11a
17
(K11a
17
)
A knot diagram
1
Linearized knot diagam
4 1 6 2 8 3 10 5 11 7 9
Solving Sequence
7,10
8
3,11
6 4 5 9 1 2
c
7
c
10
c
6
c
3
c
5
c
9
c
11
c
2
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.94953 × 10
22
u
70
− 2.28036 × 10
23
u
69
+ ··· + 2.14833 × 10
22
b − 2.53129 × 10
22
,
9.79183 × 10
20
u
70
+ 3.59725 × 10
22
u
69
+ ··· + 1.07416 × 10
22
a − 8.03639 × 10
22
, u
71
+ 5u
70
+ ··· + 16u + 1i
I
u
2
= h−3a
2
u + 2a
2
− 4au + 7b + 5a − u + 10, a
3
− a
2
u + 2a
2
+ 3au − a + 5u, u
2
− u + 1i
I
u
3
= hb, −u
3
− 2u
2
+ a − 2u, u
4
+ u
3
+ u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 81 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−5.95 × 10
22
u
70
− 2.28 × 10
23
u
69
+ · · · + 2.15 × 10
22
b − 2.53 ×
10
22
, 9.79 × 10
20
u
70
+ 3.60 × 10
22
u
69
+ · · · + 1.07 × 10
22
a − 8.04 ×
10
22
, u
71
+ 5u
70
+ · · · + 16u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
u
2
a
3
=
−0.0911577u
70
− 3.34888u
69
+ ··· − 37.5984u + 7.48153
2.76938u
70
+ 10.6146u
69
+ ··· + 12.1316u + 1.17826
a
11
=
−u
u
a
6
=
4.02087u
70
+ 14.8653u
69
+ ··· + 22.0738u − 2.91262
−2.20047u
70
− 6.62609u
69
+ ··· + 2.44001u − 0.00293030
a
4
=
−4.91020u
70
− 23.2455u
69
+ ··· − 75.9832u + 7.34450
5.57560u
70
+ 18.7187u
69
+ ··· − 10.4341u − 0.354339
a
5
=
8.28715u
70
+ 36.7438u
69
+ ··· + 99.4370u + 2.32932
−8.83708u
70
− 30.6563u
69
+ ··· − 10.5783u − 0.549932
a
9
=
−u
3
u
3
+ u
a
1
=
−u
5
− u
u
5
+ u
3
+ u
a
2
=
1.84442u
70
+ 6.91573u
69
+ ··· + 0.676442u + 9.99389
0.311963u
70
+ 1.82295u
69
+ ··· + 10.8155u + 1.16954
a
2
=
1.84442u
70
+ 6.91573u
69
+ ··· + 0.676442u + 9.99389
0.311963u
70
+ 1.82295u
69
+ ··· + 10.8155u + 1.16954
(ii) Obstruction class = −1
(iii) Cusp Shapes =
14007707892704021288689
10741642455012495551282
u
70
+
52903988225635842251755
10741642455012495551282
u
69
+ ··· +
406218822228831882964265
10741642455012495551282
u −
31847081302722889929098
5370821227506247775641
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
71
− 7u
70
+ ··· − 19u + 1
c
2
u
71
+ 35u
70
+ ··· + 91u + 1
c
3
, c
6
u
71
− 3u
70
+ ··· − 72u + 16
c
5
, c
8
u
71
+ 2u
70
+ ··· + 224u + 64
c
7
, c
10
u
71
− 5u
70
+ ··· + 16u − 1
c
9
, c
11
u
71
− 23u
70
+ ··· + 246u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
71
− 35y
70
+ ··· + 91y −1
c
2
y
71
+ 9y
70
+ ··· + 3279y −1
c
3
, c
6
y
71
+ 33y
70
+ ··· − 4800y −256
c
5
, c
8
y
71
+ 40y
70
+ ··· − 39936y −4096
c
7
, c
10
y
71
+ 23y
70
+ ··· + 246y −1
c
9
, c
11
y
71
+ 55y
70
+ ··· + 62490y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.469540 + 0.901499I
a = −2.34185 + 1.83693I
b = −0.440954 − 0.146276I
−1.31688 − 1.88106I −31.3196 + 4.6871I
u = 0.469540 − 0.901499I
a = −2.34185 − 1.83693I
b = −0.440954 + 0.146276I
−1.31688 + 1.88106I −31.3196 − 4.6871I
u = 0.703653 + 0.685371I
a = −0.410681 + 0.049842I
b = −0.285900 + 0.818152I
0.185937 − 1.104380I −1.16040 + 2.40265I
u = 0.703653 − 0.685371I
a = −0.410681 − 0.049842I
b = −0.285900 − 0.818152I
0.185937 + 1.104380I −1.16040 − 2.40265I
u = −0.066834 + 0.978657I
a = −0.76286 − 2.56276I
b = −0.149859 + 1.246530I
5.52736 − 0.93567I 4.64414 + 2.41235I
u = −0.066834 − 0.978657I
a = −0.76286 + 2.56276I
b = −0.149859 − 1.246530I
5.52736 + 0.93567I 4.64414 − 2.41235I
u = 0.199067 + 1.029270I
a = 0.844886 − 0.722840I
b = −0.903463 + 0.396432I
−0.16872 − 3.86400I 0. + 6.04330I
u = 0.199067 − 1.029270I
a = 0.844886 + 0.722840I
b = −0.903463 − 0.396432I
−0.16872 + 3.86400I 0. − 6.04330I
u = 0.228246 + 0.913383I
a = −0.23825 + 3.38061I
b = −0.223038 − 0.668311I
−1.01028 − 1.75385I 0.38756 + 7.39042I
u = 0.228246 − 0.913383I
a = −0.23825 − 3.38061I
b = −0.223038 + 0.668311I
−1.01028 + 1.75385I 0.38756 − 7.39042I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.644181 + 0.840361I
a = −1.06472 − 1.25613I
b = 0.21087 + 1.49010I
2.18680 − 0.67401I 0
u = −0.644181 − 0.840361I
a = −1.06472 + 1.25613I
b = 0.21087 − 1.49010I
2.18680 + 0.67401I 0
u = −0.170132 + 0.914729I
a = 1.00662 + 2.47886I
b = 0.419700 − 1.267450I
4.39627 + 4.60339I 3.32762 − 2.73353I
u = −0.170132 − 0.914729I
a = 1.00662 − 2.47886I
b = 0.419700 + 1.267450I
4.39627 − 4.60339I 3.32762 + 2.73353I
u = −0.836021 + 0.673858I
a = 0.109662 − 0.484018I
b = 0.672234 + 1.164290I
−2.39090 − 4.48377I 0
u = −0.836021 − 0.673858I
a = 0.109662 + 0.484018I
b = 0.672234 − 1.164290I
−2.39090 + 4.48377I 0
u = 0.682896 + 0.834787I
a = 1.99324 − 0.92672I
b = 0.617687 + 0.601618I
−3.08372 − 1.52053I 0
u = 0.682896 − 0.834787I
a = 1.99324 + 0.92672I
b = 0.617687 − 0.601618I
−3.08372 + 1.52053I 0
u = −0.832336 + 0.724886I
a = −0.670615 − 0.613985I
b = −1.075770 + 0.627927I
−6.99333 − 3.33145I 0
u = −0.832336 − 0.724886I
a = −0.670615 + 0.613985I
b = −1.075770 − 0.627927I
−6.99333 + 3.33145I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140143 + 1.101750I
a = −0.13050 − 2.45616I
b = 0.426470 + 1.144810I
4.31628 − 4.18567I 0
u = 0.140143 − 1.101750I
a = −0.13050 + 2.45616I
b = 0.426470 − 1.144810I
4.31628 + 4.18567I 0
u = −0.780059 + 0.792579I
a = 0.408945 + 0.711158I
b = 1.044280 − 0.406192I
−4.75730 + 1.60644I 0
u = −0.780059 − 0.792579I
a = 0.408945 − 0.711158I
b = 1.044280 + 0.406192I
−4.75730 − 1.60644I 0
u = −0.649958 + 0.906097I
a = 1.16875 + 1.58162I
b = 0.08760 − 1.49800I
2.40563 + 5.71061I 0
u = −0.649958 − 0.906097I
a = 1.16875 − 1.58162I
b = 0.08760 + 1.49800I
2.40563 − 5.71061I 0
u = −0.819648 + 0.758949I
a = −0.202166 + 0.947127I
b = −0.555895 − 1.022590I
−7.65318 − 0.42476I 0
u = −0.819648 − 0.758949I
a = −0.202166 − 0.947127I
b = −0.555895 + 1.022590I
−7.65318 + 0.42476I 0
u = −0.892301 + 0.672315I
a = −0.295771 + 0.358689I
b = −0.776807 − 1.153330I
−5.27544 − 10.02070I 0
u = −0.892301 − 0.672315I
a = −0.295771 − 0.358689I
b = −0.776807 + 1.153330I
−5.27544 + 10.02070I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.809277 + 0.772791I
a = 0.335402 − 0.318821I
b = 0.572324 − 0.999549I
−1.88125 + 3.19322I 0
u = 0.809277 − 0.772791I
a = 0.335402 + 0.318821I
b = 0.572324 + 0.999549I
−1.88125 − 3.19322I 0
u = 0.684814 + 0.898763I
a = 0.736483 − 0.552503I
b = 0.770057 − 0.536295I
−2.88221 − 3.75765I 0
u = 0.684814 − 0.898763I
a = 0.736483 + 0.552503I
b = 0.770057 + 0.536295I
−2.88221 + 3.75765I 0
u = 0.063523 + 0.862035I
a = −0.858693 + 0.495191I
b = 0.869259 + 0.100924I
0.623561 − 0.155557I 0.0220175 − 0.0069970I
u = 0.063523 − 0.862035I
a = −0.858693 − 0.495191I
b = 0.869259 − 0.100924I
0.623561 + 0.155557I 0.0220175 + 0.0069970I
u = 0.825029 + 0.180514I
a = −0.358331 + 0.374895I
b = −0.613697 − 1.017340I
−2.42985 − 6.27823I −7.32031 + 6.32359I
u = 0.825029 − 0.180514I
a = −0.358331 − 0.374895I
b = −0.613697 + 1.017340I
−2.42985 + 6.27823I −7.32031 − 6.32359I
u = 0.190670 + 1.155730I
a = 0.01366 + 2.28563I
b = −0.628836 − 1.153550I
2.15092 − 9.48353I 0
u = 0.190670 − 1.155730I
a = 0.01366 − 2.28563I
b = −0.628836 + 1.153550I
2.15092 + 9.48353I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.532399 + 1.050880I
a = −1.16792 + 1.12279I
b = 0.139051 − 0.972541I
1.97142 − 2.68154I 0
u = 0.532399 − 1.050880I
a = −1.16792 − 1.12279I
b = 0.139051 + 0.972541I
1.97142 + 2.68154I 0
u = 0.682581 + 0.973399I
a = −1.55596 + 1.01812I
b = −0.423358 − 0.977979I
1.01578 − 4.23738I 0
u = 0.682581 − 0.973399I
a = −1.55596 − 1.01812I
b = −0.423358 + 0.977979I
1.01578 + 4.23738I 0
u = −0.737484 + 0.947027I
a = −0.255221 + 0.689415I
b = 1.108830 + 0.298809I
−4.27963 + 4.12596I 0
u = −0.737484 − 0.947027I
a = −0.255221 − 0.689415I
b = 1.108830 − 0.298809I
−4.27963 − 4.12596I 0
u = 0.449989 + 1.115620I
a = 1.04346 − 0.97703I
b = −0.474923 + 1.017330I
0.54346 + 1.75236I 0
u = 0.449989 − 1.115620I
a = 1.04346 + 0.97703I
b = −0.474923 − 1.017330I
0.54346 − 1.75236I 0
u = 0.435093 + 0.655870I
a = −0.421928 − 0.262313I
b = 0.013074 + 0.389178I
0.058062 − 1.373770I 0.54762 + 4.59641I
u = 0.435093 − 0.655870I
a = −0.421928 + 0.262313I
b = 0.013074 − 0.389178I
0.058062 + 1.373770I 0.54762 − 4.59641I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.750193 + 0.971797I
a = 1.56758 − 0.87634I
b = 0.625386 + 1.066570I
−1.26633 − 9.05370I 0
u = 0.750193 − 0.971797I
a = 1.56758 + 0.87634I
b = 0.625386 − 1.066570I
−1.26633 + 9.05370I 0
u = −0.751292 + 0.980442I
a = −1.30409 − 1.91476I
b = −0.474824 + 1.073280I
−6.97127 + 6.31431I 0
u = −0.751292 − 0.980442I
a = −1.30409 + 1.91476I
b = −0.474824 − 1.073280I
−6.97127 − 6.31431I 0
u = −0.888822 + 0.861156I
a = −0.420743 − 0.227554I
b = −0.503579 + 0.631395I
−8.93127 + 3.93572I 0
u = −0.888822 − 0.861156I
a = −0.420743 + 0.227554I
b = −0.503579 − 0.631395I
−8.93127 − 3.93572I 0
u = −0.745302 + 1.004020I
a = 0.429820 − 0.617085I
b = −1.133830 − 0.574421I
−6.13711 + 9.23592I 0
u = −0.745302 − 1.004020I
a = 0.429820 + 0.617085I
b = −1.133830 + 0.574421I
−6.13711 − 9.23592I 0
u = −0.728006 + 1.029620I
a = 1.30483 + 1.76760I
b = 0.653700 − 1.243700I
−1.30783 + 10.33650I 0
u = −0.728006 − 1.029620I
a = 1.30483 − 1.76760I
b = 0.653700 + 1.243700I
−1.30783 − 10.33650I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.665608 + 0.272736I
a = 0.030085 − 0.514045I
b = 0.406144 + 0.846985I
−0.11266 − 1.79745I −3.68305 + 3.00636I
u = 0.665608 − 0.272736I
a = 0.030085 + 0.514045I
b = 0.406144 − 0.846985I
−0.11266 + 1.79745I −3.68305 − 3.00636I
u = −0.852550 + 0.956405I
a = 0.320716 − 0.242205I
b = −0.414388 − 0.586515I
−8.63777 + 2.49143I 0
u = −0.852550 − 0.956405I
a = 0.320716 + 0.242205I
b = −0.414388 + 0.586515I
−8.63777 − 2.49143I 0
u = −0.749415 + 1.052960I
a = −1.33912 − 1.71674I
b = −0.77993 + 1.20298I
−4.0986 + 16.1013I 0
u = −0.749415 − 1.052960I
a = −1.33912 + 1.71674I
b = −0.77993 − 1.20298I
−4.0986 − 16.1013I 0
u = 0.633866 + 0.064239I
a = −0.737841 − 1.003620I
b = −0.712988 + 0.613513I
−3.67287 − 1.17347I −10.32734 + 0.68526I
u = 0.633866 − 0.064239I
a = −0.737841 + 1.003620I
b = −0.712988 − 0.613513I
−3.67287 + 1.17347I −10.32734 − 0.68526I
u = −0.470621 + 0.142712I
a = −0.309496 + 0.762972I
b = 0.176109 + 1.095200I
2.07880 − 2.37441I −0.70861 + 4.00251I
u = −0.470621 − 0.142712I
a = −0.309496 − 0.762972I
b = 0.176109 − 1.095200I
2.07880 + 2.37441I −0.70861 − 4.00251I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0632515
a = 10.0652
b = 0.518539
−1.19409 −8.46120
12
II. I
u
2
=
h−3a
2
u+2a
2
−4au+7b+5a−u+10, a
3
−a
2
u+2a
2
+3au−a+5u, u
2
−u+1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
u − 1
a
3
=
a
3
7
a
2
u +
4
7
au + ··· −
5
7
a −
10
7
a
11
=
−u
u
a
6
=
1
7
a
2
u −
1
7
au + ··· +
3
7
a −
8
7
4
7
a
2
u +
3
7
au + ··· −
2
7
a +
3
7
a
4
=
3
7
a
2
u −
3
7
au + ··· +
2
7
a −
10
7
1
7
a
2
u −
1
7
au + ··· +
3
7
a +
6
7
a
5
=
1
7
a
2
u −
1
7
au + ··· +
3
7
a −
8
7
4
7
a
2
u +
3
7
au + ··· −
2
7
a +
3
7
a
9
=
1
u − 1
a
1
=
−1
0
a
2
=
3
7
a
2
u +
4
7
au + ··· +
2
7
a −
10
7
3
7
a
2
u +
4
7
au + ··· −
5
7
a −
10
7
a
2
=
3
7
a
2
u +
4
7
au + ··· +
2
7
a −
10
7
3
7
a
2
u +
4
7
au + ··· −
5
7
a −
10
7
(ii) Obstruction class = 1
(iii) Cusp Shapes =
18
7
a
2
u +
2
7
a
2
−
4
7
au +
19
7
a +
62
7
u −
67
7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
2
c
2
, c
6
(u
3
+ u
2
+ 2u + 1)
2
c
3
(u
3
− u
2
+ 2u − 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
c
7
, c
11
(u
2
− u + 1)
3
c
9
, c
10
(u
2
+ u + 1)
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
3
− y
2
+ 2y −1)
2
c
2
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
5
, c
8
y
6
c
7
, c
9
, c
10
c
11
(y
2
+ y + 1)
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.46996 + 0.49350I
b = −0.569840
−1.11345 − 2.02988I −2.22484 + 11.58609I
u = 0.500000 + 0.866025I
a = 1.11700 − 1.21217I
b = −0.215080 + 1.307140I
3.02413 + 0.79824I 2.65209 − 0.57512I
u = 0.500000 + 0.866025I
a = −1.14704 + 1.58470I
b = −0.215080 − 1.307140I
3.02413 − 4.85801I −0.92725 + 3.71146I
u = 0.500000 − 0.866025I
a = −1.46996 − 0.49350I
b = −0.569840
−1.11345 + 2.02988I −2.22484 − 11.58609I
u = 0.500000 − 0.866025I
a = 1.11700 + 1.21217I
b = −0.215080 − 1.307140I
3.02413 − 0.79824I 2.65209 + 0.57512I
u = 0.500000 − 0.866025I
a = −1.14704 − 1.58470I
b = −0.215080 + 1.307140I
3.02413 + 4.85801I −0.92725 − 3.71146I
16
III. I
u
3
= hb, −u
3
− 2u
2
+ a − 2u, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
u
2
a
3
=
u
3
+ 2u
2
+ 2u
0
a
11
=
−u
u
a
6
=
1
0
a
4
=
u
3
+ 2u
2
+ 2u
0
a
5
=
u
2
+ 1
−u
3
− u
2
− 1
a
9
=
−u
3
u
3
+ u
a
1
=
−u
2
− 1
u
3
+ u
2
+ 1
a
2
=
u
3
+ u
2
+ 2u − 1
u
3
+ u
2
+ 1
a
2
=
u
3
+ u
2
+ 2u − 1
u
3
+ u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
+ 5u
2
− 8
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
4
(u + 1)
4
c
3
, c
6
u
4
c
5
, c
9
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
7
u
4
+ u
3
+ u
2
+ 1
c
8
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
10
u
4
− u
3
+ u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
, c
8
, c
9
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
7
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = −0.59074 + 2.34806I
b = 0
−1.43393 − 1.41510I −11.48794 + 2.21528I
u = 0.351808 − 0.720342I
a = −0.59074 − 2.34806I
b = 0
−1.43393 + 1.41510I −11.48794 − 2.21528I
u = −0.851808 + 0.911292I
a = −0.409261 − 0.055548I
b = 0
−8.43568 + 3.16396I −4.01206 − 4.08190I
u = −0.851808 − 0.911292I
a = −0.409261 + 0.055548I
b = 0
−8.43568 − 3.16396I −4.01206 + 4.08190I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
3
+ u
2
− 1)
2
(u
71
− 7u
70
+ ··· − 19u + 1)
c
2
((u + 1)
4
)(u
3
+ u
2
+ 2u + 1)
2
(u
71
+ 35u
70
+ ··· + 91u + 1)
c
3
u
4
(u
3
− u
2
+ 2u − 1)
2
(u
71
− 3u
70
+ ··· − 72u + 16)
c
4
((u + 1)
4
)(u
3
− u
2
+ 1)
2
(u
71
− 7u
70
+ ··· − 19u + 1)
c
5
u
6
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
71
+ 2u
70
+ ··· + 224u + 64)
c
6
u
4
(u
3
+ u
2
+ 2u + 1)
2
(u
71
− 3u
70
+ ··· − 72u + 16)
c
7
((u
2
− u + 1)
3
)(u
4
+ u
3
+ u
2
+ 1)(u
71
− 5u
70
+ ··· + 16u − 1)
c
8
u
6
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
71
+ 2u
70
+ ··· + 224u + 64)
c
9
((u
2
+ u + 1)
3
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
71
− 23u
70
+ ··· + 246u + 1)
c
10
((u
2
+ u + 1)
3
)(u
4
− u
3
+ u
2
+ 1)(u
71
− 5u
70
+ ··· + 16u − 1)
c
11
((u
2
− u + 1)
3
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
71
− 23u
70
+ ··· + 246u + 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
4
)(y
3
− y
2
+ 2y −1)
2
(y
71
− 35y
70
+ ··· + 91y −1)
c
2
((y −1)
4
)(y
3
+ 3y
2
+ 2y −1)
2
(y
71
+ 9y
70
+ ··· + 3279y −1)
c
3
, c
6
y
4
(y
3
+ 3y
2
+ 2y −1)
2
(y
71
+ 33y
70
+ ··· − 4800y −256)
c
5
, c
8
y
6
(y
4
+ 5y
3
+ ··· + 2y + 1)(y
71
+ 40y
70
+ ··· − 39936y −4096)
c
7
, c
10
((y
2
+ y + 1)
3
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
71
+ 23y
70
+ ··· + 246y −1)
c
9
, c
11
((y
2
+ y + 1)
3
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
71
+ 55y
70
+ ··· + 62490y −1)
22
