11a
312
(K11a
312
)
1
Arc Sequences
7 9 1 11 10 2 4 3 5 6 8
Solving Sequence
1,7 2,4
8 3 9 6 11 5 10
c
1
c
7
c
3
c
8
c
6
c
11
c
4
c
10
c
2
, c
5
, c
9
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= hb
48
+ b
47
+ ··· + 160b + 293, 3.34435 × 10
80
u 8.50411 × 10
78
b
47
+ ··· 9.94682 × 10
80
b 4.86540 × 10
80
,
1.21498 × 10
87
b
47
+ 1.80854 × 10
89
b
46
+ ··· + 4.76053 × 10
90
a + 4.53633 × 10
91
i
I
u
2
= hu
12
3u
11
+ 3u
10
u
9
+ 2u
8
4u
7
+ 3u
6
2u
5
+ 2u
4
+ u
3
2u
2
+ 1,
u
9
+ 2u
8
u
7
+ u
6
3u
5
+ 2u
4
u
3
+ 2u
2
+ b u 1,
u
10
+ 2u
9
u
8
+ u
7
3u
6
+ 2u
5
2u
4
+ 3u
3
u
2
+ a u 1i
I
u
3
= hu
23
+ 24u
22
+ ··· + 3840u + 256, 7u
22
+ 478u
21
+ ··· + 256a 44288,
385u
22
+ 9312u
21
+ ··· + 128b + 81792i
There are 3 irreducible components with 83 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
=
hb
48
+b
47
+· · · +160b + 293, 3.34× 10
80
u 8.50 × 10
78
b
47
+· · · 9.95 × 10
80
b
4.87 × 10
80
, 1.21 × 10
87
b
47
+ 1.81 × 10
89
b
46
+ · · · + 4.76 × 10
90
a + 4.54 × 10
91
i
(i) Arc colorings
a
1
=
1
0
a
7
=
0.000255220b
47
0.0379903b
46
+ ··· 2.84235b 9.52904
b
a
2
=
0.0377351b
47
+ 0.0418803b
46
+ ··· + 9.48821b + 0.925220
b
2
a
4
=
0
0.0254283b
47
+ 0.0239377b
46
+ ··· + 2.97422b + 1.45481
a
8
=
0.000255220b
47
0.0379903b
46
+ ··· 2.84235b 9.52904
0.000364134b
47
+ 0.00613682b
46
+ ··· 1.05074b + 1.19871
a
3
=
0.0254283b
47
+ 0.0239377b
46
+ ··· + 2.97422b + 1.45481
0.0254283b
47
+ 0.0239377b
46
+ ··· + 2.97422b + 1.45481
a
9
=
0.0210767b
47
0.0454997b
46
+ ··· 4.93964b 5.07804
0.0204573b
47
0.00137254b
46
+ ··· 3.14803b + 5.64971
a
6
=
0.00440036b
47
+ 0.00369281b
46
+ ··· + 2.27005b + 1.52734
b
3
+ b
a
11
=
0.00325336b
47
0.0223904b
46
+ ··· 5.72379b 2.19641
0.00425863b
47
0.0449491b
46
+ ··· 6.99224b 9.82668
a
5
=
0.00298386b
47
0.0152709b
46
+ ··· 4.37555b 1.16930
0.0266581b
47
+ 0.0179830b
46
+ ··· + 2.88126b 1.53338
a
10
=
0.00493869b
47
0.0539919b
46
+ ··· 6.15638b 8.70294
0.00662005b
47
0.0400467b
46
+ ··· 8.53585b 11.4767
a
10
=
0.00493869b
47
0.0539919b
46
+ ··· 6.15638b 8.70294
0.00662005b
47
0.0400467b
46
+ ··· 8.53585b 11.4767
(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 = 0.877439 0.744862I
a = 0.965420 + 0.090581I
b = 1.407324 0.123988I
0.46900 + 9.27166I 4.93820 8.27362I
u = 0.877439 + 0.744862I
a = 0.965420 0.090581I
b = 1.407324 + 0.123988I
0.46900 9.27166I 4.93820 + 8.27362I
u = 0.877439 0.744862I
a = 0.970106 0.140001I
b = 1.167429 0.563919I
0.87002 + 1.69689I 2.92498 2.46866I
u = 0.877439 + 0.744862I
a = 0.970106 + 0.140001I
b = 1.167429 + 0.563919I
0.87002 1.69689I 2.92498 + 2.46866I
u = 0.754878
a = 1.190113 + 0.035905I
b = 0.82210 1.57135I
3.66858 + 6.44354I 1.59106 5.29417I
u = 0.754878
a = 1.190113 0.035905I
b = 0.82210 + 1.57135I
3.66858 6.44354I 1.59106 + 5.29417I
u = 0.877439 0.744862I
a = 1.104040 + 0.345072I
b = 0.554508 1.009701I
4.59206 + 2.82812I 9.37379 2.97945I
u = 0.877439 + 0.744862I
a = 1.104040 0.345072I
b = 0.554508 + 1.009701I
4.59206 2.82812I 9.37379 + 2.97945I
u = 0.877439 0.744862I
a = 0.655169 0.222089I
b = 0.512781 0.176265I
1.06564 + 2.82812I 7.40422 2.97945I
u = 0.877439 + 0.744862I
a = 0.655169 + 0.222089I
b = 0.512781 + 0.176265I
1.06564 2.82812I 7.40422 + 2.97945I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.877439 0.744862I
a = 0.159590 + 0.864045I
b = 0.465784 0.043673I
4.07009 + 0.24963I 0.213168 + 0.588510I
u = 0.877439 + 0.744862I
a = 0.159590 0.864045I
b = 0.465784 + 0.043673I
4.07009 0.24963I 0.213168 0.588510I
u = 0.754878
a = 0.668981 + 0.098424I
b = 0.44089 1.82899I
5.00760 1.13123I 3.60429 + 0.51079I
u = 0.754878
a = 0.668981 0.098424I
b = 0.44089 + 1.82899I
5.00760 + 1.13123I 3.60429 0.51079I
u = 0.877439 0.744862I
a = 1.54126 0.20865I
b = 0.240367 1.260872I
4.07009 + 5.40662I 0.21317 6.54740I
u = 0.877439 + 0.744862I
a = 1.54126 + 0.20865I
b = 0.240367 + 1.260872I
4.07009 5.40662I 0.21317 + 6.54740I
u = 0.877439 0.744862I
a = 0.499665 0.348447I
b = 0.220687 1.217463I
4.07009 + 0.24963I 0.213168 + 0.588510I
u = 0.877439 + 0.744862I
a = 0.499665 + 0.348447I
b = 0.220687 + 1.217463I
4.07009 0.24963I 0.213168 0.588510I
u = 0.754878
a = 1.63121 + 2.14161I
b = 0.172710 1.289021I
8.20767 + 2.57849I 6.74243 3.56796I
u = 0.754878
a = 1.63121 2.14161I
b = 0.172710 + 1.289021I
8.20767 2.57849I 6.74243 + 3.56796I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.754878
a = 0.928965 + 1.049034I
b = 0.171893 1.389675I
5.20322 0.874953
u = 0.754878
a = 0.928965 1.049034I
b = 0.171893 + 1.389675I
5.20322 0.874953
u = 0.877439 + 0.744862I
a = 0.319425 0.406274I
b = 0.003311 1.250182I
0.46900 + 3.61542I 4.93820 2.31472I
u = 0.877439 0.744862I
a = 0.319425 + 0.406274I
b = 0.003311 + 1.250182I
0.46900 3.61542I 4.93820 + 2.31472I
u = 0.877439 + 0.744862I
a = 1.41167 0.43019I
b = 0.089556 1.152971I
0.87002 1.69689I 2.92498 + 2.46866I
u = 0.877439 0.744862I
a = 1.41167 + 0.43019I
b = 0.089556 + 1.152971I
0.87002 + 1.69689I 2.92498 2.46866I
u = 0.754878
a = 1.08906 + 2.34860I
b = 0.11559 1.41262I
5.00760 + 1.13123I 3.60429 0.51079I
u = 0.754878
a = 1.08906 2.34860I
b = 0.11559 + 1.41262I
5.00760 1.13123I 3.60429 + 0.51079I
u = 0.754878
a = 1.98744 + 2.05449I
b = 0.234132 1.197833I
3.66858 6.44354I 1.59106 + 5.29417I
u = 0.754878
a = 1.98744 2.05449I
b = 0.234132 + 1.197833I
3.66858 + 6.44354I 1.59106 5.29417I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.754878
a = 1.69097 + 0.76269I
b = 0.312893 1.010356I
0.454474 2.84453
u = 0.754878
a = 1.69097 0.76269I
b = 0.312893 + 1.010356I
0.454474 2.84453
u = 0.877439 + 0.744862I
a = 1.64206 0.07485I
b = 0.328612 1.331728I
0.46900 9.27166I 4.93820 + 8.27362I
u = 0.877439 0.744862I
a = 1.64206 + 0.07485I
b = 0.328612 + 1.331728I
0.46900 + 9.27166I 4.93820 8.27362I
u = 0.877439 0.744862I
a = 0.540284 0.867399I
b = 0.347952 0.310629I
0.87002 + 3.95936I 2.92498 3.49024I
u = 0.877439 + 0.744862I
a = 0.540284 + 0.867399I
b = 0.347952 + 0.310629I
0.87002 3.95936I 2.92498 + 3.49024I
u = 0.877439 + 0.744862I
a = 0.980831 0.111936I
b = 0.383023 0.964868I
1.06564 2.82812I 7.40422 + 2.97945I
u = 0.877439 0.744862I
a = 0.980831 + 0.111936I
b = 0.383023 + 0.964868I
1.06564 + 2.82812I 7.40422 2.97945I
u = 0.877439 + 0.744862I
a = 0.715030 0.368754I
b = 0.484357 1.213986I
0.87002 3.95936I 2.92498 + 3.49024I
u = 0.877439 0.744862I
a = 0.715030 + 0.368754I
b = 0.484357 + 1.213986I
0.87002 + 3.95936I 2.92498 3.49024I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.117866 + 0.948484I
b = 0.631559 0.239514I
0.46900 + 3.61542I 4.93820 2.31472I
u = 0.877439 0.744862I
a = 0.117866 0.948484I
b = 0.631559 + 0.239514I
0.46900 3.61542I 4.93820 + 2.31472I
u = 0.754878
a = 1.002573 + 0.090934I
b = 0.66006 1.66847I
8.20767 2.57849I 6.74243 + 3.56796I
u = 0.754878
a = 1.002573 0.090934I
b = 0.66006 + 1.66847I
8.20767 + 2.57849I 6.74243 3.56796I
u = 0.877439 0.744862I
a = 0.511246 0.144564I
b = 0.790704 0.425774I
4.59206 + 2.82812I 9.37379 2.97945I
u = 0.877439 + 0.744862I
a = 0.511246 + 0.144564I
b = 0.790704 + 0.425774I
4.59206 2.82812I 9.37379 + 2.97945I
u = 0.877439 + 0.744862I
a = 0.958026 0.005356I
b = 1.294726 0.286176I
4.07009 5.40662I 0.21317 + 6.54740I
u = 0.877439 0.744862I
a = 0.958026 + 0.005356I
b = 1.294726 + 0.286176I
4.07009 + 5.40662I 0.21317 6.54740I
7
II.
I
u
2
= hu
12
3u
11
+· · ·2u
2
+1, u
9
+2u
8
+· · ·+b1, u
10
+2u
9
+· · ·+a1i
(i) Arc colorings
a
1
=
1
0
a
7
=
u
10
2u
9
+ u
8
u
7
+ 3u
6
2u
5
+ 2u
4
3u
3
+ u
2
+ u + 1
u
9
2u
8
+ u
7
u
6
+ 3u
5
2u
4
+ u
3
2u
2
+ u + 1
a
2
=
u
10
3u
9
+ 3u
8
u
7
+ 2u
6
4u
5
+ 3u
4
2u
3
+ 2u
2
+ u 1
u
11
3u
10
+ 3u
9
u
8
+ 2u
7
4u
6
+ 3u
5
2u
4
+ 2u
3
+ u
2
2u + 1
a
4
=
0
u
a
8
=
u
10
2u
9
+ u
8
u
7
+ 3u
6
2u
5
+ 2u
4
3u
3
+ u
2
+ u + 1
u
11
2u
10
+ u
9
u
8
+ 3u
7
2u
6
+ 2u
5
3u
4
+ u
3
+ u
2
+ u
a
3
=
u
u
a
9
=
u
4
u
3
+ 1
u
11
3u
10
+ 3u
9
2u
8
+ 4u
7
5u
6
+ 4u
5
4u
4
+ 3u
3
a
6
=
u
11
+ 3u
10
3u
9
+ u
8
2u
7
+ 4u
6
3u
5
+ 2u
4
u
3
2u
2
+ 2u
u
11
+ 3u
10
3u
9
+ 2u
8
4u
7
+ 5u
6
4u
5
+ 5u
4
4u
3
+ 1
a
11
=
u
9
+ 2u
8
u
7
2u
5
+ 2u
4
u
3
+ u
2
u 1
u
10
+ 2u
9
u
8
2u
6
+ 2u
5
u
4
+ u
3
u
2
2u
a
5
=
u
11
2u
10
+ u
9
+ u
7
u
6
+ u
5
u
4
u
3
+ 2u
2
2u
11
4u
10
+ 2u
9
u
8
+ 5u
7
4u
6
+ 2u
5
4u
4
+ 2u
3
+ 3u
2
+ u 1
a
10
=
u
5
+ u
4
2u + 1
u
11
+ u
10
+ 2u
9
3u
8
2u
6
+ 4u
5
2u
4
+ 3u
3
6u
2
+ 1
a
10
=
u
5
+ u
4
2u + 1
u
11
+ u
10
+ 2u
9
3u
8
2u
6
+ 4u
5
2u
4
+ 3u
3
6u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.794800 0.771002I
a = 0.600212 0.129579I
b = 0.240699 + 1.306194I
6.79522 + 1.91915I 0.40771 1.45870I
u = 0.794800 + 0.771002I
a = 0.600212 + 0.129579I
b = 0.240699 1.306194I
6.79522 1.91915I 0.40771 + 1.45870I
u = 0.585052 0.215239I
a = 0.90210 + 1.32919I
b = 0.17391 1.59240I
4.12723 1.52744I 6.19652 + 4.95399I
u = 0.585052 + 0.215239I
a = 0.90210 1.32919I
b = 0.17391 + 1.59240I
4.12723 + 1.52744I 6.19652 4.95399I
u = 0.104192 0.971564I
a = 0.471297 0.711794I
b = 0.445009 1.143310I
1.99720 + 6.23322I 3.71112 3.63849I
u = 0.104192 + 0.971564I
a = 0.471297 + 0.711794I
b = 0.445009 + 1.143310I
1.99720 6.23322I 3.71112 + 3.63849I
u = 0.756574 0.540849I
a = 1.35649 + 0.50596I
b = 0.506197 + 0.617660I
1.54867 + 1.75409I 7.03852 3.77129I
u = 0.756574 + 0.540849I
a = 1.35649 0.50596I
b = 0.506197 0.617660I
1.54867 1.75409I 7.03852 + 3.77129I
u = 0.985889 0.677032I
a = 0.921548 0.118288I
b = 0.357408 0.662175I
2.01027 + 3.15177I 2.73217 5.71624I
u = 0.985889 + 0.677032I
a = 0.921548 + 0.118288I
b = 0.357408 + 0.662175I
2.01027 3.15177I 2.73217 + 5.71624I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.241581 0.484929I
a = 0.791873 0.390324I
b = 0.229430 + 0.594825I
3.51165 + 5.19940I 5.87830 4.31149I
u = 1.241581 + 0.484929I
a = 0.791873 + 0.390324I
b = 0.229430 0.594825I
3.51165 5.19940I 5.87830 + 4.31149I
10
III. I
u
3
= hu
23
+ 24u
22
+ · · · + 3840u + 256, 7u
22
+ 478u
21
+ · · · + 256a
44288, 385u
22
+ 9312u
21
+ · · · + 128b + 81792i
(i) Arc colorings
a
1
=
1
0
a
7
=
7
256
u
22
239
128
u
21
+ ··· +
2195
2
u + 173
385
128
u
22
291
4
u
21
+ ··· 9751u 639
a
2
=
0.0625000u
22
1.43750u
21
+ ··· 119.500u 7.50000
1
16
u
22
11
8
u
21
+ ··· 112u
2
15
2
u
a
4
=
0
u
a
8
=
7
256
u
22
239
128
u
21
+ ··· +
2195
2
u + 173
323
128
u
22
+
1761
32
u
21
+ ··· 68u + 7
a
3
=
u
u
a
9
=
0.535156u
22
6.14844u
21
+ ··· + 12008.5u + 943
251
128
u
22
+
203
4
u
21
+ ··· + 10843u + 777
a
6
=
6.53906u
22
146.352u
21
+ ··· 6763u 352.500
845
128
u
22
9107
64
u
21
+ ··· +
755
2
u + 122
a
11
=
u
22
369
16
u
21
+ ··· 3695u
527
2
15
16
u
22
173
8
u
21
+ ···
7151
2
u 256
a
5
=
5
2
u
22
233
4
u
21
+ ···
50255
4
u 920
21
8
u
22
971
16
u
21
+ ··· 12023u 880
a
10
=
187
32
u
22
+
1083
8
u
21
+ ··· +
45649
2
u + 1641
17
4
u
22
+
1519
16
u
21
+ ··· + 6584u + 440
a
10
=
187
32
u
22
+
1083
8
u
21
+ ··· +
45649
2
u + 1641
17
4
u
22
+
1519
16
u
21
+ ··· + 6584u + 440
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.81045 1.25979I
a = 0.384884 + 0.000406I
b = 0.044762 + 1.270849I
5.82775 3.98753I 2.21274 + 8.17133I
u = 1.81045 + 1.25979I
a = 0.384884 0.000406I
b = 0.044762 1.270849I
5.82775 + 3.98753I 2.21274 8.17133I
u = 1.61732 0.72115I
a = 0.598438 + 0.349505I
b = 0.276976 1.131584I
2.45199 6.58203I 4.53835 + 6.99896I
u = 1.61732 + 0.72115I
a = 0.598438 0.349505I
b = 0.276976 + 1.131584I
2.45199 + 6.58203I 4.53835 6.99896I
u = 1.54739 1.95109I
a = 0.180148 0.166472I
b = 0.147192 1.228998I
7.64064 + 1.90172I 11.16155 1.95097I
u = 1.54739 + 1.95109I
a = 0.180148 + 0.166472I
b = 0.147192 + 1.228998I
7.64064 1.90172I 11.16155 + 1.95097I
u = 1.38910 0.96754I
a = 0.850202 0.022291I
b = 0.37473 + 1.45394I
7.16797 6.55570I 1.22391 + 3.26324I
u = 1.38910 + 0.96754I
a = 0.850202 + 0.022291I
b = 0.37473 1.45394I
7.16797 + 6.55570I 1.22391 3.26324I
u = 1.32811 0.93882I
a = 0.969920 + 0.035356I
b = 0.48719 1.49237I
9.7130 11.5082I 0.75618 + 6.89858I
u = 1.32811 + 0.93882I
a = 0.969920 0.035356I
b = 0.48719 + 1.49237I
9.7130 + 11.5082I 0.75618 6.89858I
12
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.29755 0.91346I
a = 1.043014 0.072514I
b = 0.57325 + 1.48723I
4.6506 16.0409I 3.32343 + 8.47375I
u = 1.29755 + 0.91346I
a = 1.043014 + 0.072514I
b = 0.57325 1.48723I
4.6506 + 16.0409I 3.32343 8.47375I
u = 0.85316 1.96961I
a = 0.019134 + 0.283785I
b = 0.318171 + 1.163071I
2.31364 + 7.21005I 0.81443 11.11700I
u = 0.85316 + 1.96961I
a = 0.019134 0.283785I
b = 0.318171 1.163071I
2.31364 7.21005I 0.81443 + 11.11700I
u = 0.682066 0.429866I
a = 1.47318 + 0.50585I
b = 0.670861 0.027425I
4.83020 5.52175I 12.07498 + 4.89921I
u = 0.682066 + 0.429866I
a = 1.47318 0.50585I
b = 0.670861 + 0.027425I
4.83020 + 5.52175I 12.07498 4.89921I
u = 0.571769 0.344867I
a = 1.53803 0.31651I
b = 0.575175 0.039007I
0.29865 2.39912I 6.29196 + 4.13143I
u = 0.571769 + 0.344867I
a = 1.53803 + 0.31651I
b = 0.575175 + 0.039007I
0.29865 + 2.39912I 6.29196 4.13143I
u = 0.521712
a = 1.80595
b = 0.450637
1.73407 6.87043
u = 0.417460 0.759198I
a = 0.953255 0.351915I
b = 0.737153 0.407888I
6.36396 + 1.94185I 12.44424 2.77963I
13
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.417460 + 0.759198I
a = 0.953255 + 0.351915I
b = 0.737153 + 0.407888I
6.36396 1.94185I 12.44424 + 2.77963I
u = 0.224766 0.469687I
a = 1.163861 0.054909I
b = 0.473749 + 0.279232I
0.892504 + 0.454173I 10.11280 4.18130I
u = 0.224766 + 0.469687I
a = 1.163861 + 0.054909I
b = 0.473749 0.279232I
0.892504 0.454173I 10.11280 + 4.18130I
14
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
8
(u
12
+ 6u
10
u
9
+ 14u
8
4u
7
+ 17u
6
6u
5
+ 12u
4
3u
3
+ 5u
2
u + 1)
(u
23
+ 10u
21
+ ··· + 3u 1)(u
48
+ u
47
+ ··· + 160u + 293)
c
2
, c
6
(u
12
+ 6u
10
+ u
9
+ 14u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 12u
4
+ 3u
3
+ 5u
2
+ u + 1)
(u
23
+ 10u
21
+ ··· + 3u 1)(u
48
+ u
47
+ ··· + 160u + 293)
c
3
(u
3
u
2
+ 1)
16
(u
12
+ 3u
11
+ 3u
10
+ u
9
+ 2u
8
+ 4u
7
+ 3u
6
+ 2u
5
+ 2u
4
u
3
2u
2
+ 1)
(u
23
+ 24u
22
+ ··· + 3840u + 256)
c
4
(u
8
3u
7
+ 7u
6
10u
5
+ 11u
4
10u
3
+ 6u
2
4u + 1)
6
(u
12
+ 2u
10
+ 3u
9
+ 4u
8
4u
7
+ 12u
6
7u
5
+ 3u
4
4u
3
+ 4u
2
+ 2u + 1)
(u
23
+ 21u
22
+ ··· 11268u 1192)
c
5
(u
8
u
7
3u
6
+ 2u
5
+ 3u
4
2u 1)
6
(u
12
6u
10
+ 13u
8
u
7
10u
6
+ 4u
5
2u
4
5u
3
+ 4u
2
+ 2u + 1)
(u
23
+ 7u
22
+ ··· + 20u 8)
c
7
, c
11
(u
12
u
11
u
10
+ u
9
+ u
8
u
7
u
5
+ 2u
4
+ 2u
3
+ 1)
(u
23
+ u
22
+ ··· + 3u
2
1)(u
48
+ 3u
47
+ ··· + 890u + 173)
c
9
, c
10
(u
8
u
7
3u
6
+ 2u
5
+ 3u
4
2u 1)
6
(u
12
6u
10
+ 13u
8
+ u
7
10u
6
4u
5
2u
4
+ 5u
3
+ 4u
2
2u + 1)
(u
23
+ 7u
22
+ ··· + 20u 8)
15
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
6
c
8
(y
12
+ 12y
11
+ ··· + 9y + 1)(y
23
+ 20y
22
+ ··· + 13y 1)
(y
48
+ 39y
47
+ ··· 564720y + 85849)
c
3
(y
3
y
2
+ 2y 1)
16
(y
12
3y
11
+ 7y
10
7y
9
+ 6y
8
+ 6y
7
7y
6
+ 14y
5
3y
3
+ 8y
2
4y + 1)
(y
23
4y
22
+ ··· + 131072y 65536)
c
4
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
17y
4
34y
3
22y
2
4y + 1)
6
(y
12
+ 4y
11
+ ··· + 4y + 1)(y
23
+ 9y
22
+ ··· + 1.91157 × 10
7
y 1420864)
c
5
, c
9
, c
10
(y
8
7y
7
+ 19y
6
22y
5
+ 3y
4
+ 14y
3
6y
2
4y + 1)
6
(y
12
12y
11
+ ··· + 4y + 1)(y
23
19y
22
+ ··· + 144y 64)
c
7
, c
11
(y
12
3y
11
+ 5y
10
5y
9
+ 5y
8
+ y
7
+ y
5
+ 10y
4
4y
3
+ 4y
2
+ 1)
(y
23
3y
22
+ ··· + 6y 1)(y
48
13y
47
+ ··· 826008y + 29929)
16