12n
0205
(K12n
0205
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 9 3 11 5 8 6 10
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
= h1.70976 × 10
62
u
52
− 3.03954 × 10
60
u
51
+ ··· + 8.90112 × 10
63
b − 1.06077 × 10
64
,
− 1.10028 × 10
63
u
52
− 1.18132 × 10
64
u
51
+ ··· + 9.89014 × 10
62
a − 1.33065 × 10
64
,
u
53
+ 11u
52
+ ··· + 27u + 1i
I
u
2
= ha
6
+ 2a
4
+ 3a
2
+ b + 2, a
9
− a
8
+ 2a
7
− a
6
+ 3a
5
− a
4
+ 2a
3
+ a + 1, u − 1i
I
u
3
= hu
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 68 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
= h1.71 × 10
62
u
52
− 3.04 × 10
60
u
51
+ · · · + 8.90 × 10
63
b − 1.06 ×
10
64
, −1.10 × 10
63
u
52
− 1.18 × 10
64
u
51
+ · · · + 9.89 × 10
62
a − 1.33 ×
10
64
, u
53
+ 11u
52
+ · · · + 27u + 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
=
1.11250u
52
+ 11.9444u
51
+ ··· + 116.277u + 13.4543
−0.0192084u
52
+ 0.000341478u
51
+ ··· + 15.5915u + 1.19173
a
9
=
1.11250u
52
+ 11.9444u
51
+ ··· + 116.277u + 13.4543
−0.382334u
52
− 3.37450u
51
+ ··· + 8.79186u + 0.898684
a
12
=
−0.851461u
52
− 9.05934u
51
+ ··· − 65.4023u − 7.59764
0.902652u
52
+ 8.13404u
51
+ ··· + 10.0567u − 0.0126855
a
6
=
−0.0355732u
52
− 0.584596u
51
+ ··· + 13.1513u − 0.387998
0.349645u
52
+ 3.23765u
51
+ ··· + 1.90889u + 0.0261483
a
7
=
0.130529u
52
+ 1.68645u
51
+ ··· + 35.4466u + 5.88903
0.154225u
52
+ 1.43278u
51
+ ··· + 4.53267u + 0.381154
a
11
=
−0.284754u
52
− 3.11922u
51
+ ··· − 39.9792u − 6.27018
0.427550u
52
+ 3.88507u
51
+ ··· − 1.47440u − 0.445947
a
8
=
0.284754u
52
+ 3.11922u
51
+ ··· + 39.9792u + 6.27018
0.154225u
52
+ 1.43278u
51
+ ··· + 4.53267u + 0.381154
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.225150u
52
− 2.33690u
51
+ ··· − 27.9440u − 9.85542
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
+ 63u
52
+ ··· + 371u + 1
c
2
, c
4
u
53
− 11u
52
+ ··· + 27u − 1
c
3
, c
7
u
53
− 2u
52
+ ··· + 2560u + 512
c
5
, c
11
u
53
+ 3u
52
+ ··· + 3u + 1
c
6
9(9u
53
− 30u
52
+ ··· − 9820u − 5144)
c
8
, c
10
u
53
− 8u
52
+ ··· + 936u − 81
c
9
u
53
+ 2u
52
+ ··· + 22464u − 5184
c
12
9(9u
53
− 6u
52
+ ··· + 279223u − 329)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
− 135y
52
+ ··· + 162995y −1
c
2
, c
4
y
53
− 63y
52
+ ··· + 371y −1
c
3
, c
7
y
53
+ 54y
52
+ ··· + 6815744y −262144
c
5
, c
11
y
53
+ 37y
52
+ ··· + 11y −1
c
6
81(81y
53
− 3132y
52
+ ··· + 2.63839 × 10
8
y −2.64607 × 10
7
)
c
8
, c
10
y
53
− 54y
52
+ ··· + 624672y −6561
c
9
y
53
− 36y
52
+ ··· − 140341248y −26873856
c
12
81(81y
53
− 4590y
52
+ ··· + 7.81268 × 10
10
y −108241)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.740987 + 0.599213I
a = 1.57596 − 0.73751I
b = 0.321377 − 0.617776I
−4.33713 − 4.43867I −10.24927 + 6.85756I
u = 0.740987 − 0.599213I
a = 1.57596 + 0.73751I
b = 0.321377 + 0.617776I
−4.33713 + 4.43867I −10.24927 − 6.85756I
u = 1.029610 + 0.245825I
a = 0.125397 + 0.344874I
b = 0.310362 + 0.858643I
−2.07856 − 0.90512I 0
u = 1.029610 − 0.245825I
a = 0.125397 − 0.344874I
b = 0.310362 − 0.858643I
−2.07856 + 0.90512I 0
u = 1.014220 + 0.368097I
a = 0.17089 + 1.53157I
b = 1.88007 − 0.54448I
−7.18708 − 1.12498I −14.8807 + 0.I
u = 1.014220 − 0.368097I
a = 0.17089 − 1.53157I
b = 1.88007 + 0.54448I
−7.18708 + 1.12498I −14.8807 + 0.I
u = 1.14783
a = 0.526566
b = 2.18865
−2.44483 0
u = 0.822832 + 0.202810I
a = 0.184579 − 0.579850I
b = 0.34533 + 2.28724I
−3.14584 − 0.60875I −6.43020 − 7.79756I
u = 0.822832 − 0.202810I
a = 0.184579 + 0.579850I
b = 0.34533 − 2.28724I
−3.14584 + 0.60875I −6.43020 + 7.79756I
u = −0.724671 + 0.356426I
a = −0.056116 + 0.976114I
b = 0.178762 + 0.417119I
0.78284 − 1.50580I 1.85337 + 3.47450I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724671 − 0.356426I
a = −0.056116 − 0.976114I
b = 0.178762 − 0.417119I
0.78284 + 1.50580I 1.85337 − 3.47450I
u = 1.229490 + 0.119531I
a = −1.077010 + 0.000602I
b = −2.50917 + 2.03905I
−5.64518 + 2.18249I 0
u = 1.229490 − 0.119531I
a = −1.077010 − 0.000602I
b = −2.50917 − 2.03905I
−5.64518 − 2.18249I 0
u = 0.578578 + 0.484586I
a = −1.018420 + 0.280436I
b = −0.415921 + 0.414378I
−0.90481 − 1.57510I −3.08858 + 5.02134I
u = 0.578578 − 0.484586I
a = −1.018420 − 0.280436I
b = −0.415921 − 0.414378I
−0.90481 + 1.57510I −3.08858 − 5.02134I
u = −0.708934 + 0.120407I
a = −0.92683 − 1.44462I
b = −0.469500 − 0.468379I
−4.72794 − 6.87040I −1.05460 + 3.48446I
u = −0.708934 − 0.120407I
a = −0.92683 + 1.44462I
b = −0.469500 + 0.468379I
−4.72794 + 6.87040I −1.05460 − 3.48446I
u = −1.188110 + 0.522041I
a = −0.065515 − 0.516096I
b = −0.181732 − 0.422617I
−1.55881 + 5.25423I 0
u = −1.188110 − 0.522041I
a = −0.065515 + 0.516096I
b = −0.181732 + 0.422617I
−1.55881 − 5.25423I 0
u = 0.713723 + 1.108540I
a = −1.145180 + 0.691529I
b = −1.004520 + 0.127758I
−11.4354 − 9.7069I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.713723 − 1.108540I
a = −1.145180 − 0.691529I
b = −1.004520 − 0.127758I
−11.4354 + 9.7069I 0
u = 0.645363 + 1.159150I
a = −0.411472 + 1.090720I
b = −0.475717 + 0.405091I
−11.21080 + 2.39200I 0
u = 0.645363 − 1.159150I
a = −0.411472 − 1.090720I
b = −0.475717 − 0.405091I
−11.21080 − 2.39200I 0
u = 0.536755 + 0.402568I
a = 0.923406 − 0.659788I
b = 0.89484 − 1.39101I
−3.70920 + 0.68240I −10.13112 + 2.63548I
u = 0.536755 − 0.402568I
a = 0.923406 + 0.659788I
b = 0.89484 + 1.39101I
−3.70920 − 0.68240I −10.13112 − 2.63548I
u = 0.709864 + 1.162520I
a = 0.713217 − 0.733177I
b = 0.685394 − 0.156529I
−6.83584 − 3.76717I 0
u = 0.709864 − 1.162520I
a = 0.713217 + 0.733177I
b = 0.685394 + 0.156529I
−6.83584 + 3.76717I 0
u = −0.190058 + 0.453543I
a = −1.217760 + 0.413382I
b = −0.101388 + 0.374695I
1.01456 − 1.24993I 3.91266 + 3.38096I
u = −0.190058 − 0.453543I
a = −1.217760 − 0.413382I
b = −0.101388 − 0.374695I
1.01456 + 1.24993I 3.91266 − 3.38096I
u = −1.63891 + 0.08655I
a = −0.523277 − 0.000961I
b = −2.42482 − 0.70129I
−11.54620 + 0.81534I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63891 − 0.08655I
a = −0.523277 + 0.000961I
b = −2.42482 + 0.70129I
−11.54620 − 0.81534I 0
u = −1.65289 + 0.15939I
a = 0.875260 − 0.410425I
b = 2.21311 − 0.23469I
−8.77075 + 4.08365I 0
u = −1.65289 − 0.15939I
a = 0.875260 + 0.410425I
b = 2.21311 + 0.23469I
−8.77075 − 4.08365I 0
u = −1.70501 + 0.03615I
a = −0.395981 − 0.689977I
b = −1.41927 + 0.04910I
−12.33890 + 1.47775I 0
u = −1.70501 − 0.03615I
a = −0.395981 + 0.689977I
b = −1.41927 − 0.04910I
−12.33890 − 1.47775I 0
u = −1.70201 + 0.18739I
a = −1.42791 + 0.60902I
b = −2.95092 + 0.61814I
−12.9006 + 7.5876I 0
u = −1.70201 − 0.18739I
a = −1.42791 − 0.60902I
b = −2.95092 − 0.61814I
−12.9006 − 7.5876I 0
u = −0.276292 + 0.038780I
a = 3.14779 − 2.19159I
b = 0.509597 − 0.650771I
−1.03321 + 2.55519I 0.02559 − 3.47308I
u = −0.276292 − 0.038780I
a = 3.14779 + 2.19159I
b = 0.509597 + 0.650771I
−1.03321 − 2.55519I 0.02559 + 3.47308I
u = 1.73015 + 0.03085I
a = 0.952566 − 0.310448I
b = 2.31647 − 0.61550I
−13.7945 + 6.0358I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73015 − 0.03085I
a = 0.952566 + 0.310448I
b = 2.31647 + 0.61550I
−13.7945 − 6.0358I 0
u = −1.69334 + 0.39921I
a = 1.073220 − 0.496311I
b = 2.64306 − 0.19760I
−19.2132 + 15.4269I 0
u = −1.69334 − 0.39921I
a = 1.073220 + 0.496311I
b = 2.64306 + 0.19760I
−19.2132 − 15.4269I 0
u = −1.70276 + 0.44597I
a = 0.904826 − 0.036221I
b = 1.90592 + 0.31921I
−18.7129 + 3.6964I 0
u = −1.70276 − 0.44597I
a = 0.904826 + 0.036221I
b = 1.90592 − 0.31921I
−18.7129 − 3.6964I 0
u = −1.71139 + 0.41302I
a = −0.918462 + 0.320773I
b = −2.22054 + 0.11225I
−14.6527 + 9.7412I 0
u = −1.71139 − 0.41302I
a = −0.918462 − 0.320773I
b = −2.22054 − 0.11225I
−14.6527 − 9.7412I 0
u = 1.76059
a = −0.828656
b = −2.05351
−9.31076 0
u = −1.76959 + 0.06263I
a = 1.07789 + 1.41573I
b = 1.99778 + 1.80741I
−17.5158 + 2.8823I 0
u = −1.76959 − 0.06263I
a = 1.07789 − 1.41573I
b = 1.99778 − 1.80741I
−17.5158 − 2.8823I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.016819 + 0.167581I
a = −4.99549 − 3.00427I
b = −1.226480 + 0.616758I
−4.36101 − 1.13066I −3.77707 + 1.04050I
u = −0.016819 − 0.167581I
a = −4.99549 + 3.00427I
b = −1.226480 − 0.616758I
−4.36101 + 1.13066I −3.77707 − 1.04050I
u = −0.0499663
a = 9.21094
b = 0.593977
−1.26040 −8.84480
10
II.
I
u
2
= ha
6
+ 2a
4
+ 3a
2
+ b + 2, a
9
− a
8
+ 2a
7
− a
6
+ 3a
5
− a
4
+ 2a
3
+ a + 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
+ 2a − 1
a
6
=
a
4
−a
8
− a
6
− a
4
+ a
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 = −4a
8
+ 8a
7
− 13a
6
+ 9a
5
− 17a
4
+ 16a
3
− 13a
2
+ 4a − 16
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
8
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
9
, c
12
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
10
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
11
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
8
, c
10
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
9
, c
12
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.140343 + 0.966856I
b = −0.218072 + 0.482572I
0.13850 + 2.09337I −4.94317 − 6.62869I
u = 1.00000
a = −0.140343 − 0.966856I
b = −0.218072 − 0.482572I
0.13850 − 2.09337I −4.94317 + 6.62869I
u = 1.00000
a = −0.628449 + 0.875112I
b = −0.037875 + 0.791187I
−2.26187 + 2.45442I −8.11682 − 3.00529I
u = 1.00000
a = −0.628449 − 0.875112I
b = −0.037875 − 0.791187I
−2.26187 − 2.45442I −8.11682 + 3.00529I
u = 1.00000
a = 0.796005 + 0.733148I
b = 0.80973 − 2.39258I
−6.01628 + 1.33617I −10.09079 + 3.07774I
u = 1.00000
a = 0.796005 − 0.733148I
b = 0.80973 + 2.39258I
−6.01628 − 1.33617I −10.09079 − 3.07774I
u = 1.00000
a = 0.728966 + 0.986295I
b = 0.417942 + 0.357732I
−5.24306 − 7.08493I −14.1334 + 8.8789I
u = 1.00000
a = 0.728966 − 0.986295I
b = 0.417942 − 0.357732I
−5.24306 + 7.08493I −14.1334 − 8.8789I
u = 1.00000
a = −0.512358
b = −2.94345
−2.84338 −25.4320
14
III. I
u
3
= hu
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
2
3
u
5
−
4
9
u
4
+ ··· +
8
9
u +
1
9
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
11
=
−2u
5
+ 3u
3
− 2u
−
4
3
u
5
−
4
3
u
4
+
2
3
u
2
+
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
+
47
9
u
4
−
4
3
u
3
−
19
9
u
2
−
20
3
u −
80
9
15
(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)
16
(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)
17
(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
−3.53554 − 0.92430I −15.9578 + 1.1630I
u = 1.002190 − 0.295542I
a = 0
b = 0.49282 + 2.03411I
−3.53554 + 0.92430I −15.9578 − 1.1630I
u = −0.428243 + 0.664531I
a = 0
b = −0.384438 − 0.080017I
0.245672 − 0.924305I −7.47464 − 1.75692I
u = −0.428243 − 0.664531I
a = 0
b = −0.384438 + 0.080017I
0.245672 + 0.924305I −7.47464 + 1.75692I
u = −1.073950 + 0.558752I
a = 0
b = 0.391622 + 0.105509I
−1.64493 + 5.69302I −7.2342 − 14.2758I
u = −1.073950 − 0.558752I
a = 0
b = 0.391622 − 0.105509I
−1.64493 − 5.69302I −7.2342 + 14.2758I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
53
+ 63u
52
+ ··· + 371u + 1)
c
2
((u − 1)
9
)(u
6
+ u
5
+ ··· + u + 1)(u
53
− 11u
52
+ ··· + 27u − 1)
c
3
u
9
(u
6
− u
5
+ ··· − u + 1)(u
53
− 2u
52
+ ··· + 2560u + 512)
c
4
((u + 1)
9
)(u
6
− u
5
+ ··· − u + 1)(u
53
− 11u
52
+ ··· + 27u − 1)
c
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
53
+ 3u
52
+ ··· + 3u + 1)
c
6
81(9u
6
− 12u
5
+ 2u
4
+ u
3
+ 4u
2
− 4u + 1)
· (u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (9u
53
− 30u
52
+ ··· − 9820u − 5144)
c
7
u
9
(u
6
+ u
5
+ ··· + u + 1)(u
53
− 2u
52
+ ··· + 2560u + 512)
c
8
(u − 1)
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
53
− 8u
52
+ ··· + 936u − 81)
c
9
u
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
53
+ 2u
52
+ ··· + 22464u − 5184)
c
10
(u + 1)
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
53
− 8u
52
+ ··· + 936u − 81)
c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
53
+ 3u
52
+ ··· + 3u + 1)
c
12
81(9u
6
+ 30u
5
+ 41u
4
+ 30u
3
+ 15u
2
+ 5u + 1)
· (u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (9u
53
− 6u
52
+ ··· + 279223u − 329)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
53
− 135y
52
+ ··· + 162995y −1)
c
2
, c
4
(y −1)
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
53
− 63y
52
+ ··· + 371y −1)
c
3
, c
7
y
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
53
+ 54y
52
+ ··· + 6815744y −262144)
c
5
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
53
+ 37y
52
+ ··· + 11y −1)
c
6
6561(81y
6
− 108y
5
+ 100y
4
− 63y
3
+ 28y
2
− 8y + 1)
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (81y
53
− 3132y
52
+ ··· + 263838736y −26460736)
c
8
, c
10
(y −1)
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
53
− 54y
52
+ ··· + 624672y −6561)
c
9
y
6
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
53
− 36y
52
+ ··· − 140341248y −26873856)
c
12
6561(81y
6
− 162y
5
+ 151y
4
+ 48y
3
+ 7y
2
+ 5y + 1)
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (81y
53
− 4590y
52
+ ··· + 78126767425y −108241)
20
