11a
102
(K11a
102
)
A knot diagram
1
Linearized knot diagam
6 1 7 10 2 4 3 11 5 8 9
Solving Sequence
2,5
6 1
3,10
4 7 9 11 8
c
5
c
1
c
2
c
4
c
6
c
9
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.87536 × 10
21
u
41
− 3.96737 × 10
21
u
40
+ ··· + 5.90778 × 10
21
b − 6.72165 × 10
21
,
2.13130 × 10
22
u
41
− 4.18187 × 10
22
u
40
+ ··· + 7.08933 × 10
22
a − 3.54422 × 10
23
, u
42
− 2u
41
+ ··· − 36u + 9i
I
u
2
= h−u
12
− 4u
10
− 3u
9
− 6u
8
− 9u
7
− 7u
6
− 9u
5
− 7u
4
− 3u
3
− 3u
2
+ b + 1,
− u
13
− u
12
− 4u
11
− 6u
10
− 8u
9
− 12u
8
− 11u
7
− 11u
6
− 9u
5
− 3u
4
− u
3
+ u
2
+ a + 3u + 1,
u
15
+ 5u
13
+ 3u
12
+ 10u
11
+ 12u
10
+ 14u
9
+ 18u
8
+ 17u
7
+ 13u
6
+ 13u
5
+ 5u
4
+ 3u
3
+ u
2
− u − 1i
I
u
3
= hb, u
3
+ 2u
2
+ 2a + 3u + 1, u
4
+ u
3
+ u
2
+ 1i
I
u
4
= hau + 5b − 2a − 3u + 1, a
2
− a + 5u + 4, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 65 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
=
h2.88×10
21
u
41
−3.97×10
21
u
40
+· · ·+5.91×10
21
b−6.72×10
21
, 2.13×10
22
u
41
−
4.18 × 10
22
u
40
+ · · · + 7.09 × 10
22
a − 3.54 × 10
23
, u
42
− 2u
41
+ · · · − 36u + 9i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
10
=
−0.300635u
41
+ 0.589882u
40
+ ··· − 15.7376u + 4.99938
−0.486707u
41
+ 0.671550u
40
+ ··· − 9.85137u + 1.13776
a
4
=
0.279236u
41
− 0.941462u
40
+ ··· + 18.2040u − 4.05148
0.463095u
41
− 1.13764u
40
+ ··· + 27.2892u − 7.18073
a
7
=
0.797859u
41
− 1.13262u
40
+ ··· + 15.2674u − 0.433684
0.308200u
41
− 0.215226u
40
+ ··· − 6.59502u + 3.37739
a
9
=
0.186072u
41
− 0.0816676u
40
+ ··· − 5.88625u + 3.86161
−0.486707u
41
+ 0.671550u
40
+ ··· − 9.85137u + 1.13776
a
11
=
−0.377575u
41
+ 0.483319u
40
+ ··· + 4.32261u − 2.55226
−0.157428u
41
+ 0.0210348u
40
+ ··· + 8.77277u − 2.82010
a
8
=
0.626320u
41
− 0.755435u
40
+ ··· + 11.7778u + 0.221051
0.157428u
41
− 0.0210348u
40
+ ··· − 8.77277u + 2.82010
a
8
=
0.626320u
41
− 0.755435u
40
+ ··· + 11.7778u + 0.221051
0.157428u
41
− 0.0210348u
40
+ ··· − 8.77277u + 2.82010
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3375308932150515076741
15754069295721805208896
u
41
−
7093505981346082336715
15754069295721805208896
u
40
+ ··· −
990909890095625692917289
15754069295721805208896
u +
306048621353866106187553
15754069295721805208896
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
42
− 2u
41
+ ··· − 36u + 9
c
2
u
42
+ 18u
41
+ ··· + 936u + 81
c
3
, c
6
, c
7
u
42
− 2u
41
+ ··· − 48u + 9
c
4
, c
9
u
42
− 2u
41
+ ··· − 48u + 64
c
8
, c
10
, c
11
u
42
− 4u
41
+ ··· + 3u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
42
+ 18y
41
+ ··· + 936y + 81
c
2
y
42
+ 18y
41
+ ··· + 43092y + 6561
c
3
, c
6
, c
7
y
42
+ 42y
41
+ ··· + 648y + 81
c
4
, c
9
y
42
+ 24y
41
+ ··· + 37632y + 4096
c
8
, c
10
, c
11
y
42
− 40y
41
+ ··· + 431y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.321244 + 0.924907I
a = 0.68951 − 2.35177I
b = 0.16746 − 1.77078I
−8.34619 + 1.31277I −3.80780 − 5.75825I
u = 0.321244 − 0.924907I
a = 0.68951 + 2.35177I
b = 0.16746 + 1.77078I
−8.34619 − 1.31277I −3.80780 + 5.75825I
u = −0.781793 + 0.668749I
a = −0.179012 − 0.710623I
b = 0.864043 − 0.487802I
6.85342 − 1.08907I 3.57208 + 1.87970I
u = −0.781793 − 0.668749I
a = −0.179012 + 0.710623I
b = 0.864043 + 0.487802I
6.85342 + 1.08907I 3.57208 − 1.87970I
u = 0.786749 + 0.566093I
a = −0.122149 − 0.366661I
b = −0.176094 + 1.096880I
−4.33907 + 0.92313I −6.58218 − 1.96577I
u = 0.786749 − 0.566093I
a = −0.122149 + 0.366661I
b = −0.176094 − 1.096880I
−4.33907 − 0.92313I −6.58218 + 1.96577I
u = 1.010940 + 0.277119I
a = 0.118893 + 0.317524I
b = −0.708157 + 1.185080I
−0.13244 − 8.79986I −2.66885 + 5.03818I
u = 1.010940 − 0.277119I
a = 0.118893 − 0.317524I
b = −0.708157 − 1.185080I
−0.13244 + 8.79986I −2.66885 − 5.03818I
u = 0.443155 + 0.836892I
a = 0.077559 + 0.409124I
b = 0.533447 − 0.314098I
−0.14555 + 1.89662I −0.46549 − 4.15100I
u = 0.443155 − 0.836892I
a = 0.077559 − 0.409124I
b = 0.533447 + 0.314098I
−0.14555 − 1.89662I −0.46549 + 4.15100I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.854547 + 0.372087I
a = 0.040427 − 0.627535I
b = 0.641022 − 1.066170I
5.09584 − 4.47116I 1.35353 + 3.51083I
u = 0.854547 − 0.372087I
a = 0.040427 + 0.627535I
b = 0.641022 + 1.066170I
5.09584 + 4.47116I 1.35353 − 3.51083I
u = −0.349226 + 1.057360I
a = 0.73971 + 2.07726I
b = −0.065056 + 1.043400I
−3.60913 − 1.10388I −10.34002 + 1.20607I
u = −0.349226 − 1.057360I
a = 0.73971 − 2.07726I
b = −0.065056 − 1.043400I
−3.60913 + 1.10388I −10.34002 − 1.20607I
u = 0.551141 + 1.033680I
a = −0.68540 + 2.16562I
b = 0.285987 + 1.305530I
1.07465 + 4.16567I −3.63331 − 3.63134I
u = 0.551141 − 1.033680I
a = −0.68540 − 2.16562I
b = 0.285987 − 1.305530I
1.07465 − 4.16567I −3.63331 + 3.63134I
u = 0.438210 + 1.089350I
a = −0.210411 − 0.547185I
b = −1.120410 + 0.266857I
−5.07603 + 3.61628I −8.76999 − 3.97464I
u = 0.438210 − 1.089350I
a = −0.210411 + 0.547185I
b = −1.120410 − 0.266857I
−5.07603 − 3.61628I −8.76999 + 3.97464I
u = 0.629402 + 0.513854I
a = −0.454894 + 1.264650I
b = −0.532736 + 1.051670I
2.61565 + 0.48442I −1.18826 − 1.33056I
u = 0.629402 − 0.513854I
a = −0.454894 − 1.264650I
b = −0.532736 − 1.051670I
2.61565 − 0.48442I −1.18826 + 1.33056I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.705333 + 0.962448I
a = −0.390598 + 0.325640I
b = −0.865578 − 0.213500I
5.99098 − 4.47238I 2.83567 + 4.51985I
u = −0.705333 − 0.962448I
a = −0.390598 − 0.325640I
b = −0.865578 + 0.213500I
5.99098 + 4.47238I 2.83567 − 4.51985I
u = −0.715912 + 0.371485I
a = 0.682256 + 1.165700I
b = −1.056740 + 0.582481I
1.90495 + 2.38439I −0.748912 − 0.739188I
u = −0.715912 − 0.371485I
a = 0.682256 − 1.165700I
b = −1.056740 − 0.582481I
1.90495 − 2.38439I −0.748912 + 0.739188I
u = −0.515614 + 1.080020I
a = −1.12031 − 1.77848I
b = 0.439748 − 1.104040I
−2.45148 − 5.86761I −6.25811 + 7.21816I
u = −0.515614 − 1.080020I
a = −1.12031 + 1.77848I
b = 0.439748 + 1.104040I
−2.45148 + 5.86761I −6.25811 − 7.21816I
u = −0.107934 + 0.771038I
a = −1.21133 + 1.83186I
b = 0.383646 + 0.488117I
−2.24911 − 0.80040I −10.34390 − 2.30566I
u = −0.107934 − 0.771038I
a = −1.21133 − 1.83186I
b = 0.383646 − 0.488117I
−2.24911 + 0.80040I −10.34390 + 2.30566I
u = −0.565953 + 1.102330I
a = 0.712921 − 0.245709I
b = 1.324750 + 0.452245I
−0.22800 − 7.29302I −3.85885 + 5.40090I
u = −0.565953 − 1.102330I
a = 0.712921 + 0.245709I
b = 1.324750 − 0.452245I
−0.22800 + 7.29302I −3.85885 − 5.40090I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.207458 + 1.224160I
a = −0.48946 − 1.74308I
b = −0.26287 − 1.45352I
−11.12090 + 1.23717I −12.55029 − 0.91395I
u = −0.207458 − 1.224160I
a = −0.48946 + 1.74308I
b = −0.26287 + 1.45352I
−11.12090 − 1.23717I −12.55029 + 0.91395I
u = 0.611787 + 1.141700I
a = 0.77774 − 1.97693I
b = −0.578718 − 1.259990I
2.78819 + 9.89486I −2.06286 − 7.44629I
u = 0.611787 − 1.141700I
a = 0.77774 + 1.97693I
b = −0.578718 + 1.259990I
2.78819 − 9.89486I −2.06286 + 7.44629I
u = −0.604626 + 1.165380I
a = 1.06930 + 1.51130I
b = −0.62853 + 1.29344I
−8.35687 − 9.85804I −8.74565 + 6.87807I
u = −0.604626 − 1.165380I
a = 1.06930 − 1.51130I
b = −0.62853 − 1.29344I
−8.35687 + 9.85804I −8.74565 − 6.87807I
u = −0.959413 + 0.912281I
a = 0.315723 + 0.170462I
b = −0.128054 + 0.731912I
4.54070 − 3.45793I −8.56940 + 4.77216I
u = −0.959413 − 0.912281I
a = 0.315723 − 0.170462I
b = −0.128054 − 0.731912I
4.54070 + 3.45793I −8.56940 − 4.77216I
u = 0.239207 + 0.573323I
a = 0.793218 + 0.179899I
b = −0.296599 − 0.453205I
0.165616 + 1.199760I 1.09413 − 6.46841I
u = 0.239207 − 0.573323I
a = 0.793218 − 0.179899I
b = −0.296599 + 0.453205I
0.165616 − 1.199760I 1.09413 + 6.46841I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626883 + 1.232800I
a = −0.73702 + 1.79556I
b = 0.77943 + 1.32376I
−3.0695 + 14.6861I −5.13652 − 8.10029I
u = 0.626883 − 1.232800I
a = −0.73702 − 1.79556I
b = 0.77943 − 1.32376I
−3.0695 − 14.6861I −5.13652 + 8.10029I
9
II.
I
u
2
= h−u
12
−4u
10
+· · ·+b+1, −u
13
−u
12
+· · ·+a+1, u
15
+5u
13
+· · ·−u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
10
=
u
13
+ u
12
+ ··· − 3u − 1
u
12
+ 4u
10
+ 3u
9
+ 6u
8
+ 9u
7
+ 7u
6
+ 9u
5
+ 7u
4
+ 3u
3
+ 3u
2
− 1
a
4
=
−u
u
3
+ u
a
7
=
−u
2
+ 1
u
4
a
9
=
u
13
+ 4u
11
+ 2u
10
+ 5u
9
+ 6u
8
+ 2u
7
+ 4u
6
− 4u
4
− 2u
3
− 4u
2
− 3u
u
12
+ 4u
10
+ 3u
9
+ 6u
8
+ 9u
7
+ 7u
6
+ 9u
5
+ 7u
4
+ 3u
3
+ 3u
2
− 1
a
11
=
u
6
+ 3u
4
+ 2u
3
+ 2u
2
+ 2u + 1
−u
6
− 2u
4
− u
2
a
8
=
−u
4
− u
2
+ 1
u
6
+ 2u
4
+ u
2
a
8
=
−u
4
− u
2
+ 1
u
6
+ 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
12
+ 16u
10
+ 8u
9
+ 24u
8
+ 24u
7
+ 24u
6
+ 24u
5
+ 20u
4
+ 4u
3
+ 8u
2
− 4u − 6
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
u
15
+ 5u
13
+ ··· − u − 1
c
2
u
15
+ 10u
14
+ ··· + 3u − 1
c
4
, c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
c
8
, c
10
, c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
3
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
y
15
+ 10y
14
+ ··· + 3y −1
c
2
y
15
− 10y
14
+ ··· + 15y −1
c
4
, c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
3
c
8
, c
10
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
3
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.392556 + 0.928076I
a = 1.56131 − 1.04952I
b = −0.339110 − 0.822375I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.392556 − 0.928076I
a = 1.56131 + 1.04952I
b = −0.339110 + 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = −0.874669 + 0.344338I
a = −0.285415 − 0.003942I
b = 0.455697 + 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −0.874669 − 0.344338I
a = −0.285415 + 0.003942I
b = 0.455697 − 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −0.239239 + 1.082450I
a = −0.99209 − 1.41160I
b = 0.766826
−2.40108 −3.48114 + 0.I
u = −0.239239 − 1.082450I
a = −0.99209 + 1.41160I
b = 0.766826
−2.40108 −3.48114 + 0.I
u = 0.620645 + 1.060090I
a = −1.22012 + 0.88709I
b = 0.455697 + 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = 0.620645 − 1.060090I
a = −1.22012 − 0.88709I
b = 0.455697 − 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = 0.157939 + 1.235430I
a = −0.78772 + 1.73286I
b = −0.339110 + 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.157939 − 1.235430I
a = −0.78772 − 1.73286I
b = −0.339110 − 0.822375I
−0.32910 + 1.53058I −2.51511 − 4.43065I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.550495 + 0.307358I
a = 0.512065 − 0.335441I
b = −0.339110 − 0.822375I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = −0.550495 − 0.307358I
a = 0.512065 + 0.335441I
b = −0.339110 + 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.25402 + 1.40443I
a = 0.67600 − 1.30157I
b = 0.455697 − 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = 0.25402 − 1.40443I
a = 0.67600 + 1.30157I
b = 0.455697 + 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = 0.478478
a = −1.92805
b = 0.766826
−2.40108 −3.48110
14
III. I
u
3
= hb, u
3
+ 2u
2
+ 2a + 3u + 1, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
3
+ u
2
+ 1
a
10
=
−
1
2
u
3
− u
2
−
3
2
u −
1
2
0
a
4
=
1
0
a
7
=
u
2
+ 1
−u
2
a
9
=
−
1
2
u
3
− u
2
−
3
2
u −
1
2
0
a
11
=
−
1
2
u
3
− u
2
−
5
2
u −
1
2
u
3
+ u
a
8
=
u
−u
3
− u
a
8
=
u
−u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1
4
u
3
−
7
2
u
2
−
23
4
u −
11
4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
+ u
2
+ 1
c
2
, c
6
, c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
3
u
4
− u
3
+ 3u
2
− 2u + 1
c
4
, c
9
u
4
c
5
u
4
+ u
3
+ u
2
+ 1
c
8
(u − 1)
4
c
10
, c
11
(u + 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
2
, c
3
, c
6
c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
4
, c
9
y
4
c
8
, c
10
, c
11
(y −1)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = −0.38053 − 1.53420I
b = 0
−1.85594 + 1.41510I −3.26394 − 5.88934I
u = 0.351808 − 0.720342I
a = −0.38053 + 1.53420I
b = 0
−1.85594 − 1.41510I −3.26394 + 5.88934I
u = −0.851808 + 0.911292I
a = 0.130534 − 0.427872I
b = 0
5.14581 − 3.16396I 2.13894 − 0.11292I
u = −0.851808 − 0.911292I
a = 0.130534 + 0.427872I
b = 0
5.14581 + 3.16396I 2.13894 + 0.11292I
18
IV. I
u
4
= hau + 5b − 2a − 3u + 1, a
2
− a + 5u + 4, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
1
a
1
=
−u
0
a
3
=
u
u
a
10
=
a
−
1
5
au +
2
5
a +
3
5
u −
1
5
a
4
=
2
5
au +
1
5
a −
6
5
u −
8
5
2
5
au +
1
5
a −
1
5
u −
8
5
a
7
=
1
5
au −
2
5
a −
8
5
u +
11
5
1
5
au −
2
5
a −
8
5
u +
6
5
a
9
=
1
5
au +
3
5
a −
3
5
u +
1
5
−
1
5
au +
2
5
a +
3
5
u −
1
5
a
11
=
−2u + 1
1
5
au −
2
5
a −
8
5
u +
1
5
a
8
=
1
5
au −
2
5
a −
8
5
u +
6
5
1
5
au −
2
5
a −
8
5
u +
1
5
a
8
=
1
5
au −
2
5
a −
8
5
u +
6
5
1
5
au −
2
5
a −
8
5
u +
1
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
(u
2
+ 1)
2
c
2
(u + 1)
4
c
4
, c
9
u
4
+ 3u
2
+ 1
c
8
(u
2
+ u − 1)
2
c
10
, c
11
(u
2
− u − 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
(y + 1)
4
c
2
(y −1)
4
c
4
, c
9
(y
2
+ 3y + 1)
2
c
8
, c
10
, c
11
(y
2
− 3y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.61803 + 2.23607I
b = 1.61803I
−8.88264 −8.00000
u = 1.000000I
a = 1.61803 − 2.23607I
b = − 0.618034I
−0.986960 −8.00000
u = − 1.000000I
a = −0.61803 − 2.23607I
b = − 1.61803I
−8.88264 −8.00000
u = − 1.000000I
a = 1.61803 + 2.23607I
b = 0.618034I
−0.986960 −8.00000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ 1)
2
)(u
4
− u
3
+ u
2
+ 1)(u
15
+ 5u
13
+ ··· − u − 1)
· (u
42
− 2u
41
+ ··· − 36u + 9)
c
2
((u + 1)
4
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
15
+ 10u
14
+ ··· + 3u − 1)
· (u
42
+ 18u
41
+ ··· + 936u + 81)
c
3
((u
2
+ 1)
2
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
15
+ 5u
13
+ ··· − u − 1)
· (u
42
− 2u
41
+ ··· − 48u + 9)
c
4
, c
9
u
4
(u
4
+ 3u
2
+ 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
· (u
42
− 2u
41
+ ··· − 48u + 64)
c
5
((u
2
+ 1)
2
)(u
4
+ u
3
+ u
2
+ 1)(u
15
+ 5u
13
+ ··· − u − 1)
· (u
42
− 2u
41
+ ··· − 36u + 9)
c
6
, c
7
((u
2
+ 1)
2
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
15
+ 5u
13
+ ··· − u − 1)
· (u
42
− 2u
41
+ ··· − 48u + 9)
c
8
(u − 1)
4
(u
2
+ u − 1)
2
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
3
· (u
42
− 4u
41
+ ··· + 3u + 4)
c
10
, c
11
(u + 1)
4
(u
2
− u − 1)
2
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
3
· (u
42
− 4u
41
+ ··· + 3u + 4)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y + 1)
4
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
15
+ 10y
14
+ ··· + 3y −1)
· (y
42
+ 18y
41
+ ··· + 936y + 81)
c
2
((y −1)
4
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
15
− 10y
14
+ ··· + 15y −1)
· (y
42
+ 18y
41
+ ··· + 43092y + 6561)
c
3
, c
6
, c
7
((y + 1)
4
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
15
+ 10y
14
+ ··· + 3y −1)
· (y
42
+ 42y
41
+ ··· + 648y + 81)
c
4
, c
9
y
4
(y
2
+ 3y + 1)
2
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
3
· (y
42
+ 24y
41
+ ··· + 37632y + 4096)
c
8
, c
10
, c
11
(y −1)
4
(y
2
− 3y + 1)
2
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
3
· (y
42
− 40y
41
+ ··· + 431y + 16)
24
