12n
0208
(K12n
0208
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 10 3 11 5 8 6 9
Solving Sequence
3,5
2 1
4,10
9 12 6 7 11 8
c
2
c
1
c
4
c
9
c
12
c
5
c
6
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h6.08795 × 10
88
u
64
+ 5.17375 × 10
89
u
63
+ ··· + 3.20686 × 10
88
b − 2.93483 × 10
88
,
4.89867 × 10
87
u
64
+ 3.97189 × 10
88
u
63
+ ··· + 3.56318 × 10
87
a + 1.88337 × 10
88
, u
65
+ 10u
64
+ ··· − 11u − 1i
I
u
2
= h−a
6
+ 2a
4
− 3a
2
+ b + 2, a
8
− a
7
− a
6
+ 2a
5
+ a
4
− 2a
3
+ 2a − 1, u − 1i
I
u
3
= h−u
5
− 4u
4
− 3u
3
+ 2u
2
+ 3b + 3u + 1, a, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 79 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
=
h6.09×10
88
u
64
+5.17×10
89
u
63
+· · ·+3.21×10
88
b−2.93×10
88
, 4.90×10
87
u
64
+
3.97 × 10
88
u
63
+ · · · + 3.56 × 10
87
a + 1.88 × 10
88
, u
65
+ 10u
64
+ · · · − 11u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
−1.37480u
64
− 11.1470u
63
+ ··· + 1.59486u − 5.28564
−1.89841u
64
− 16.1334u
63
+ ··· + 13.3331u + 0.915173
a
9
=
−1.37480u
64
− 11.1470u
63
+ ··· + 1.59486u − 5.28564
−5.70850u
64
− 48.6155u
63
+ ··· + 40.5692u + 3.51616
a
12
=
−0.0863684u
64
− 0.904473u
63
+ ··· − 10.1953u + 2.73218
4.03669u
64
+ 33.9170u
63
+ ··· − 25.9308u − 2.40433
a
6
=
2.43925u
64
+ 21.4354u
63
+ ··· − 19.0226u − 2.35834
−0.459002u
64
− 3.41692u
63
+ ··· + 0.298030u − 0.146156
a
7
=
−3.90567u
64
− 32.4081u
63
+ ··· + 19.3485u − 1.64653
3.74879u
64
+ 31.7029u
63
+ ··· − 24.6208u − 2.74300
a
11
=
0.156882u
64
+ 0.705201u
63
+ ··· + 5.27226u + 4.38953
6.31020u
64
+ 53.4331u
63
+ ··· − 41.9173u − 3.84100
a
8
=
−0.156882u
64
− 0.705201u
63
+ ··· − 5.27226u − 4.38953
3.74879u
64
+ 31.7029u
63
+ ··· − 24.6208u − 2.74300
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.74709u
64
+ 73.9059u
63
+ ··· − 57.9278u + 8.32578
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
+ 68u
64
+ ··· + 59u + 1
c
2
, c
4
u
65
− 10u
64
+ ··· − 11u + 1
c
3
, c
7
u
65
− 2u
64
+ ··· + 640u − 256
c
5
, c
11
u
65
+ 3u
64
+ ··· + 3u + 1
c
6
9(9u
65
+ 18u
64
+ ··· − 294572u − 29917)
c
8
, c
10
u
65
+ 8u
64
+ ··· + 1080u + 81
c
9
u
65
+ 2u
64
+ ··· − 19008u − 5184
c
12
9(9u
65
+ 42u
64
+ ··· + 608293u + 315227)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
− 132y
64
+ ··· + 7503y −1
c
2
, c
4
y
65
− 68y
64
+ ··· + 59y −1
c
3
, c
7
y
65
+ 48y
64
+ ··· + 901120y −65536
c
5
, c
11
y
65
+ 37y
64
+ ··· + 11y −1
c
6
81(81y
65
+ 5796y
64
+ ··· + 1.08032 × 10
10
y −8.95027 × 10
8
)
c
8
, c
10
y
65
− 30y
64
+ ··· + 422172y −6561
c
9
y
65
+ 36y
64
+ ··· − 462827520y −26873856
c
12
81(81y
65
− 558y
64
+ ··· − 1.06335 × 10
12
y −9.93681 × 10
10
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.456314 + 0.879364I
a = 1.131230 + 0.584791I
b = 1.72707 − 0.08743I
−5.91253 − 0.89151I 0
u = 0.456314 − 0.879364I
a = 1.131230 − 0.584791I
b = 1.72707 + 0.08743I
−5.91253 + 0.89151I 0
u = 0.999495 + 0.144370I
a = −0.300725 − 0.528299I
b = 0.76050 − 4.52365I
−0.766193 − 0.710691I 0
u = 0.999495 − 0.144370I
a = −0.300725 + 0.528299I
b = 0.76050 + 4.52365I
−0.766193 + 0.710691I 0
u = 0.926759 + 0.319800I
a = 0.034852 + 0.405826I
b = 0.504999 + 0.295737I
−1.70444 − 0.86317I 0
u = 0.926759 − 0.319800I
a = 0.034852 − 0.405826I
b = 0.504999 − 0.295737I
−1.70444 + 0.86317I 0
u = 0.675546 + 0.796801I
a = −0.79995 − 1.32569I
b = −1.84324 + 0.02675I
−6.56044 − 4.64446I 0
u = 0.675546 − 0.796801I
a = −0.79995 + 1.32569I
b = −1.84324 − 0.02675I
−6.56044 + 4.64446I 0
u = −0.467867 + 0.830676I
a = −0.486235 + 0.347007I
b = −0.515074 + 0.067949I
3.05269 − 0.72062I 0
u = −0.467867 − 0.830676I
a = −0.486235 − 0.347007I
b = −0.515074 − 0.067949I
3.05269 + 0.72062I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.08705
a = −0.457326
b = 2.56265
−0.408756 0
u = 0.455394 + 1.021320I
a = −0.764046 − 0.815756I
b = −1.49226 − 0.53436I
−0.92912 − 5.51849I 0
u = 0.455394 − 1.021320I
a = −0.764046 + 0.815756I
b = −1.49226 + 0.53436I
−0.92912 + 5.51849I 0
u = −0.968998 + 0.625550I
a = 0.061077 − 0.528566I
b = 0.485762 − 0.040171I
1.52187 + 6.09633I 0
u = −0.968998 − 0.625550I
a = 0.061077 + 0.528566I
b = 0.485762 + 0.040171I
1.52187 − 6.09633I 0
u = 0.527094 + 1.026630I
a = 0.794808 + 1.110310I
b = 1.76347 + 0.85154I
−4.34514 − 11.16830I 0
u = 0.527094 − 1.026630I
a = 0.794808 − 1.110310I
b = 1.76347 − 0.85154I
−4.34514 + 11.16830I 0
u = 0.857226 + 0.787857I
a = 0.559234 + 0.678465I
b = 1.170350 − 0.209373I
−2.21134 − 0.65096I 0
u = 0.857226 − 0.787857I
a = 0.559234 − 0.678465I
b = 1.170350 + 0.209373I
−2.21134 + 0.65096I 0
u = −0.802152
a = 1.20099
b = −0.170389
5.22479 24.0830
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.201410 + 0.069070I
a = 0.819602 − 0.047913I
b = 0.256683 + 1.354200I
−2.66486 − 2.32248I 0
u = 1.201410 − 0.069070I
a = 0.819602 + 0.047913I
b = 0.256683 − 1.354200I
−2.66486 + 2.32248I 0
u = 0.682090 + 0.350060I
a = −0.700589 + 0.542937I
b = 0.70615 + 2.83263I
−1.45078 + 0.59119I 2.85675 + 3.51070I
u = 0.682090 − 0.350060I
a = −0.700589 − 0.542937I
b = 0.70615 − 2.83263I
−1.45078 − 0.59119I 2.85675 − 3.51070I
u = 0.805635 + 0.937608I
a = −0.980560 − 0.441826I
b = −1.26976 + 0.73991I
−5.14289 + 4.65238I 0
u = 0.805635 − 0.937608I
a = −0.980560 + 0.441826I
b = −1.26976 − 0.73991I
−5.14289 − 4.65238I 0
u = −0.749176 + 0.103391I
a = −1.04340 − 1.06042I
b = 0.210161 − 0.079232I
1.17561 + 6.59366I 15.1731 − 8.7497I
u = −0.749176 − 0.103391I
a = −1.04340 + 1.06042I
b = 0.210161 + 0.079232I
1.17561 − 6.59366I 15.1731 + 8.7497I
u = 0.417480 + 0.517521I
a = −1.49219 + 1.44433I
b = 1.31694 + 1.34577I
−0.61197 − 3.88642I 5.46114 + 8.74938I
u = 0.417480 − 0.517521I
a = −1.49219 − 1.44433I
b = 1.31694 − 1.34577I
−0.61197 + 3.88642I 5.46114 − 8.74938I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48357 + 0.08066I
a = −0.203578 − 0.981777I
b = −0.810009 − 0.273620I
−8.45370 + 1.77642I 0
u = 1.48357 − 0.08066I
a = −0.203578 + 0.981777I
b = −0.810009 + 0.273620I
−8.45370 − 1.77642I 0
u = −1.49118 + 0.02637I
a = −0.46060 + 1.34932I
b = 0.464845 − 0.172950I
−4.34300 + 1.86014I 0
u = −1.49118 − 0.02637I
a = −0.46060 − 1.34932I
b = 0.464845 + 0.172950I
−4.34300 − 1.86014I 0
u = 0.384990 + 0.309899I
a = 1.60352 − 0.03292I
b = −1.17235 − 0.91495I
1.19155 − 0.95389I 10.21513 + 0.37317I
u = 0.384990 − 0.309899I
a = 1.60352 + 0.03292I
b = −1.17235 + 0.91495I
1.19155 + 0.95389I 10.21513 − 0.37317I
u = −1.52385 + 0.08329I
a = −1.032020 + 0.513949I
b = 1.42841 − 0.28527I
−5.31966 + 2.30754I 0
u = −1.52385 − 0.08329I
a = −1.032020 − 0.513949I
b = 1.42841 + 0.28527I
−5.31966 − 2.30754I 0
u = −1.52244 + 0.13410I
a = 1.48434 + 0.04778I
b = −1.60893 + 0.57560I
−7.12119 + 6.12750I 0
u = −1.52244 − 0.13410I
a = 1.48434 − 0.04778I
b = −1.60893 − 0.57560I
−7.12119 − 6.12750I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55086 + 0.16341I
a = −0.059513 + 0.770911I
b = 0.538883 + 0.255788I
−3.79735 − 2.57206I 0
u = 1.55086 − 0.16341I
a = −0.059513 − 0.770911I
b = 0.538883 − 0.255788I
−3.79735 + 2.57206I 0
u = −1.53316 + 0.36124I
a = 0.156811 + 0.866115I
b = −1.71885 + 0.05723I
−12.27680 + 5.48243I 0
u = −1.53316 − 0.36124I
a = 0.156811 − 0.866115I
b = −1.71885 − 0.05723I
−12.27680 − 5.48243I 0
u = −1.59050 + 0.05802I
a = 0.423270 − 0.120131I
b = −3.06479 + 0.46878I
−9.22847 + 0.59840I 0
u = −1.59050 − 0.05802I
a = 0.423270 + 0.120131I
b = −3.06479 − 0.46878I
−9.22847 − 0.59840I 0
u = 1.60342 + 0.11053I
a = 0.272856 − 0.890825I
b = −0.447120 − 0.410542I
−7.04530 − 8.03742I 0
u = 1.60342 − 0.11053I
a = 0.272856 + 0.890825I
b = −0.447120 + 0.410542I
−7.04530 + 8.03742I 0
u = −1.56938 + 0.38944I
a = −0.329304 − 0.941370I
b = 1.79802 − 0.50487I
−7.46828 + 10.68780I 0
u = −1.56938 − 0.38944I
a = −0.329304 + 0.941370I
b = 1.79802 + 0.50487I
−7.46828 − 10.68780I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61283 + 0.24938I
a = −0.355232 − 1.312240I
b = 1.67813 + 0.08130I
−14.1808 + 8.5511I 0
u = −1.61283 − 0.24938I
a = −0.355232 + 1.312240I
b = 1.67813 − 0.08130I
−14.1808 − 8.5511I 0
u = −1.59165 + 0.38058I
a = 0.364333 + 1.077600I
b = −2.06415 + 0.66485I
−11.1904 + 16.3453I 0
u = −1.59165 − 0.38058I
a = 0.364333 − 1.077600I
b = −2.06415 − 0.66485I
−11.1904 − 16.3453I 0
u = −1.63466 + 0.20895I
a = 0.388083 + 0.905964I
b = −1.42883 + 0.12631I
−10.53090 + 4.21781I 0
u = −1.63466 − 0.20895I
a = 0.388083 − 0.905964I
b = −1.42883 − 0.12631I
−10.53090 − 4.21781I 0
u = 0.191133 + 0.275831I
a = 2.96128 + 1.01345I
b = −0.373282 − 0.817737I
1.45815 − 1.19485I 9.19775 + 4.74594I
u = 0.191133 − 0.275831I
a = 2.96128 − 1.01345I
b = −0.373282 + 0.817737I
1.45815 + 1.19485I 9.19775 − 4.74594I
u = −0.295126 + 0.054794I
a = 2.87388 − 2.22523I
b = 0.487604 − 0.180053I
−2.55567 − 2.51492I 6.71386 + 3.00902I
u = −0.295126 − 0.054794I
a = 2.87388 + 2.22523I
b = 0.487604 + 0.180053I
−2.55567 + 2.51492I 6.71386 − 3.00902I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70229 + 0.22811I
a = −0.005540 − 0.755493I
b = 1.037080 + 0.107357I
−13.75280 − 0.18156I 0
u = −1.70229 − 0.22811I
a = −0.005540 + 0.755493I
b = 1.037080 − 0.107357I
−13.75280 + 0.18156I 0
u = −0.052582 + 0.159560I
a = −5.33288 − 2.93386I
b = −0.380996 + 0.381397I
1.04936 + 1.32007I 10.95788 − 0.41796I
u = −0.052582 − 0.159560I
a = −5.33288 + 2.93386I
b = −0.380996 − 0.381397I
1.04936 − 1.32007I 10.95788 + 0.41796I
u = −0.110381
a = −4.90925
b = −0.349777
0.709590 14.3470
11
II.
I
u
2
= h−a
6
+ 2a
4
− 3a
2
+ b + 2, a
8
− a
7
− a
6
+ 2a
5
+ a
4
− 2a
3
+ 2a − 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
4
=
1
0
a
10
=
a
a
6
− 2a
4
+ 3a
2
− 2
a
9
=
a
a
6
− 2a
4
+ 3a
2
+ a − 2
a
12
=
a
2
a
7
− 2a
5
+ 3a
3
+ a
2
− 2a − 1
a
6
=
a
4
−a
6
+ 2a
4
− 3a
2
− a + 2
a
7
=
a
6
+ a
2
0
a
11
=
a
6
+ a
2
a
6
− 2a
4
+ 3a
2
− 2
a
8
=
a
6
+ a
2
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −a
7
+ 4a
6
+ 2a
5
− 5a
4
− 3a
3
+ 5a
2
+ 5a − 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
6
, c
8
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
9
, c
12
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
10
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
11
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
6
, c
8
, c
10
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
9
, c
12
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.570868 + 0.730671I
b = −0.89335 + 2.72444I
−0.604279 − 1.131230I 6.13774 + 5.30650I
u = 1.00000
a = 0.570868 − 0.730671I
b = −0.89335 − 2.72444I
−0.604279 + 1.131230I 6.13774 − 5.30650I
u = 1.00000
a = −0.855237 + 0.665892I
b = 0.195703 − 0.910609I
−3.80435 − 2.57849I −1.88107 + 3.45077I
u = 1.00000
a = −0.855237 − 0.665892I
b = 0.195703 + 0.910609I
−3.80435 + 2.57849I −1.88107 − 3.45077I
u = 1.00000
a = −1.09818
b = 0.463171
4.85780 0.988100
u = 1.00000
a = 1.031810 + 0.655470I
b = −0.471534 − 0.216354I
0.73474 + 6.44354I −1.17016 − 2.68172I
u = 1.00000
a = 1.031810 − 0.655470I
b = −0.471534 + 0.216354I
0.73474 − 6.44354I −1.17016 + 2.68172I
u = 1.00000
a = 0.603304
b = −1.12481
−0.799899 1.83890
15
III. I
u
3
= h−u
5
− 4u
4
− 3u
3
+ 2u
2
+ 3b + 3u + 1, a, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
0
1
3
u
5
+
4
3
u
4
+ ··· − u −
1
3
a
9
=
0
1
3
u
5
+
4
3
u
4
+ ··· − u −
1
3
a
12
=
−u
2
+ 1
7
9
u
5
+
14
9
u
4
+ ··· −
11
9
u −
5
9
a
6
=
u
5
− 2u
3
+ u
4
3
u
5
+
4
9
u
4
+ ··· +
10
9
u −
1
9
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
11
=
−2u
5
+ 3u
3
− 2u
−
2
3
u
5
+
4
3
u
4
+ ··· − 2u −
1
3
a
8
=
2u
5
− 3u
3
+ 2u
u
5
− u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1
9
u
5
+
25
9
u
4
+
4
3
u
3
−
53
9
u
2
−
4
3
u +
116
9
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
6
9(9u
6
+ 12u
5
+ 2u
4
− u
3
+ 4u
2
+ 4u + 1)
c
8
(u + 1)
6
c
9
u
6
c
10
(u − 1)
6
c
11
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
12
9(9u
6
− 30u
5
+ 41u
4
− 30u
3
+ 15u
2
− 5u + 1)
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
6
81(81y
6
− 108y
5
+ 100y
4
− 63y
3
+ 28y
2
− 8y + 1)
c
8
, c
10
(y −1)
6
c
9
y
6
c
12
81(81y
6
− 162y
5
+ 151y
4
+ 48y
3
+ 7y
2
+ 5y + 1)
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0
b = −0.49282 + 2.03411I
−0.245672 − 0.924305I 8.52440 + 0.42550I
u = 1.002190 − 0.295542I
a = 0
b = −0.49282 − 2.03411I
−0.245672 + 0.924305I 8.52440 − 0.42550I
u = −0.428243 + 0.664531I
a = 0
b = 0.384438 + 0.080017I
3.53554 − 0.92430I 14.9081 + 3.3454I
u = −0.428243 − 0.664531I
a = 0
b = 0.384438 − 0.080017I
3.53554 + 0.92430I 14.9081 − 3.3454I
u = −1.073950 + 0.558752I
a = 0
b = −0.391622 − 0.105509I
1.64493 + 5.69302I 7.23419 + 3.25470I
u = −1.073950 − 0.558752I
a = 0
b = −0.391622 + 0.105509I
1.64493 − 5.69302I 7.23419 − 3.25470I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
65
+ 68u
64
+ ··· + 59u + 1)
c
2
((u − 1)
8
)(u
6
+ u
5
+ ··· + u + 1)(u
65
− 10u
64
+ ··· − 11u + 1)
c
3
u
8
(u
6
− u
5
+ ··· − u + 1)(u
65
− 2u
64
+ ··· + 640u − 256)
c
4
((u + 1)
8
)(u
6
− u
5
+ ··· − u + 1)(u
65
− 10u
64
+ ··· − 11u + 1)
c
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
65
+ 3u
64
+ ··· + 3u + 1)
c
6
81(9u
6
+ 12u
5
+ 2u
4
− u
3
+ 4u
2
+ 4u + 1)
· (u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (9u
65
+ 18u
64
+ ··· − 294572u − 29917)
c
7
u
8
(u
6
+ u
5
+ ··· + u + 1)(u
65
− 2u
64
+ ··· + 640u − 256)
c
8
(u + 1)
6
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
65
+ 8u
64
+ ··· + 1080u + 81)
c
9
u
6
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
65
+ 2u
64
+ ··· − 19008u − 5184)
c
10
(u − 1)
6
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
65
+ 8u
64
+ ··· + 1080u + 81)
c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
65
+ 3u
64
+ ··· + 3u + 1)
c
12
81(9u
6
− 30u
5
+ 41u
4
− 30u
3
+ 15u
2
− 5u + 1)
· (u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (9u
65
+ 42u
64
+ ··· + 608293u + 315227)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
8
)(y
6
+ y
5
+ ··· + 3y + 1)(y
65
− 132y
64
+ ··· + 7503y −1)
c
2
, c
4
(y −1)
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
65
− 68y
64
+ ··· + 59y −1)
c
3
, c
7
y
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
65
+ 48y
64
+ ··· + 901120y −65536)
c
5
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
65
+ 37y
64
+ ··· + 11y −1)
c
6
6561(81y
6
− 108y
5
+ 100y
4
− 63y
3
+ 28y
2
− 8y + 1)
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (81y
65
+ 5796y
64
+ ··· + 10803168570y −895026889)
c
8
, c
10
(y −1)
6
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
65
− 30y
64
+ ··· + 422172y −6561)
c
9
y
6
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
65
+ 36y
64
+ ··· − 462827520y −26873856)
c
12
6561(81y
6
− 162y
5
+ 151y
4
+ 48y
3
+ 7y
2
+ 5y + 1)
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (81y
65
− 558y
64
+ ··· − 1063347056943y −99368061529)
21
