11a
138
(K11a
138
)
1
Arc Sequences
6 1 11 10 2 9 4 3 5 7 8
Solving Sequence
2,5 6,9
7 10 1 3 4 8 11
c
5
c
6
c
9
c
1
c
2
c
4
c
8
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
14
u
13
+ 4u
12
4u
11
+ 9u
10
9u
9
+ 14u
8
13u
7
+ 14u
6
11u
5
+ 10u
4
6u
3
+ 4u
2
2u + 1,
2u
12
+ u
11
6u
10
+ 3u
9
10u
8
+ 6u
7
11u
6
+ 6u
5
5u
4
+ u
3
2u
2
+ b,
2u
13
u
12
+ 7u
11
4u
10
+ 13u
9
9u
8
+ 16u
7
12u
6
+ 10u
5
8u
4
+ 4u
3
2u
2
+ a + u 1i
I
u
2
= hu
94
+ 18u
92
+ ··· 86u + 19,
2.53312 × 10
131
u
93
+ 5.50106 × 10
132
u
92
+ ··· + 3.94596 × 10
132
b + 5.66772 × 10
133
,
2.57397 × 10
133
u
93
+ 8.81637 × 10
133
u
92
+ ··· + 7.49732 × 10
133
a + 2.04074 × 10
135
i
There are 2 irreducible components with 108 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
14
u
13
+· · ·2u+1, 2u
12
+u
11
+· · ·2u
2
+b, 2u
13
u
12
+· · ·+a1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
9
=
2u
13
+ u
12
+ ··· u + 1
2u
12
u
11
+ 6u
10
3u
9
+ 10u
8
6u
7
+ 11u
6
6u
5
+ 5u
4
u
3
+ 2u
2
a
7
=
2u
13
+ u
12
+ ··· 4u + 3
u
13
+ u
12
+ ··· 3u + 1
a
10
=
2u
13
+ u
12
+ ··· u + 1
2u
12
+ 6u
10
+ 10u
8
u
7
+ 11u
6
u
5
+ 5u
4
+ 3u
2
+ 1
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
4
=
3u
13
u
12
+ ··· + 2u
2
1
u
12
2u
11
+ ··· + 5u
2
3u
a
8
=
2u
13
+ u
12
+ ··· + 2u
2
+ 1
u
12
+ 2u
10
+ u
9
+ 2u
8
+ 2u
7
+ 4u
5
4u
4
+ 5u
3
2u
2
+ 2u 1
a
11
=
u
13
+ u
12
4u
11
+ 3u
10
8u
9
+ 5u
8
11u
7
+ 5u
6
8u
5
3u
3
u
2
u
13
u
12
+ ··· 3u
2
+ u
a
11
=
u
13
+ u
12
4u
11
+ 3u
10
8u
9
+ 5u
8
11u
7
+ 5u
6
8u
5
3u
3
u
2
u
13
u
12
+ ··· 3u
2
+ u
(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 = 0.741847 1.006643I
a = 0.003263 + 0.366777I
b = 0.108563 + 0.977487I
0.27543 + 3.16621I 5.01739 7.56548I
u = 0.741847 + 1.006643I
a = 0.003263 0.366777I
b = 0.108563 0.977487I
0.27543 3.16621I 5.01739 + 7.56548I
u = 0.473825 0.725334I
a = 1.97318 0.92036I
b = 1.72162 1.13904I
1.64938 + 1.47694I 29.7777 30.0683I
u = 0.473825 + 0.725334I
a = 1.97318 + 0.92036I
b = 1.72162 + 1.13904I
1.64938 1.47694I 29.7777 + 30.0683I
u = 0.218324 0.879322I
a = 0.477042 + 0.303428I
b = 0.01938 + 1.82516I
3.70335 + 0.96919I 0.59112 6.46740I
u = 0.218324 + 0.879322I
a = 0.477042 0.303428I
b = 0.01938 1.82516I
3.70335 0.96919I 0.59112 + 6.46740I
u = 0.041315 1.259018I
a = 0.907114 + 0.143819I
b = 1.251142 + 0.537115I
0.636777 + 1.162526I 0.38748 2.64720I
u = 0.041315 + 1.259018I
a = 0.907114 0.143819I
b = 1.251142 0.537115I
0.636777 1.162526I 0.38748 + 2.64720I
u = 0.595922 0.607204I
a = 1.28945 + 0.76662I
b = 0.401010 0.733331I
4.21333 + 4.10072I 5.58747 4.56335I
u = 0.595922 + 0.607204I
a = 1.28945 0.76662I
b = 0.401010 + 0.733331I
4.21333 4.10072I 5.58747 + 4.56335I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.629454 1.045366I
a = 0.676415 + 0.741655I
b = 1.60069 + 2.02182I
2.82526 9.05252I 3.02000 + 9.52611I
u = 0.629454 + 1.045366I
a = 0.676415 0.741655I
b = 1.60069 2.02182I
2.82526 + 9.05252I 3.02000 9.52611I
u = 0.667304 0.401977I
a = 0.60527 1.48268I
b = 0.683901 0.483831I
4.15226 5.01003I 2.89129 + 5.27661I
u = 0.667304 + 0.401977I
a = 0.60527 + 1.48268I
b = 0.683901 + 0.483831I
4.15226 + 5.01003I 2.89129 5.27661I
4
II. I
u
2
= hu
94
+ 18u
92
+ · · · 86u + 19, 2.53 × 10
131
u
93
+ 5.50 × 10
132
u
92
+
· · · + 3.95 × 10
132
b + 5.67 × 10
133
, 2.57 × 10
133
u
93
+ 8.82 × 10
133
u
92
+ · · · +
7.50 × 10
133
a + 2.04 × 10
135
i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
9
=
0.343319u
93
1.17594u
92
+ ··· + 47.4340u 27.2196
0.0641953u
93
1.39410u
92
+ ··· + 61.0894u 14.3633
a
7
=
1.05091u
93
+ 1.36980u
92
+ ··· 265.448u + 70.0756
2.35688u
93
+ 1.14947u
92
+ ··· + 183.126u 43.4592
a
10
=
0.343319u
93
1.17594u
92
+ ··· + 47.4340u 27.2196
1.31423u
93
2.20414u
92
+ ··· 33.5181u + 7.97945
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
4
=
2.22029u
93
+ 2.60768u
92
+ ··· + 46.8092u 1.07893
2.01186u
93
+ 2.36152u
92
+ ··· 36.5637u + 19.4508
a
8
=
0.225703u
93
1.08401u
92
+ ··· + 66.3412u 32.3715
0.266213u
93
2.07444u
92
+ ··· + 89.5245u 23.9322
a
11
=
0.0928990u
93
+ 1.21606u
92
+ ··· 162.039u + 48.0660
1.06053u
93
0.0379060u
92
+ ··· + 130.596u 38.9836
a
11
=
0.0928990u
93
+ 1.21606u
92
+ ··· 162.039u + 48.0660
1.06053u
93
0.0379060u
92
+ ··· + 130.596u 38.9836
(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 = 1.154048 0.229156I
a = 0.018819 + 1.027699I
b = 0.001395 + 0.509713I
4.11766 + 6.08651I 1.89585 12.90814I
u = 1.154048 + 0.229156I
a = 0.018819 1.027699I
b = 0.001395 0.509713I
4.11766 6.08651I 1.89585 + 12.90814I
u = 0.958234 0.600549I
a = 0.978364 0.861185I
b = 0.095930 0.416213I
7.78536 3.65950I 7.19328 + 3.10117I
u = 0.958234 + 0.600549I
a = 0.978364 + 0.861185I
b = 0.095930 + 0.416213I
7.78536 + 3.65950I 7.19328 3.10117I
u = 0.890802 0.990398I
a = 0.597327 + 0.594627I
b = 0.03778 + 1.43011I
2.07734 + 3.40281I 2.52976 3.87991I
u = 0.890802 + 0.990398I
a = 0.597327 0.594627I
b = 0.03778 1.43011I
2.07734 3.40281I 2.52976 + 3.87991I
u = 0.788570 0.519422I
a = 1.096853 + 0.333282I
b = 0.132574 + 0.469825I
0.81606 6.58212I 0.06641 + 5.80487I
u = 0.788570 + 0.519422I
a = 1.096853 0.333282I
b = 0.132574 0.469825I
0.81606 + 6.58212I 0.06641 5.80487I
u = 0.772806 0.634311I
a = 0.965714 + 0.666676I
b = 0.729722 0.142198I
2.72382 3.59329I 1.36149 + 3.84627I
u = 0.772806 + 0.634311I
a = 0.965714 0.666676I
b = 0.729722 + 0.142198I
2.72382 + 3.59329I 1.36149 3.84627I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.745984 0.804640I
a = 0.935224 0.845126I
b = 0.056334 0.827532I
6.26917 + 2.63292I 5.69618 3.39145I
u = 0.745984 + 0.804640I
a = 0.935224 + 0.845126I
b = 0.056334 + 0.827532I
6.26917 2.63292I 5.69618 + 3.39145I
u = 0.737805 1.096794I
a = 0.703640 0.952177I
b = 0.91653 2.05044I
6.23852 + 9.84950I 4.39001 7.64089I
u = 0.737805 + 1.096794I
a = 0.703640 + 0.952177I
b = 0.91653 + 2.05044I
6.23852 9.84950I 4.39001 + 7.64089I
u = 0.732135 0.860734I
a = 0.905163 0.802490I
b = 0.11865 1.59187I
6.12499 + 2.78185I 6.38795 2.74253I
u = 0.732135 + 0.860734I
a = 0.905163 + 0.802490I
b = 0.11865 + 1.59187I
6.12499 2.78185I 6.38795 + 2.74253I
u = 0.712836 0.893503I
a = 0.842198 0.774077I
b = 0.57020 1.78608I
6.00363 + 2.90156I 5.29122 2.98759I
u = 0.712836 + 0.893503I
a = 0.842198 + 0.774077I
b = 0.57020 + 1.78608I
6.00363 2.90156I 5.29122 + 2.98759I
u = 0.695476 0.779469I
a = 1.37745 + 0.59069I
b = 0.0257528 + 0.0934147I
6.51815 3.45234I 5.48898 + 1.92372I
u = 0.695476 + 0.779469I
a = 1.37745 0.59069I
b = 0.0257528 0.0934147I
6.51815 + 3.45234I 5.48898 1.92372I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.685534 1.022396I
a = 0.570647 + 0.767577I
b = 1.20915 + 2.40312I
1.56372 + 9.12407I 4.29429 9.46951I
u = 0.685534 + 1.022396I
a = 0.570647 0.767577I
b = 1.20915 2.40312I
1.56372 9.12407I 4.29429 + 9.46951I
u = 0.675420 0.918989I
a = 0.698394 + 1.177555I
b = 1.12883 + 2.25849I
6.09111 + 8.73034I 4.17794 8.47803I
u = 0.675420 + 0.918989I
a = 0.698394 1.177555I
b = 1.12883 2.25849I
6.09111 8.73034I 4.17794 + 8.47803I
u = 0.671783 0.586083I
a = 0.242407 + 0.178172I
b = 0.256270 0.946203I
2.58045 2.08956I 3.02938 + 2.37261I
u = 0.671783 + 0.586083I
a = 0.242407 0.178172I
b = 0.256270 + 0.946203I
2.58045 + 2.08956I 3.02938 2.37261I
u = 0.655731 1.063816I
a = 0.322649 0.952140I
b = 0.08535 1.84948I
0.78035 + 12.02031I 2.29206 10.05499I
u = 0.655731 + 1.063816I
a = 0.322649 + 0.952140I
b = 0.08535 + 1.84948I
0.78035 12.02031I 2.29206 + 10.05499I
u = 0.626927 1.026074I
a = 0.072642 + 0.169203I
b = 0.855407 + 0.727862I
1.27843 + 7.16623I 0.13912 7.53857I
u = 0.626927 + 1.026074I
a = 0.072642 0.169203I
b = 0.855407 0.727862I
1.27843 7.16623I 0.13912 + 7.53857I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.526379 0.975572I
a = 0.285436 + 0.628695I
b = 0.02471 + 1.80111I
2.74009 + 4.79051I 7.62795 7.28564I
u = 0.526379 + 0.975572I
a = 0.285436 0.628695I
b = 0.02471 1.80111I
2.74009 4.79051I 7.62795 + 7.28564I
u = 0.372193 0.319512I
a = 1.119171 0.597617I
b = 0.351039 0.342846I
1.35478 0.87382I 4.52639 + 1.86312I
u = 0.372193 + 0.319512I
a = 1.119171 + 0.597617I
b = 0.351039 + 0.342846I
1.35478 + 0.87382I 4.52639 1.86312I
u = 0.274173 0.962209I
a = 0.071947 + 0.432940I
b = 0.52961 + 1.71858I
4.34588 + 0.86890I 13.9925 2.3122I
u = 0.274173 + 0.962209I
a = 0.071947 0.432940I
b = 0.52961 1.71858I
4.34588 0.86890I 13.9925 + 2.3122I
u = 0.236372 0.894495I
a = 0.397500 0.466475I
b = 0.377840 0.459884I
1.55461 1.18795I 5.25040 + 3.52680I
u = 0.236372 + 0.894495I
a = 0.397500 + 0.466475I
b = 0.377840 + 0.459884I
1.55461 + 1.18795I 5.25040 3.52680I
u = 0.191973 1.387138I
a = 0.723180 + 0.023604I
b = 0.910688 + 0.247145I
0.794911 0.333244I 4.07684 2.62495I
u = 0.191973 + 1.387138I
a = 0.723180 0.023604I
b = 0.910688 0.247145I
0.794911 + 0.333244I 4.07684 + 2.62495I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.182172 1.261938I
a = 0.909401 0.518285I
b = 1.25783 1.26326I
1.47238 + 10.24953I 3.11527 8.40903I
u = 0.182172 + 1.261938I
a = 0.909401 + 0.518285I
b = 1.25783 + 1.26326I
1.47238 10.24953I 3.11527 + 8.40903I
u = 0.000285 1.159922I
a = 0.094852 0.884856I
b = 0.21406 1.79560I
5.00871 4.94387I 6.82451 + 5.88311I
u = 0.000285 + 1.159922I
a = 0.094852 + 0.884856I
b = 0.21406 + 1.79560I
5.00871 + 4.94387I 6.82451 5.88311I
u = 0.047677 0.756229I
a = 1.33053 + 0.60668I
b = 2.36212 + 0.17230I
2.25517 5.11870I 2.20140 + 6.13323I
u = 0.047677 + 0.756229I
a = 1.33053 0.60668I
b = 2.36212 0.17230I
2.25517 + 5.11870I 2.20140 6.13323I
u = 0.055511 1.062534I
a = 0.835539 + 0.334959I
b = 1.43176 + 1.34547I
3.10746 3.06338I 6.90352 + 6.63954I
u = 0.055511 + 1.062534I
a = 0.835539 0.334959I
b = 1.43176 1.34547I
3.10746 + 3.06338I 6.90352 6.63954I
u = 0.074483 0.887023I
a = 0.652703 + 0.497524I
b = 0.16006 + 2.09086I
4.11297 0.07058I 8.74341 0.53456I
u = 0.074483 + 0.887023I
a = 0.652703 0.497524I
b = 0.16006 2.09086I
4.11297 + 0.07058I 8.74341 + 0.53456I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.187919 1.179453I
a = 1.019440 + 0.000848I
b = 1.71614 + 0.56134I
1.19365 + 1.54765I 8.46781 7.31335I
u = 0.187919 + 1.179453I
a = 1.019440 0.000848I
b = 1.71614 0.56134I
1.19365 1.54765I 8.46781 + 7.31335I
u = 0.326338 0.736385I
a = 1.80513 0.54254I
b = 1.161276 0.172700I
1.27718 1.12906I 1.89401 + 8.56512I
u = 0.326338 + 0.736385I
a = 1.80513 + 0.54254I
b = 1.161276 + 0.172700I
1.27718 + 1.12906I 1.89401 8.56512I
u = 0.331512 0.359265I
a = 2.06138 0.17441I
b = 1.083545 0.188636I
1.80205 1.10971I 0.93812 3.27932I
u = 0.331512 + 0.359265I
a = 2.06138 + 0.17441I
b = 1.083545 + 0.188636I
1.80205 + 1.10971I 0.93812 + 3.27932I
u = 0.345824 1.101662I
a = 0.561890 0.724085I
b = 0.599705 1.193738I
0.62322 2.44856I 2.57464 + 7.28809I
u = 0.345824 + 1.101662I
a = 0.561890 + 0.724085I
b = 0.599705 + 1.193738I
0.62322 + 2.44856I 2.57464 7.28809I
u = 0.348886 0.562301I
a = 1.91763 + 0.75028I
b = 0.718764 0.485022I
3.26202 + 4.12377I 3.82614 3.00808I
u = 0.348886 + 0.562301I
a = 1.91763 0.75028I
b = 0.718764 + 0.485022I
3.26202 4.12377I 3.82614 + 3.00808I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.525700 0.752927I
a = 1.54462 + 1.55397I
b = 1.27059 + 1.88705I
1.74995 1.48935I 34.1539 + 39.5645I
u = 0.525700 + 0.752927I
a = 1.54462 1.55397I
b = 1.27059 1.88705I
1.74995 + 1.48935I 34.1539 39.5645I
u = 0.558579 0.339705I
a = 1.39393 + 1.53590I
b = 0.510988 0.126573I
3.25748 + 4.05422I 1.13185 3.03795I
u = 0.558579 + 0.339705I
a = 1.39393 1.53590I
b = 0.510988 + 0.126573I
3.25748 4.05422I 1.13185 + 3.03795I
u = 0.566930 0.359574I
a = 0.86644 1.30126I
b = 0.381966 0.343860I
1.32685 1.54158I 1.03113 + 4.33342I
u = 0.566930 + 0.359574I
a = 0.86644 + 1.30126I
b = 0.381966 + 0.343860I
1.32685 + 1.54158I 1.03113 4.33342I
u = 0.580548 0.957210I
a = 0.864386 1.095100I
b = 0.45989 1.49085I
1.01885 3.00871I 7.67842 5.76703I
u = 0.580548 + 0.957210I
a = 0.864386 + 1.095100I
b = 0.45989 + 1.49085I
1.01885 + 3.00871I 7.67842 + 5.76703I
u = 0.592379 0.857518I
a = 1.48158 + 1.10986I
b = 0.77672 + 1.77752I
2.76989 2.34388I 8.73657 + 1.69893I
u = 0.592379 + 0.857518I
a = 1.48158 1.10986I
b = 0.77672 1.77752I
2.76989 + 2.34388I 8.73657 1.69893I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.596735 1.047627I
a = 0.809716 + 0.781497I
b = 1.51544 + 2.39054I
1.55735 8.77630I 4.68174 + 8.29059I
u = 0.596735 + 1.047627I
a = 0.809716 0.781497I
b = 1.51544 2.39054I
1.55735 + 8.77630I 4.68174 8.29059I
u = 0.603887 1.145813I
a = 0.314663 0.682171I
b = 0.297242 1.239135I
0.76570 2.63619I 8.70822 + 0.52578I
u = 0.603887 + 1.145813I
a = 0.314663 + 0.682171I
b = 0.297242 + 1.239135I
0.76570 + 2.63619I 8.70822 0.52578I
u = 0.634876 0.844268I
a = 0.951142 0.740289I
b = 1.43828 0.46615I
5.15766 6.81146I 3.76128 + 9.14677I
u = 0.634876 + 0.844268I
a = 0.951142 + 0.740289I
b = 1.43828 + 0.46615I
5.15766 + 6.81146I 3.76128 9.14677I
u = 0.641346 0.865360I
a = 0.861053 0.657168I
b = 1.26818 2.74958I
5.09034 + 1.82821I 4.00840 1.79500I
u = 0.641346 + 0.865360I
a = 0.861053 + 0.657168I
b = 1.26818 + 2.74958I
5.09034 1.82821I 4.00840 + 1.79500I
u = 0.655266 0.957538I
a = 0.695496 + 0.346942I
b = 0.382605 + 1.343720I
0.56730 4.67706I 4.98504 + 7.99066I
u = 0.655266 + 0.957538I
a = 0.695496 0.346942I
b = 0.382605 1.343720I
0.56730 + 4.67706I 4.98504 7.99066I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.666004 0.953204I
a = 0.388918 0.151109I
b = 0.291873 + 0.079820I
0.27532 2.65301I 1.48368 0.43332I
u = 0.666004 + 0.953204I
a = 0.388918 + 0.151109I
b = 0.291873 0.079820I
0.27532 + 2.65301I 1.48368 + 0.43332I
u = 0.668968 0.720659I
a = 0.307459 0.791136I
b = 0.493035 0.906763I
0.151749 0.477282I 3.82978 1.44096I
u = 0.668968 + 0.720659I
a = 0.307459 + 0.791136I
b = 0.493035 + 0.906763I
0.151749 + 0.477282I 3.82978 + 1.44096I
u = 0.734623 1.141254I
a = 0.722524 + 0.594953I
b = 1.14467 + 1.59039I
5.26894 8.76068I 4.41884 + 7.51477I
u = 0.734623 + 1.141254I
a = 0.722524 0.594953I
b = 1.14467 1.59039I
5.26894 + 8.76068I 4.41884 7.51477I
u = 0.735857 1.101584I
a = 0.714256 0.936075I
b = 1.03733 2.31889I
4.6871 18.0471I 0.90658 + 9.95509I
u = 0.735857 + 1.101584I
a = 0.714256 + 0.936075I
b = 1.03733 + 2.31889I
4.6871 + 18.0471I 0.90658 9.95509I
u = 0.850683 0.581825I
a = 0.426900 + 0.073951I
b = 0.005625 0.457661I
1.11160 3.31196I 0.24905 + 8.80050I
u = 0.850683 + 0.581825I
a = 0.426900 0.073951I
b = 0.005625 + 0.457661I
1.11160 + 3.31196I 0.24905 8.80050I
14
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.951027 0.599721I
a = 1.021364 0.873477I
b = 0.369019 0.349339I
6.25206 + 11.87072I 2.93072 6.04856I
u = 0.951027 + 0.599721I
a = 1.021364 + 0.873477I
b = 0.369019 + 0.349339I
6.25206 11.87072I 2.93072 + 6.04856I
u = 1.005510 0.537423I
a = 0.555244 + 0.968467I
b = 0.307934 + 0.279965I
7.14357 + 2.45971I 7.03746 2.89681I
u = 1.005510 + 0.537423I
a = 0.555244 0.968467I
b = 0.307934 0.279965I
7.14357 2.45971I 7.03746 + 2.89681I
15
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
14
u
13
+ ··· 2u + 1)(u
94
+ 18u
92
+ ··· 86u + 19)
c
2
(u
14
+ 7u
13
+ ··· + 4u + 1)(u
94
+ 36u
93
+ ··· + 8108u + 361)
c
3
(u
14
2u
13
+ ··· + 2u + 1)(u
94
+ 5u
93
+ ··· + 88u + 11)
c
4
(u
14
2u
13
+ ··· + 4u + 1)(u
94
+ u
93
+ ··· + 724u + 59)
c
5
(u
14
+ u
13
+ ··· + 2u + 1)(u
94
+ 18u
92
+ ··· 86u + 19)
c
6
(u
14
6u
13
+ ··· 5u + 1)(u
94
+ u
93
+ ··· + 33u + 781)
c
7
(u
14
+ u
12
+ ··· + 4u + 1)(u
94
+ 3u
93
+ ··· 872u + 184)
c
8
(u
14
+ 2u
13
+ ··· 4u + 1)(u
94
+ u
93
+ ··· 6u + 1)
c
9
(u
14
+ 2u
13
+ ··· 4u + 1)(u
94
+ u
93
+ ··· + 724u + 59)
c
10
(u
14
u
13
+ ··· + 6u + 1)(u
94
+ 2u
93
+ ··· + 22u + 1)
c
11
(u
14
+ 2u
13
+ ··· 3u + 1)(u
94
+ 3u
93
+ ··· 519u + 19)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
14
+ 7y
13
+ ··· + 4y + 1)(y
94
+ 36y
93
+ ··· + 8108y + 361)
c
2
(y
14
+ 3y
13
+ ··· + 8y + 1)(y
94
+ 48y
93
+ ··· + 1.32356 × 10
7
y + 130321)
c
3
(y
14
+ 14y
12
+ ··· + 4y + 1)(y
94
+ 9y
93
+ ··· + 7084y + 121)
c
4
(y
14
+ 8y
13
+ ··· + 8y + 1)(y
94
+ 69y
93
+ ··· 23148y + 3481)
c
6
(y
14
+ 10y
13
+ ··· + 21y + 1)
(y
94
+ 27y
93
+ ··· + 20468921y + 609961)
c
7
(y
14
+ 2y
13
+ ··· + 8y + 1)(y
94
+ 23y
93
+ ··· + 1507232y + 33856)
c
8
(y
14
6y
13
+ ··· 2y + 1)(y
94
5y
93
+ ··· 10y + 1)
c
9
(y
14
+ 8y
13
+ ··· + 8y + 1)(y
94
+ 69y
93
+ ··· 23148y + 3481)
c
10
(y
14
+ 3y
13
+ ··· + 6y + 1)(y
94
+ 8y
93
+ ··· 18y + 1)
c
11
(y
14
+ 4y
13
+ ··· 9y + 1)(y
94
15y
93
+ ··· 72597y + 361)
17