12a
1235
(K12a
1235
)
A knot diagram
1
Linearized knot diagam
5 6 9 10 11 3 12 1 4 2 7 8
Solving Sequence
7,12
8 1
3,9
4 6 2 11 5 10
c
7
c
12
c
8
c
3
c
6
c
2
c
11
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.86883 × 10
97
u
82
− 1.55584 × 10
98
u
81
+ ··· + 7.14764 × 10
98
b − 1.16306 × 10
99
,
− 1.14478 × 10
98
u
82
− 2.39182 × 10
98
u
81
+ ··· + 7.14764 × 10
98
a − 3.16119 × 10
99
, u
83
+ u
82
+ ··· + 9u − 1i
I
u
2
= h−u
14
+ 10u
12
+ u
11
− 39u
10
− 8u
9
+ 75u
8
+ 23u
7
− 74u
6
− 29u
5
+ 35u
4
+ 17u
3
− 6u
2
+ b − 5u + 1,
u
15
− u
14
+ ··· + a − 1, u
17
− 12u
15
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 100 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
= h−2.87×10
97
u
82
−1.56×10
98
u
81
+· · ·+7.15×10
98
b−1.16×10
99
, −1.14×
10
98
u
82
−2.39×10
98
u
81
+· · ·+7.15×10
98
a−3.16×10
99
, u
83
+u
82
+· · ·+9u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
0.160162u
82
+ 0.334631u
81
+ ··· − 0.747532u + 4.42271
0.0401367u
82
+ 0.217672u
81
+ ··· + 0.925102u + 1.62720
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
0.213196u
82
+ 0.466612u
81
+ ··· + 0.0323716u + 5.97524
0.00962191u
82
+ 0.239696u
81
+ ··· + 0.902950u + 1.65279
a
6
=
0.428885u
82
+ 0.918419u
81
+ ··· + 1.55236u + 8.53499
0.0169089u
82
+ 0.434079u
81
+ ··· − 0.349604u + 3.04904
a
2
=
−0.826939u
82
− 1.72921u
81
+ ··· − 4.55454u − 10.5230
0.0411460u
82
− 0.623126u
81
+ ··· + 2.08602u − 3.87008
a
11
=
u
u
a
5
=
0.428878u
82
+ 0.873387u
81
+ ··· + 1.79165u + 8.46262
0.0169013u
82
+ 0.389047u
81
+ ··· − 0.110312u + 2.97668
a
10
=
−0.958590u
82
− 0.625662u
81
+ ··· − 3.45210u − 8.51747
−0.504620u
82
− 0.211045u
81
+ ··· − 2.58924u − 2.59056
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.80406u
82
+ 2.42592u
81
+ ··· + 2.92566u + 25.5968
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
83
+ 5u
82
+ ··· + 719u − 479
c
2
, c
6
u
83
− 28u
81
+ ··· − 22u − 73
c
3
, c
4
, c
9
u
83
− u
82
+ ··· − 4u + 8
c
5
u
83
+ u
82
+ ··· + 34u − 1
c
7
, c
8
, c
11
c
12
u
83
− u
82
+ ··· + 9u + 1
c
10
u
83
− 2u
82
+ ··· + 736u + 1561
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
83
+ 9y
82
+ ··· + 384757y −229441
c
2
, c
6
y
83
− 56y
82
+ ··· + 97428y −5329
c
3
, c
4
, c
9
y
83
− 83y
82
+ ··· − 304y −64
c
5
y
83
+ y
82
+ ··· + 750y −1
c
7
, c
8
, c
11
c
12
y
83
− 99y
82
+ ··· + 83y −1
c
10
y
83
− 34y
82
+ ··· + 95556644y −2436721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.768082 + 0.691197I
a = 0.252642 + 1.292600I
b = −1.33555 + 0.56553I
7.6353 − 12.3651I 0
u = 0.768082 − 0.691197I
a = 0.252642 − 1.292600I
b = −1.33555 − 0.56553I
7.6353 + 12.3651I 0
u = −0.866895 + 0.373017I
a = 0.922412 − 0.077651I
b = −0.597906 − 0.120958I
2.82259 − 0.53209I 0
u = −0.866895 − 0.373017I
a = 0.922412 + 0.077651I
b = −0.597906 + 0.120958I
2.82259 + 0.53209I 0
u = 0.235435 + 0.882232I
a = 0.296158 + 0.219377I
b = −1.254670 − 0.403627I
9.25233 + 7.20437I 0
u = 0.235435 − 0.882232I
a = 0.296158 − 0.219377I
b = −1.254670 + 0.403627I
9.25233 − 7.20437I 0
u = −0.731931 + 0.526717I
a = −0.55919 + 1.43057I
b = 1.251280 + 0.487251I
1.12377 + 8.38932I 0
u = −0.731931 − 0.526717I
a = −0.55919 − 1.43057I
b = 1.251280 − 0.487251I
1.12377 − 8.38932I 0
u = −0.502172 + 0.729866I
a = 0.808477 − 1.017140I
b = −0.836691 − 0.506283I
3.26194 + 4.42234I 0
u = −0.502172 − 0.729866I
a = 0.808477 + 1.017140I
b = −0.836691 + 0.506283I
3.26194 − 4.42234I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741521 + 0.479666I
a = 0.61796 + 1.69432I
b = 1.180280 + 0.049298I
7.90154 + 3.78747I 0
u = −0.741521 − 0.479666I
a = 0.61796 − 1.69432I
b = 1.180280 − 0.049298I
7.90154 − 3.78747I 0
u = 0.759993 + 0.438039I
a = 0.51802 − 1.64118I
b = 1.39103 − 0.62751I
7.59156 − 2.88645I 0
u = 0.759993 − 0.438039I
a = 0.51802 + 1.64118I
b = 1.39103 + 0.62751I
7.59156 + 2.88645I 0
u = 1.065910 + 0.374554I
a = 0.230666 − 0.271570I
b = 0.886114 + 0.262946I
−0.720339 + 0.792513I 0
u = 1.065910 − 0.374554I
a = 0.230666 + 0.271570I
b = 0.886114 − 0.262946I
−0.720339 − 0.792513I 0
u = 0.835796 + 0.060616I
a = −0.741566 − 0.326162I
b = −0.139599 − 0.295553I
−1.73821 − 0.12176I 0
u = 0.835796 − 0.060616I
a = −0.741566 + 0.326162I
b = −0.139599 + 0.295553I
−1.73821 + 0.12176I 0
u = −0.605321 + 0.578215I
a = 0.022688 + 0.194967I
b = −0.662120 + 0.544490I
2.82569 + 0.10655I 0
u = −0.605321 − 0.578215I
a = 0.022688 − 0.194967I
b = −0.662120 − 0.544490I
2.82569 − 0.10655I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.774756 + 0.279655I
a = 0.409521 − 0.846501I
b = 0.075986 − 0.890444I
−2.46982 + 3.44779I 0
u = −0.774756 − 0.279655I
a = 0.409521 + 0.846501I
b = 0.075986 + 0.890444I
−2.46982 − 3.44779I 0
u = 0.598146 + 0.543807I
a = −0.747680 − 0.822006I
b = 0.797769 − 0.293360I
−0.78891 − 1.85485I 0
u = 0.598146 − 0.543807I
a = −0.747680 + 0.822006I
b = 0.797769 + 0.293360I
−0.78891 + 1.85485I 0
u = 0.666365 + 0.433298I
a = −0.252771 − 1.104390I
b = −0.032199 − 1.198920I
3.54914 − 6.33411I 0. + 8.16822I
u = 0.666365 − 0.433298I
a = −0.252771 + 1.104390I
b = −0.032199 + 1.198920I
3.54914 + 6.33411I 0. − 8.16822I
u = −0.137211 + 0.664955I
a = −1.008040 + 0.313227I
b = 1.111180 − 0.371677I
2.87567 − 4.41134I 3.53322 + 5.88957I
u = −0.137211 − 0.664955I
a = −1.008040 − 0.313227I
b = 1.111180 + 0.371677I
2.87567 + 4.41134I 3.53322 − 5.88957I
u = 0.555148 + 0.350297I
a = 1.40971 + 1.37443I
b = −1.219220 + 0.311712I
1.52584 − 2.93851I 2.21348 + 8.51205I
u = 0.555148 − 0.350297I
a = 1.40971 − 1.37443I
b = −1.219220 − 0.311712I
1.52584 + 2.93851I 2.21348 − 8.51205I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.284960 + 0.532591I
a = −0.606372 − 0.317238I
b = −1.101640 + 0.237984I
4.61964 − 2.27072I 0
u = −1.284960 − 0.532591I
a = −0.606372 + 0.317238I
b = −1.101640 − 0.237984I
4.61964 + 2.27072I 0
u = −0.499318 + 0.304404I
a = 0.15040 − 2.11729I
b = −1.091140 − 0.571643I
1.74936 + 2.54506I 4.42588 − 10.86296I
u = −0.499318 − 0.304404I
a = 0.15040 + 2.11729I
b = −1.091140 + 0.571643I
1.74936 − 2.54506I 4.42588 + 10.86296I
u = 0.452167 + 0.325212I
a = 0.58482 + 2.60510I
b = −1.002000 − 0.101348I
1.85705 + 0.45025I 3.87420 + 1.56486I
u = 0.452167 − 0.325212I
a = 0.58482 − 2.60510I
b = −1.002000 + 0.101348I
1.85705 − 0.45025I 3.87420 − 1.56486I
u = −0.054260 + 0.528821I
a = −0.542993 − 0.539629I
b = 1.44268 + 0.17108I
9.81715 − 0.31683I 9.58825 − 0.96575I
u = −0.054260 − 0.528821I
a = −0.542993 + 0.539629I
b = 1.44268 − 0.17108I
9.81715 + 0.31683I 9.58825 + 0.96575I
u = 1.49008
a = 0.452163
b = 1.68796
4.72540 0
u = 1.49221 + 0.03214I
a = −0.02163 + 1.51967I
b = 0.808869 + 0.200589I
−0.82324 − 4.29800I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49221 − 0.03214I
a = −0.02163 − 1.51967I
b = 0.808869 − 0.200589I
−0.82324 + 4.29800I 0
u = −0.420439 + 0.274945I
a = −0.115243 − 0.576490I
b = −1.037550 + 0.209794I
1.89083 − 0.25563I 4.66041 − 1.63586I
u = −0.420439 − 0.274945I
a = −0.115243 + 0.576490I
b = −1.037550 − 0.209794I
1.89083 + 0.25563I 4.66041 + 1.63586I
u = −1.50758 + 0.03846I
a = 0.68100 − 1.96909I
b = 0.998445 − 0.934747I
−1.10641 − 2.50144I 0
u = −1.50758 − 0.03846I
a = 0.68100 + 1.96909I
b = 0.998445 + 0.934747I
−1.10641 + 2.50144I 0
u = −1.51416
a = 1.76375
b = 2.20627
4.11044 0
u = −1.54919 + 0.07124I
a = −0.47695 − 1.54171I
b = −0.924141 − 0.190121I
−5.00465 + 0.83960I 0
u = −1.54919 − 0.07124I
a = −0.47695 + 1.54171I
b = −0.924141 + 0.190121I
−5.00465 − 0.83960I 0
u = 1.56347 + 0.06819I
a = −0.78560 + 1.75556I
b = −1.14540 + 0.90049I
−5.34195 − 3.77537I 0
u = 1.56347 − 0.06819I
a = −0.78560 − 1.75556I
b = −1.14540 − 0.90049I
−5.34195 + 3.77537I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57107 + 0.09416I
a = −0.166949 − 1.254180I
b = −1.38879 − 0.41637I
−5.75176 + 4.51699I 0
u = −1.57107 − 0.09416I
a = −0.166949 + 1.254180I
b = −1.38879 + 0.41637I
−5.75176 − 4.51699I 0
u = 1.55834 + 0.24296I
a = −0.02366 + 1.51038I
b = −0.963467 + 0.634147I
−3.58166 − 8.00557I 0
u = 1.55834 − 0.24296I
a = −0.02366 − 1.51038I
b = −0.963467 − 0.634147I
−3.58166 + 8.00557I 0
u = 1.57285 + 0.14448I
a = −0.592693 − 1.011330I
b = −0.679658 − 0.812394I
−4.48210 − 2.61438I 0
u = 1.57285 − 0.14448I
a = −0.592693 + 1.011330I
b = −0.679658 + 0.812394I
−4.48210 + 2.61438I 0
u = 0.085058 + 0.399319I
a = −0.716080 − 0.440615I
b = 0.043328 + 0.425943I
0.023615 − 1.107130I 0.24981 + 5.47165I
u = 0.085058 − 0.399319I
a = −0.716080 + 0.440615I
b = 0.043328 − 0.425943I
0.023615 + 1.107130I 0.24981 − 5.47165I
u = −1.58914 + 0.16134I
a = 0.135384 + 1.207830I
b = 1.053060 + 0.533761I
−8.22990 + 4.45911I 0
u = −1.58914 − 0.16134I
a = 0.135384 − 1.207830I
b = 1.053060 − 0.533761I
−8.22990 − 4.45911I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59660 + 0.07112I
a = −0.407344 + 0.653461I
b = −1.263460 + 0.332042I
−5.48564 − 0.54881I 0
u = 1.59660 − 0.07112I
a = −0.407344 − 0.653461I
b = −1.263460 − 0.332042I
−5.48564 + 0.54881I 0
u = −1.59450 + 0.12611I
a = −0.39069 + 1.82656I
b = −0.22128 + 1.47922I
−4.13693 + 8.41109I 0
u = −1.59450 − 0.12611I
a = −0.39069 − 1.82656I
b = −0.22128 − 1.47922I
−4.13693 − 8.41109I 0
u = 0.201705 + 0.326921I
a = 2.77973 + 1.57851I
b = 0.449464 + 0.725917I
4.91629 + 3.36888I 3.38585 − 1.71367I
u = 0.201705 − 0.326921I
a = 2.77973 − 1.57851I
b = 0.449464 − 0.725917I
4.91629 − 3.36888I 3.38585 + 1.71367I
u = 1.61261 + 0.15634I
a = 0.39427 − 1.52840I
b = 1.35704 − 0.60605I
−6.81274 − 10.95820I 0
u = 1.61261 − 0.15634I
a = 0.39427 + 1.52840I
b = 1.35704 + 0.60605I
−6.81274 + 10.95820I 0
u = 1.61775 + 0.14984I
a = 0.88961 − 1.28448I
b = 0.998630 − 0.221072I
−0.12435 − 6.19456I 0
u = 1.61775 − 0.14984I
a = 0.88961 + 1.28448I
b = 0.998630 + 0.221072I
−0.12435 + 6.19456I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62616 + 0.06822I
a = 0.30884 + 1.49012I
b = 0.105281 + 1.165260I
−10.74930 − 4.72000I 0
u = 1.62616 − 0.06822I
a = 0.30884 − 1.49012I
b = 0.105281 − 1.165260I
−10.74930 + 4.72000I 0
u = −1.62426 + 0.13524I
a = 0.97669 + 1.71202I
b = 1.25823 + 0.93663I
−0.55167 + 5.09041I 0
u = −1.62426 − 0.13524I
a = 0.97669 − 1.71202I
b = 1.25823 − 0.93663I
−0.55167 − 5.09041I 0
u = −1.62996 + 0.21685I
a = −0.53811 − 1.61542I
b = −1.38415 − 0.71622I
−0.3993 + 15.8170I 0
u = −1.62996 − 0.21685I
a = −0.53811 + 1.61542I
b = −1.38415 + 0.71622I
−0.3993 − 15.8170I 0
u = −0.132784 + 0.329558I
a = 2.33743 − 2.97261I
b = 0.332026 + 0.247657I
4.91640 + 3.48534I 6.06358 − 0.28376I
u = −0.132784 − 0.329558I
a = 2.33743 + 2.97261I
b = 0.332026 − 0.247657I
4.91640 − 3.48534I 6.06358 + 0.28376I
u = −1.64700 + 0.01472I
a = −0.044159 − 0.956622I
b = 0.183647 − 0.730460I
−10.48590 − 0.17400I 0
u = −1.64700 − 0.01472I
a = −0.044159 + 0.956622I
b = 0.183647 + 0.730460I
−10.48590 + 0.17400I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.71576
a = 0.0355812
b = 0.301602
−10.8584 0
u = 1.83402
a = −0.726582
b = −0.854030
−7.54790 0
u = 0.106735
a = 4.49766
b = 1.77073
10.1184 26.6560
13
II.
I
u
2
= h−u
14
+10u
12
+· · ·+b+1, u
15
−u
14
+· · ·+a−1, u
17
−12u
15
+· · ·+2u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
−u
15
+ u
14
+ ··· + 3u + 1
u
14
− 10u
12
+ ··· + 5u − 1
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
2u
14
+ u
13
+ ··· + 4u − 1
u
15
+ u
14
+ ··· + 4u − 2
a
6
=
−u
16
− u
15
+ ··· + 2u + 2
−u
15
− u
14
+ ··· − u + 4
a
2
=
−u
16
− u
15
+ ··· + 2u + 2
−u
15
− 3u
14
+ ··· − 5u + 4
a
11
=
u
u
a
5
=
−u
16
− u
15
+ ··· + u + 2
−u
15
− 2u
14
+ ··· − 2u + 4
a
10
=
−u
16
+ 10u
14
+ ··· + u − 1
−2u
16
+ 22u
14
+ ··· + 5u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
16
+ 4u
15
+ 73u
14
− 38u
13
− 367u
12
+ 133u
11
+ 984u
10
−
199u
9
− 1511u
8
+ 83u
7
+ 1323u
6
+ 86u
5
− 622u
4
− 97u
3
+ 148u
2
+ 27u − 26
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 3u
14
+ ··· − 2u + 1
c
2
u
17
− 3u
16
+ ··· − 3u + 1
c
3
, c
4
u
17
− 10u
15
+ ··· + 2u − 1
c
5
u
17
+ 2u
14
+ ··· + u + 1
c
6
u
17
+ 3u
16
+ ··· − 3u − 1
c
7
, c
8
u
17
− 12u
15
+ ··· + 2u + 1
c
9
u
17
− 10u
15
+ ··· + 2u + 1
c
10
u
17
− 3u
16
+ ··· − 3u + 1
c
11
, c
12
u
17
− 12u
15
+ ··· + 2u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 12y
15
+ ··· − 6y −1
c
2
, c
6
y
17
− 17y
16
+ ··· + 17y −1
c
3
, c
4
, c
9
y
17
− 20y
16
+ ··· + 12y −1
c
5
y
17
− 6y
15
+ ··· + 3y −1
c
7
, c
8
, c
11
c
12
y
17
− 24y
16
+ ··· + 24y −1
c
10
y
17
− 11y
16
+ ··· + 9y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.003650 + 0.195846I
a = 0.414207 − 0.465164I
b = 0.873230 + 0.151297I
−0.428333 + 0.312530I 2.43654 + 3.06657I
u = 1.003650 − 0.195846I
a = 0.414207 + 0.465164I
b = 0.873230 − 0.151297I
−0.428333 − 0.312530I 2.43654 − 3.06657I
u = −1.061240 + 0.385002I
a = 0.662692 − 0.347814I
b = −0.641197 + 0.217090I
2.74449 − 1.32796I 0.90153 + 5.25483I
u = −1.061240 − 0.385002I
a = 0.662692 + 0.347814I
b = −0.641197 − 0.217090I
2.74449 + 1.32796I 0.90153 − 5.25483I
u = −1.20350
a = −1.13612
b = −1.50640
6.94121 5.07090
u = −0.418970 + 0.407394I
a = 0.74760 − 2.87715I
b = −0.698605 − 0.479518I
4.81038 + 4.20124I 4.41894 − 9.88963I
u = −0.418970 − 0.407394I
a = 0.74760 + 2.87715I
b = −0.698605 + 0.479518I
4.81038 − 4.20124I 4.41894 + 9.88963I
u = 1.52501
a = −1.23243
b = −2.01362
3.55547 −6.47810
u = 0.421778 + 0.203629I
a = −1.04051 − 2.49094I
b = 1.068590 − 0.399623I
1.43687 − 1.83764I −0.929561 + 0.761877I
u = 0.421778 − 0.203629I
a = −1.04051 + 2.49094I
b = 1.068590 + 0.399623I
1.43687 + 1.83764I −0.929561 − 0.761877I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56066 + 0.06072I
a = 0.55652 + 1.55091I
b = 1.220760 + 0.593258I
−5.52285 + 2.78715I −0.957635 − 0.257577I
u = −1.56066 − 0.06072I
a = 0.55652 − 1.55091I
b = 1.220760 − 0.593258I
−5.52285 − 2.78715I −0.957635 + 0.257577I
u = 1.57362 + 0.12841I
a = −0.57428 + 1.80929I
b = −0.719013 + 0.744031I
−2.18394 − 6.16611I −0.54092 + 5.12639I
u = 1.57362 − 0.12841I
a = −0.57428 − 1.80929I
b = −0.719013 − 0.744031I
−2.18394 + 6.16611I −0.54092 − 5.12639I
u = −0.290981
a = 0.180347
b = −1.79429
9.95562 −22.8560
u = −1.72992
a = 0.608202
b = 0.582363
−10.5244 10.2120
u = 1.78304
a = 0.0475599
b = −0.475597
−8.35124 −5.60590
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− 3u
14
+ ··· − 2u + 1)(u
83
+ 5u
82
+ ··· + 719u − 479)
c
2
(u
17
− 3u
16
+ ··· − 3u + 1)(u
83
− 28u
81
+ ··· − 22u − 73)
c
3
, c
4
(u
17
− 10u
15
+ ··· + 2u − 1)(u
83
− u
82
+ ··· − 4u + 8)
c
5
(u
17
+ 2u
14
+ ··· + u + 1)(u
83
+ u
82
+ ··· + 34u − 1)
c
6
(u
17
+ 3u
16
+ ··· − 3u − 1)(u
83
− 28u
81
+ ··· − 22u − 73)
c
7
, c
8
(u
17
− 12u
15
+ ··· + 2u + 1)(u
83
− u
82
+ ··· + 9u + 1)
c
9
(u
17
− 10u
15
+ ··· + 2u + 1)(u
83
− u
82
+ ··· − 4u + 8)
c
10
(u
17
− 3u
16
+ ··· − 3u + 1)(u
83
− 2u
82
+ ··· + 736u + 1561)
c
11
, c
12
(u
17
− 12u
15
+ ··· + 2u − 1)(u
83
− u
82
+ ··· + 9u + 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
− 12y
15
+ ··· − 6y −1)(y
83
+ 9y
82
+ ··· + 384757y −229441)
c
2
, c
6
(y
17
− 17y
16
+ ··· + 17y −1)(y
83
− 56y
82
+ ··· + 97428y −5329)
c
3
, c
4
, c
9
(y
17
− 20y
16
+ ··· + 12y −1)(y
83
− 83y
82
+ ··· − 304y −64)
c
5
(y
17
− 6y
15
+ ··· + 3y −1)(y
83
+ y
82
+ ··· + 750y −1)
c
7
, c
8
, c
11
c
12
(y
17
− 24y
16
+ ··· + 24y −1)(y
83
− 99y
82
+ ··· + 83y −1)
c
10
(y
17
− 11y
16
+ ··· + 9y −1)
· (y
83
− 34y
82
+ ··· + 95556644y −2436721)
20
