11n
182
(K11n
182
)
1
Arc Sequences
9 7 1 10 11 3 5 3 4 7 8
Solving Sequence
5,7 8,11
1 10 4 3 6 9 2
c
7
c
11
c
10
c
4
c
3
c
6
c
9
c
1
c
2
, c
5
, c
8
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= hu
3
u
2
+ 1, u
2
+ b + u, u
2
+ a u + 1i
I
u
2
= hu
14
6u
13
+ 12u
12
6u
11
3u
10
23u
9
+ 59u
8
22u
7
43u
6
+ 45u
5
7u
4
16u
3
+ 14u
2
5u + 1,
9465u
13
+ 105704u
12
+ ··· + 142097b + 758363,
321146u
13
1972182u
12
+ ··· + 142097a 941645i
I
u
3
= hu
23
+ u
22
+ ··· + 5u 1,
383665719756u
22
403814607772u
21
+ ··· + 2663810305417a + 3383102148608,
1681985907858u
22
+ 2329472807543u
21
+ ··· + 2663810305417b + 10554558520247i
I
u
4
= hu
40
+ 3u
39
+ ··· + 25u + 29,
2.03505 × 10
58
u
39
2.48829 × 10
58
u
38
+ ··· + 1.88428 × 10
60
b + 4.52119 × 10
60
,
1.45903 × 10
61
u
39
3.01592 × 10
61
u
38
+ ··· + 1.09288 × 10
61
a 5.99270 × 10
62
i
There are 4 irreducible components with 80 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
3
u
2
+ 1, u
2
+ b + u, u
2
+ a u + 1i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
8
=
u
u
a
11
=
u
2
+ u 1
u
2
u
a
1
=
u 1
u
a
10
=
u
2
+ u 1
0
a
4
=
1
0
a
3
=
u
2
u + 1
u
2
a
6
=
u
2
2u + 2
u 1
a
9
=
u
2
+ u 1
0
a
2
=
u
2
u + 1
u
a
2
=
u
2
u + 1
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 = 0.754878
a = 2.32472
b = 1.32472
6.19175 9.27303
u = 0.877439 0.744862I
a = 0.337641 + 0.562280I
b = 0.662359 0.562280I
1.45094 + 3.77083I 4.63651 3.93596I
u = 0.877439 + 0.744862I
a = 0.337641 0.562280I
b = 0.662359 + 0.562280I
1.45094 3.77083I 4.63651 + 3.93596I
3
II. I
u
2
= hu
14
6u
13
+ · · · 5u + 1, 9465u
13
+ 105704u
12
+ · · · + 142097b +
758363, 3.21 × 10
5
u
13
1.97 × 10
6
u
12
+ · · · + 1.42 × 10
5
a 9.42 × 10
5
i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
8
=
u
u
a
11
=
2.26005u
13
+ 13.8791u
12
+ ··· 27.5620u + 6.62678
0.0666094u
13
0.743886u
12
+ ··· + 15.8374u 5.33694
a
1
=
2.39439u
13
+ 14.5567u
12
+ ··· 25.7651u + 5.80207
0.0677284u
13
1.42143u
12
+ ··· + 14.0405u 4.51223
a
10
=
2.26005u
13
+ 13.8791u
12
+ ··· 27.5620u + 6.62678
0.570723u
13
4.50220u
12
+ ··· + 19.6916u 5.65578
a
4
=
0.336939u
13
+ 3.08824u
12
+ ··· 6.82863u + 0.847337
5.90976u
13
33.9443u
12
+ ··· + 45.8070u 5.25817
a
3
=
1.99691u
13
+ 10.1599u
12
+ ··· + 1.44262u 3.05527
7.06231u
13
39.8158u
12
+ ··· + 51.4874u 5.69548
a
6
=
1.18340u
13
6.73052u
12
+ ··· + 10.9924u 3.10981
4.90166u
13
28.1312u
12
+ ··· + 39.4711u 3.82170
a
9
=
6.08505u
13
+ 34.8617u
12
+ ··· 50.4636u + 6.93151
4.37804u
13
30.3049u
12
+ ··· + 115.751u 34.2887
a
2
=
1.99691u
13
+ 10.1599u
12
+ ··· + 1.44262u 3.05527
6.53593u
13
36.6448u
12
+ ··· + 44.3765u 3.87393
a
2
=
1.99691u
13
+ 10.1599u
12
+ ··· + 1.44262u 3.05527
6.53593u
13
36.6448u
12
+ ··· + 44.3765u 3.87393
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.04271 1.08370I
a = 0.002884 0.969351I
b = 1.075051 + 0.267284I
0.20871 5.48705I 1.09915 + 7.96619I
u = 1.04271 + 1.08370I
a = 0.002884 + 0.969351I
b = 1.075051 0.267284I
0.20871 + 5.48705I 1.09915 7.96619I
u = 0.807415 0.203980I
a = 0.10958 2.23687I
b = 0.26229 + 1.50919I
7.86115 0.79658I 13.7450 5.5444I
u = 0.807415 + 0.203980I
a = 0.10958 + 2.23687I
b = 0.26229 1.50919I
7.86115 + 0.79658I 13.7450 + 5.5444I
u = 0.198097 0.363970I
a = 0.736142 + 0.733828I
b = 0.17445 2.40689I
0.0877733 6.94848
u = 0.198097 + 0.363970I
a = 0.736142 0.733828I
b = 0.17445 + 2.40689I
0.0877733 6.94848
u = 0.328860 0.493680I
a = 2.96408 2.28060I
b = 0.026964 + 1.011554I
0.20871 + 5.48705I 1.09915 7.96619I
u = 0.328860 + 0.493680I
a = 2.96408 + 2.28060I
b = 0.026964 1.011554I
0.20871 5.48705I 1.09915 + 7.96619I
u = 0.841811 0.182190I
a = 1.193665 + 0.497510I
b = 0.497274 0.152979I
7.19586 + 4.79737I 15.3799 10.7291I
u = 0.841811 + 0.182190I
a = 1.193665 0.497510I
b = 0.497274 + 0.152979I
7.19586 4.79737I 15.3799 + 10.7291I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.36446 1.14498I
a = 0.203095 0.643481I
b = 0.442580 + 1.172072I
7.19586 + 4.79737I 15.3799 10.7291I
u = 1.36446 + 1.14498I
a = 0.203095 + 0.643481I
b = 0.442580 1.172072I
7.19586 4.79737I 15.3799 + 10.7291I
u = 2.11690 0.04289I
a = 0.237160 0.132344I
b = 0.020398 + 0.369670I
7.86115 0.79658I 13.7450 5.5444I
u = 2.11690 + 0.04289I
a = 0.237160 + 0.132344I
b = 0.020398 0.369670I
7.86115 + 0.79658I 13.7450 + 5.5444I
6
III. I
u
3
=
hu
23
+u
22
+· · · +5u1, 3.84×10
11
u
22
4.04×10
11
u
21
+· · · +2.66×10
12
a+
3.38 × 10
12
, 1.68 × 10
12
u
22
+ 2.33 × 10
12
u
21
+ · · · + 2.66 × 10
12
b + 1.06 × 10
13
i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
8
=
u
u
a
11
=
0.144029u
22
+ 0.151593u
21
+ ··· 1.08601u 1.27002
0.631421u
22
0.874489u
21
+ ··· 7.69922u 3.96220
a
1
=
0.310226u
22
+ 0.0138814u
21
+ ··· 1.77614u 1.03452
0.797619u
22
0.736778u
21
+ ··· 7.00909u 4.19771
a
10
=
0.144029u
22
+ 0.151593u
21
+ ··· 1.08601u 1.27002
0.920460u
22
0.868993u
21
+ ··· 7.59301u 3.95464
a
4
=
0.912866u
22
0.998970u
21
+ ··· 8.37651u 5.16448
3.28484u
22
3.99636u
21
+ ··· 37.7495u 22.8331
a
3
=
0.616521u
22
0.640256u
21
+ ··· 5.79085u 5.47471
3.34568u
22
3.95337u
21
+ ··· 37.5399u 22.0355
a
6
=
1.00555u
22
1.06597u
21
+ ··· 9.76296u 4.89081
3.34747u
22
3.83718u
21
+ ··· 36.5637u 22.6866
a
9
=
4.35302u
22
+ 4.90315u
21
+ ··· + 46.3267u + 27.5774
18.3336u
22
+ 21.1309u
21
+ ··· + 204.984u + 122.419
a
2
=
0.616521u
22
+ 0.640256u
21
+ ··· + 5.79085u + 5.47471
3.64135u
22
+ 4.01792u
21
+ ··· + 38.0377u + 22.0593
a
2
=
0.616521u
22
+ 0.640256u
21
+ ··· + 5.79085u + 5.47471
3.64135u
22
+ 4.01792u
21
+ ··· + 38.0377u + 22.0593
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.23451 0.89988I
a = 0.199211 + 1.217360I
b = 1.41673 1.05728I
0.6169 16.3897I 0.60357 + 8.49133I
u = 1.23451 + 0.89988I
a = 0.199211 1.217360I
b = 1.41673 + 1.05728I
0.6169 + 16.3897I 0.60357 8.49133I
u = 1.08075
a = 1.86531
b = 1.44953
5.56139 4.10584
u = 0.929406 0.853194I
a = 0.299340 0.953399I
b = 1.54142 + 1.02397I
5.11296 9.53315I 2.57549 + 7.49079I
u = 0.929406 + 0.853194I
a = 0.299340 + 0.953399I
b = 1.54142 1.02397I
5.11296 + 9.53315I 2.57549 7.49079I
u = 0.734602
a = 1.14183
b = 0.741140
3.46093 0.434274
u = 0.728418 0.872189I
a = 0.641628 0.187788I
b = 1.106466 0.450129I
3.37848 + 2.40469I 1.77991 2.36658I
u = 0.728418 + 0.872189I
a = 0.641628 + 0.187788I
b = 1.106466 + 0.450129I
3.37848 2.40469I 1.77991 + 2.36658I
u = 0.555624 0.905584I
a = 0.49767 1.86139I
b = 0.838883 0.107334I
1.86354 5.26744I 5.28915 + 6.74191I
u = 0.555624 + 0.905584I
a = 0.49767 + 1.86139I
b = 0.838883 + 0.107334I
1.86354 + 5.26744I 5.28915 6.74191I
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.501300 0.715167I
a = 0.53363 + 1.67929I
b = 1.007000 + 0.109890I
6.01384 1.36939I 7.91646 + 4.62007I
u = 0.501300 + 0.715167I
a = 0.53363 1.67929I
b = 1.007000 0.109890I
6.01384 + 1.36939I 7.91646 4.62007I
u = 0.150085
a = 1.44080
b = 5.51897
0.0107219 320.580
u = 0.188306 0.473727I
a = 0.561105 + 0.795614I
b = 0.130616 0.595336I
0.294559 + 1.131281I 2.80927 6.63257I
u = 0.188306 + 0.473727I
a = 0.561105 0.795614I
b = 0.130616 + 0.595336I
0.294559 1.131281I 2.80927 + 6.63257I
u = 0.704512 0.984779I
a = 0.628487 0.870126I
b = 0.434960 + 0.791403I
2.32908 + 5.49763I 4.79992 7.26042I
u = 0.704512 + 0.984779I
a = 0.628487 + 0.870126I
b = 0.434960 0.791403I
2.32908 5.49763I 4.79992 + 7.26042I
u = 1.000303 0.806208I
a = 0.264755 0.418974I
b = 1.004092 + 0.312053I
0.46558 + 3.81570I 4.70967 3.05268I
u = 1.000303 + 0.806208I
a = 0.264755 + 0.418974I
b = 1.004092 0.312053I
0.46558 3.81570I 4.70967 + 3.05268I
u = 1.049548 0.569449I
a = 0.513573 0.507114I
b = 0.293138 0.162200I
5.59031 + 2.93906I 3.96701 3.47635I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.049548 + 0.569449I
a = 0.513573 + 0.507114I
b = 0.293138 + 0.162200I
5.59031 2.93906I 3.96701 + 3.47635I
u = 1.33922 0.68743I
a = 0.582622 + 0.923168I
b = 1.28811 0.58522I
3.36043 + 7.89416I 1.16388 6.61187I
u = 1.33922 + 0.68743I
a = 0.582622 0.923168I
b = 1.28811 + 0.58522I
3.36043 7.89416I 1.16388 + 6.61187I
10
IV. I
u
4
=
hu
40
+3u
39
+· · ·+25u+29, 2.04×10
58
u
39
2.49×10
58
u
38
+· · ·+1.88×10
60
b+
4.52× 10
60
, 1.46× 10
61
u
39
3.02 × 10
61
u
38
+· · · +1.09 × 10
61
a 5.99 × 10
62
i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
8
=
u
u
a
11
=
1.33503u
39
+ 2.75960u
38
+ ··· + 0.413666u + 54.8339
0.0108002u
39
+ 0.0132055u
38
+ ··· 1.11313u 2.39943
a
1
=
0.374199u
39
+ 0.688438u
38
+ ··· + 7.82546u + 18.1578
0.971632u
39
+ 2.08436u
38
+ ··· 8.52492u + 34.2767
a
10
=
1.33503u
39
+ 2.75960u
38
+ ··· + 0.413666u + 54.8339
0.910032u
39
+ 1.97988u
38
+ ··· 8.69159u + 33.7200
a
4
=
0.152095u
39
0.219259u
38
+ ··· + 1.01612u 17.0248
0.341579u
39
+ 0.789913u
38
+ ··· 4.55561u + 8.59539
a
3
=
0.546014u
39
1.19788u
38
+ ··· + 1.34233u 22.2151
0.668479u
39
1.57360u
38
+ ··· + 20.5062u 30.0110
a
6
=
0.494965u
39
+ 1.19837u
38
+ ··· 20.9731u + 19.1383
0.295920u
39
+ 0.574218u
38
+ ··· + 4.15014u + 7.15990
a
9
=
0.790885u
39
1.77259u
38
+ ··· + 16.8230u 26.2982
1.50570u
39
3.31129u
38
+ ··· + 17.1505u 56.3917
a
2
=
0.546014u
39
+ 1.19788u
38
+ ··· 1.34233u + 22.2151
0.992044u
39
+ 2.31414u
38
+ ··· 25.3365u + 42.7757
a
2
=
0.546014u
39
+ 1.19788u
38
+ ··· 1.34233u + 22.2151
0.992044u
39
+ 2.31414u
38
+ ··· 25.3365u + 42.7757
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.29816 1.03823I
a = 0.132816 0.844585I
b = 1.297611 + 0.357812I
0.39627 4.88151I 5.90664 + 1.87878I
u = 1.29816 + 1.03823I
a = 0.132816 + 0.844585I
b = 1.297611 0.357812I
0.39627 + 4.88151I 5.90664 1.87878I
u = 1.28977
a = 0.128344
b = 1.68398
2.04716 7.60148
u = 1.23114 0.76536I
a = 0.476691 0.906587I
b = 0.863473 + 0.702581I
1.76779 6.66107I 3.08867 + 6.78923I
u = 1.23114 + 0.76536I
a = 0.476691 + 0.906587I
b = 0.863473 0.702581I
1.76779 + 6.66107I 3.08867 6.78923I
u = 1.009225 0.784248I
a = 0.08237 + 1.47371I
b = 1.18197 1.01982I
2.54638 8.54122I 0.95116 + 7.30579I
u = 1.009225 + 0.784248I
a = 0.08237 1.47371I
b = 1.18197 + 1.01982I
2.54638 + 8.54122I 0.95116 7.30579I
u = 0.937408 0.876311I
a = 0.815021 + 0.665202I
b = 0.807207 + 0.324120I
5.13837 + 3.10653I 2.77090 3.27458I
u = 0.937408 + 0.876311I
a = 0.815021 0.665202I
b = 0.807207 0.324120I
5.13837 3.10653I 2.77090 + 3.27458I
u = 0.843881 0.602804I
a = 0.449541 1.099597I
b = 1.65148 + 0.86732I
5.13837 3.10653I 2.77090 + 3.27458I
12
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.843881 + 0.602804I
a = 0.449541 + 1.099597I
b = 1.65148 0.86732I
5.13837 + 3.10653I 2.77090 3.27458I
u = 0.804574 1.002742I
a = 0.048065 + 0.330310I
b = 1.239703 0.163443I
0.78911 3.05252I 1.27188 + 4.35560I
u = 0.804574 + 1.002742I
a = 0.048065 0.330310I
b = 1.239703 + 0.163443I
0.78911 + 3.05252I 1.27188 4.35560I
u = 0.795151
a = 2.86303
b = 0.339716
2.04716 7.60148
u = 0.778748 0.245271I
a = 0.30833 + 2.34067I
b = 0.27350 1.63668I
7.62987 1.01721I 5.24970 + 11.81252I
u = 0.778748 + 0.245271I
a = 0.30833 2.34067I
b = 0.27350 + 1.63668I
7.62987 + 1.01721I 5.24970 11.81252I
u = 0.733508 0.115684I
a = 1.44067 + 0.39693I
b = 0.664252 0.160838I
6.94055 4.65557I 9.06224 2.69200I
u = 0.733508 + 0.115684I
a = 1.44067 0.39693I
b = 0.664252 + 0.160838I
6.94055 + 4.65557I 9.06224 + 2.69200I
u = 0.65753 1.37826I
a = 0.427813 0.242372I
b = 0.995696 0.575456I
2.54638 + 8.54122I 0.95116 7.30579I
u = 0.65753 + 1.37826I
a = 0.427813 + 0.242372I
b = 0.995696 + 0.575456I
2.54638 8.54122I 0.95116 + 7.30579I
13
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.424536 0.808576I
a = 0.315037 + 0.509796I
b = 0.784427 0.777948I
0.703344 + 0.559674I 1.56320 4.51761I
u = 0.424536 + 0.808576I
a = 0.315037 0.509796I
b = 0.784427 + 0.777948I
0.703344 0.559674I 1.56320 + 4.51761I
u = 0.139241 0.695732I
a = 0.214033 0.868341I
b = 0.925655 + 0.211889I
0.28152 2.20542I 2.09891 + 2.63579I
u = 0.139241 + 0.695732I
a = 0.214033 + 0.868341I
b = 0.925655 0.211889I
0.28152 + 2.20542I 2.09891 2.63579I
u = 0.570217 0.118702I
a = 0.87440 + 4.53720I
b = 0.173500 1.090053I
0.39627 4.88151I 5.90664 + 1.87878I
u = 0.570217 + 0.118702I
a = 0.87440 4.53720I
b = 0.173500 + 1.090053I
0.39627 + 4.88151I 5.90664 1.87878I
u = 0.603347 0.367132I
a = 0.528457 + 1.092615I
b = 0.22072 1.72024I
0.703344 + 0.559674I 1.56320 4.51761I
u = 0.603347 + 0.367132I
a = 0.528457 1.092615I
b = 0.22072 + 1.72024I
0.703344 0.559674I 1.56320 + 4.51761I
u = 0.724639 0.605856I
a = 1.12874 + 1.60910I
b = 0.544982 1.041209I
0.78911 + 3.05252I 1.27188 4.35560I
u = 0.724639 + 0.605856I
a = 1.12874 1.60910I
b = 0.544982 + 1.041209I
0.78911 3.05252I 1.27188 + 4.35560I
14
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.773777 0.786429I
a = 0.118397 + 1.066554I
b = 0.642415 0.696940I
0.28152 + 2.20542I 2.09891 2.63579I
u = 0.773777 + 0.786429I
a = 0.118397 1.066554I
b = 0.642415 + 0.696940I
0.28152 2.20542I 2.09891 + 2.63579I
u = 0.893885 0.284008I
a = 0.19736 + 1.43941I
b = 0.69923 1.89210I
1.76779 + 6.66107I 3.08867 6.78923I
u = 0.893885 + 0.284008I
a = 0.19736 1.43941I
b = 0.69923 + 1.89210I
1.76779 6.66107I 3.08867 + 6.78923I
u = 1.048818 0.339914I
a = 0.036709 1.123555I
b = 0.097868 + 1.079940I
4.78547 5.34389
u = 1.048818 + 0.339914I
a = 0.036709 + 1.123555I
b = 0.097868 1.079940I
4.78547 5.34389
u = 1.31598 1.12343I
a = 0.248036 0.701090I
b = 0.469023 + 1.259785I
6.94055 + 4.65557I 9.06224 + 2.69200I
u = 1.31598 + 1.12343I
a = 0.248036 + 0.701090I
b = 0.469023 1.259785I
6.94055 4.65557I 9.06224 2.69200I
u = 2.19127 0.09123I
a = 0.280856 0.026788I
b = 0.357723 0.224098I
7.62987 1.01721I 5.24970 + 11.81252I
u = 2.19127 + 0.09123I
a = 0.280856 + 0.026788I
b = 0.357723 + 0.224098I
7.62987 + 1.01721I 5.24970 11.81252I
15
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
10
(u
3
2u
2
+ u 1)(u
14
+ 3u
13
+ ··· + 8u + 4)(u
23
6u
21
+ ··· 40u 4)
(u
40
+ 9u
38
+ ··· + 244u 44)
c
2
(u
3
+ 2u
2
+ u + 1)(u
7
2u
6
+ 2u
5
3u
4
+ 3u
2
u + 1)
2
(1 + 8u + 52u
2
+ 114u
3
+ 19u
4
199u
5
268u
6
66u
7
+ 293u
8
+ 356u
9
18u
10
248u
11
114u
12
+ 31u
13
+ 55u
14
+ 33u
15
u
16
15u
17
5u
18
+ 2u
19
+ u
20
)
2
(u
23
3u
22
+ ··· + 47u 8)
c
3
, c
7
(u
3
+ u
2
1)(u
14
+ 6u
13
+ ··· + 5u + 1)(u
23
+ u
22
+ ··· + 5u 1)
(u
40
+ 3u
39
+ ··· + 25u + 29)
c
4
, c
9
u
3
(u
14
3u
12
17u
10
+ 114u
8
277u
6
+ 352u
4
236u
2
+ 67)
(11 + 25u + 18u
2
80u
3
+ 10u
4
+ 99u
5
28u
6
70u
7
13u
8
+ 57u
9
+ 50u
10
68u
11
29u
12
+ 60u
13
5u
14
32u
15
+ 13u
16
+ 9u
17
6u
18
u
19
+ u
20
)
2
(u
23
+ 9u
22
+ ··· 40u 16)
c
5
, c
8
(u
3
u 1)(u
14
+ 9u
12
+ ··· 3u + 1)(u
23
+ 6u
22
+ ··· + 22u + 5)
(u
40
u
39
+ ··· + 47u 169)
c
6
(u
3
2u
2
+ u 1)(u
7
+ 2u
6
+ 2u
5
+ 3u
4
3u
2
u 1)
2
(1 + 8u + 52u
2
+ 114u
3
+ 19u
4
199u
5
268u
6
66u
7
+ 293u
8
+ 356u
9
18u
10
248u
11
114u
12
+ 31u
13
+ 55u
14
+ 33u
15
u
16
15u
17
5u
18
+ 2u
19
+ u
20
)
2
(u
23
3u
22
+ ··· + 47u 8)
c
11
(u
3
+ u
2
1)(u
7
2u
6
+ 3u
5
3u
4
5u
3
+ 2u
2
+ 5u + 3)
2
(1 + 7u + 7u
2
+ 26u
3
+ 46u
4
+ 73u
5
+ 16u
6
+ 222u
7
109u
8
+ 227u
9
235u
10
+ 160u
11
83u
12
+ 54u
13
50u
14
2u
15
+ 2u
16
+ 2u
18
u
19
+ u
20
)
2
(u
23
+ 4u
22
+ ··· 7u 34)
16
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
10
(y
3
2y
2
3y 1)(y
14
+ 15y
13
+ ··· + 96y + 16)
(y
23
12y
22
+ ··· + 448y 16)(y
40
+ 18y
39
+ ··· 94208y + 1936)
c
2
, c
6
(y
3
2y
2
3y 1)(y
7
8y
5
+ y
4
+ 18y
3
3y
2
5y 1)
2
(1 + 40y + 918y
2
8372y
3
+ 1.95 × 10
4
y
4
9997y
5
2.26 × 10
4
y
6
+ 2.39 × 10
4
y
7
+ 3.76 × 10
4
y
8
1.02 × 10
5
y
9
+ 1.01 × 10
5
y
10
4.89 × 10
4
y
11
+ 3844y
12
+ 1.04 × 10
4
y
13
6891y
14
+ 1827y
15
+ 89y
16
237y
17
+ 83y
18
14y
19
+ y
20
)
2
(y
23
13y
22
+ ··· + 1233y 64)
c
3
, c
7
(y
3
y
2
+ 2y 1)(y
14
12y
13
+ ··· + 3y + 1)
(y
23
5y
22
+ ··· + 41y 1)(y
40
19y
39
+ ··· 12747y + 841)
c
4
, c
9
y
3
(y
7
3y
6
17y
5
+ 114y
4
277y
3
+ 352y
2
236y + 67)
2
(121 1021y + 4104y
2
1.04 × 10
4
y
3
+ 1.87 × 10
4
y
4
2.60 × 10
4
y
5
+ 2.93 × 10
4
y
6
2.93 × 10
4
y
7
+ 2.90 × 10
4
y
8
2.94 × 10
4
y
9
+ 2.75 × 10
4
y
10
2.15 × 10
4
y
11
+ 1.36 × 10
4
y
12
7428y
13
+ 3823y
14
1922y
15
+ 867y
16
311y
17
+ 80y
18
13y
19
+ y
20
)
2
(y
23
43y
22
+ ··· 1088y 256)
c
5
, c
8
(y
3
2y
2
+ y 1)(y
14
+ 18y
13
+ ··· + 11y + 1)
(y
23
46y
22
+ ··· + 344y 25)(y
40
+ 7y
39
+ ··· 530503y + 28561)
c
11
(y
3
y
2
+ 2y 1)(9 + 13y 36y
2
+ 79y
3
21y
4
13y
5
+ 2y
6
+ y
7
)
2
(1 35y 223y
2
1022y
3
4782y
4
2.06 × 10
4
y
5
5.97 × 10
4
y
6
1.18 × 10
5
y
7
1.31 × 10
5
y
8
8.63 × 10
4
y
9
2.44 × 10
4
y
10
+ 996y
11
+ 1.39 × 10
4
y
12
+ 5124y
13
+ 1680y
14
686y
15
254y
16
96y
17
+ 8y
18
+ 3y
19
+ y
20
)
2
(y
23
+ 6y
22
+ ··· 12055y 1156)
17