12a
0028
(K12a
0028
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 4 8 1 7 11
Solving Sequence
7,11
12
1,3
2 6 4 5 10 8 9
c
11
c
12
c
1
c
6
c
3
c
5
c
10
c
7
c
9
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
73
− 2u
72
+ ··· + b − 1, −u
75
+ 3u
74
+ ··· + 2a − 1, u
76
− 3u
75
+ ··· − 4u + 1i
I
u
2
= hb, a + u + 1, u
2
+ u + 1i
I
u
3
= hb, a − 1, u
15
+ 3u
13
+ 6u
11
+ u
10
+ 7u
9
+ 2u
8
+ 6u
7
+ 3u
6
+ 5u
5
+ 2u
4
+ 3u
3
+ u
2
+ 2u + 1i
I
u
4
= hb, a − 1, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 95 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
= hu
73
−2u
72
+· · ·+b−1, −u
75
+3u
74
+· · ·+2a−1, u
76
−3u
75
+· · ·−4u+1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
3
=
1
2
u
75
−
3
2
u
74
+ ··· + 4u +
1
2
−u
73
+ 2u
72
+ ··· − 3u + 1
a
2
=
−
1
2
u
75
+
3
2
u
74
+ ··· + 2u +
5
2
−u
37
− 7u
35
+ ··· − 4u
2
− u
a
6
=
u
u
3
+ u
a
4
=
u
75
− u
74
+ ··· + 2u + 1
3u
75
−
11
2
u
74
+ ··· +
5
2
u −
1
2
a
5
=
−u
75
+ 3u
74
+ ··· − 8u + 1
−
1
2
u
74
+ u
73
+ ··· +
5
2
u −
1
2
a
10
=
u
4
+ u
2
+ 1
u
4
a
8
=
−u
9
− 2u
7
− 3u
5
− 2u
3
− u
−u
9
− u
7
− u
5
+ u
a
9
=
u
14
+ 3u
12
+ 6u
10
+ 7u
8
+ 6u
6
+ 4u
4
+ 2u
2
+ 1
u
14
+ 2u
12
+ 3u
10
+ 2u
8
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
11
2
u
75
− 19u
74
+ ··· +
27
2
u − 7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 35u
75
+ ··· − 12u
2
+ 1
c
2
, c
5
u
76
+ 3u
75
+ ··· + 2u + 1
c
3
u
76
− 3u
75
+ ··· − 2u + 1
c
4
, c
8
u
76
+ 4u
75
+ ··· + 16u + 16
c
6
, c
11
u
76
− 3u
75
+ ··· − 4u + 1
c
7
, c
9
u
76
+ 20u
75
+ ··· + 1152u + 256
c
10
, c
12
u
76
− 27u
75
+ ··· + 156u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
+ 15y
75
+ ··· − 24y + 1
c
2
, c
5
y
76
+ 35y
75
+ ··· − 12y
2
+ 1
c
3
y
76
− 5y
75
+ ··· − 96y + 1
c
4
, c
8
y
76
− 20y
75
+ ··· − 1152y + 256
c
6
, c
11
y
76
+ 27y
75
+ ··· + 156y
2
+ 1
c
7
, c
9
y
76
+ 60y
75
+ ··· + 712704y + 65536
c
10
, c
12
y
76
+ 47y
75
+ ··· + 312y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.820067 + 0.580500I
a = −1.05528 − 2.33587I
b = 0.24200 − 2.52038I
0.28459 + 11.09290I 0
u = 0.820067 − 0.580500I
a = −1.05528 + 2.33587I
b = 0.24200 + 2.52038I
0.28459 − 11.09290I 0
u = 0.784162 + 0.610183I
a = 0.218261 − 1.162730I
b = 1.28826 − 0.84685I
−2.88911 + 3.62351I 0
u = 0.784162 − 0.610183I
a = 0.218261 + 1.162730I
b = 1.28826 + 0.84685I
−2.88911 − 3.62351I 0
u = 0.804404 + 0.574368I
a = 1.08811 + 1.63791I
b = −0.04056 + 1.69896I
2.31596 + 5.81698I 0
u = 0.804404 − 0.574368I
a = 1.08811 − 1.63791I
b = −0.04056 − 1.69896I
2.31596 − 5.81698I 0
u = −0.266450 + 1.003770I
a = −0.051209 − 0.894123I
b = 0.382872 + 0.726383I
−0.37911 + 6.19852I 0
u = −0.266450 − 1.003770I
a = −0.051209 + 0.894123I
b = 0.382872 − 0.726383I
−0.37911 − 6.19852I 0
u = −0.758972 + 0.572804I
a = −1.15206 + 2.58616I
b = 0.38835 + 2.61192I
1.30562 − 4.85760I −4.00000 + 2.81637I
u = −0.758972 − 0.572804I
a = −1.15206 − 2.58616I
b = 0.38835 − 2.61192I
1.30562 + 4.85760I −4.00000 − 2.81637I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.614417 + 0.865433I
a = 0.80686 − 1.36588I
b = −0.59195 − 1.44117I
−0.59560 + 2.40827I 0
u = −0.614417 − 0.865433I
a = 0.80686 + 1.36588I
b = −0.59195 + 1.44117I
−0.59560 − 2.40827I 0
u = −0.682974 + 0.815558I
a = −2.87082 + 1.38786I
b = −0.95465 + 3.40719I
−3.11243 − 0.72332I 0
u = −0.682974 − 0.815558I
a = −2.87082 − 1.38786I
b = −0.95465 − 3.40719I
−3.11243 + 0.72332I 0
u = −0.215813 + 0.910718I
a = 0.265261 + 0.121375I
b = −0.586596 − 0.385311I
1.49867 + 2.13083I 0. − 5.38892I
u = −0.215813 − 0.910718I
a = 0.265261 − 0.121375I
b = −0.586596 + 0.385311I
1.49867 − 2.13083I 0. + 5.38892I
u = 0.737672 + 0.767805I
a = 1.05157 + 1.41551I
b = −0.22256 + 1.66158I
−4.16374 + 0.54928I 0
u = 0.737672 − 0.767805I
a = 1.05157 − 1.41551I
b = −0.22256 − 1.66158I
−4.16374 − 0.54928I 0
u = −0.744701 + 0.542472I
a = 1.18253 − 1.67888I
b = −0.01927 − 1.66588I
3.09050 + 0.22669I −1.99230 − 2.08336I
u = −0.744701 − 0.542472I
a = 1.18253 + 1.67888I
b = −0.01927 + 1.66588I
3.09050 − 0.22669I −1.99230 + 2.08336I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.774528 + 0.755664I
a = −1.82547 − 1.78464I
b = −0.27849 − 2.85903I
−6.90483 + 4.88361I 0
u = 0.774528 − 0.755664I
a = −1.82547 + 1.78464I
b = −0.27849 + 2.85903I
−6.90483 − 4.88361I 0
u = −0.636867 + 0.654546I
a = 1.10871 + 1.19060I
b = 1.71940 + 0.17017I
−1.56601 + 1.58828I −7.89253 − 2.90076I
u = −0.636867 − 0.654546I
a = 1.10871 − 1.19060I
b = 1.71940 − 0.17017I
−1.56601 − 1.58828I −7.89253 + 2.90076I
u = 0.639841 + 0.879271I
a = −0.543599 + 0.737979I
b = −0.075619 + 0.338430I
−0.96997 − 4.97477I 0
u = 0.639841 − 0.879271I
a = −0.543599 − 0.737979I
b = −0.075619 − 0.338430I
−0.96997 + 4.97477I 0
u = 0.716966 + 0.538440I
a = −0.779361 + 0.668048I
b = 0.292228 + 0.497426I
1.60658 − 2.39995I −4.54324 + 1.90730I
u = 0.716966 − 0.538440I
a = −0.779361 − 0.668048I
b = 0.292228 − 0.497426I
1.60658 + 2.39995I −4.54324 − 1.90730I
u = −0.528629 + 0.969740I
a = −0.495625 − 0.870919I
b = −0.596905 + 0.163211I
−0.23592 + 3.03712I 0
u = −0.528629 − 0.969740I
a = −0.495625 + 0.870919I
b = −0.596905 − 0.163211I
−0.23592 − 3.03712I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.014582 + 1.106940I
a = 0.698613 + 0.845252I
b = 0.83233 − 1.27996I
6.97493 − 3.72971I 0
u = 0.014582 − 1.106940I
a = 0.698613 − 0.845252I
b = 0.83233 + 1.27996I
6.97493 + 3.72971I 0
u = 0.759065 + 0.810624I
a = −0.21510 − 2.16462I
b = 1.83924 − 1.72824I
−7.82704 − 2.79074I 0
u = 0.759065 − 0.810624I
a = −0.21510 + 2.16462I
b = 1.83924 + 1.72824I
−7.82704 + 2.79074I 0
u = −0.003461 + 1.114350I
a = −0.484952 − 0.498420I
b = −1.039760 + 0.702363I
8.62942 + 1.55231I 0
u = −0.003461 − 1.114350I
a = −0.484952 + 0.498420I
b = −1.039760 − 0.702363I
8.62942 − 1.55231I 0
u = −0.678647 + 0.889200I
a = −0.99601 + 3.18933I
b = 2.29317 + 2.94183I
−2.88720 + 5.97422I 0
u = −0.678647 − 0.889200I
a = −0.99601 − 3.18933I
b = 2.29317 − 2.94183I
−2.88720 − 5.97422I 0
u = −0.756171 + 0.426179I
a = −0.797372 − 0.584543I
b = 0.344833 − 0.560635I
1.18722 + 7.92961I −5.68516 − 7.58189I
u = −0.756171 − 0.426179I
a = −0.797372 + 0.584543I
b = 0.344833 + 0.560635I
1.18722 − 7.92961I −5.68516 + 7.58189I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.040806 + 1.132090I
a = −0.446780 + 0.376335I
b = −0.941823 − 0.709155I
8.37243 + 4.62112I 0
u = −0.040806 − 1.132090I
a = −0.446780 − 0.376335I
b = −0.941823 + 0.709155I
8.37243 − 4.62112I 0
u = −0.054219 + 1.140020I
a = 0.589590 − 0.733142I
b = 0.70115 + 1.27546I
6.50055 + 9.90761I 0
u = −0.054219 − 1.140020I
a = 0.589590 + 0.733142I
b = 0.70115 − 1.27546I
6.50055 − 9.90761I 0
u = 0.735374 + 0.908373I
a = −1.93507 − 0.56007I
b = −1.05640 − 2.40281I
−7.52975 − 2.85954I 0
u = 0.735374 − 0.908373I
a = −1.93507 + 0.56007I
b = −1.05640 + 2.40281I
−7.52975 + 2.85954I 0
u = 0.707706 + 0.935010I
a = 1.03539 + 1.48069I
b = −0.48512 + 1.88720I
−3.65836 − 6.05326I 0
u = 0.707706 − 0.935010I
a = 1.03539 − 1.48069I
b = −0.48512 − 1.88720I
−3.65836 + 6.05326I 0
u = −0.632430 + 1.003530I
a = −1.272460 − 0.506257I
b = −1.24027 + 1.30625I
−0.49083 + 3.41773I 0
u = −0.632430 − 1.003530I
a = −1.272460 + 0.506257I
b = −1.24027 − 1.30625I
−0.49083 − 3.41773I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727570 + 0.952707I
a = −1.41975 − 2.28891I
b = 1.28428 − 2.82954I
−6.30922 − 10.55470I 0
u = 0.727570 − 0.952707I
a = −1.41975 + 2.28891I
b = 1.28428 + 2.82954I
−6.30922 + 10.55470I 0
u = −0.014242 + 0.784224I
a = 0.639035 − 0.926041I
b = −0.869179 − 0.194601I
2.08815 + 1.38840I 2.95491 − 3.97928I
u = −0.014242 − 0.784224I
a = 0.639035 + 0.926041I
b = −0.869179 + 0.194601I
2.08815 − 1.38840I 2.95491 + 3.97928I
u = −0.619260 + 1.054980I
a = −0.429463 − 0.595270I
b = −0.312184 − 0.533722I
4.72824 + 2.31494I 0
u = −0.619260 − 1.054980I
a = −0.429463 + 0.595270I
b = −0.312184 + 0.533722I
4.72824 − 2.31494I 0
u = −0.650542 + 1.042030I
a = 1.34113 − 1.51578I
b = −0.49049 − 2.32412I
4.53764 + 5.08932I 0
u = −0.650542 − 1.042030I
a = 1.34113 + 1.51578I
b = −0.49049 + 2.32412I
4.53764 − 5.08932I 0
u = 0.655264 + 1.042540I
a = −0.467205 + 0.606561I
b = −0.260958 + 0.532361I
4.45459 − 8.18431I 0
u = 0.655264 − 1.042540I
a = −0.467205 − 0.606561I
b = −0.260958 − 0.532361I
4.45459 + 8.18431I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663246 + 1.039230I
a = −2.27057 + 1.76444I
b = 0.36310 + 3.31027I
2.67522 + 10.26500I 0
u = −0.663246 − 1.039230I
a = −2.27057 − 1.76444I
b = 0.36310 − 3.31027I
2.67522 − 10.26500I 0
u = 0.681711 + 1.035000I
a = −1.189270 + 0.104639I
b = −0.94885 − 1.58563I
−1.62052 − 9.16663I 0
u = 0.681711 − 1.035000I
a = −1.189270 − 0.104639I
b = −0.94885 + 1.58563I
−1.62052 + 9.16663I 0
u = 0.677356 + 1.053730I
a = 1.29035 + 1.43391I
b = −0.40380 + 2.25686I
3.74543 − 11.38940I 0
u = 0.677356 − 1.053730I
a = 1.29035 − 1.43391I
b = −0.40380 − 2.25686I
3.74543 + 11.38940I 0
u = 0.684596 + 1.057450I
a = −2.07654 − 1.62476I
b = 0.33793 − 3.06189I
1.7152 − 16.7334I 0
u = 0.684596 − 1.057450I
a = −2.07654 + 1.62476I
b = 0.33793 + 3.06189I
1.7152 + 16.7334I 0
u = −0.607659 + 0.388530I
a = 0.330601 + 0.231355I
b = 0.754959 + 0.436898I
−1.72401 + 1.26068I −9.61689 − 3.20971I
u = −0.607659 − 0.388530I
a = 0.330601 − 0.231355I
b = 0.754959 − 0.436898I
−1.72401 − 1.26068I −9.61689 + 3.20971I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141223 + 0.694571I
a = −0.45492 + 1.73909I
b = 0.930270 − 0.034337I
1.00182 − 2.99656I 0.34736 + 1.79586I
u = 0.141223 − 0.694571I
a = −0.45492 − 1.73909I
b = 0.930270 + 0.034337I
1.00182 + 2.99656I 0.34736 − 1.79586I
u = −0.606989 + 0.079902I
a = −0.801617 − 0.099145I
b = 0.509633 − 0.600376I
−3.65273 + 3.42052I −12.40083 − 4.88890I
u = −0.606989 − 0.079902I
a = −0.801617 + 0.099145I
b = 0.509633 + 0.600376I
−3.65273 − 3.42052I −12.40083 + 4.88890I
u = 0.214408 + 0.135150I
a = 0.38448 + 2.43399I
b = 0.411442 − 0.639233I
−0.32678 + 1.73919I −2.49698 − 4.03216I
u = 0.214408 − 0.135150I
a = 0.38448 − 2.43399I
b = 0.411442 + 0.639233I
−0.32678 − 1.73919I −2.49698 + 4.03216I
12
II. I
u
2
= hb, a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u − 1
a
1
=
−u
−u − 1
a
3
=
−u − 1
0
a
2
=
−u − 1
−u − 1
a
6
=
u
u + 1
a
4
=
0
1
a
5
=
0
1
a
10
=
0
u
a
8
=
0
u
a
9
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u − 7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
12
u
2
− u + 1
c
2
, c
10
, c
11
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
u
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
10
c
11
, c
12
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
y
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 0
4.05977I −3.00000 − 6.92820I
u = −0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 0
− 4.05977I −3.00000 + 6.92820I
16
III. I
u
3
= hb, a − 1, u
15
+ 3u
13
+ · · · + 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
3
=
1
0
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
0
u
a
10
=
u
4
+ u
2
+ 1
u
4
a
8
=
−u
9
− 2u
7
− 3u
5
− 2u
3
− u
−u
9
− u
7
− u
5
+ u
a
9
=
u
14
+ 3u
12
+ 6u
10
+ 7u
8
+ 6u
6
+ 4u
4
+ 2u
2
+ 1
u
14
+ 2u
12
+ 3u
10
+ 2u
8
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
10
− 8u
8
− 12u
6
− 4u
5
− 8u
4
− 4u
3
− 4u
2
− 4u − 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 6u
14
+ ··· + 2u − 1
c
2
, c
5
, c
6
c
11
u
15
+ 3u
13
+ ··· + 2u + 1
c
3
u
15
+ 3u
13
+ ··· − 4u + 1
c
4
, c
8
(u
3
− u
2
+ 1)
5
c
7
, c
9
(u
3
+ u
2
+ 2u + 1)
5
c
10
, c
12
u
15
− 6u
14
+ ··· + 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
y
15
+ 6y
14
+ ··· + 18y −1
c
2
, c
5
, c
6
c
11
y
15
+ 6y
14
+ ··· + 2y −1
c
3
y
15
+ 6y
14
+ ··· − 14y −1
c
4
, c
8
(y
3
− y
2
+ 2y −1)
5
c
7
, c
9
(y
3
+ 3y
2
+ 2y −1)
5
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.633840 + 0.835010I
a = 1.00000
b = 0
−1.11345 −9.01951 + 0.I
u = 0.633840 − 0.835010I
a = 1.00000
b = 0
−1.11345 −9.01951 + 0.I
u = −0.406029 + 0.986492I
a = 1.00000
b = 0
−1.11345 −9.01951 + 0.I
u = −0.406029 − 0.986492I
a = 1.00000
b = 0
−1.11345 −9.01951 + 0.I
u = 0.752750 + 0.551515I
a = 1.00000
b = 0
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 0.752750 − 0.551515I
a = 1.00000
b = 0
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.048319 + 1.089120I
a = 1.00000
b = 0
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.048319 − 1.089120I
a = 1.00000
b = 0
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.742775 + 0.457992I
a = 1.00000
b = 0
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.742775 − 0.457992I
a = 1.00000
b = 0
3.02413 − 2.82812I −2.49024 + 2.97945I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.644158 + 1.035000I
a = 1.00000
b = 0
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.644158 − 1.035000I
a = 1.00000
b = 0
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.605814 + 1.063630I
a = 1.00000
b = 0
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.605814 − 1.063630I
a = 1.00000
b = 0
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.455622
a = 1.00000
b = 0
−1.11345 −9.01950
21
IV. I
u
4
= hb, a − 1, u
2
+ u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u − 1
a
1
=
−u
−u − 1
a
3
=
1
0
a
2
=
1
−u − 1
a
6
=
u
u + 1
a
4
=
0
u
a
5
=
0
u
a
10
=
0
u
a
8
=
0
u
a
9
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
12
u
2
− u + 1
c
2
, c
10
, c
11
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
u
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
10
c
11
, c
12
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.00000
b = 0
0 0
u = −0.500000 − 0.866025I
a = 1.00000
b = 0
0 0
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
15
+ 6u
14
+ ··· + 2u − 1)(u
76
+ 35u
75
+ ··· − 12u
2
+ 1)
c
2
((u
2
+ u + 1)
2
)(u
15
+ 3u
13
+ ··· + 2u + 1)(u
76
+ 3u
75
+ ··· + 2u + 1)
c
3
((u
2
− u + 1)
2
)(u
15
+ 3u
13
+ ··· − 4u + 1)(u
76
− 3u
75
+ ··· − 2u + 1)
c
4
, c
8
u
4
(u
3
− u
2
+ 1)
5
(u
76
+ 4u
75
+ ··· + 16u + 16)
c
5
((u
2
− u + 1)
2
)(u
15
+ 3u
13
+ ··· + 2u + 1)(u
76
+ 3u
75
+ ··· + 2u + 1)
c
6
((u
2
− u + 1)
2
)(u
15
+ 3u
13
+ ··· + 2u + 1)(u
76
− 3u
75
+ ··· − 4u + 1)
c
7
, c
9
u
4
(u
3
+ u
2
+ 2u + 1)
5
(u
76
+ 20u
75
+ ··· + 1152u + 256)
c
10
((u
2
+ u + 1)
2
)(u
15
− 6u
14
+ ··· + 2u + 1)(u
76
− 27u
75
+ ··· + 156u
2
+ 1)
c
11
((u
2
+ u + 1)
2
)(u
15
+ 3u
13
+ ··· + 2u + 1)(u
76
− 3u
75
+ ··· − 4u + 1)
c
12
((u
2
− u + 1)
2
)(u
15
− 6u
14
+ ··· + 2u + 1)(u
76
− 27u
75
+ ··· + 156u
2
+ 1)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
15
+ 6y
14
+ ··· + 18y −1)(y
76
+ 15y
75
+ ··· − 24y + 1)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
15
+ 6y
14
+ ··· + 2y −1)(y
76
+ 35y
75
+ ··· − 12y
2
+ 1)
c
3
((y
2
+ y + 1)
2
)(y
15
+ 6y
14
+ ··· − 14y −1)(y
76
− 5y
75
+ ··· − 96y + 1)
c
4
, c
8
y
4
(y
3
− y
2
+ 2y −1)
5
(y
76
− 20y
75
+ ··· − 1152y + 256)
c
6
, c
11
((y
2
+ y + 1)
2
)(y
15
+ 6y
14
+ ··· + 2y −1)(y
76
+ 27y
75
+ ··· + 156y
2
+ 1)
c
7
, c
9
y
4
(y
3
+ 3y
2
+ 2y −1)
5
(y
76
+ 60y
75
+ ··· + 712704y + 65536)
c
10
, c
12
((y
2
+ y + 1)
2
)(y
15
+ 6y
14
+ ··· + 18y −1)
· (y
76
+ 47y
75
+ ··· + 312y + 1)
27
