12n
0703
(K12n
0703
)
A knot diagram
1
Linearized knot diagam
4 6 7 8 9 10 4 12 2 3 9 7
Solving Sequence
4,8 5,12
9 6 7 1 2 3 11 10
c
4
c
8
c
5
c
7
c
12
c
1
c
3
c
11
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.60229 × 10
96
u
54
+ 2.91450 × 10
96
u
53
+ ··· + 1.26296 × 10
98
b − 3.52131 × 10
97
,
1.21366 × 10
98
u
54
+ 2.79487 × 10
98
u
53
+ ··· + 1.32611 × 10
99
a + 1.28362 × 10
100
, u
55
+ 2u
54
+ ··· + 10u − 21i
I
u
2
= h−u
14
− 2u
13
+ 8u
12
+ 16u
11
− 24u
10
− 45u
9
+ 38u
8
+ 56u
7
− 34u
6
− 29u
5
+ 9u
4
+ 4u
3
+ 9u
2
+ b + u + 1,
− 2u
14
− 2u
13
+ ··· + a + 5,
u
15
+ 3u
14
− 6u
13
− 24u
12
+ 8u
11
+ 69u
10
+ 7u
9
− 94u
8
− 22u
7
+ 63u
6
+ 20u
5
− 13u
4
− 14u
3
− 10u
2
− 1i
I
u
3
= hb
2
+ b − a, a
2
+ a + 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 74 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
=
h1.60×10
96
u
54
+2.91×10
96
u
53
+· · ·+1.26×10
98
b−3.52×10
97
, 1.21×10
98
u
54
+
2.79 × 10
98
u
53
+ · · · + 1.33 × 10
99
a + 1.28 × 10
100
, u
55
+ 2u
54
+ · · · + 10u − 21i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
12
=
−0.0915205u
54
− 0.210758u
53
+ ··· − 20.1374u − 9.67965
−0.0126868u
54
− 0.0230768u
53
+ ··· + 4.47039u + 0.278815
a
9
=
0.0149847u
54
+ 0.0198107u
53
+ ··· + 7.10770u + 2.36249
0.0166454u
54
+ 0.0346016u
53
+ ··· + 4.03014u + 0.137160
a
6
=
−0.110827u
54
− 0.258163u
53
+ ··· − 29.3739u − 6.63387
0.0161463u
54
+ 0.0324579u
53
+ ··· + 0.912590u − 0.403284
a
7
=
u
u
a
1
=
−0.100369u
54
− 0.231157u
53
+ ··· − 21.4928u − 10.3099
−0.0215354u
54
− 0.0434760u
53
+ ··· + 3.11502u − 0.351471
a
2
=
−0.0788337u
54
− 0.187681u
53
+ ··· − 24.6078u − 9.95846
−0.0215354u
54
− 0.0434760u
53
+ ··· + 3.11502u − 0.351471
a
3
=
−u
2
+ 1
−u
2
a
11
=
0.112884u
54
+ 0.258117u
53
+ ··· + 33.6265u + 7.39414
−0.00613650u
54
− 0.00991033u
53
+ ··· + 2.47671u + 1.02640
a
10
=
0.115245u
54
+ 0.257703u
53
+ ··· + 28.9349u + 5.85332
−0.00189354u
54
− 0.00106986u
53
+ ··· + 2.46134u + 1.14169
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0893522u
54
+ 0.122027u
53
+ ··· − 35.4397u − 10.8689
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
+ 7u
54
+ ··· − 107283u + 5687
c
2
u
55
− 2u
54
+ ··· + 11u + 1
c
3
, c
4
, c
7
u
55
+ 2u
54
+ ··· + 10u − 21
c
5
u
55
+ u
54
+ ··· − 11533u − 4223
c
6
u
55
+ 2u
54
+ ··· − 28u + 47
c
8
, c
11
u
55
+ 3u
54
+ ··· − 23u − 7
c
9
u
55
− 5u
53
+ ··· + 136u − 48
c
10
u
55
+ 17u
53
+ ··· + 586u − 227
c
12
u
55
+ u
54
+ ··· − 5060u − 2767
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
− 99y
54
+ ··· + 1442878657y −32341969
c
2
y
55
+ 2y
54
+ ··· + 75y −1
c
3
, c
4
, c
7
y
55
− 76y
54
+ ··· + 6862y −441
c
5
y
55
+ 29y
54
+ ··· − 23722333y −17833729
c
6
y
55
− 12y
54
+ ··· + 71378y −2209
c
8
, c
11
y
55
+ 5y
54
+ ··· + 2125y −49
c
9
y
55
− 10y
54
+ ··· + 63808y −2304
c
10
y
55
+ 34y
54
+ ··· − 605918y −51529
c
12
y
55
− 107y
54
+ ··· − 5436606y −7656289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.843879 + 0.544766I
a = 1.298890 − 0.127602I
b = 1.156400 + 0.474581I
−3.16540 + 3.11054I −14.1931 − 9.0876I
u = −0.843879 − 0.544766I
a = 1.298890 + 0.127602I
b = 1.156400 − 0.474581I
−3.16540 − 3.11054I −14.1931 + 9.0876I
u = 0.948829 + 0.204011I
a = −0.942145 − 0.845434I
b = −0.842082 − 0.113281I
−2.44958 − 4.10717I −10.9496 + 9.7884I
u = 0.948829 − 0.204011I
a = −0.942145 + 0.845434I
b = −0.842082 + 0.113281I
−2.44958 + 4.10717I −10.9496 − 9.7884I
u = −0.037941 + 1.123190I
a = −0.309131 − 0.625328I
b = −0.250371 − 0.018761I
−1.10227 + 4.51894I 0
u = −0.037941 − 1.123190I
a = −0.309131 + 0.625328I
b = −0.250371 + 0.018761I
−1.10227 − 4.51894I 0
u = −1.090260 + 0.307766I
a = −0.153294 − 0.936767I
b = −0.727540 + 0.848969I
−2.42178 − 2.55675I 0
u = −1.090260 − 0.307766I
a = −0.153294 + 0.936767I
b = −0.727540 − 0.848969I
−2.42178 + 2.55675I 0
u = 0.792699 + 0.232053I
a = −1.39064 − 0.28620I
b = −1.170460 + 0.185340I
−4.12045 − 1.98383I −18.7598 + 3.0273I
u = 0.792699 − 0.232053I
a = −1.39064 + 0.28620I
b = −1.170460 − 0.185340I
−4.12045 + 1.98383I −18.7598 − 3.0273I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.150340 + 0.254911I
a = −0.425744 + 0.326070I
b = −1.380530 − 0.225219I
−1.61488 + 0.87614I 0
u = −1.150340 − 0.254911I
a = −0.425744 − 0.326070I
b = −1.380530 + 0.225219I
−1.61488 − 0.87614I 0
u = −1.124160 + 0.427568I
a = 0.599114 + 0.157148I
b = 0.573870 + 0.680404I
−2.81458 + 0.86949I 0
u = −1.124160 − 0.427568I
a = 0.599114 − 0.157148I
b = 0.573870 − 0.680404I
−2.81458 − 0.86949I 0
u = 1.213070 + 0.090501I
a = 0.454982 − 0.314837I
b = 0.627652 + 1.153370I
−3.98050 − 5.51374I 0
u = 1.213070 − 0.090501I
a = 0.454982 + 0.314837I
b = 0.627652 − 1.153370I
−3.98050 + 5.51374I 0
u = 0.742164 + 0.235850I
a = 0.299105 + 1.265320I
b = −0.453999 + 1.033190I
2.30362 + 3.30557I −2.87153 − 3.56943I
u = 0.742164 − 0.235850I
a = 0.299105 − 1.265320I
b = −0.453999 − 1.033190I
2.30362 − 3.30557I −2.87153 + 3.56943I
u = −1.301400 + 0.156837I
a = 0.251488 + 1.049080I
b = −0.057943 + 0.886147I
−1.28653 − 3.07187I 0
u = −1.301400 − 0.156837I
a = 0.251488 − 1.049080I
b = −0.057943 − 0.886147I
−1.28653 + 3.07187I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.078130 + 0.779868I
a = 0.937931 + 0.091074I
b = 1.219160 + 0.105261I
−4.41965 − 10.75660I 0
u = 1.078130 − 0.779868I
a = 0.937931 − 0.091074I
b = 1.219160 − 0.105261I
−4.41965 + 10.75660I 0
u = −1.062820 + 0.800842I
a = −0.700193 − 0.073534I
b = −0.941274 + 0.263175I
−4.22067 + 1.89516I 0
u = −1.062820 − 0.800842I
a = −0.700193 + 0.073534I
b = −0.941274 − 0.263175I
−4.22067 − 1.89516I 0
u = −0.181860 + 0.623471I
a = 1.072740 − 0.311332I
b = 0.846917 + 0.444278I
1.18559 + 2.23449I −0.71696 − 3.13365I
u = −0.181860 − 0.623471I
a = 1.072740 + 0.311332I
b = 0.846917 − 0.444278I
1.18559 − 2.23449I −0.71696 + 3.13365I
u = 1.344180 + 0.263000I
a = 0.033573 − 0.599843I
b = −0.307839 + 0.697502I
−3.77877 − 5.48694I 0
u = 1.344180 − 0.263000I
a = 0.033573 + 0.599843I
b = −0.307839 − 0.697502I
−3.77877 + 5.48694I 0
u = −0.554000
a = 0.302766
b = −0.620774
−1.07952 −9.55000
u = 0.003980 + 0.413867I
a = 1.88223 + 0.89459I
b = 0.131386 + 0.662442I
0.54485 + 2.00796I −2.63887 − 4.05218I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.003980 − 0.413867I
a = 1.88223 − 0.89459I
b = 0.131386 − 0.662442I
0.54485 − 2.00796I −2.63887 + 4.05218I
u = −0.183724 + 0.367833I
a = 0.58192 + 1.74816I
b = −0.299016 + 0.515843I
−1.46466 + 0.28580I −10.27103 − 1.57830I
u = −0.183724 − 0.367833I
a = 0.58192 − 1.74816I
b = −0.299016 − 0.515843I
−1.46466 − 0.28580I −10.27103 + 1.57830I
u = 1.65391
a = 0.249685
b = 1.86192
−9.07692 0
u = −1.66786 + 0.09211I
a = 0.751228 − 0.535995I
b = 2.66084 − 0.38730I
−12.75570 + 3.35483I 0
u = −1.66786 − 0.09211I
a = 0.751228 + 0.535995I
b = 2.66084 + 0.38730I
−12.75570 − 3.35483I 0
u = −1.72061 + 0.05114I
a = 0.679921 − 0.682618I
b = 2.27477 − 0.94586I
−12.03510 + 5.10367I 0
u = −1.72061 − 0.05114I
a = 0.679921 + 0.682618I
b = 2.27477 + 0.94586I
−12.03510 − 5.10367I 0
u = −0.145583 + 0.234667I
a = −2.42652 + 0.00455I
b = −0.11826 + 1.67678I
0.55411 + 4.57385I −7.8171 − 13.5503I
u = −0.145583 − 0.234667I
a = −2.42652 − 0.00455I
b = −0.11826 − 1.67678I
0.55411 − 4.57385I −7.8171 + 13.5503I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.266031 + 0.033873I
a = 0.13429 + 5.34542I
b = 0.444871 − 0.069784I
3.84010 + 3.87958I −14.7891 − 1.0481I
u = 0.266031 − 0.033873I
a = 0.13429 − 5.34542I
b = 0.444871 + 0.069784I
3.84010 − 3.87958I −14.7891 + 1.0481I
u = 1.73181 + 0.18076I
a = −0.720894 − 0.731345I
b = −2.16250 − 0.49231I
−12.24970 − 6.15405I 0
u = 1.73181 − 0.18076I
a = −0.720894 + 0.731345I
b = −2.16250 + 0.49231I
−12.24970 + 6.15405I 0
u = −1.77155 + 0.23587I
a = −0.696419 + 0.603643I
b = −2.34613 + 0.51535I
−14.1664 + 14.9969I 0
u = −1.77155 − 0.23587I
a = −0.696419 − 0.603643I
b = −2.34613 − 0.51535I
−14.1664 − 14.9969I 0
u = −1.78772 + 0.04019I
a = −0.733763 − 0.585348I
b = −2.15718 − 0.56893I
−15.0134 + 6.2911I 0
u = −1.78772 − 0.04019I
a = −0.733763 + 0.585348I
b = −2.15718 + 0.56893I
−15.0134 − 6.2911I 0
u = 1.77789 + 0.25574I
a = 0.657004 + 0.451249I
b = 2.28450 + 0.38651I
−13.8622 − 6.3433I 0
u = 1.77789 − 0.25574I
a = 0.657004 − 0.451249I
b = 2.28450 − 0.38651I
−13.8622 + 6.3433I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.79768 + 0.03453I
a = 0.527842 − 0.629408I
b = 1.97284 − 0.48816I
−13.39870 + 1.16047I 0
u = 1.79768 − 0.03453I
a = 0.527842 + 0.629408I
b = 1.97284 + 0.48816I
−13.39870 − 1.16047I 0
u = 1.82600 + 0.05971I
a = −0.823032 − 0.428595I
b = −2.11304 − 0.47973I
−14.0479 − 3.0438I 0
u = 1.82600 − 0.05971I
a = −0.823032 + 0.428595I
b = −2.11304 + 0.47973I
−14.0479 + 3.0438I 0
u = −2.00544
a = 0.242799
b = 1.02879
−7.47069 0
10
II. I
u
2
=
h−u
14
−2u
13
+· · ·+b+1, −2u
14
−2u
13
+· · ·+a+5, u
15
+3u
14
+· · ·−10u
2
−1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
12
=
2u
14
+ 2u
13
+ ··· − u − 5
u
14
+ 2u
13
+ ··· − u − 1
a
9
=
4u
14
+ 9u
13
+ ··· − 16u − 3
10u
14
+ 17u
13
+ ··· + 5u − 7
a
6
=
5u
14
+ 7u
13
+ ··· + 11u + 1
11u
14
+ 17u
13
+ ··· + 7u − 8
a
7
=
u
u
a
1
=
8u
14
+ 10u
13
+ ··· − 44u
2
− 8
7u
14
+ 10u
13
+ ··· − 43u
2
− 4
a
2
=
u
14
− 9u
12
+ ··· − u
2
− 4
7u
14
+ 10u
13
+ ··· − 43u
2
− 4
a
3
=
−u
2
+ 1
−u
2
a
11
=
−u
14
− u
13
+ ··· − 3u + 4
−11u
14
− 16u
13
+ ··· − 3u + 7
a
10
=
13u
14
+ 22u
13
+ ··· + 2u − 6
15u
14
+ 25u
13
+ ··· + 9u − 11
(ii) Obstruction class = 1
(iii) Cusp Shapes = 26u
14
+ 43u
13
− 216u
12
− 339u
11
+ 679u
10
+ 927u
9
− 1096u
8
−
1104u
7
+ 928u
6
+ 563u
5
− 215u
4
− 149u
3
− 204u
2
+ 32u − 15
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 8u
14
+ ··· + 175u − 43
c
2
u
15
− 3u
14
+ ··· + 2u
2
− 1
c
3
, c
4
u
15
+ 3u
14
+ ··· − 10u
2
− 1
c
5
u
15
− u
14
+ ··· − u
2
− 1
c
6
u
15
+ u
13
+ ··· + u + 1
c
7
u
15
− 3u
14
+ ··· + 10u
2
+ 1
c
8
u
15
− 4u
14
+ ··· + u + 1
c
9
u
15
− u
14
+ ··· + 27u − 13
c
10
u
15
+ u
14
+ ··· − 7u
2
− 1
c
11
u
15
+ 4u
14
+ ··· + u − 1
c
12
u
15
− 2u
14
+ ··· + u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 2y
14
+ ··· − 15815y −1849
c
2
y
15
− 3y
14
+ ··· + 4y −1
c
3
, c
4
, c
7
y
15
− 21y
14
+ ··· − 20y −1
c
5
y
15
+ 3y
14
+ ··· − 2y −1
c
6
y
15
+ 2y
14
+ ··· − 3y −1
c
8
, c
11
y
15
+ 10y
14
+ ··· − 3y −1
c
9
y
15
+ 5y
14
+ ··· + 131y −169
c
10
y
15
+ 15y
14
+ ··· − 14y −1
c
12
y
15
+ 4y
14
+ ··· − 37y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.860177 + 0.509187I
a = −1.021030 + 0.032473I
b = −0.879433 + 0.229899I
−2.90182 − 2.03075I −10.03062 + 3.32590I
u = 0.860177 − 0.509187I
a = −1.021030 − 0.032473I
b = −0.879433 − 0.229899I
−2.90182 + 2.03075I −10.03062 − 3.32590I
u = 1.320510 + 0.166851I
a = −0.090859 + 0.980403I
b = −0.175878 + 0.242981I
−0.02472 + 2.27007I −5.66786 − 3.21825I
u = 1.320510 − 0.166851I
a = −0.090859 − 0.980403I
b = −0.175878 − 0.242981I
−0.02472 − 2.27007I −5.66786 + 3.21825I
u = −1.347170 + 0.162955I
a = −0.160946 + 0.533747I
b = −0.22492 − 1.70994I
−3.25137 + 6.18801I −3.54918 − 9.67050I
u = −1.347170 − 0.162955I
a = −0.160946 − 0.533747I
b = −0.22492 + 1.70994I
−3.25137 − 6.18801I −3.54918 + 9.67050I
u = −1.42579 + 0.12850I
a = 0.070901 − 0.902606I
b = 0.289612 − 1.144560I
−0.93716 + 5.50758I −6.26875 − 6.01276I
u = −1.42579 − 0.12850I
a = 0.070901 + 0.902606I
b = 0.289612 + 1.144560I
−0.93716 − 5.50758I −6.26875 + 6.01276I
u = −0.206520 + 0.508428I
a = 0.860914 − 0.633967I
b = −0.115881 − 1.290910I
0.74360 − 3.97923I −4.72626 + 2.68613I
u = −0.206520 − 0.508428I
a = 0.860914 + 0.633967I
b = −0.115881 + 1.290910I
0.74360 + 3.97923I −4.72626 − 2.68613I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.071627 + 0.286359I
a = −4.47522 − 0.75940I
b = −0.277531 − 0.478076I
4.21917 − 3.97249I 6.01465 + 6.05055I
u = 0.071627 − 0.286359I
a = −4.47522 + 0.75940I
b = −0.277531 + 0.478076I
4.21917 + 3.97249I 6.01465 − 6.05055I
u = −1.72665 + 0.09660I
a = 0.721441 − 0.590290I
b = 2.34637 − 0.60996I
−12.29270 + 4.25654I −10.89997 − 2.52513I
u = −1.72665 − 0.09660I
a = 0.721441 + 0.590290I
b = 2.34637 + 0.60996I
−12.29270 − 4.25654I −10.89997 + 2.52513I
u = 1.90762
a = 0.189589
b = 1.07533
−7.29848 9.25600
15
III. I
u
3
= hb
2
+ b − a, a
2
+ a + 1, u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
1
a
5
=
1
1
a
12
=
a
b
a
9
=
a + 1
−ba + 1
a
6
=
−b
ba + a
a
7
=
1
1
a
1
=
−b + 2a
a
a
2
=
−b + a
a
a
3
=
0
−1
a
11
=
a + 1
−ba − a
a
10
=
a + 1
−ba + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3ba − a − 9
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
2
− u + 1)
2
c
2
u
4
− 2u
3
+ 2u
2
− u + 1
c
3
, c
4
(u − 1)
4
c
5
, c
6
u
4
− u
3
− u
2
+ u + 1
c
7
(u + 1)
4
c
9
u
4
c
10
, c
11
(u
2
+ u + 1)
2
c
12
u
4
+ 2u
2
+ 3u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
c
11
(y
2
+ y + 1)
2
c
2
y
4
+ 2y
2
+ 3y + 1
c
3
, c
4
, c
7
(y −1)
4
c
5
, c
6
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
9
y
4
c
12
y
4
+ 4y
3
+ 6y
2
− 5y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.500000 + 0.866025I
b = 0.070696 + 0.758745I
−1.64493 + 2.02988I −10.57732 − 1.82047I
u = 1.00000
a = −0.500000 + 0.866025I
b = −1.070700 − 0.758745I
−1.64493 + 2.02988I −4.92268 − 2.50966I
u = 1.00000
a = −0.500000 − 0.866025I
b = 0.070696 − 0.758745I
−1.64493 − 2.02988I −10.57732 + 1.82047I
u = 1.00000
a = −0.500000 − 0.866025I
b = −1.070700 + 0.758745I
−1.64493 − 2.02988I −4.92268 + 2.50966I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
15
− 8u
14
+ ··· + 175u − 43)
· (u
55
+ 7u
54
+ ··· − 107283u + 5687)
c
2
(u
4
− 2u
3
+ 2u
2
− u + 1)(u
15
− 3u
14
+ ··· + 2u
2
− 1)
· (u
55
− 2u
54
+ ··· + 11u + 1)
c
3
, c
4
((u − 1)
4
)(u
15
+ 3u
14
+ ··· − 10u
2
− 1)(u
55
+ 2u
54
+ ··· + 10u − 21)
c
5
(u
4
− u
3
− u
2
+ u + 1)(u
15
− u
14
+ ··· − u
2
− 1)
· (u
55
+ u
54
+ ··· − 11533u − 4223)
c
6
(u
4
− u
3
− u
2
+ u + 1)(u
15
+ u
13
+ ··· + u + 1)
· (u
55
+ 2u
54
+ ··· − 28u + 47)
c
7
((u + 1)
4
)(u
15
− 3u
14
+ ··· + 10u
2
+ 1)(u
55
+ 2u
54
+ ··· + 10u − 21)
c
8
((u
2
− u + 1)
2
)(u
15
− 4u
14
+ ··· + u + 1)(u
55
+ 3u
54
+ ··· − 23u − 7)
c
9
u
4
(u
15
− u
14
+ ··· + 27u − 13)(u
55
− 5u
53
+ ··· + 136u − 48)
c
10
((u
2
+ u + 1)
2
)(u
15
+ u
14
+ ··· − 7u
2
− 1)
· (u
55
+ 17u
53
+ ··· + 586u − 227)
c
11
((u
2
+ u + 1)
2
)(u
15
+ 4u
14
+ ··· + u − 1)(u
55
+ 3u
54
+ ··· − 23u − 7)
c
12
(u
4
+ 2u
2
+ 3u + 1)(u
15
− 2u
14
+ ··· + u + 1)
· (u
55
+ u
54
+ ··· − 5060u − 2767)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
15
+ 2y
14
+ ··· − 15815y −1849)
· (y
55
− 99y
54
+ ··· + 1442878657y −32341969)
c
2
(y
4
+ 2y
2
+ 3y + 1)(y
15
− 3y
14
+ ··· + 4y −1)
· (y
55
+ 2y
54
+ ··· + 75y −1)
c
3
, c
4
, c
7
((y −1)
4
)(y
15
− 21y
14
+ ··· − 20y −1)
· (y
55
− 76y
54
+ ··· + 6862y −441)
c
5
(y
4
− 3y
3
+ 5y
2
− 3y + 1)(y
15
+ 3y
14
+ ··· − 2y −1)
· (y
55
+ 29y
54
+ ··· − 23722333y −17833729)
c
6
(y
4
− 3y
3
+ 5y
2
− 3y + 1)(y
15
+ 2y
14
+ ··· − 3y −1)
· (y
55
− 12y
54
+ ··· + 71378y −2209)
c
8
, c
11
((y
2
+ y + 1)
2
)(y
15
+ 10y
14
+ ··· − 3y −1)
· (y
55
+ 5y
54
+ ··· + 2125y −49)
c
9
y
4
(y
15
+ 5y
14
+ ··· + 131y −169)(y
55
− 10y
54
+ ··· + 63808y −2304)
c
10
((y
2
+ y + 1)
2
)(y
15
+ 15y
14
+ ··· − 14y −1)
· (y
55
+ 34y
54
+ ··· − 605918y −51529)
c
12
(y
4
+ 4y
3
+ 6y
2
− 5y + 1)(y
15
+ 4y
14
+ ··· − 37y −1)
· (y
55
− 107y
54
+ ··· − 5436606y −7656289)
21
