12a
0305
(K12a
0305
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 7 2 1 11 12 5 9 4
Solving Sequence
2,6
3 7 1 8
5,10
11 4 12 9
c
2
c
6
c
1
c
7
c
5
c
10
c
4
c
12
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
89
− u
88
+ ··· + b − 2u, u
87
+ 14u
85
+ ··· + a + 1, u
92
+ 2u
91
+ ··· + 3u − 1i
I
u
2
= hu
8
− u
7
+ u
6
− u
5
+ u
4
− u
3
+ b − u, −u
6
− u
4
− u
2
+ a − u, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 101 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−u
89
−u
88
+· · ·+b−2u, u
87
+14u
85
+· · ·+a+1, u
92
+2u
91
+· · ·+3u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
1
=
u
2
+ 1
−u
4
a
8
=
u
7
+ 2u
5
+ 2u
3
+ 2u
−u
9
− u
7
− u
5
+ u
a
5
=
u
3
u
3
+ u
a
10
=
−u
87
− 14u
85
+ ··· − 3u − 1
u
89
+ u
88
+ ··· + 3u
2
+ 2u
a
11
=
2u
91
+ 2u
90
+ ··· + 4u
2
− 2
2u
91
+ u
90
+ ··· + 6u
2
+ u
a
4
=
−u
14
− 3u
12
− 6u
10
− 9u
8
− 8u
6
− 6u
4
− 2u
2
+ 1
u
16
+ 2u
14
+ 4u
12
+ 4u
10
+ 2u
8
− 2u
4
− 2u
2
a
12
=
u
26
+ 5u
24
+ ··· − u
2
+ 1
−u
28
− 4u
26
+ ··· + 10u
6
+ 3u
4
a
9
=
u
91
+ u
90
+ ··· + u
2
− 1
u
91
+ u
90
+ ··· + 4u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
91
− 2u
90
+ ··· + 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
92
+ 30u
91
+ ··· − 15u + 1
c
2
, c
6
u
92
− 2u
91
+ ··· − 3u − 1
c
3
u
92
− 2u
91
+ ··· − 19073u − 4777
c
4
, c
10
u
92
− u
91
+ ··· + 512u + 512
c
7
u
92
+ 10u
91
+ ··· − 2595u − 175
c
8
, c
9
, c
11
u
92
− 10u
91
+ ··· + 9u − 1
c
12
u
92
+ 6u
91
+ ··· + 93765u + 53361
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
92
+ 66y
91
+ ··· − 223y + 1
c
2
, c
6
y
92
+ 30y
91
+ ··· − 15y + 1
c
3
y
92
− 18y
91
+ ··· − 956098667y + 22819729
c
4
, c
10
y
92
− 57y
91
+ ··· − 1835008y + 262144
c
7
y
92
+ 6y
91
+ ··· + 948825y + 30625
c
8
, c
9
, c
11
y
92
− 90y
91
+ ··· − 3y + 1
c
12
y
92
+ 42y
91
+ ··· − 115995084723y + 2847396321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.238579 + 0.976043I
a = 0.192909 − 0.693401I
b = −0.304491 − 0.860553I
−5.41288 − 2.84467I 0
u = −0.238579 − 0.976043I
a = 0.192909 + 0.693401I
b = −0.304491 + 0.860553I
−5.41288 + 2.84467I 0
u = −0.131476 + 0.996623I
a = 0.210814 + 0.343582I
b = 0.521220 + 0.022009I
−2.04930 − 2.60188I 0
u = −0.131476 − 0.996623I
a = 0.210814 − 0.343582I
b = 0.521220 − 0.022009I
−2.04930 + 2.60188I 0
u = −0.761512 + 0.636187I
a = 0.16026 − 2.38247I
b = 1.56743 − 1.52368I
−7.42452 − 1.21614I 0
u = −0.761512 − 0.636187I
a = 0.16026 + 2.38247I
b = 1.56743 + 1.52368I
−7.42452 + 1.21614I 0
u = −0.781538 + 0.684375I
a = 0.25605 + 2.82276I
b = −1.81816 + 2.53546I
0.155477 + 1.294890I 0
u = −0.781538 − 0.684375I
a = 0.25605 − 2.82276I
b = −1.81816 − 2.53546I
0.155477 − 1.294890I 0
u = 0.098394 + 1.038460I
a = 0.07502 + 1.54246I
b = 0.567259 − 0.826734I
−5.85938 + 1.27529I 0
u = 0.098394 − 1.038460I
a = 0.07502 − 1.54246I
b = 0.567259 + 0.826734I
−5.85938 − 1.27529I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.796526 + 0.681227I
a = 1.180110 − 0.586282I
b = −0.184618 − 1.380540I
−1.36598 − 3.95919I 0
u = 0.796526 − 0.681227I
a = 1.180110 + 0.586282I
b = −0.184618 + 1.380540I
−1.36598 + 3.95919I 0
u = −0.113967 + 1.047090I
a = −0.317702 − 0.526590I
b = −0.972673 + 0.055257I
−7.57114 − 3.91705I 0
u = −0.113967 − 1.047090I
a = −0.317702 + 0.526590I
b = −0.972673 − 0.055257I
−7.57114 + 3.91705I 0
u = 0.128444 + 1.048180I
a = 0.42689 − 1.60839I
b = −0.356284 + 0.752529I
−5.07389 + 6.38810I 0
u = 0.128444 − 1.048180I
a = 0.42689 + 1.60839I
b = −0.356284 − 0.752529I
−5.07389 − 6.38810I 0
u = −0.806783 + 0.685584I
a = 0.09380 − 3.06953I
b = 2.61016 − 2.39283I
1.26879 + 6.37618I 0
u = −0.806783 − 0.685584I
a = 0.09380 + 3.06953I
b = 2.61016 + 2.39283I
1.26879 − 6.37618I 0
u = −0.743166 + 0.754535I
a = 1.13339 + 1.20352I
b = 0.73726 + 1.94182I
1.43085 + 0.04969I 0
u = −0.743166 − 0.754535I
a = 1.13339 − 1.20352I
b = 0.73726 − 1.94182I
1.43085 − 0.04969I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822268 + 0.680379I
a = −0.26921 + 3.00155I
b = −2.83495 + 2.02876I
−4.87607 + 10.56990I 0
u = −0.822268 − 0.680379I
a = −0.26921 − 3.00155I
b = −2.83495 − 2.02876I
−4.87607 − 10.56990I 0
u = 0.068444 + 1.066700I
a = −0.119803 − 1.063560I
b = −0.669699 + 0.996000I
−13.26790 − 1.71324I 0
u = 0.068444 − 1.066700I
a = −0.119803 + 1.063560I
b = −0.669699 − 0.996000I
−13.26790 + 1.71324I 0
u = 0.794586 + 0.715154I
a = −0.701553 + 0.368801I
b = 0.106681 + 0.861927I
4.11451 − 2.13885I 0
u = 0.794586 − 0.715154I
a = −0.701553 − 0.368801I
b = 0.106681 − 0.861927I
4.11451 + 2.13885I 0
u = 0.523406 + 0.932221I
a = −2.86628 + 1.08586I
b = −1.70161 + 2.54061I
−2.88968 − 0.50850I 0
u = 0.523406 − 0.932221I
a = −2.86628 − 1.08586I
b = −1.70161 − 2.54061I
−2.88968 + 0.50850I 0
u = −0.603531 + 0.883423I
a = −0.405753 + 0.377637I
b = −0.456391 + 0.312778I
0.27502 − 2.36293I 0
u = −0.603531 − 0.883423I
a = −0.405753 − 0.377637I
b = −0.456391 − 0.312778I
0.27502 + 2.36293I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141577 + 1.066640I
a = −0.64547 + 1.36105I
b = 0.165043 − 0.846640I
−11.4205 + 10.4846I 0
u = 0.141577 − 1.066640I
a = −0.64547 − 1.36105I
b = 0.165043 + 0.846640I
−11.4205 − 10.4846I 0
u = 0.483733 + 0.961923I
a = 2.62934 − 0.98848I
b = 1.77034 − 2.05250I
−9.44292 − 4.26740I 0
u = 0.483733 − 0.961923I
a = 2.62934 + 0.98848I
b = 1.77034 + 2.05250I
−9.44292 + 4.26740I 0
u = 0.041839 + 0.919641I
a = 1.46421 + 0.47733I
b = 0.510800 − 0.847804I
−3.71389 + 0.94541I −10.08955 + 0.I
u = 0.041839 − 0.919641I
a = 1.46421 − 0.47733I
b = 0.510800 + 0.847804I
−3.71389 − 0.94541I −10.08955 + 0.I
u = 0.738617 + 0.792436I
a = 0.08397 + 1.76696I
b = 1.79864 + 0.87393I
0.61740 + 2.17666I 0
u = 0.738617 − 0.792436I
a = 0.08397 − 1.76696I
b = 1.79864 − 0.87393I
0.61740 − 2.17666I 0
u = 0.780023 + 0.757512I
a = −0.138766 − 1.011260I
b = −1.111500 − 0.321008I
4.83837 − 0.28034I 0
u = 0.780023 − 0.757512I
a = −0.138766 + 1.011260I
b = −1.111500 + 0.321008I
4.83837 + 0.28034I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.545981 + 0.946335I
a = 0.786190 − 0.801145I
b = 0.983452 − 0.814754I
−5.14496 − 1.95841I 0
u = −0.545981 − 0.946335I
a = 0.786190 + 0.801145I
b = 0.983452 + 0.814754I
−5.14496 + 1.95841I 0
u = 0.819340 + 0.747466I
a = 0.811111 + 0.583349I
b = 0.969514 − 0.641469I
1.33460 − 1.79462I 0
u = 0.819340 − 0.747466I
a = 0.811111 − 0.583349I
b = 0.969514 + 0.641469I
1.33460 + 1.79462I 0
u = 0.569272 + 0.952059I
a = 3.05755 − 0.71634I
b = 2.21583 − 2.69381I
−3.18636 + 4.50271I 0
u = 0.569272 − 0.952059I
a = 3.05755 + 0.71634I
b = 2.21583 + 2.69381I
−3.18636 − 4.50271I 0
u = −0.765440 + 0.803103I
a = −0.818029 − 0.295898I
b = −1.30883 − 0.73438I
3.29801 − 4.00356I 0
u = −0.765440 − 0.803103I
a = −0.818029 + 0.295898I
b = −1.30883 + 0.73438I
3.29801 + 4.00356I 0
u = −0.133642 + 0.866499I
a = −0.704930 + 0.358994I
b = −0.183847 + 0.660585I
−0.97407 − 1.60778I −2.42278 + 5.49433I
u = −0.133642 − 0.866499I
a = −0.704930 − 0.358994I
b = −0.183847 − 0.660585I
−0.97407 + 1.60778I −2.42278 − 5.49433I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.788650 + 0.825251I
a = 0.429590 − 0.032526I
b = 1.320190 + 0.022577I
−2.36074 − 7.57914I 0
u = −0.788650 − 0.825251I
a = 0.429590 + 0.032526I
b = 1.320190 − 0.022577I
−2.36074 + 7.57914I 0
u = 0.580403 + 0.990368I
a = −2.76821 + 0.58596I
b = −2.31851 + 2.48526I
−10.22640 + 7.87203I 0
u = 0.580403 − 0.990368I
a = −2.76821 − 0.58596I
b = −2.31851 − 2.48526I
−10.22640 − 7.87203I 0
u = 0.704163 + 0.934133I
a = 1.48699 + 1.28974I
b = 2.52056 − 0.39514I
0.17844 + 3.32501I 0
u = 0.704163 − 0.934133I
a = 1.48699 − 1.28974I
b = 2.52056 + 0.39514I
0.17844 − 3.32501I 0
u = −0.729358 + 0.927928I
a = 0.48537 + 1.40074I
b = −0.176884 + 1.006650I
2.91207 − 1.65574I 0
u = −0.729358 − 0.927928I
a = 0.48537 − 1.40074I
b = −0.176884 − 1.006650I
2.91207 + 1.65574I 0
u = −0.705139 + 0.959518I
a = −1.85262 − 1.43236I
b = −0.85947 − 1.99272I
0.80377 − 5.57265I 0
u = −0.705139 − 0.959518I
a = −1.85262 + 1.43236I
b = −0.85947 + 1.99272I
0.80377 + 5.57265I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759357 + 0.917611I
a = 0.154740 − 1.175150I
b = 0.453810 − 0.286093I
−2.64654 + 1.75870I 0
u = −0.759357 − 0.917611I
a = 0.154740 + 1.175150I
b = 0.453810 + 0.286093I
−2.64654 − 1.75870I 0
u = 0.727371 + 0.965715I
a = −0.751407 − 0.816273I
b = −1.54104 + 0.06209I
4.20110 + 5.97753I 0
u = 0.727371 − 0.965715I
a = −0.751407 + 0.816273I
b = −1.54104 − 0.06209I
4.20110 − 5.97753I 0
u = −0.685625 + 1.015050I
a = 2.70888 − 0.73049I
b = 3.23800 + 0.79506I
−8.54521 − 4.28248I 0
u = −0.685625 − 1.015050I
a = 2.70888 + 0.73049I
b = 3.23800 − 0.79506I
−8.54521 + 4.28248I 0
u = −0.707286 + 1.005200I
a = −3.58502 + 0.61898I
b = −3.77645 − 1.63082I
−0.81196 − 6.92992I 0
u = −0.707286 − 1.005200I
a = −3.58502 − 0.61898I
b = −3.77645 + 1.63082I
−0.81196 + 6.92992I 0
u = 0.722334 + 0.994639I
a = 0.737532 − 0.314068I
b = 0.384875 − 1.089600I
3.26407 + 7.86054I 0
u = 0.722334 − 0.994639I
a = 0.737532 + 0.314068I
b = 0.384875 + 1.089600I
3.26407 − 7.86054I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.712416 + 1.010960I
a = −1.204580 + 0.587426I
b = −0.61714 + 1.85907I
−2.36288 + 9.65056I 0
u = 0.712416 − 1.010960I
a = −1.204580 − 0.587426I
b = −0.61714 − 1.85907I
−2.36288 − 9.65056I 0
u = 0.747422 + 0.985363I
a = −0.024978 + 1.031910I
b = 1.13289 + 0.99412I
0.60476 + 7.66863I 0
u = 0.747422 − 0.985363I
a = −0.024978 − 1.031910I
b = 1.13289 − 0.99412I
0.60476 − 7.66863I 0
u = −0.718187 + 1.012530I
a = 3.69458 − 1.31136I
b = 4.36717 + 1.27660I
0.27703 − 12.11510I 0
u = −0.718187 − 1.012530I
a = 3.69458 + 1.31136I
b = 4.36717 − 1.27660I
0.27703 + 12.11510I 0
u = −0.722974 + 1.020340I
a = −3.42871 + 1.57766I
b = −4.41694 − 0.95821I
−5.9102 − 16.3665I 0
u = −0.722974 − 1.020340I
a = −3.42871 − 1.57766I
b = −4.41694 + 0.95821I
−5.9102 + 16.3665I 0
u = 0.609690 + 0.383304I
a = 1.39793 − 1.53881I
b = −0.79199 − 1.39508I
−8.70626 − 3.35319I −6.31043 + 0.88458I
u = 0.609690 − 0.383304I
a = 1.39793 + 1.53881I
b = −0.79199 + 1.39508I
−8.70626 + 3.35319I −6.31043 − 0.88458I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642810 + 0.198730I
a = −0.90695 + 1.72665I
b = 0.82727 + 1.31383I
−7.33603 + 8.13323I −4.06363 − 5.79146I
u = 0.642810 − 0.198730I
a = −0.90695 − 1.72665I
b = 0.82727 − 1.31383I
−7.33603 − 8.13323I −4.06363 + 5.79146I
u = −0.628906
a = 1.21805
b = 0.115016
−2.33416 −3.59530
u = 0.586802 + 0.202280I
a = 0.91801 − 1.51754I
b = −0.88316 − 1.33256I
−1.11584 + 4.25818I −1.35985 − 6.31874I
u = 0.586802 − 0.202280I
a = 0.91801 + 1.51754I
b = −0.88316 + 1.33256I
−1.11584 − 4.25818I −1.35985 + 6.31874I
u = −0.560782 + 0.239213I
a = 1.05446 − 1.13653I
b = 0.336700 − 0.124705I
−3.54932 − 1.95688I −3.33049 + 3.24146I
u = −0.560782 − 0.239213I
a = 1.05446 + 1.13653I
b = 0.336700 + 0.124705I
−3.54932 + 1.95688I −3.33049 − 3.24146I
u = 0.505945 + 0.290277I
a = −1.21465 + 1.33169I
b = 0.81248 + 1.21732I
−1.83395 − 0.43175I −4.17282 − 0.00864I
u = 0.505945 − 0.290277I
a = −1.21465 − 1.33169I
b = 0.81248 − 1.21732I
−1.83395 + 0.43175I −4.17282 + 0.00864I
u = −0.514009 + 0.086156I
a = −0.670765 + 0.702252I
b = −0.126844 + 0.092730I
1.31136 − 0.58307I 6.08435 + 1.47406I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.514009 − 0.086156I
a = −0.670765 − 0.702252I
b = −0.126844 − 0.092730I
1.31136 + 0.58307I 6.08435 − 1.47406I
u = 0.260294
a = −1.68667
b = 0.872774
−1.21528 −9.67220
14
II. I
u
2
= hu
8
− u
7
+ u
6
− u
5
+ u
4
− u
3
+ b − u, −u
6
− u
4
− u
2
+ a − u, u
9
−
u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
1
=
u
2
+ 1
−u
4
a
8
=
u
7
+ 2u
5
+ 2u
3
+ 2u
−u
8
+ u
7
− u
6
+ 2u
5
− u
4
+ 2u
3
+ 2u + 1
a
5
=
u
3
u
3
+ u
a
10
=
u
6
+ u
4
+ u
2
+ u
−u
8
+ u
7
− u
6
+ u
5
− u
4
+ u
3
+ u
a
11
=
u
6
+ u
4
+ u
2
+ u
−u
8
+ u
7
− u
6
+ u
5
− u
4
+ u
3
+ u
a
4
=
u
3
u
3
+ u
a
12
=
−u
7
− 2u
5
− 2u
3
− 2u
u
8
− u
7
+ u
6
− 2u
5
+ u
4
− 2u
3
− 2u − 1
a
9
=
u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 3u
−2u
8
+ 2u
7
− 2u
6
+ 3u
5
− 2u
4
+ 3u
3
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
7
+ 4u
6
− 5u
5
+ 5u
4
− 10u
3
+ 5u
2
− u − 1
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
2
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
3
, c
12
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
4
, c
10
u
9
c
6
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
7
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
8
, c
9
(u − 1)
9
c
11
(u + 1)
9
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
2
, c
6
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
3
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
4
, c
10
y
9
c
7
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
8
, c
9
, c
11
(y −1)
9
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = −0.855828 + 0.530357I
b = −0.154190 − 0.257272I
−3.42837 − 2.09337I −7.72019 + 4.44592I
u = −0.140343 − 0.966856I
a = −0.855828 − 0.530357I
b = −0.154190 + 0.257272I
−3.42837 + 2.09337I −7.72019 − 4.44592I
u = −0.628449 + 0.875112I
a = −0.77654 + 1.46791I
b = −1.76111 + 0.42995I
−1.02799 − 2.45442I −7.83797 + 2.47153I
u = −0.628449 − 0.875112I
a = −0.77654 − 1.46791I
b = −1.76111 − 0.42995I
−1.02799 + 2.45442I −7.83797 − 2.47153I
u = 0.796005 + 0.733148I
a = −0.852888 + 0.566992I
b = −0.430151 + 1.332530I
2.72642 − 1.33617I 1.031098 + 0.174453I
u = 0.796005 − 0.733148I
a = −0.852888 − 0.566992I
b = −0.430151 − 1.332530I
2.72642 + 1.33617I 1.031098 − 0.174453I
u = 0.728966 + 0.986295I
a = 1.06667 − 0.97795I
b = 0.23704 − 1.46509I
1.95319 + 7.08493I −0.87316 − 5.18429I
u = 0.728966 − 0.986295I
a = 1.06667 + 0.97795I
b = 0.23704 + 1.46509I
1.95319 − 7.08493I −0.87316 + 5.18429I
u = −0.512358
a = −0.162845
b = −0.783184
−0.446489 2.80040
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
92
+ 30u
91
+ ··· − 15u + 1)
c
2
(u
9
− u
8
+ ··· + u + 1)(u
92
− 2u
91
+ ··· − 3u − 1)
c
3
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
92
− 2u
91
+ ··· − 19073u − 4777)
c
4
, c
10
u
9
(u
92
− u
91
+ ··· + 512u + 512)
c
6
(u
9
+ u
8
+ ··· + u − 1)(u
92
− 2u
91
+ ··· − 3u − 1)
c
7
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
92
+ 10u
91
+ ··· − 2595u − 175)
c
8
, c
9
((u − 1)
9
)(u
92
− 10u
91
+ ··· + 9u − 1)
c
11
((u + 1)
9
)(u
92
− 10u
91
+ ··· + 9u − 1)
c
12
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
92
+ 6u
91
+ ··· + 93765u + 53361)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
92
+ 66y
91
+ ··· − 223y + 1)
c
2
, c
6
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
92
+ 30y
91
+ ··· − 15y + 1)
c
3
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
92
− 18y
91
+ ··· − 956098667y + 22819729)
c
4
, c
10
y
9
(y
92
− 57y
91
+ ··· − 1835008y + 262144)
c
7
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
92
+ 6y
91
+ ··· + 948825y + 30625)
c
8
, c
9
, c
11
((y −1)
9
)(y
92
− 90y
91
+ ··· − 3y + 1)
c
12
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
92
+ 42y
91
+ ··· − 115995084723y + 2847396321)
20
