12n
0490
(K12n
0490
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 11 1 12 3 1 4 8
Solving Sequence
8,12
9
1,4
3 7 11 5 6 2 10
c
8
c
12
c
3
c
7
c
11
c
4
c
6
c
2
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
25
+ 33u
24
+ ··· + 4b + 36, 17u
25
+ 196u
24
+ ··· + 32a + 656, u
26
+ 12u
25
+ ··· + 288u + 32i
I
u
2
= h−333638458a
9
u
2
+ 2803980318a
8
u
2
+ ··· − 878011078a − 1380422771,
a
9
u
2
+ 5a
8
u
2
+ ··· + 528a + 584, u
3
− u
2
+ 2u − 1i
I
u
3
= h2u
17
+ 15u
15
+ ··· + b + 2, 2u
16
− 2u
15
+ ··· + a + 4, u
18
− u
17
+ ··· − 4u + 1i
* 3 irreducible components of dim
C
= 0, with total 74 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
= h3u
25
+ 33u
24
+ · · · + 4b + 36, 17u
25
+ 196u
24
+ · · · + 32a +
656, u
26
+ 12u
25
+ · · · + 288u + 32i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
4
=
−0.531250u
25
− 6.12500u
24
+ ··· − 148.500u − 20.5000
−
3
4
u
25
−
33
4
u
24
+ ··· −
155
2
u − 9
a
3
=
−
9
32
u
25
−
21
8
u
24
+ ··· − 16u −
7
2
1
2
u
25
+
23
4
u
24
+ ··· +
149
2
u + 7
a
7
=
u
2
+ 1
u
2
a
11
=
−
19
32
u
25
−
105
16
u
24
+ ··· − 134u − 16
−
3
16
u
25
−
17
8
u
24
+ ··· − 11u − 1
a
5
=
2.87500u
25
+ 30.5625u
24
+ ··· + 671.750u + 82.5000
−
23
16
u
25
−
137
8
u
24
+ ··· −
483
2
u − 26
a
6
=
−
57
32
u
25
−
157
8
u
24
+ ··· −
1077
2
u − 68
3
4
u
25
+
69
8
u
24
+ ··· + 116u + 13
a
2
=
−
1
32
u
25
−
3
16
u
24
+ ··· + 23u + 3
9
16
u
25
+
51
8
u
24
+ ··· + 155u + 19
a
10
=
1
32
u
25
+
3
16
u
24
+ ··· − 21u − 2
7
16
u
25
+
37
8
u
24
+ ··· + 102u + 13
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
7
4
u
25
− 20u
24
+ ··· − 292u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
+ 9u
25
+ ··· + 96u + 64
c
2
, c
5
u
26
+ 9u
25
+ ··· + 24u + 8
c
3
, c
4
, c
9
c
11
u
26
+ 8u
24
+ ··· + 3u + 1
c
6
, c
10
u
26
+ u
25
+ ··· + 14u + 1
c
7
, c
8
, c
12
u
26
− 12u
25
+ ··· − 288u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 19y
25
+ ··· − 8704y + 4096
c
2
, c
5
y
26
− 9y
25
+ ··· − 96y + 64
c
3
, c
4
, c
9
c
11
y
26
+ 16y
25
+ ··· + 5y + 1
c
6
, c
10
y
26
+ 39y
25
+ ··· − 50y + 1
c
7
, c
8
, c
12
y
26
+ 22y
25
+ ··· + 512y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373580 + 0.933614I
a = 0.280319 + 0.410765I
b = 0.406899 + 0.387993I
−0.83502 − 2.62007I 5.29205 + 6.35608I
u = −0.373580 − 0.933614I
a = 0.280319 − 0.410765I
b = 0.406899 − 0.387993I
−0.83502 + 2.62007I 5.29205 − 6.35608I
u = −0.977022 + 0.289560I
a = −0.999855 + 0.807238I
b = −0.329282 − 0.190408I
5.86673 − 2.98457I 2.91733 + 2.32225I
u = −0.977022 − 0.289560I
a = −0.999855 − 0.807238I
b = −0.329282 + 0.190408I
5.86673 + 2.98457I 2.91733 − 2.32225I
u = −1.040460 + 0.290353I
a = 0.885056 − 0.906575I
b = 0.321883 + 0.239511I
4.93150 − 9.47568I 1.22997 + 6.65192I
u = −1.040460 − 0.290353I
a = 0.885056 + 0.906575I
b = 0.321883 − 0.239511I
4.93150 + 9.47568I 1.22997 − 6.65192I
u = −0.893372 + 0.672431I
a = 0.616422 − 0.459995I
b = 0.580795 + 0.074295I
−1.98248 − 3.07677I −3.82004 + 5.96476I
u = −0.893372 − 0.672431I
a = 0.616422 + 0.459995I
b = 0.580795 − 0.074295I
−1.98248 + 3.07677I −3.82004 − 5.96476I
u = −0.658604 + 1.099520I
a = −0.357985 + 0.662624I
b = −0.744381 + 0.825205I
3.47939 − 2.75359I 0. + 1.54097I
u = −0.658604 − 1.099520I
a = −0.357985 − 0.662624I
b = −0.744381 − 0.825205I
3.47939 + 2.75359I 0. − 1.54097I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.737527 + 1.134930I
a = 0.473155 − 0.623862I
b = 1.037410 − 0.669242I
2.46178 + 3.30067I −1.81816 − 2.93564I
u = −0.737527 − 1.134930I
a = 0.473155 + 0.623862I
b = 1.037410 + 0.669242I
2.46178 − 3.30067I −1.81816 + 2.93564I
u = −0.500184 + 0.273597I
a = −1.113850 + 0.000222I
b = −0.361841 − 0.000040I
1.011870 − 0.620695I 7.41936 + 3.02549I
u = −0.500184 − 0.273597I
a = −1.113850 − 0.000222I
b = −0.361841 + 0.000040I
1.011870 + 0.620695I 7.41936 − 3.02549I
u = 0.345460 + 0.396654I
a = 0.416298 + 0.809635I
b = 0.415031 − 0.528152I
−1.54818 + 1.01569I −2.49851 + 1.48185I
u = 0.345460 − 0.396654I
a = 0.416298 − 0.809635I
b = 0.415031 + 0.528152I
−1.54818 − 1.01569I −2.49851 − 1.48185I
u = −0.12954 + 1.47954I
a = 0.663655 + 0.382952I
b = 1.94741 + 0.15396I
−4.82392 − 2.67431I 0
u = −0.12954 − 1.47954I
a = 0.663655 − 0.382952I
b = 1.94741 − 0.15396I
−4.82392 + 2.67431I 0
u = −0.39186 + 1.47047I
a = 1.031950 + 0.307632I
b = 2.57514 + 0.41031I
0.23550 − 7.89653I 0
u = −0.39186 − 1.47047I
a = 1.031950 − 0.307632I
b = 2.57514 − 0.41031I
0.23550 + 7.89653I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.42139 + 1.47806I
a = −1.077660 − 0.235946I
b = −2.67192 − 0.32255I
−0.7052 − 14.6997I 0. + 7.55199I
u = −0.42139 − 1.47806I
a = −1.077660 + 0.235946I
b = −2.67192 + 0.32255I
−0.7052 + 14.6997I 0. − 7.55199I
u = 0.04653 + 1.56180I
a = −0.561335 − 0.336020I
b = −1.91553 + 0.15501I
−8.47892 + 2.46726I 0
u = 0.04653 − 1.56180I
a = −0.561335 + 0.336020I
b = −1.91553 − 0.15501I
−8.47892 − 2.46726I 0
u = −0.26846 + 1.59618I
a = −0.756170 − 0.252389I
b = −2.26161 − 0.13367I
−9.48266 − 7.26585I 0
u = −0.26846 − 1.59618I
a = −0.756170 + 0.252389I
b = −2.26161 + 0.13367I
−9.48266 + 7.26585I 0
7
II. I
u
2
= h−3.34 × 10
8
a
9
u
2
+ 2.80 × 10
9
a
8
u
2
+ · · · − 8.78 × 10
8
a − 1.38 ×
10
9
, a
9
u
2
+ 5a
8
u
2
+ · · · + 528a + 584, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
4
=
a
0.209620a
9
u
2
− 1.76170a
8
u
2
+ ··· + 0.551640a + 0.867297
a
3
=
−0.209620a
9
u
2
+ 1.76170a
8
u
2
+ ··· + 0.448360a − 0.867297
−1.52915a
9
u
2
+ 2.83867a
8
u
2
+ ··· + 1.28335a + 1.54825
a
7
=
u
2
+ 1
u
2
a
11
=
−a
2
u
−1.83712a
9
u
2
+ 2.43089a
8
u
2
+ ··· − 0.217188a + 3.13850
a
5
=
a
3
u
2
+ a
−2.20070a
9
u
2
+ 2.46990a
8
u
2
+ ··· − 1.35859a + 2.49562
a
6
=
1.87891a
9
u
2
− 3.01206a
8
u
2
+ ··· − 0.212937a − 1.75521
2.51980a
9
u
2
− 2.23306a
8
u
2
+ ··· + 1.62064a − 2.93193
a
2
=
−0.232543a
9
u
2
+ 1.95512a
8
u
2
+ ··· + 0.115174a + 0.454433
−a
2
u
2
+ 2u − 2
a
10
=
2.70862a
9
u
2
− 2.33692a
8
u
2
+ ··· + 1.65477a − 1.76434
0.871503a
9
u
2
+ 0.0939733a
8
u
2
+ ··· + 1.43758a + 1.37417
(ii) Obstruction class = −1
(iii) Cusp Shapes =
640570216
1591637129
a
9
u
2
+
5775444576
1591637129
a
8
u
2
+ ··· +
12123611228
1591637129
a +
11646488850
1591637129
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
6
c
2
, c
5
(u
5
− u
4
+ u
2
+ u − 1)
6
c
3
, c
4
, c
9
c
11
u
30
− u
29
+ ··· + 1390u + 773
c
6
, c
10
u
30
− 3u
29
+ ··· − 9926u + 2939
c
7
, c
8
, c
12
(u
3
+ u
2
+ 2u + 1)
10
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
6
c
2
, c
5
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
6
c
3
, c
4
, c
9
c
11
y
30
+ 15y
29
+ ··· + 5878292y + 597529
c
6
, c
10
y
30
+ 19y
29
+ ··· − 67383832y + 8637721
c
7
, c
8
, c
12
(y
3
+ 3y
2
+ 2y −1)
10
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.014630 + 0.047968I
b = −2.30589 − 0.97577I
−8.84111 + 2.82812I −11.11859 − 2.97945I
u = 0.215080 + 1.307140I
a = 0.771849 − 0.683924I
b = 1.093870 − 0.106141I
−6.13913 + 5.04209I −2.62407 − 7.20234I
u = 0.215080 + 1.307140I
a = −1.115000 − 0.034024I
b = −2.93266 − 0.29143I
−6.13913 + 5.04209I −2.62407 − 7.20234I
u = 0.215080 + 1.307140I
a = −0.784986 + 0.155927I
b = −2.90073 + 1.14869I
2.99936 + 6.15987I −1.59102 − 5.34173I
u = 0.215080 + 1.307140I
a = 1.217270 + 0.148472I
b = 2.62933 + 0.23436I
−6.13913 + 0.61415I −2.62407 + 1.24344I
u = 0.215080 + 1.307140I
a = 0.305785 + 1.223910I
b = 0.871169 + 0.998250I
2.99936 − 0.50362I −1.59102 − 0.61717I
u = 0.215080 + 1.307140I
a = 0.683723 − 0.136389I
b = 2.59396 − 1.27411I
2.99936 − 0.50362I −1.59102 − 0.61717I
u = 0.215080 + 1.307140I
a = −0.127449 − 1.308880I
b = −0.575167 − 1.111610I
2.99936 + 6.15987I −1.59102 − 5.34173I
u = 0.215080 + 1.307140I
a = 1.290360 − 0.282036I
b = 2.26738 + 0.12156I
−8.84111 + 2.82812I −11.11859 − 2.97945I
u = 0.215080 + 1.307140I
a = −0.564558 + 0.306692I
b = −0.833786 − 0.795800I
−6.13913 + 0.61415I −2.62407 + 1.24344I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 − 1.307140I
a = −1.014630 − 0.047968I
b = −2.30589 + 0.97577I
−8.84111 − 2.82812I −11.11859 + 2.97945I
u = 0.215080 − 1.307140I
a = 0.771849 + 0.683924I
b = 1.093870 + 0.106141I
−6.13913 − 5.04209I −2.62407 + 7.20234I
u = 0.215080 − 1.307140I
a = −1.115000 + 0.034024I
b = −2.93266 + 0.29143I
−6.13913 − 5.04209I −2.62407 + 7.20234I
u = 0.215080 − 1.307140I
a = −0.784986 − 0.155927I
b = −2.90073 − 1.14869I
2.99936 − 6.15987I −1.59102 + 5.34173I
u = 0.215080 − 1.307140I
a = 1.217270 − 0.148472I
b = 2.62933 − 0.23436I
−6.13913 − 0.61415I −2.62407 − 1.24344I
u = 0.215080 − 1.307140I
a = 0.305785 − 1.223910I
b = 0.871169 − 0.998250I
2.99936 + 0.50362I −1.59102 + 0.61717I
u = 0.215080 − 1.307140I
a = 0.683723 + 0.136389I
b = 2.59396 + 1.27411I
2.99936 + 0.50362I −1.59102 + 0.61717I
u = 0.215080 − 1.307140I
a = −0.127449 + 1.308880I
b = −0.575167 + 1.111610I
2.99936 − 6.15987I −1.59102 + 5.34173I
u = 0.215080 − 1.307140I
a = 1.290360 + 0.282036I
b = 2.26738 − 0.12156I
−8.84111 − 2.82812I −11.11859 + 2.97945I
u = 0.215080 − 1.307140I
a = −0.564558 − 0.306692I
b = −0.833786 + 0.795800I
−6.13913 − 0.61415I −2.62407 − 1.24344I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = −0.494172 + 1.023630I
b = 0.055265 + 0.919402I
−2.00154 − 2.21397I 3.90519 + 4.22289I
u = 0.569840
a = −0.494172 − 1.023630I
b = 0.055265 − 0.919402I
−2.00154 + 2.21397I 3.90519 − 4.22289I
u = 0.569840
a = −1.81678 + 0.97410I
b = −0.401412 − 1.037940I
7.13694 + 3.33174I 4.93825 − 2.36228I
u = 0.569840
a = −1.81678 − 0.97410I
b = −0.401412 + 1.037940I
7.13694 − 3.33174I 4.93825 + 2.36228I
u = 0.569840
a = 1.73970 + 1.26637I
b = 0.470359 − 0.966293I
7.13694 + 3.33174I 4.93825 − 2.36228I
u = 0.569840
a = 1.73970 − 1.26637I
b = 0.470359 + 0.966293I
7.13694 − 3.33174I 4.93825 + 2.36228I
u = 0.569840
a = 0.18462 + 2.19674I
b = 0.221651 − 0.130016I
−2.00154 + 2.21397I 3.90519 − 4.22289I
u = 0.569840
a = 0.18462 − 2.19674I
b = 0.221651 + 0.130016I
−2.00154 − 2.21397I 3.90519 + 4.22289I
u = 0.569840
a = −0.27573 + 2.20498I
b = 0.246656 + 0.540491I
−4.70353 −4.58932 + 0.I
u = 0.569840
a = −0.27573 − 2.20498I
b = 0.246656 − 0.540491I
−4.70353 −4.58932 + 0.I
13
III.
I
u
3
= h2u
17
+15u
15
+· · ·+b+2, 2u
16
−2u
15
+· · ·+a+4, u
18
−u
17
+· · ·−4u+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
4
=
−2u
16
+ 2u
15
+ ··· − 4u − 4
−2u
17
− 15u
15
+ ··· + 4u − 2
a
3
=
2u
17
− 4u
16
+ ··· − 21u
2
− 4
−3u
16
+ 4u
15
+ ··· + 6u − 2
a
7
=
u
2
+ 1
u
2
a
11
=
−2u
17
+ 2u
16
+ ··· − 22u + 5
−u
17
+ 2u
16
+ ··· − 4u + 2
a
5
=
u
17
− 3u
16
+ ··· + 13u − 2
−3u
17
− 21u
15
+ ··· + 19u − 5
a
6
=
u
17
− 2u
16
+ ··· + 27u − 5
−2u
17
+ u
16
+ ··· + 6u − 3
a
2
=
−u
16
− 8u
14
+ ··· − 15u + 1
−u
16
+ u
15
+ ··· − 19u
2
+ 3u
a
10
=
−2u
17
+ u
16
+ ··· − 19u + 4
−u
17
+ u
16
+ ··· − u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
17
+ 7u
16
− 24u
15
+ 61u
14
− 112u
13
+ 219u
12
− 282u
11
+
425u
10
− 445u
9
+ 493u
8
− 466u
7
+ 358u
6
− 299u
5
+ 167u
4
− 81u
3
+ 44u
2
+ 7u − 5
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 8u
17
+ ··· − 8u + 1
c
2
u
18
+ 2u
17
+ ··· + 2u + 1
c
3
, c
11
u
18
+ 7u
16
+ ··· + 13u
2
+ 1
c
4
, c
9
u
18
+ 7u
16
+ ··· + 13u
2
+ 1
c
5
u
18
− 2u
17
+ ··· − 2u + 1
c
6
, c
10
u
18
+ u
17
+ ··· + u + 1
c
7
, c
8
u
18
− u
17
+ ··· − 4u + 1
c
12
u
18
+ u
17
+ ··· + 4u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 12y
17
+ ··· + 16y + 1
c
2
, c
5
y
18
− 8y
17
+ ··· − 8y + 1
c
3
, c
4
, c
9
c
11
y
18
+ 14y
17
+ ··· + 26y + 1
c
6
, c
10
y
18
+ 5y
17
+ ··· − 9y + 1
c
7
, c
8
, c
12
y
18
+ 19y
17
+ ··· + 26y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.548156 + 0.847238I
a = −0.223507 + 0.171449I
b = −0.275267 − 0.419395I
−1.41562 − 2.18118I −2.40356 + 0.24504I
u = −0.548156 − 0.847238I
a = −0.223507 − 0.171449I
b = −0.275267 + 0.419395I
−1.41562 + 2.18118I −2.40356 − 0.24504I
u = −0.289325 + 0.967313I
a = −0.214015 − 0.827701I
b = 1.143520 − 0.792525I
4.75616 − 4.41472I 1.35648 + 3.62940I
u = −0.289325 − 0.967313I
a = −0.214015 + 0.827701I
b = 1.143520 + 0.792525I
4.75616 + 4.41472I 1.35648 − 3.62940I
u = −0.301562 + 1.039980I
a = −0.015170 + 0.829040I
b = −1.39264 + 0.54596I
4.48430 + 2.10133I 1.59454 − 2.04993I
u = −0.301562 − 1.039980I
a = −0.015170 − 0.829040I
b = −1.39264 − 0.54596I
4.48430 − 2.10133I 1.59454 + 2.04993I
u = 0.826816 + 0.217598I
a = −0.35619 − 1.39245I
b = −0.265916 − 0.214656I
−4.52038 + 1.43762I −3.35124 − 4.60330I
u = 0.826816 − 0.217598I
a = −0.35619 + 1.39245I
b = −0.265916 + 0.214656I
−4.52038 − 1.43762I −3.35124 + 4.60330I
u = 0.278515 + 1.287490I
a = −1.123880 + 0.058895I
b = −2.12241 − 0.53151I
−7.92752 + 2.43301I −1.35565 + 0.52411I
u = 0.278515 − 1.287490I
a = −1.123880 − 0.058895I
b = −2.12241 + 0.53151I
−7.92752 − 2.43301I −1.35565 − 0.52411I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.094154 + 1.349150I
a = −0.996965 + 0.368074I
b = −2.30279 − 0.39041I
−7.09698 + 2.98270I −3.08593 − 3.04995I
u = 0.094154 − 1.349150I
a = −0.996965 − 0.368074I
b = −2.30279 + 0.39041I
−7.09698 − 2.98270I −3.08593 + 3.04995I
u = −0.01485 + 1.49543I
a = 0.746594 − 0.367613I
b = 2.22443 + 0.33307I
−9.34606 − 2.01452I −7.23332 − 0.16467I
u = −0.01485 − 1.49543I
a = 0.746594 + 0.367613I
b = 2.22443 − 0.33307I
−9.34606 + 2.01452I −7.23332 + 0.16467I
u = 0.35110 + 1.52606I
a = 0.830916 − 0.030800I
b = 2.13840 + 0.29887I
−10.29080 + 5.91942I −5.83679 − 3.74571I
u = 0.35110 − 1.52606I
a = 0.830916 + 0.030800I
b = 2.13840 − 0.29887I
−10.29080 − 5.91942I −5.83679 + 3.74571I
u = 0.103300 + 0.232173I
a = −3.64778 − 2.10197I
b = −0.147325 − 0.979951I
−3.18667 − 2.11613I −5.18453 + 3.64144I
u = 0.103300 − 0.232173I
a = −3.64778 + 2.10197I
b = −0.147325 + 0.979951I
−3.18667 + 2.11613I −5.18453 − 3.64144I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
6
)(u
18
− 8u
17
+ ··· − 8u + 1)
· (u
26
+ 9u
25
+ ··· + 96u + 64)
c
2
((u
5
− u
4
+ u
2
+ u − 1)
6
)(u
18
+ 2u
17
+ ··· + 2u + 1)
· (u
26
+ 9u
25
+ ··· + 24u + 8)
c
3
, c
11
(u
18
+ 7u
16
+ ··· + 13u
2
+ 1)(u
26
+ 8u
24
+ ··· + 3u + 1)
· (u
30
− u
29
+ ··· + 1390u + 773)
c
4
, c
9
(u
18
+ 7u
16
+ ··· + 13u
2
+ 1)(u
26
+ 8u
24
+ ··· + 3u + 1)
· (u
30
− u
29
+ ··· + 1390u + 773)
c
5
((u
5
− u
4
+ u
2
+ u − 1)
6
)(u
18
− 2u
17
+ ··· − 2u + 1)
· (u
26
+ 9u
25
+ ··· + 24u + 8)
c
6
, c
10
(u
18
+ u
17
+ ··· + u + 1)(u
26
+ u
25
+ ··· + 14u + 1)
· (u
30
− 3u
29
+ ··· − 9926u + 2939)
c
7
, c
8
((u
3
+ u
2
+ 2u + 1)
10
)(u
18
− u
17
+ ··· − 4u + 1)
· (u
26
− 12u
25
+ ··· − 288u + 32)
c
12
((u
3
+ u
2
+ 2u + 1)
10
)(u
18
+ u
17
+ ··· + 4u + 1)
· (u
26
− 12u
25
+ ··· − 288u + 32)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
6
)(y
18
+ 12y
17
+ ··· + 16y + 1)
· (y
26
+ 19y
25
+ ··· − 8704y + 4096)
c
2
, c
5
((y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
6
)(y
18
− 8y
17
+ ··· − 8y + 1)
· (y
26
− 9y
25
+ ··· − 96y + 64)
c
3
, c
4
, c
9
c
11
(y
18
+ 14y
17
+ ··· + 26y + 1)(y
26
+ 16y
25
+ ··· + 5y + 1)
· (y
30
+ 15y
29
+ ··· + 5878292y + 597529)
c
6
, c
10
(y
18
+ 5y
17
+ ··· − 9y + 1)(y
26
+ 39y
25
+ ··· − 50y + 1)
· (y
30
+ 19y
29
+ ··· − 67383832y + 8637721)
c
7
, c
8
, c
12
((y
3
+ 3y
2
+ 2y −1)
10
)(y
18
+ 19y
17
+ ··· + 26y + 1)
· (y
26
+ 22y
25
+ ··· + 512y + 1024)
20
