.82369I
b = 0.300650 + 1.185315I
2.86988 7.90451I 1.41287 + 11.07621I
u = 0.614408 + 0.531789I
a = 2.38039 0.82369I
b = 0.300650 1.185315I
2.86988 + 7.90451I 1.41287 11.07621I
u = 0.36709 1.73288I
a = 0.077770 0.578892I
b = 0.268637 0.926272I
0.17356 + 4.65502I 2.68890 10.30148I
u = 0.36709 + 1.73288I
a = 0.077770 + 0.578892I
b = 0.268637 + 0.926272I
0.17356 4.65502I 2.68890 + 10.30148I
u = 0.345949 0.681576I
a = 0.799172 + 0.488356I
b = 0.400085 + 0.779941I
0.45850 + 1.90438I 4.87683 2.73751I
u = 0.345949 + 0.681576I
a = 0.799172 0.488356I
b = 0.400085 0.779941I
0.45850 1.90438I 4.87683 + 2.73751I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.315066 0.794489I
a = 0.077165 + 0.269831I
b = 1.075547 0.160757I
9.64122 + 1.15165I 12.31029 + 1.33137I
u = 0.315066 + 0.794489I
a = 0.077165 0.269831I
b = 1.075547 + 0.160757I
9.64122 1.15165I 12.31029 1.33137I
u = 0.115180
a = 1.46083
b = 1.83723
10.0236 89.3531
u = 0.217059 0.310973I
a = 0.577538 0.940146I
b = 0.794294 0.196262I
1.43199 0.10841I 9.03393 1.67726I
u = 0.217059 + 0.310973I
a = 0.577538 + 0.940146I
b = 0.794294 + 0.196262I
1.43199 + 0.10841I 9.03393 + 1.67726I
u = 0.229874 1.178066I
a = 0.472863 + 0.491184I
b = 0.354699 0.723101I
7.08647 + 3.90826I 9.31273 0.42676I
u = 0.229874 + 1.178066I
a = 0.472863 0.491184I
b = 0.354699 + 0.723101I
7.08647 3.90826I 9.31273 + 0.42676I
u = 0.267524 0.594606I
a = 2.87446 + 2.84318I
b = 0.268404 + 0.857891I
6.81415 + 6.82656I 7.91716 9.86777I
u = 0.267524 + 0.594606I
a = 2.87446 2.84318I
b = 0.268404 0.857891I
6.81415 6.82656I 7.91716 + 9.86777I
u = 0.332170 0.629742I
a = 0.085108 0.607459I
b = 0.512801 + 0.532408I
0.40811 + 2.17817I 5.56775 5.52206I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.332170 + 0.629742I
a = 0.085108 + 0.607459I
b = 0.512801 0.532408I
0.40811 2.17817I 5.56775 + 5.52206I
u = 0.362510 0.110765I
a = 1.21537 + 2.06664I
b = 0.622034 0.798019I
4.81925 + 2.14563I 8.40267 3.44502I
u = 0.362510 + 0.110765I
a = 1.21537 2.06664I
b = 0.622034 + 0.798019I
4.81925 2.14563I 8.40267 + 3.44502I
u = 0.387502 1.003568I
a = 0.075758 0.290850I
b = 0.102432 + 0.587595I
0.58871 + 2.37016I 4.17793 + 0.20978I
u = 0.387502 + 1.003568I
a = 0.075758 + 0.290850I
b = 0.102432 0.587595I
0.58871 2.37016I 4.17793 0.20978I
u = 0.533022 0.705164I
a = 0.313368 + 0.555005I
b = 0.766287 0.483773I
5.63533 + 2.97696I 10.49191 3.67148I
u = 0.533022 + 0.705164I
a = 0.313368 0.555005I
b = 0.766287 + 0.483773I
5.63533 2.97696I 10.49191 + 3.67148I
u = 0.548587 0.896368I
a = 0.374783 0.947309I
b = 0.61912 1.42748I
4.61143 + 7.37584I 10.2448 10.2846I
u = 0.548587 + 0.896368I
a = 0.374783 + 0.947309I
b = 0.61912 + 1.42748I
4.61143 7.37584I 10.2448 + 10.2846I
u = 0.695545 0.304864I
a = 0.16589 3.29163I
b = 0.194990 0.972525I
0.49529 + 4.30405I 0.74509 9.00558I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.695545 + 0.304864I
a = 0.16589 + 3.29163I
b = 0.194990 + 0.972525I
0.49529 4.30405I 0.74509 + 9.00558I
u = 0.751296 0.617383I
a = 0.397295 + 0.125727I
b = 0.560357 + 0.063304I
1.03837 + 1.54696I 1.67898 4.77723I
u = 0.751296 + 0.617383I
a = 0.397295 0.125727I
b = 0.560357 0.063304I
1.03837 1.54696I 1.67898 + 4.77723I
u = 0.85835 1.24200I
a = 0.510868 + 0.408341I
b = 0.058412 + 0.928721I
1.12675 + 3.01989I 1.45420 3.67592I
u = 0.85835 + 1.24200I
a = 0.510868 0.408341I
b = 0.058412 0.928721I
1.12675 3.01989I 1.45420 + 3.67592I
u = 0.864539 0.448586I
a = 0.484886 1.139655I
b = 0.563658 0.873301I
1.161848 + 0.746665I 0.192569 0.288737I
u = 0.864539 + 0.448586I
a = 0.484886 + 1.139655I
b = 0.563658 + 0.873301I
1.161848 0.746665I 0.192569 + 0.288737I
u = 0.882883 0.965266I
a = 0.385935 + 0.016752I
b = 0.549004 0.248370I
3.28529 + 3.22075I 7.79433 4.35674I
u = 0.882883 + 0.965266I
a = 0.385935 0.016752I
b = 0.549004 + 0.248370I
3.28529 3.22075I 7.79433 + 4.35674I
u = 0.895956 0.430676I
a = 1.51300 0.95295I
b = 0.073479 0.979835I
2.63186 0.30603I 4.47610 0.84684I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.895956 + 0.430676I
a = 1.51300 + 0.95295I
b = 0.073479 + 0.979835I
2.63186 + 0.30603I 4.47610 + 0.84684I
u = 0.896562 0.724352I
a = 0.401782 + 1.011935I
b = 0.580851 + 1.289204I
1.90539 + 5.37165I 4.99409 10.30612I
u = 0.896562 + 0.724352I
a = 0.401782 1.011935I
b = 0.580851 1.289204I
1.90539 5.37165I 4.99409 + 10.30612I
u = 0.983911
a = 0.545112
b = 0.664036
2.27296 3.80779
u = 1.098757 0.158169I
a = 0.462035 1.052923I
b = 0.591230 1.087056I
3.27941 + 2.28675I 3.82551 1.37856I
u = 1.098757 + 0.158169I
a = 0.462035 + 1.052923I
b = 0.591230 + 1.087056I
3.27941 2.28675I 3.82551 + 1.37856I
u = 1.26078 1.24731I
a = 0.702035 + 1.182958I
b = 0.444333 + 1.113407I
0.79244 + 7.21107I 2.35901 8.61847I
u = 1.26078 + 1.24731I
a = 0.702035 1.182958I
b = 0.444333 1.113407I
0.79244 7.21107I 2.35901 + 8.61847I
u = 1.37243 1.03477I
a = 0.535648 1.177408I
b = 0.428397 1.160104I
4.10700 + 5.44401I 7.49868 9.59248I
u = 1.37243 + 1.03477I
a = 0.535648 + 1.177408I
b = 0.428397 + 1.160104I
4.10700 5.44401I 7.49868 + 9.59248I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.37453 1.19947I
a = 0.207842 1.093092I
b = 0.337940 1.350438I
0.04809 + 6.65339I 2.74381 8.91641I
u = 1.37453 + 1.19947I
a = 0.207842 + 1.093092I
b = 0.337940 + 1.350438I
0.04809 6.65339I 2.74381 + 8.91641I
u = 1.41569 0.95577I
a = 0.213894 + 1.241579I
b = 0.307225 + 1.253980I
4.35734 + 4.93840I 7.58655 6.46522I
u = 1.41569 + 0.95577I
a = 0.213894 1.241579I
b = 0.307225 1.253980I
4.35734 4.93840I 7.58655 + 6.46522I
u = 1.53020 0.59826I
a = 0.045437 1.408482I
b = 0.191400 1.188395I
0.78403 + 3.10651I 0.40975 1.77947I
u = 1.53020 + 0.59826I
a = 0.045437 + 1.408482I
b = 0.191400 + 1.188395I
0.78403 3.10651I 0.40975 + 1.77947I
u = 1.61598 0.75808I
a = 0.476895 + 1.058481I
b = 0.461674 + 1.165624I
0.88817 + 4.15422I 0.79456 1.86780I
u = 1.61598 + 0.75808I
a = 0.476895 1.058481I
b = 0.461674 1.165624I
0.88817 4.15422I 0.79456 + 1.86780I
14
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
17
2u
16
+ ··· 4u 1)(u
88
+ 9u
87
+ ··· 24u 1)
c
2
(u
17
3u
15
+ ··· + 2u + 1)(u
88
+ u
87
+ ··· 1530u 73)
c
3
(u
17
+ 9u
16
+ ··· + 12u + 1)(u
88
+ 2u
87
+ ··· + 1392u + 133)
c
4
(u
17
8u
16
+ ··· + 10u 1)(u
88
+ 3u
87
+ ··· 6998u + 2363)
c
5
(u
17
2u
16
+ ··· + 2u 1)(u
88
+ 3u
87
+ ··· + 12u 1)
c
6
(u
17
2u
16
+ ··· + 2u 1)(u
88
+ u
87
+ ··· 9888u 1216)
c
7
(u
17
u
16
+ ··· + u 1)(u
88
+ 26u
86
+ ··· + 35u 19)
c
8
(u
17
+ 2u
16
+ ··· + 2u + 1)(u
88
+ 3u
87
+ ··· + 12u 1)
c
9
(u
17
+ 2u
16
+ ··· + 2u + 1)(u
88
+ 3u
87
+ ··· + 12u 1)
c
10
(u
17
+ 4u
16
+ ··· + 2u 1)(u
88
+ 5u
87
+ ··· + 32u 1)
c
11
(u
17
+ u
16
+ ··· + u + 1)(u
88
+ 26u
86
+ ··· + 35u 19)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
17
14y
16
+ ··· + 12y 1)(y
88
15y
87
+ ··· + 48y + 1)
c
2
(y
17
6y
16
+ ··· 8y
2
1)(y
88
+ 17y
87
+ ··· + 439816y + 5329)
c
3
(y
17
+ y
16
+ ··· + 18y 1)(y
88
16y
87
+ ··· 1724598y + 17689)
c
4
(y
17
+ 2y
16
+ ··· + 4y 1)
(y
88
23y
87
+ ··· 69312708y + 5583769)
c
5
(y
17
18y
16
+ ··· + 18y 1)(y
88
87y
87
+ ··· + 6y + 1)
c
6
(y
17
+ 6y
16
+ ··· + 12y 1)
(y
88
7y
87
+ ··· 41894912y + 1478656)
c
7
, c
11
(y
17
+ 9y
16
+ ··· 13y 1)(y
88
+ 52y
87
+ ··· + 8009y + 361)
c
8
(y
17
18y
16
+ ··· + 18y 1)(y
88
87y
87
+ ··· + 6y + 1)
c
9
(y
17
18y
16
+ ··· + 18y 1)(y
88
87y
87
+ ··· + 6y + 1)
c
10
(y
17
12y
16
+ ··· + 14y 1)(y
88
9y
87
+ ··· 42y + 1)
16