11a
113
(K11a
113
)
A knot diagram
1
Linearized knot diagam
6 1 11 9 2 10 3 4 5 7 8
Solving Sequence
2,5 6,9
10 7 1 3 4 8 11
c
5
c
9
c
6
c
1
c
2
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.34839 × 10
80
u
67
+ 3.68124 × 10
80
u
66
+ ··· + 1.27153 × 10
82
b − 1.90765 × 10
82
,
6.93735 × 10
81
u
67
− 9.19994 × 10
80
u
66
+ ··· + 1.27153 × 10
82
a − 4.71008 × 10
82
, u
68
+ 12u
66
+ ··· + 14u + 1i
I
u
2
= hu
12
+ 3u
10
+ 7u
8
+ 9u
6
+ u
5
+ 8u
4
+ 2u
3
+ 4u
2
+ b + u + 2,
u
13
+ 3u
12
+ 6u
11
+ 10u
10
+ 14u
9
+ 20u
8
+ 22u
7
+ 25u
6
+ 23u
5
+ 22u
4
+ 17u
3
+ 11u
2
+ a + 4u + 3,
u
14
+ u
13
+ 4u
12
+ 3u
11
+ 9u
10
+ 6u
9
+ 13u
8
+ 8u
7
+ 13u
6
+ 8u
5
+ 9u
4
+ 4u
3
+ 4u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 82 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
=
h5.35×10
80
u
67
+3.68×10
80
u
66
+· · ·+1.27×10
82
b−1.91×10
82
, 6.94×10
81
u
67
−
9.20 × 10
80
u
66
+ · · · + 1.27 × 10
82
a − 4.71 × 10
82
, u
68
+ 12u
66
+ · · · + 14u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
9
=
−0.545593u
67
+ 0.0723536u
66
+ ··· − 2.02184u + 3.70427
−0.0420628u
67
− 0.0289514u
66
+ ··· − 1.69314u + 1.50029
a
10
=
−0.587656u
67
+ 0.0434022u
66
+ ··· − 3.71498u + 5.20456
−0.0420628u
67
− 0.0289514u
66
+ ··· − 1.69314u + 1.50029
a
7
=
−0.355881u
67
+ 0.380128u
66
+ ··· + 8.26080u − 6.73774
−0.194171u
67
+ 0.115092u
66
+ ··· − 1.69115u − 2.69071
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
4
=
−0.444897u
67
− 0.0337046u
66
+ ··· − 7.30208u + 6.51254
0.126760u
67
− 0.101224u
66
+ ··· − 0.515987u + 2.55578
a
8
=
−0.322518u
67
+ 0.382112u
66
+ ··· + 7.92528u − 6.76024
−0.224672u
67
+ 0.0956000u
66
+ ··· − 5.25233u − 2.97848
a
11
=
−1.65034u
67
+ 0.264278u
66
+ ··· − 36.4509u − 9.08954
−0.600905u
67
+ 0.0210170u
66
+ ··· − 17.9861u − 3.94419
a
11
=
−1.65034u
67
+ 0.264278u
66
+ ··· − 36.4509u − 9.08954
−0.600905u
67
+ 0.0210170u
66
+ ··· − 17.9861u − 3.94419
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.99975u
67
+ 0.337333u
66
+ ··· − 36.0266u − 0.689887
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
68
+ 12u
66
+ ··· − 14u + 1
c
2
u
68
+ 24u
67
+ ··· − 66u + 1
c
3
u
68
+ 5u
67
+ ··· + 1376u + 161
c
4
, c
8
, c
9
u
68
+ u
67
+ ··· − 13u − 19
c
6
, c
10
u
68
+ u
67
+ ··· + 99u − 13
c
7
u
68
− u
67
+ ··· − 83u − 123
c
11
u
68
+ 5u
67
+ ··· − 131u − 179
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
68
+ 24y
67
+ ··· − 66y + 1
c
2
y
68
+ 48y
67
+ ··· − 11082y + 1
c
3
y
68
− 23y
67
+ ··· − 1710480y + 25921
c
4
, c
8
, c
9
y
68
− 75y
67
+ ··· − 1537y + 361
c
6
, c
10
y
68
− 61y
67
+ ··· + 17369y + 169
c
7
y
68
+ 17y
67
+ ··· + 422135y + 15129
c
11
y
68
+ 21y
67
+ ··· + 1105527y + 32041
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.056691 + 0.998319I
a = 0.429493 − 0.794328I
b = −1.354540 − 0.227994I
1.84313 + 3.63375I 5.00000 + 0.I
u = 0.056691 − 0.998319I
a = 0.429493 + 0.794328I
b = −1.354540 + 0.227994I
1.84313 − 3.63375I 5.00000 + 0.I
u = −0.737376 + 0.671219I
a = −2.08721 + 0.27350I
b = 1.58093 + 0.06731I
11.54460 + 0.21877I 17.6771 + 0.I
u = −0.737376 − 0.671219I
a = −2.08721 − 0.27350I
b = 1.58093 − 0.06731I
11.54460 − 0.21877I 17.6771 + 0.I
u = 0.124547 + 0.983422I
a = 0.010360 − 0.721178I
b = 0.219106 − 0.623961I
−3.12233 − 0.57125I 0
u = 0.124547 − 0.983422I
a = 0.010360 + 0.721178I
b = 0.219106 + 0.623961I
−3.12233 + 0.57125I 0
u = −0.350162 + 0.974636I
a = −0.417402 − 1.047070I
b = 0.832916 − 0.285678I
−1.26804 − 2.79796I 0
u = −0.350162 − 0.974636I
a = −0.417402 + 1.047070I
b = 0.832916 + 0.285678I
−1.26804 + 2.79796I 0
u = 0.786533 + 0.684928I
a = −1.66355 + 0.54319I
b = 1.72387 − 0.29020I
12.09960 − 0.83840I 0
u = 0.786533 − 0.684928I
a = −1.66355 − 0.54319I
b = 1.72387 + 0.29020I
12.09960 + 0.83840I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830250 + 0.658865I
a = −0.250221 + 0.410875I
b = 0.798752 − 0.772203I
5.67993 − 5.34809I 0
u = 0.830250 − 0.658865I
a = −0.250221 − 0.410875I
b = 0.798752 + 0.772203I
5.67993 + 5.34809I 0
u = −0.749134 + 0.751065I
a = −2.64257 − 0.98796I
b = 1.50979 + 0.07061I
7.17486 + 3.06656I 0
u = −0.749134 − 0.751065I
a = −2.64257 + 0.98796I
b = 1.50979 − 0.07061I
7.17486 − 3.06656I 0
u = −0.906668 + 0.562915I
a = −0.063631 + 0.203600I
b = 0.565448 + 0.170026I
4.68598 − 2.04595I 0
u = −0.906668 − 0.562915I
a = −0.063631 − 0.203600I
b = 0.565448 − 0.170026I
4.68598 + 2.04595I 0
u = 0.789964 + 0.729685I
a = −2.20736 + 1.00128I
b = 1.50674 + 0.17499I
7.19896 + 3.40495I 0
u = 0.789964 − 0.729685I
a = −2.20736 − 1.00128I
b = 1.50674 − 0.17499I
7.19896 − 3.40495I 0
u = −0.024461 + 1.086200I
a = −0.840798 − 0.156923I
b = −1.47061 + 0.12446I
6.24502 − 0.43169I 0
u = −0.024461 − 1.086200I
a = −0.840798 + 0.156923I
b = −1.47061 − 0.12446I
6.24502 + 0.43169I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.668707 + 0.865207I
a = 0.704861 + 0.333087I
b = −0.616750 + 0.357372I
4.01661 + 1.17981I 0
u = 0.668707 − 0.865207I
a = 0.704861 − 0.333087I
b = −0.616750 − 0.357372I
4.01661 − 1.17981I 0
u = 0.679050 + 0.858235I
a = −0.77402 + 1.29486I
b = 0.400623 + 0.354831I
4.03879 + 4.03484I 0
u = 0.679050 − 0.858235I
a = −0.77402 − 1.29486I
b = 0.400623 − 0.354831I
4.03879 − 4.03484I 0
u = −0.710320 + 0.840348I
a = −1.094730 − 0.412872I
b = 0.418566 − 1.103500I
4.26526 − 0.78149I 0
u = −0.710320 − 0.840348I
a = −1.094730 + 0.412872I
b = 0.418566 + 1.103500I
4.26526 + 0.78149I 0
u = −0.703267 + 0.893390I
a = −0.176298 + 0.303056I
b = −0.611742 − 1.091160I
4.10083 − 4.63563I 0
u = −0.703267 − 0.893390I
a = −0.176298 − 0.303056I
b = −0.611742 + 1.091160I
4.10083 + 4.63563I 0
u = 0.564977 + 0.999135I
a = −1.220080 + 0.538963I
b = 0.536796 + 0.482587I
−0.51569 + 6.32863I 0
u = 0.564977 − 0.999135I
a = −1.220080 − 0.538963I
b = 0.536796 − 0.482587I
−0.51569 − 6.32863I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493291 + 1.042080I
a = −0.032396 − 0.417531I
b = 0.538420 + 0.338146I
−0.59382 − 3.25955I 0
u = −0.493291 − 1.042080I
a = −0.032396 + 0.417531I
b = 0.538420 − 0.338146I
−0.59382 + 3.25955I 0
u = −0.152408 + 1.170190I
a = −0.442695 + 0.367195I
b = −0.308154 + 0.476045I
−1.12613 − 4.69478I 0
u = −0.152408 − 1.170190I
a = −0.442695 − 0.367195I
b = −0.308154 − 0.476045I
−1.12613 + 4.69478I 0
u = −0.709893 + 0.967350I
a = 2.26969 + 1.36925I
b = −1.55119 + 0.14708I
6.51252 − 8.62631I 0
u = −0.709893 − 0.967350I
a = 2.26969 − 1.36925I
b = −1.55119 − 0.14708I
6.51252 + 8.62631I 0
u = −0.072290 + 0.784893I
a = 1.44712 + 1.00338I
b = −0.867537 + 0.492868I
0.479696 + 1.218850I 3.82242 − 2.62908I
u = −0.072290 − 0.784893I
a = 1.44712 − 1.00338I
b = −0.867537 − 0.492868I
0.479696 − 1.218850I 3.82242 + 2.62908I
u = −1.036660 + 0.628687I
a = 1.76825 + 0.21237I
b = −1.62760 − 0.23134I
13.7366 + 9.0871I 0
u = −1.036660 − 0.628687I
a = 1.76825 − 0.21237I
b = −1.62760 + 0.23134I
13.7366 − 9.0871I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.687079 + 1.010450I
a = 1.32026 + 2.12559I
b = −1.51603 + 0.10725I
10.52170 − 5.68294I 0
u = −0.687079 − 1.010450I
a = 1.32026 − 2.12559I
b = −1.51603 − 0.10725I
10.52170 + 5.68294I 0
u = 0.742606 + 0.989112I
a = 1.71217 − 0.97802I
b = −1.52663 + 0.03900I
6.41405 + 2.38016I 0
u = 0.742606 − 0.989112I
a = 1.71217 + 0.97802I
b = −1.52663 − 0.03900I
6.41405 − 2.38016I 0
u = 0.560580 + 0.511556I
a = 1.077470 − 0.460333I
b = −0.359314 + 0.358132I
0.85594 − 1.76487I 7.42480 + 4.84873I
u = 0.560580 − 0.511556I
a = 1.077470 + 0.460333I
b = −0.359314 − 0.358132I
0.85594 + 1.76487I 7.42480 − 4.84873I
u = 0.713931 + 1.015970I
a = 1.41258 − 1.55830I
b = −1.65304 − 0.39573I
11.09840 + 6.52113I 0
u = 0.713931 − 1.015970I
a = 1.41258 + 1.55830I
b = −1.65304 + 0.39573I
11.09840 − 6.52113I 0
u = 0.725112 + 1.032960I
a = 1.016130 − 0.612765I
b = −0.696435 − 0.914112I
4.55307 + 11.17470I 0
u = 0.725112 − 1.032960I
a = 1.016130 + 0.612765I
b = −0.696435 + 0.914112I
4.55307 − 11.17470I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.506212 + 0.514162I
a = 1.000830 − 0.052860I
b = −0.358987 + 0.452126I
1.004420 − 0.901476I 8.36804 + 5.20975I
u = −0.506212 − 0.514162I
a = 1.000830 + 0.052860I
b = −0.358987 − 0.452126I
1.004420 + 0.901476I 8.36804 − 5.20975I
u = −0.772141 + 1.064070I
a = 0.404218 + 0.523737I
b = −0.378482 + 0.463468I
3.24077 − 4.14481I 0
u = −0.772141 − 1.064070I
a = 0.404218 − 0.523737I
b = −0.378482 − 0.463468I
3.24077 + 4.14481I 0
u = 1.281700 + 0.464275I
a = 1.66046 − 0.06858I
b = −1.54861 + 0.02461I
11.85000 + 1.49284I 0
u = 1.281700 − 0.464275I
a = 1.66046 + 0.06858I
b = −1.54861 − 0.02461I
11.85000 − 1.49284I 0
u = −0.784798 + 1.129230I
a = −1.46411 − 1.43292I
b = 1.61931 − 0.29900I
12.1505 − 15.6778I 0
u = −0.784798 − 1.129230I
a = −1.46411 + 1.43292I
b = 1.61931 + 0.29900I
12.1505 + 15.6778I 0
u = 0.035097 + 0.578937I
a = 2.16601 − 0.21856I
b = 0.030110 + 0.376253I
0.96062 − 1.38974I 4.85505 + 5.15507I
u = 0.035097 − 0.578937I
a = 2.16601 + 0.21856I
b = 0.030110 − 0.376253I
0.96062 + 1.38974I 4.85505 − 5.15507I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22199 + 1.44135I
a = −0.308371 + 0.423417I
b = 1.49524 + 0.11629I
4.95386 + 6.63333I 0
u = 0.22199 − 1.44135I
a = −0.308371 − 0.423417I
b = 1.49524 − 0.11629I
4.95386 − 6.63333I 0
u = 0.91649 + 1.24644I
a = −1.34038 + 1.01266I
b = 1.49909 + 0.12802I
9.50152 + 6.18867I 0
u = 0.91649 − 1.24644I
a = −1.34038 − 1.01266I
b = 1.49909 − 0.12802I
9.50152 − 6.18867I 0
u = −0.422490
a = 1.36125
b = −0.753301
1.14898 8.76770
u = −0.041792 + 0.289775I
a = 4.68550 + 1.04734I
b = 1.215190 − 0.166969I
4.61196 − 3.48976I 13.3589 + 6.7779I
u = −0.041792 − 0.289775I
a = 4.68550 − 1.04734I
b = 1.215190 + 0.166969I
4.61196 + 3.48976I 13.3589 − 6.7779I
u = −0.0980352
a = 3.51954
b = 1.66282
10.1505 −0.505670
11
II.
I
u
2
= hu
12
+ 3u
10
+ · · · + b + 2, u
13
+ 3u
12
+ · · · + a + 3, u
14
+ u
13
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
9
=
−u
13
− 3u
12
+ ··· − 4u − 3
−u
12
− 3u
10
− 7u
8
− 9u
6
− u
5
− 8u
4
− 2u
3
− 4u
2
− u − 2
a
10
=
−u
13
− 4u
12
+ ··· − 5u − 5
−u
12
− 3u
10
− 7u
8
− 9u
6
− u
5
− 8u
4
− 2u
3
− 4u
2
− u − 2
a
7
=
2u
13
+ 2u
12
+ ··· + u + 2
u
13
+ 2u
12
+ ··· + 2u + 1
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
4
=
u
13
+ 4u
12
+ ··· + 2u + 4
u
13
+ u
12
+ ··· + 3u + 2
a
8
=
u
13
+ u
12
+ 2u
11
+ u
10
+ 3u
9
+ 2u
8
+ 2u
7
+ u
6
+ u
5
+ u
4
− u
2
+ 2
u
13
+ 2u
12
+ ··· + 2u + 1
a
11
=
u
13
− 2u
12
+ ··· + 3u − 2
−u
12
− u
11
+ ··· − u − 2
a
11
=
u
13
− 2u
12
+ ··· + 3u − 2
−u
12
− u
11
+ ··· − u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −4u
13
−6u
12
−15u
11
−18u
10
−31u
9
−36u
8
−41u
7
−48u
6
−37u
5
−43u
4
−25u
3
−22u
2
−8u+3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− u
13
+ ··· − u + 1
c
2
u
14
+ 7u
13
+ ··· + 7u + 1
c
3
u
14
− 2u
12
+ 3u
10
+ u
8
− 6u
7
+ 2u
6
+ 6u
5
− 6u
4
+ u
3
+ 3u
2
− 3u + 1
c
4
u
14
− 8u
12
+ ··· − 2u
2
+ 1
c
5
u
14
+ u
13
+ ··· + u + 1
c
6
u
14
− 2u
13
+ ··· − 2u + 1
c
7
u
14
+ 2u
12
+ 2u
11
+ 4u
10
+ 3u
9
+ 8u
8
+ u
7
+ 9u
6
+ 3u
5
+ 2u
4
+ 5u
3
+ 1
c
8
, c
9
u
14
− 8u
12
+ ··· − 2u
2
+ 1
c
10
u
14
+ 2u
13
+ ··· + 2u + 1
c
11
u
14
+ 2u
12
+ 3u
11
+ 3u
10
+ 4u
9
+ 5u
8
+ 6u
7
+ 5u
6
+ 2u
5
+ u
4
− 2u
3
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
14
+ 7y
13
+ ··· + 7y + 1
c
2
y
14
+ 7y
13
+ ··· + 3y + 1
c
3
y
14
− 4y
13
+ ··· − 3y + 1
c
4
, c
8
, c
9
y
14
− 16y
13
+ ··· − 4y + 1
c
6
, c
10
y
14
− 14y
13
+ ··· − 10y + 1
c
7
y
14
+ 4y
13
+ ··· + 4y
2
+ 1
c
11
y
14
+ 4y
13
+ ··· + 2y
2
+ 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734849 + 0.838959I
a = −0.333800 + 0.436998I
b = −0.139966 + 0.587557I
3.61664 + 2.81352I 9.64591 − 2.83616I
u = 0.734849 − 0.838959I
a = −0.333800 − 0.436998I
b = −0.139966 − 0.587557I
3.61664 − 2.81352I 9.64591 + 2.83616I
u = 0.418839 + 1.066630I
a = 0.150053 + 0.914839I
b = 0.560131 − 0.227043I
−0.01874 + 3.80056I 10.63694 − 6.25439I
u = 0.418839 − 1.066630I
a = 0.150053 − 0.914839I
b = 0.560131 + 0.227043I
−0.01874 − 3.80056I 10.63694 + 6.25439I
u = −0.316820 + 1.106540I
a = −0.741155 − 0.065388I
b = 1.252080 − 0.108337I
2.59324 − 5.04325I 8.06202 + 6.26470I
u = −0.316820 − 1.106540I
a = −0.741155 + 0.065388I
b = 1.252080 + 0.108337I
2.59324 + 5.04325I 8.06202 − 6.26470I
u = −0.675866 + 0.491616I
a = −1.82024 + 0.02181I
b = 1.62719 + 0.06521I
10.70220 − 0.32675I 11.36618 + 5.14991I
u = −0.675866 − 0.491616I
a = −1.82024 − 0.02181I
b = 1.62719 − 0.06521I
10.70220 + 0.32675I 11.36618 − 5.14991I
u = −0.201031 + 0.762183I
a = −1.75035 + 0.68281I
b = −1.248670 − 0.185999I
4.04298 + 2.85458I 6.73494 − 0.49707I
u = −0.201031 − 0.762183I
a = −1.75035 − 0.68281I
b = −1.248670 + 0.185999I
4.04298 − 2.85458I 6.73494 + 0.49707I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.330549 + 0.694071I
a = 2.11814 − 0.09358I
b = −0.549066 − 0.437412I
1.43631 − 0.60321I 11.13684 − 2.07841I
u = 0.330549 − 0.694071I
a = 2.11814 + 0.09358I
b = −0.549066 + 0.437412I
1.43631 + 0.60321I 11.13684 + 2.07841I
u = −0.790520 + 1.084840I
a = 1.37736 + 1.39149I
b = −1.50170 + 0.16073I
8.88116 − 5.55392I 8.91716 + 2.29843I
u = −0.790520 − 1.084840I
a = 1.37736 − 1.39149I
b = −1.50170 − 0.16073I
8.88116 + 5.55392I 8.91716 − 2.29843I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
− u
13
+ ··· − u + 1)(u
68
+ 12u
66
+ ··· − 14u + 1)
c
2
(u
14
+ 7u
13
+ ··· + 7u + 1)(u
68
+ 24u
67
+ ··· − 66u + 1)
c
3
(u
14
− 2u
12
+ 3u
10
+ u
8
− 6u
7
+ 2u
6
+ 6u
5
− 6u
4
+ u
3
+ 3u
2
− 3u + 1)
· (u
68
+ 5u
67
+ ··· + 1376u + 161)
c
4
(u
14
− 8u
12
+ ··· − 2u
2
+ 1)(u
68
+ u
67
+ ··· − 13u − 19)
c
5
(u
14
+ u
13
+ ··· + u + 1)(u
68
+ 12u
66
+ ··· − 14u + 1)
c
6
(u
14
− 2u
13
+ ··· − 2u + 1)(u
68
+ u
67
+ ··· + 99u − 13)
c
7
(u
14
+ 2u
12
+ 2u
11
+ 4u
10
+ 3u
9
+ 8u
8
+ u
7
+ 9u
6
+ 3u
5
+ 2u
4
+ 5u
3
+ 1)
· (u
68
− u
67
+ ··· − 83u − 123)
c
8
, c
9
(u
14
− 8u
12
+ ··· − 2u
2
+ 1)(u
68
+ u
67
+ ··· − 13u − 19)
c
10
(u
14
+ 2u
13
+ ··· + 2u + 1)(u
68
+ u
67
+ ··· + 99u − 13)
c
11
(u
14
+ 2u
12
+ 3u
11
+ 3u
10
+ 4u
9
+ 5u
8
+ 6u
7
+ 5u
6
+ 2u
5
+ u
4
− 2u
3
+ 1)
· (u
68
+ 5u
67
+ ··· − 131u − 179)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
14
+ 7y
13
+ ··· + 7y + 1)(y
68
+ 24y
67
+ ··· − 66y + 1)
c
2
(y
14
+ 7y
13
+ ··· + 3y + 1)(y
68
+ 48y
67
+ ··· − 11082y + 1)
c
3
(y
14
− 4y
13
+ ··· − 3y + 1)(y
68
− 23y
67
+ ··· − 1710480y + 25921)
c
4
, c
8
, c
9
(y
14
− 16y
13
+ ··· − 4y + 1)(y
68
− 75y
67
+ ··· − 1537y + 361)
c
6
, c
10
(y
14
− 14y
13
+ ··· − 10y + 1)(y
68
− 61y
67
+ ··· + 17369y + 169)
c
7
(y
14
+ 4y
13
+ ··· + 4y
2
+ 1)(y
68
+ 17y
67
+ ··· + 422135y + 15129)
c
11
(y
14
+ 4y
13
+ ··· + 2y
2
+ 1)(y
68
+ 21y
67
+ ··· + 1105527y + 32041)
18
