11a
157
(K11a
157
)
A knot diagram
1
Linearized knot diagam
6 1 10 8 2 4 11 5 3 7 9
Solving Sequence
2,5
6 1
3,9
10 8 4 11 7
c
5
c
1
c
2
c
9
c
8
c
4
c
11
c
7
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−116u
51
− 310u
50
+ ··· + 2304b + 7136, −3775u
52
− 16066u
51
+ ··· + 52992a + 229724,
u
53
+ 4u
52
+ ··· − 92u − 46i
I
u
2
= h−a
2
u + 2b + a − 2, a
3
+ 2a
2
u − au + 2a + 2, u
2
− u + 1i
I
u
3
= hb + 1, 6a + u + 4, u
2
+ 2i
I
u
4
= hb
2
au + b
3
− bu − au − b + u − 1, u
2
− u + 1i
I
v
1
= ha, b
3
− b − 1, v − 1i
I
v
2
= ha, b − 1, v − 1i
* 5 irreducible components of dim
C
= 0, with total 65 representations.
* 1 irreducible components of dim
C
= 1
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−116u
51
− 310u
50
+ · · · + 2304b + 7136, −3775u
52
− 16066u
51
+
· · · + 52992a + 229724, u
53
+ 4u
52
+ · · · − 92u − 46i
(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
9
=
0.0712372u
52
+ 0.303178u
51
+ ··· − 8.73049u − 4.33507
0.0503472u
51
+ 0.134549u
50
+ ··· − 1.31510u − 3.09722
a
10
=
0.184518u
52
+ 0.705088u
51
+ ··· − 14.9597u − 6.29167
0.0625000u
52
+ 0.159722u
51
+ ··· − 1.55729u − 1.65972
a
8
=
0.0712372u
52
+ 0.353525u
51
+ ··· − 10.0456u − 7.43229
0.0503472u
51
+ 0.134549u
50
+ ··· − 1.31510u − 3.09722
a
4
=
0.119226u
52
+ 0.443048u
51
+ ··· − 9.10745u − 4.01302
0.00520833u
52
− 0.0195313u
51
+ ··· + 1.50521u + 0.684896
a
11
=
−0.0306839u
52
− 0.0914855u
51
+ ··· + 4.15433u + 4.34635
0.109375u
52
+ 0.342448u
51
+ ··· − 4.84375u − 0.565104
a
7
=
−0.0805405u
52
− 0.300460u
51
+ ··· + 7.03842u + 4.68750
−0.0625000u
52
− 0.165799u
51
+ ··· + 0.802083u + 1.18924
a
7
=
−0.0805405u
52
− 0.300460u
51
+ ··· + 7.03842u + 4.68750
−0.0625000u
52
− 0.165799u
51
+ ··· + 0.802083u + 1.18924
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1153
1728
u
52
+
1951
864
u
51
+ ··· −
7271
216
u +
1
4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
53
+ 4u
52
+ ··· − 92u − 46
c
2
u
53
+ 24u
52
+ ··· + 3496u − 2116
c
3
, c
9
9(9u
53
− 18u
52
+ ··· − 77u − 19)
c
4
, c
8
9(9u
53
+ 18u
52
+ ··· − 9u − 19)
c
6
16(16u
53
− 16u
52
+ ··· + 103779u − 3609)
c
7
, c
10
u
53
+ 6u
52
+ ··· − 5832u − 1706
c
11
16(16u
53
+ 32u
52
+ ··· − 16641u − 6003)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
53
+ 24y
52
+ ··· + 3496y − 2116
c
2
y
53
+ 12y
52
+ ··· + 393508288y − 4477456
c
3
, c
9
81(81y
53
− 3510y
52
+ ··· + 3421y − 361)
c
4
, c
8
81(81y
53
− 2214y
52
+ ··· + 7149y − 361)
c
6
256(256y
53
+ 6016y
52
+ ··· + 9.94255 × 10
9
y − 1.30249 × 10
7
)
c
7
, c
10
y
53
− 30y
52
+ ··· − 5573800y − 2910436
c
11
256(256y
53
− 6528y
52
+ ··· − 3.68087 × 10
8
y − 3.60360 × 10
7
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.809668 + 0.591571I
a = −0.38862 + 1.53061I
b = −0.262654 − 1.151540I
9.44289 + 4.62072I 10.24286 − 2.08237I
u = −0.809668 − 0.591571I
a = −0.38862 − 1.53061I
b = −0.262654 + 1.151540I
9.44289 − 4.62072I 10.24286 + 2.08237I
u = 0.932904 + 0.475451I
a = 0.719049 + 0.844934I
b = −1.26960 − 0.64309I
6.27152 − 10.90750I 7.14898 + 5.53843I
u = 0.932904 − 0.475451I
a = 0.719049 − 0.844934I
b = −1.26960 + 0.64309I
6.27152 + 10.90750I 7.14898 − 5.53843I
u = 0.880838 + 0.326928I
a = −0.164167 + 0.799269I
b = −0.573186 − 0.653434I
7.95194 + 1.12051I 10.90095 + 0.04798I
u = 0.880838 − 0.326928I
a = −0.164167 − 0.799269I
b = −0.573186 + 0.653434I
7.95194 − 1.12051I 10.90095 − 0.04798I
u = −0.817792 + 0.679811I
a = 0.418946 − 0.981125I
b = 0.303446 + 0.604240I
4.38963 + 0.38285I 8.33080 + 0.50210I
u = −0.817792 − 0.679811I
a = 0.418946 + 0.981125I
b = 0.303446 − 0.604240I
4.38963 − 0.38285I 8.33080 − 0.50210I
u = 0.994126 + 0.446360I
a = −0.477878 − 0.579642I
b = 1.071810 + 0.473560I
2.22320 − 4.60694I 5.52820 + 4.35998I
u = 0.994126 − 0.446360I
a = −0.477878 + 0.579642I
b = 1.071810 − 0.473560I
2.22320 + 4.60694I 5.52820 − 4.35998I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.611609 + 0.908410I
a = −1.30709 + 0.63481I
b = 0.809891 + 0.174593I
0.872134 + 1.079720I 0. + 2.41019I
u = 0.611609 − 0.908410I
a = −1.30709 − 0.63481I
b = 0.809891 − 0.174593I
0.872134 − 1.079720I 0. − 2.41019I
u = 0.170302 + 1.087830I
a = 0.635126 + 0.069933I
b = 0.001690 + 0.649953I
3.08054 + 4.00121I 5.97068 − 4.06106I
u = 0.170302 − 1.087830I
a = 0.635126 − 0.069933I
b = 0.001690 − 0.649953I
3.08054 − 4.00121I 5.97068 + 4.06106I
u = 0.626566 + 0.643943I
a = 1.22653 − 0.71815I
b = −0.826327 + 0.364980I
1.59094 + 3.76796I 4.39825 − 7.64009I
u = 0.626566 − 0.643943I
a = 1.22653 + 0.71815I
b = −0.826327 − 0.364980I
1.59094 − 3.76796I 4.39825 + 7.64009I
u = −0.128610 + 1.112310I
a = 0.653956 − 0.300609I
b = 1.275160 − 0.403466I
−4.15345 + 3.73758I −2.48655 − 3.09856I
u = −0.128610 − 1.112310I
a = 0.653956 + 0.300609I
b = 1.275160 + 0.403466I
−4.15345 − 3.73758I −2.48655 + 3.09856I
u = −0.949759 + 0.608985I
a = 0.264387 + 0.875055I
b = −0.908688 − 0.564102I
6.99581 − 5.82913I 8.82739 + 6.38685I
u = −0.949759 − 0.608985I
a = 0.264387 − 0.875055I
b = −0.908688 + 0.564102I
6.99581 + 5.82913I 8.82739 − 6.38685I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.496009 + 1.017750I
a = 1.36846 − 1.83838I
b = 0.878140 + 0.204929I
0.67079 − 3.09135I 0. + 5.67301I
u = −0.496009 − 1.017750I
a = 1.36846 + 1.83838I
b = 0.878140 − 0.204929I
0.67079 + 3.09135I 0. − 5.67301I
u = −0.724250 + 0.436534I
a = 1.15534 − 0.92210I
b = −1.151270 + 0.693551I
0.72806 + 5.75739I 4.99130 − 5.10418I
u = −0.724250 − 0.436534I
a = 1.15534 + 0.92210I
b = −1.151270 − 0.693551I
0.72806 − 5.75739I 4.99130 + 5.10418I
u = −0.434366 + 0.666743I
a = 0.33515 − 2.08440I
b = −0.607875 + 0.260312I
1.88416 − 0.85038I 6.25673 − 3.20224I
u = −0.434366 − 0.666743I
a = 0.33515 + 2.08440I
b = −0.607875 − 0.260312I
1.88416 + 0.85038I 6.25673 + 3.20224I
u = −0.212305 + 1.189430I
a = −0.778145 + 0.361047I
b = −1.237090 + 0.111866I
−6.51253 − 1.42478I 0
u = −0.212305 − 1.189430I
a = −0.778145 − 0.361047I
b = −1.237090 − 0.111866I
−6.51253 + 1.42478I 0
u = −0.686889 + 1.004730I
a = 0.343976 − 0.826525I
b = −0.085142 + 0.784336I
3.37147 − 6.01200I 0
u = −0.686889 − 1.004730I
a = 0.343976 + 0.826525I
b = −0.085142 − 0.784336I
3.37147 + 6.01200I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572191 + 1.085580I
a = −0.52093 + 1.70529I
b = −1.240970 − 0.438253I
−4.09769 − 6.18849I 0
u = −0.572191 − 1.085580I
a = −0.52093 − 1.70529I
b = −1.240970 + 0.438253I
−4.09769 + 6.18849I 0
u = −0.601851 + 1.072670I
a = 0.51488 − 1.93050I
b = 1.31349 + 0.76096I
−1.10548 − 10.82140I 0
u = −0.601851 − 1.072670I
a = 0.51488 + 1.93050I
b = 1.31349 − 0.76096I
−1.10548 + 10.82140I 0
u = 0.055611 + 0.764069I
a = −0.284386 + 0.734524I
b = 0.575442 − 0.355913I
−1.00556 + 1.44727I −1.64819 − 5.47738I
u = 0.055611 − 0.764069I
a = −0.284386 − 0.734524I
b = 0.575442 + 0.355913I
−1.00556 − 1.44727I −1.64819 + 5.47738I
u = −0.673460 + 1.041740I
a = −0.955719 + 0.894786I
b = 0.132760 − 1.273430I
8.08301 − 10.18320I 0
u = −0.673460 − 1.041740I
a = −0.955719 − 0.894786I
b = 0.132760 + 1.273430I
8.08301 + 10.18320I 0
u = −0.681987 + 0.321709I
a = −0.724827 + 0.615572I
b = 1.078220 − 0.328843I
−1.99983 + 1.37832I −0.467710 − 0.890691I
u = −0.681987 − 0.321709I
a = −0.724827 − 0.615572I
b = 1.078220 + 0.328843I
−1.99983 − 1.37832I −0.467710 + 0.890691I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.780684 + 1.053130I
a = −0.293135 − 0.040674I
b = 0.683599 − 0.489569I
5.65031 − 0.44478I 0
u = −0.780684 − 1.053130I
a = −0.293135 + 0.040674I
b = 0.683599 + 0.489569I
5.65031 + 0.44478I 0
u = 0.013214 + 1.311610I
a = 0.807998 − 0.074133I
b = 1.204730 + 0.451072I
−0.35444 − 8.20749I 0
u = 0.013214 − 1.311610I
a = 0.807998 + 0.074133I
b = 1.204730 − 0.451072I
−0.35444 + 8.20749I 0
u = 0.680239 + 1.136940I
a = 0.55415 + 1.83786I
b = 1.35544 − 0.64421I
4.2476 + 16.8128I 0
u = 0.680239 − 1.136940I
a = 0.55415 − 1.83786I
b = 1.35544 + 0.64421I
4.2476 − 16.8128I 0
u = 0.695044 + 1.161580I
a = −0.43161 − 1.48086I
b = −1.215140 + 0.489831I
0.03277 + 10.71240I 0
u = 0.695044 − 1.161580I
a = −0.43161 + 1.48086I
b = −1.215140 − 0.489831I
0.03277 − 10.71240I 0
u = 0.621820 + 1.215440I
a = 0.821143 + 0.925875I
b = 0.823061 − 0.470093I
5.26202 + 4.45797I 0
u = 0.621820 − 1.215440I
a = 0.821143 − 0.925875I
b = 0.823061 + 0.470093I
5.26202 − 4.45797I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.12822 + 1.49963I
a = −0.590311 − 0.032839I
b = −0.946332 − 0.195707I
−4.67412 − 0.82373I 0
u = 0.12822 − 1.49963I
a = −0.590311 + 0.032839I
b = −0.946332 + 0.195707I
−4.67412 + 0.82373I 0
u = 0.318662
a = 2.19545
b = −0.365228
1.00464 11.4100
10
II. I
u
2
= h−a
2
u + 2b + a − 2, a
3
+ 2a
2
u − au + 2a + 2, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u + 1
a
1
=
−u
u − 1
a
3
=
1
0
a
9
=
a
1
2
a
2
u −
1
2
a + 1
a
10
=
1
2
a
2
u +
1
2
a + 1
1
2
a
2
u −
1
2
a + 1
a
8
=
1
2
a
2
u +
1
2
a + 1
1
2
a
2
u −
1
2
a + 1
a
4
=
1
2
a
2
u +
1
2
a + 1
−
1
2
a
2
u +
1
2
a
2
−
1
2
au + a − u
a
11
=
−
1
2
a
2
u −
1
2
a − 1
−
1
2
a
2
u +
1
2
a − 1
a
7
=
1
2
a
2
u +
1
2
a + 1
1
2
a
2
u −
1
2
a + 1
a
7
=
1
2
a
2
u +
1
2
a + 1
1
2
a
2
u −
1
2
a + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u + 2
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
, c
4
, c
6
c
8
, c
9
u
6
− 2u
4
− u
3
+ u
2
+ u + 1
c
7
, c
10
u
6
c
11
u
6
− 4u
5
+ 6u
4
− 3u
3
− u
2
+ u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
3
c
3
, c
4
, c
6
c
8
, c
9
y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1
c
7
, c
10
y
6
c
11
y
6
− 4y
5
+ 10y
4
− 11y
3
+ 19y
2
− 3y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.412728 + 1.011420I
b = 0.218964 − 0.666188I
2.02988I 0. − 3.46410I
u = 0.500000 + 0.866025I
a = −0.562490 − 0.528127I
b = 1.033350 + 0.428825I
2.02988I 0. − 3.46410I
u = 0.500000 + 0.866025I
a = −0.85024 − 2.21534I
b = −1.252310 + 0.237364I
2.02988I 0. − 3.46410I
u = 0.500000 − 0.866025I
a = 0.412728 − 1.011420I
b = 0.218964 + 0.666188I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = −0.562490 + 0.528127I
b = 1.033350 − 0.428825I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = −0.85024 + 2.21534I
b = −1.252310 − 0.237364I
− 2.02988I 0. + 3.46410I
14
III. I
u
3
= hb + 1, 6a + u + 4, u
2
+ 2i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
2
a
1
=
−u
−u
a
3
=
2u
3u
a
9
=
−
1
6
u −
2
3
−1
a
10
=
−
13
6
u −
2
3
−3u − 1
a
8
=
−
1
6
u −
5
3
−1
a
4
=
−
1
6
u −
2
3
−1
a
11
=
−
23
18
u −
1
9
−
4
3
u −
1
3
a
7
=
−
5
18
u +
8
9
−
1
3
u +
5
3
a
7
=
−
5
18
u +
8
9
−
1
3
u +
5
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
10
u
2
+ 2
c
2
(u + 2)
2
c
3
, c
4
(u + 1)
2
c
6
, c
11
3(3u
2
− 2u + 1)
c
8
, c
9
(u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
10
(y + 2)
2
c
2
(y − 4)
2
c
3
, c
4
, c
8
c
9
(y − 1)
2
c
6
, c
11
9(9y
2
+ 2y + 1)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −0.666667 − 0.235702I
b = −1.00000
−4.93480 0
u = − 1.414210I
a = −0.666667 + 0.235702I
b = −1.00000
−4.93480 0
18
IV. I
u
4
= hb
2
au + b
3
− bu − au − b + u − 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u + 1
a
1
=
−u
u − 1
a
3
=
1
0
a
9
=
a
b
a
10
=
b + a
b
a
8
=
b + a
b
a
4
=
−b
2
− ba + 1
−b
2
a
11
=
−bau − a
2
u + a
2
− u
−b
2
u − bau + ba + u − 1
a
7
=
bau + a
2
u − a
2
+ b + a + u
b
2
u + bau − ba + b − u + 1
a
7
=
bau + a
2
u − a
2
+ b + a + u
b
2
u + bau − ba + b − u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u + 8
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
19
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
1.64493 − 2.02988I 6.00000 − 3.46410I
20
V. I
v
1
= ha, b
3
− b − 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
6
=
1
0
a
1
=
1
0
a
3
=
1
0
a
9
=
0
b
a
10
=
b
b
a
8
=
b
b
a
4
=
−b
2
+ 1
−b
2
a
11
=
1
b
2
a
7
=
b + 1
b
2
+ b
a
7
=
b + 1
b
2
+ b
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
3
c
3
, c
4
, c
8
c
9
, c
11
u
3
− u + 1
c
6
u
3
+ 2u
2
+ u + 1
c
7
, c
10
(u − 1)
3
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
3
c
3
, c
4
, c
8
c
9
, c
11
y
3
− 2y
2
+ y − 1
c
6
y
3
− 2y
2
− 3y − 1
c
7
, c
10
(y − 1)
3
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.662359 + 0.562280I
1.64493 6.00000
v = 1.00000
a = 0
b = −0.662359 − 0.562280I
1.64493 6.00000
v = 1.00000
a = 0
b = 1.32472
1.64493 6.00000
24
VI. I
v
2
= ha, b − 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
6
=
1
0
a
1
=
1
0
a
3
=
1
0
a
9
=
0
1
a
10
=
1
1
a
8
=
1
1
a
4
=
0
−1
a
11
=
1
1
a
7
=
1
1
a
7
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
u
c
3
, c
4
, c
11
u − 1
c
6
, c
8
, c
9
u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
y
c
3
, c
4
, c
6
c
8
, c
9
, c
11
y − 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
0 0
28
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
4
(u
2
+ 2)(u
2
− u + 1)
3
(u
53
+ 4u
52
+ ··· − 92u − 46)
c
2
u
4
(u + 2)
2
(u
2
+ u + 1)
3
(u
53
+ 24u
52
+ ··· + 3496u − 2116)
c
3
9(u − 1)(u + 1)
2
(u
3
− u + 1)(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
· (9u
53
− 18u
52
+ ··· − 77u − 19)
c
4
9(u − 1)(u + 1)
2
(u
3
− u + 1)(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
· (9u
53
+ 18u
52
+ ··· − 9u − 19)
c
6
48(u + 1)(3u
2
− 2u + 1)(u
3
+ 2u
2
+ u + 1)(u
6
− 2u
4
+ ··· + u + 1)
· (16u
53
− 16u
52
+ ··· + 103779u − 3609)
c
7
, c
10
u
7
(u − 1)
3
(u
2
+ 2)(u
53
+ 6u
52
+ ··· − 5832u − 1706)
c
8
9(u − 1)
2
(u + 1)(u
3
− u + 1)(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
· (9u
53
+ 18u
52
+ ··· − 9u − 19)
c
9
9(u − 1)
2
(u + 1)(u
3
− u + 1)(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
· (9u
53
− 18u
52
+ ··· − 77u − 19)
c
11
48(u − 1)(3u
2
− 2u + 1)(u
3
− u + 1)(u
6
− 4u
5
+ ··· + u + 1)
· (16u
53
+ 32u
52
+ ··· − 16641u − 6003)
29
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
4
(y + 2)
2
(y
2
+ y + 1)
3
(y
53
+ 24y
52
+ ··· + 3496y − 2116)
c
2
y
4
(y − 4)
2
(y
2
+ y + 1)
3
· (y
53
+ 12y
52
+ ··· + 393508288y − 4477456)
c
3
, c
9
81(y − 1)
3
(y
3
− 2y
2
+ y − 1)(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
· (81y
53
− 3510y
52
+ ··· + 3421y − 361)
c
4
, c
8
81(y − 1)
3
(y
3
− 2y
2
+ y − 1)(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
· (81y
53
− 2214y
52
+ ··· + 7149y − 361)
c
6
2304(y − 1)(9y
2
+ 2y + 1)(y
3
− 2y
2
− 3y − 1)
· (y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
· (256y
53
+ 6016y
52
+ ··· + 9942551577y − 13024881)
c
7
, c
10
y
7
(y − 1)
3
(y + 2)
2
(y
53
− 30y
52
+ ··· − 5573800y − 2910436)
c
11
2304(y − 1)(9y
2
+ 2y + 1)(y
3
− 2y
2
+ y − 1)
· (y
6
− 4y
5
+ 10y
4
− 11y
3
+ 19y
2
− 3y + 1)
· (256y
53
− 6528y
52
+ ··· − 368087463y − 36036009)
30
