12n
0197
(K12n
0197
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 10 4 12 7 6 8 9
Solving Sequence
4,7
8
3,10
6 11 12 9 5 2 1
c
7
c
3
c
6
c
10
c
11
c
9
c
5
c
2
c
1
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.18355 × 10
119
u
63
− 1.02834 × 10
120
u
62
+ ··· + 6.77073 × 10
121
b − 4.36658 × 10
121
,
1.74383 × 10
121
u
63
+ 1.62828 × 10
121
u
62
+ ··· + 6.09366 × 10
122
a − 5.03534 × 10
122
,
u
64
+ 2u
63
+ ··· − 36u − 36i
I
u
2
= h−3u
2
a + au + 3u
2
+ 5b − 2a − u + 7, −4u
2
a + a
2
+ 2au + 7u
2
− 6a − 2u + 17, u
3
− u
2
+ 2u − 1i
I
u
3
= hb, −2u
2
+ a − u − 3, u
3
+ u
2
+ 2u + 1i
I
v
1
= ha, b − 3v + 1, 3v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 75 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−8.18 × 10
119
u
63
− 1.03 × 10
120
u
62
+ · · · + 6.77 × 10
121
b − 4.37 ×
10
121
, 1.74 × 10
121
u
63
+ 1.63 × 10
121
u
62
+ · · · + 6.09 × 10
122
a − 5.04 ×
10
122
, u
64
+ 2u
63
+ · · · − 36u − 36i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
10
=
−0.0286172u
63
− 0.0267209u
62
+ ··· + 6.11396u + 0.826324
0.0120867u
63
+ 0.0151881u
62
+ ··· − 2.44925u + 0.644920
a
6
=
−0.00662501u
63
+ 0.00268962u
62
+ ··· + 0.595026u − 0.834195
−0.00664903u
63
− 0.0289554u
62
+ ··· + 1.40621u + 1.36782
a
11
=
−0.0183635u
63
− 0.0249695u
62
+ ··· + 5.48546u − 0.126144
0.00140169u
63
+ 0.0235025u
62
+ ··· − 1.73632u − 1.16399
a
12
=
−0.0101569u
63
+ 0.00172136u
62
+ ··· + 3.98696u − 1.71340
−0.00147268u
63
+ 0.0111679u
62
+ ··· − 1.07088u − 0.793992
a
9
=
−0.0165305u
63
− 0.0115329u
62
+ ··· + 3.66471u + 1.47124
0.0120867u
63
+ 0.0151881u
62
+ ··· − 2.44925u + 0.644920
a
5
=
−0.00128622u
63
− 0.00466939u
62
+ ··· + 2.09437u − 0.413947
−0.000693282u
63
− 0.0414084u
62
+ ··· + 0.539582u + 3.47925
a
2
=
0.00597049u
63
− 0.0314814u
62
+ ··· − 1.43299u + 3.96869
0.0313178u
63
+ 0.0159753u
62
+ ··· − 0.686893u + 1.99154
a
1
=
0.000592942u
63
− 0.0367390u
62
+ ··· − 1.55479u + 3.89320
0.0243989u
63
+ 0.00752519u
62
+ ··· − 0.804368u + 2.11396
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.144774u
63
+ 0.289389u
62
+ ··· − 34.9857u − 14.7964
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
+ 34u
63
+ ··· + 295u + 81
c
2
, c
4
u
64
− 6u
63
+ ··· − 41u + 9
c
3
, c
7
u
64
+ 2u
63
+ ··· − 36u − 36
c
5
u
64
+ 2u
63
+ ··· + 14008u + 1448
c
6
, c
9
, c
10
u
64
− 2u
63
+ ··· − 8u + 8
c
8
, c
11
, c
12
u
64
− 5u
63
+ ··· + 77u − 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
− 2y
63
+ ··· − 197995y + 6561
c
2
, c
4
y
64
− 34y
63
+ ··· − 295y + 81
c
3
, c
7
y
64
+ 24y
63
+ ··· + 8136y + 1296
c
5
y
64
− 28y
63
+ ··· − 37440y + 2096704
c
6
, c
9
, c
10
y
64
+ 56y
63
+ ··· − 2240y + 64
c
8
, c
11
, c
12
y
64
− 25y
63
+ ··· − 103635y + 2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.371724 + 0.987147I
a = 0.34956 − 2.12621I
b = −0.00833 + 1.56770I
7.22646 − 4.24018I −1.56965 + 6.79694I
u = 0.371724 − 0.987147I
a = 0.34956 + 2.12621I
b = −0.00833 − 1.56770I
7.22646 + 4.24018I −1.56965 − 6.79694I
u = −0.851897 + 0.643385I
a = 0.219665 + 0.339736I
b = 0.734413 − 0.053249I
−1.92756 + 0.31252I −6.62839 − 0.48650I
u = −0.851897 − 0.643385I
a = 0.219665 − 0.339736I
b = 0.734413 + 0.053249I
−1.92756 − 0.31252I −6.62839 + 0.48650I
u = 0.289154 + 0.883310I
a = −1.66383 + 1.15257I
b = −0.190882 − 1.354230I
7.93884 − 1.04658I 3.28663 + 0.78986I
u = 0.289154 − 0.883310I
a = −1.66383 − 1.15257I
b = −0.190882 + 1.354230I
7.93884 + 1.04658I 3.28663 − 0.78986I
u = −0.120473 + 0.912958I
a = −0.51004 + 2.46185I
b = −0.10152 − 1.51750I
8.40492 + 0.01731I 2.49939 − 0.84899I
u = −0.120473 − 0.912958I
a = −0.51004 − 2.46185I
b = −0.10152 + 1.51750I
8.40492 − 0.01731I 2.49939 + 0.84899I
u = 0.638572 + 0.640695I
a = 0.148291 − 0.920775I
b = −0.286756 + 0.783489I
1.31901 − 1.54000I −0.73504 + 2.22693I
u = 0.638572 − 0.640695I
a = 0.148291 + 0.920775I
b = −0.286756 − 0.783489I
1.31901 + 1.54000I −0.73504 − 2.22693I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.143236 + 0.877205I
a = −0.725073 − 0.333935I
b = −0.656856 + 0.176920I
2.97594 − 1.87605I −2.44251 + 2.63726I
u = 0.143236 − 0.877205I
a = −0.725073 + 0.333935I
b = −0.656856 − 0.176920I
2.97594 + 1.87605I −2.44251 − 2.63726I
u = 0.756304 + 0.458360I
a = 0.306352 − 0.919317I
b = −0.060789 + 0.914710I
1.28520 − 1.55606I −1.54627 + 3.90847I
u = 0.756304 − 0.458360I
a = 0.306352 + 0.919317I
b = −0.060789 − 0.914710I
1.28520 + 1.55606I −1.54627 − 3.90847I
u = −0.504418 + 0.998062I
a = −1.100990 − 0.549182I
b = −0.289271 + 1.203540I
6.09312 + 5.38431I 0. − 6.40891I
u = −0.504418 − 0.998062I
a = −1.100990 + 0.549182I
b = −0.289271 − 1.203540I
6.09312 − 5.38431I 0. + 6.40891I
u = 0.762958 + 0.831010I
a = 0.183769 − 0.405771I
b = 0.955269 + 0.141940I
−5.62436 − 4.28044I −6.00000 + 4.50614I
u = 0.762958 − 0.831010I
a = 0.183769 + 0.405771I
b = 0.955269 − 0.141940I
−5.62436 + 4.28044I −6.00000 − 4.50614I
u = −0.729450 + 0.880042I
a = 1.24966 + 1.57057I
b = 0.348427 − 1.115220I
−2.00749 − 0.07198I −6.00000 + 0.I
u = −0.729450 − 0.880042I
a = 1.24966 − 1.57057I
b = 0.348427 + 1.115220I
−2.00749 + 0.07198I −6.00000 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.582893 + 0.626983I
a = 0.109115 − 0.762611I
b = 0.575665 + 1.168030I
−2.52052 − 1.08813I −6.33441 − 3.27535I
u = −0.582893 − 0.626983I
a = 0.109115 + 0.762611I
b = 0.575665 − 1.168030I
−2.52052 + 1.08813I −6.33441 + 3.27535I
u = 1.100450 + 0.340054I
a = 0.124200 + 0.922793I
b = 0.300318 − 1.253550I
1.78771 + 3.40756I 0
u = 1.100450 − 0.340054I
a = 0.124200 − 0.922793I
b = 0.300318 + 1.253550I
1.78771 − 3.40756I 0
u = −0.737565 + 0.903046I
a = 0.122843 + 0.600237I
b = −0.619828 − 0.958033I
−1.91355 + 5.66807I 0
u = −0.737565 − 0.903046I
a = 0.122843 − 0.600237I
b = −0.619828 + 0.958033I
−1.91355 − 5.66807I 0
u = 0.726823 + 0.936403I
a = 0.033280 + 0.795146I
b = −0.808810 − 0.058894I
−5.29747 − 1.38613I 0
u = 0.726823 − 0.936403I
a = 0.033280 − 0.795146I
b = −0.808810 + 0.058894I
−5.29747 + 1.38613I 0
u = −0.943462 + 0.748807I
a = 0.402673 + 0.687146I
b = −0.352033 − 1.214350I
−1.75143 − 2.80069I 0
u = −0.943462 − 0.748807I
a = 0.402673 − 0.687146I
b = −0.352033 + 1.214350I
−1.75143 + 2.80069I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.530839 + 1.085190I
a = −1.18992 − 2.38726I
b = −0.357475 + 1.308410I
−1.02207 + 5.58763I 0
u = −0.530839 − 1.085190I
a = −1.18992 + 2.38726I
b = −0.357475 − 1.308410I
−1.02207 − 5.58763I 0
u = −0.638350 + 0.458185I
a = −1.42772 + 1.84164I
b = 0.058032 + 1.284130I
4.43558 − 0.95010I −3.68053 + 0.16501I
u = −0.638350 − 0.458185I
a = −1.42772 − 1.84164I
b = 0.058032 − 1.284130I
4.43558 + 0.95010I −3.68053 − 0.16501I
u = 0.991904 + 0.750159I
a = 0.148320 − 0.337014I
b = 0.819310 − 0.137492I
−4.97229 + 4.33638I 0
u = 0.991904 − 0.750159I
a = 0.148320 + 0.337014I
b = 0.819310 + 0.137492I
−4.97229 − 4.33638I 0
u = 0.745865 + 1.004160I
a = 0.98676 − 1.53664I
b = 0.322497 + 1.317150I
2.39311 − 4.14386I 0
u = 0.745865 − 1.004160I
a = 0.98676 + 1.53664I
b = 0.322497 − 1.317150I
2.39311 + 4.14386I 0
u = −0.760147 + 1.058960I
a = −0.086257 − 0.649687I
b = −0.798556 + 0.238433I
−0.69248 + 5.71971I 0
u = −0.760147 − 1.058960I
a = −0.086257 + 0.649687I
b = −0.798556 − 0.238433I
−0.69248 − 5.71971I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.146270 + 0.626192I
a = 0.042638 − 0.906852I
b = 0.358907 + 1.357570I
−0.26204 − 8.58996I 0
u = −1.146270 − 0.626192I
a = 0.042638 + 0.906852I
b = 0.358907 − 1.357570I
−0.26204 + 8.58996I 0
u = −0.807059 + 1.031940I
a = 0.96063 + 1.40654I
b = 0.42783 − 1.37511I
−0.85936 + 9.21399I 0
u = −0.807059 − 1.031940I
a = 0.96063 − 1.40654I
b = 0.42783 + 1.37511I
−0.85936 − 9.21399I 0
u = 0.830339 + 1.065580I
a = −0.173021 + 0.690884I
b = −0.914977 − 0.285555I
−3.96299 − 10.98490I 0
u = 0.830339 − 1.065580I
a = −0.173021 − 0.690884I
b = −0.914977 + 0.285555I
−3.96299 + 10.98490I 0
u = 0.567499 + 0.274781I
a = 4.46367 − 0.22909I
b = 0.02424 + 1.46247I
5.03811 + 0.63967I −9.48403 − 2.81401I
u = 0.567499 − 0.274781I
a = 4.46367 + 0.22909I
b = 0.02424 − 1.46247I
5.03811 − 0.63967I −9.48403 + 2.81401I
u = −0.620354
a = 0.588745
b = 0.303129
−0.902009 −11.9970
u = −0.384122 + 0.467062I
a = 1.95525 + 0.79572I
b = −0.104623 − 0.484898I
−1.32609 − 0.73040I −4.44163 − 2.02837I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.384122 − 0.467062I
a = 1.95525 − 0.79572I
b = −0.104623 + 0.484898I
−1.32609 + 0.73040I −4.44163 + 2.02837I
u = −0.183247 + 1.393890I
a = 0.208751 − 0.090637I
b = −0.371033 + 0.044917I
4.27685 + 3.00285I 0
u = −0.183247 − 1.393890I
a = 0.208751 + 0.090637I
b = −0.371033 − 0.044917I
4.27685 − 3.00285I 0
u = −0.149689 + 0.573511I
a = 0.227207 + 0.623159I
b = 0.689304 − 0.758710I
−1.26637 + 2.57337I 0.88170 − 9.10964I
u = −0.149689 − 0.573511I
a = 0.227207 − 0.623159I
b = 0.689304 + 0.758710I
−1.26637 − 2.57337I 0.88170 + 9.10964I
u = 0.71093 + 1.24560I
a = −1.02150 + 1.90643I
b = −0.33731 − 1.40946I
4.54460 − 9.84680I 0
u = 0.71093 − 1.24560I
a = −1.02150 − 1.90643I
b = −0.33731 + 1.40946I
4.54460 + 9.84680I 0
u = −0.82496 + 1.19188I
a = −1.14346 − 1.72247I
b = −0.37895 + 1.44957I
1.5598 + 15.6517I 0
u = −0.82496 − 1.19188I
a = −1.14346 + 1.72247I
b = −0.37895 − 1.44957I
1.5598 − 15.6517I 0
u = 0.27583 + 1.49962I
a = 0.22042 − 2.09601I
b = −0.085375 + 1.278350I
8.14760 − 1.49578I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27583 − 1.49962I
a = 0.22042 + 2.09601I
b = −0.085375 − 1.278350I
8.14760 + 1.49578I 0
u = 0.05777 + 1.52528I
a = −0.11056 + 2.18220I
b = −0.151020 − 1.302210I
8.53543 − 4.95851I 0
u = 0.05777 − 1.52528I
a = −0.11056 − 2.18220I
b = −0.151020 + 1.302210I
8.53543 + 4.95851I 0
u = 0.471301
a = 5.67876
b = 0.217221
0.391402 −51.7770
11
II. I
u
2
= h−3u
2
a + au + 3u
2
+ 5b − 2a − u + 7, −4u
2
a + a
2
+ 2au + 7u
2
−
6a − 2u + 17, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
u
u
2
− u + 1
a
10
=
a
3
5
u
2
a −
3
5
u
2
+ ··· +
2
5
a −
7
5
a
6
=
−
3
5
u
2
a +
33
5
u
2
+ ··· −
7
5
a +
47
5
2
a
11
=
−
3
5
u
2
a +
3
5
u
2
+ ··· −
7
5
a +
7
5
−
3
5
u
2
a +
3
5
u
2
+ ··· −
2
5
a +
7
5
a
12
=
−
3
5
u
2
a +
3
5
u
2
+ ··· −
7
5
a +
12
5
−
3
5
u
2
a +
8
5
u
2
+ ··· −
2
5
a +
7
5
a
9
=
3
5
u
2
a −
3
5
u
2
+ ··· +
7
5
a −
7
5
3
5
u
2
a −
3
5
u
2
+ ··· +
2
5
a −
7
5
a
5
=
−1
0
a
2
=
u
2
+ 1
u
2
− u + 1
a
1
=
1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 4u − 4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
(u
3
+ u
2
+ 2u + 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
9
c
10
(u
2
+ 2)
3
c
8
(u − 1)
6
c
11
, c
12
(u + 1)
6
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
9
c
10
(y + 2)
6
c
8
, c
11
, c
12
(y −1)
6
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.79801 + 1.99502I
b = − 1.414210I
9.60386 − 2.82812I 3.50976 + 2.97945I
u = 0.215080 + 1.307140I
a = −0.28159 − 2.36019I
b = 1.414210I
9.60386 − 2.82812I 3.50976 + 2.97945I
u = 0.215080 − 1.307140I
a = −0.79801 − 1.99502I
b = 1.414210I
9.60386 + 2.82812I 3.50976 − 2.97945I
u = 0.215080 − 1.307140I
a = −0.28159 + 2.36019I
b = − 1.414210I
9.60386 + 2.82812I 3.50976 − 2.97945I
u = 0.569840
a = 3.07960 + 2.94099I
b = 1.414210I
5.46628 −3.01950
u = 0.569840
a = 3.07960 − 2.94099I
b = − 1.414210I
5.46628 −3.01950
15
III. I
u
3
= hb, −2u
2
+ a − u − 3, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
u
−u
2
− u − 1
a
10
=
2u
2
+ u + 3
0
a
6
=
1
0
a
11
=
2u
2
+ u + 3
0
a
12
=
2u
2
+ u + 2
−u
2
a
9
=
2u
2
+ u + 3
0
a
5
=
1
0
a
2
=
−u
2
− 1
−u
2
− u − 1
a
1
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 2u + 12
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
, c
9
c
10
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
(u + 1)
3
c
11
, c
12
(u − 1)
3
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
c
5
, c
6
, c
9
c
10
y
3
c
8
, c
11
, c
12
(y −1)
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.539798 + 0.182582I
b = 0
4.66906 + 2.82812I 4.92040 + 0.36516I
u = −0.215080 − 1.307140I
a = −0.539798 − 0.182582I
b = 0
4.66906 − 2.82812I 4.92040 − 0.36516I
u = −0.569840
a = 3.07960
b = 0
0.531480 12.1590
19
IV. I
v
1
= ha, b − 3v + 1, 3v
2
− 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
3
=
v
0
a
10
=
0
3v − 1
a
6
=
1
−3v + 2
a
11
=
−3v + 1
3v − 2
a
12
=
−1
3v − 2
a
9
=
3v − 1
3v − 1
a
5
=
2
−3v + 3
a
2
=
v − 2
3v − 3
a
1
=
−2
3v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v −
25
3
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
7
u
2
c
4
(u + 1)
2
c
5
, c
8
, c
9
c
10
u
2
+ u + 1
c
6
, c
11
, c
12
u
2
− u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
7
y
2
c
5
, c
6
, c
8
c
9
, c
10
, c
11
c
12
y
2
+ y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.288675I
a = 0
b = 0.500000 + 0.866025I
−1.64493 − 2.02988I −6.33333 + 1.15470I
v = 0.500000 − 0.288675I
a = 0
b = 0.500000 − 0.866025I
−1.64493 + 2.02988I −6.33333 − 1.15470I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
3
− u
2
+ 2u − 1)
3
(u
64
+ 34u
63
+ ··· + 295u + 81)
c
2
((u − 1)
2
)(u
3
+ u
2
− 1)
3
(u
64
− 6u
63
+ ··· − 41u + 9)
c
3
u
2
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
64
+ 2u
63
+ ··· − 36u − 36)
c
4
((u + 1)
2
)(u
3
− u
2
+ 1)
3
(u
64
− 6u
63
+ ··· − 41u + 9)
c
5
u
3
(u
2
+ 2)
3
(u
2
+ u + 1)(u
64
+ 2u
63
+ ··· + 14008u + 1448)
c
6
u
3
(u
2
+ 2)
3
(u
2
− u + 1)(u
64
− 2u
63
+ ··· − 8u + 8)
c
7
u
2
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
64
+ 2u
63
+ ··· − 36u − 36)
c
8
((u − 1)
6
)(u + 1)
3
(u
2
+ u + 1)(u
64
− 5u
63
+ ··· + 77u − 49)
c
9
, c
10
u
3
(u
2
+ 2)
3
(u
2
+ u + 1)(u
64
− 2u
63
+ ··· − 8u + 8)
c
11
, c
12
((u − 1)
3
)(u + 1)
6
(u
2
− u + 1)(u
64
− 5u
63
+ ··· + 77u − 49)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
3
+ 3y
2
+ 2y − 1)
3
(y
64
− 2y
63
+ ··· − 197995y + 6561)
c
2
, c
4
((y − 1)
2
)(y
3
− y
2
+ 2y − 1)
3
(y
64
− 34y
63
+ ··· − 295y + 81)
c
3
, c
7
y
2
(y
3
+ 3y
2
+ 2y − 1)
3
(y
64
+ 24y
63
+ ··· + 8136y + 1296)
c
5
y
3
(y + 2)
6
(y
2
+ y + 1)(y
64
− 28y
63
+ ··· − 37440y + 2096704)
c
6
, c
9
, c
10
y
3
(y + 2)
6
(y
2
+ y + 1)(y
64
+ 56y
63
+ ··· − 2240y + 64)
c
8
, c
11
, c
12
((y − 1)
9
)(y
2
+ y + 1)(y
64
− 25y
63
+ ··· − 103635y + 2401)
25
