12n
0280
(K12n
0280
)
A knot diagram
1
Linearized knot diagam
3 6 7 11 9 2 5 11 12 5 7 9
Solving Sequence
2,7
6 3 4
1,9
5 12 10 11 8
c
6
c
2
c
3
c
1
c
5
c
12
c
9
c
11
c
8
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
18
+ 4u
17
+ ··· + b − 1, −u
19
+ 5u
18
+ ··· + 2a + 4, u
20
− 5u
19
+ ··· − 10u + 2i
I
u
2
= hu
9
+ 2u
8
+ 4u
7
+ 4u
6
+ 5u
5
+ 4u
4
+ 4u
3
+ 2u
2
+ b + u + 1,
− u
10
− 4u
9
− 7u
8
− 10u
7
− 9u
6
− 11u
5
− 10u
4
− 8u
3
− 4u
2
+ 2a − 3u − 4,
u
11
+ 2u
10
+ 5u
9
+ 6u
8
+ 9u
7
+ 9u
6
+ 10u
5
+ 8u
4
+ 6u
3
+ 5u
2
+ 2u + 2i
I
u
3
= h−u
7
a − 3u
5
a − u
6
+ u
4
a − 4u
3
a − 2u
4
+ u
2
a + u
3
− 2au − u
2
+ b + a + u + 1,
− 2u
7
a + 5u
7
+ ··· − a − 4, u
8
+ u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
− 1i
* 3 irreducible components of dim
C
= 0, with total 47 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
18
+4u
17
+· · ·+b −1, −u
19
+5u
18
+· · ·+2a +4, u
20
−5u
19
+· · ·−10u +2i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
1
2
u
19
−
5
2
u
18
+ ··· + 10u − 2
u
18
− 4u
17
+ ··· − 3u + 1
a
5
=
3
2
u
19
−
13
2
u
18
+ ··· + u + 1
−u
18
+ 5u
17
+ ··· + 11u − 3
a
12
=
−
3
2
u
19
+
13
2
u
18
+ ··· − 7u + 1
u
19
− 4u
18
+ ··· + 5u − 1
a
10
=
2u
19
− 10u
18
+ ··· + 13u − 2
−2u
19
+ 8u
18
+ ··· − 9u + 2
a
11
=
−
5
2
u
19
+
21
2
u
18
+ ··· − 12u + 2
u
19
− 4u
18
+ ··· + 5u − 1
a
8
=
1
2
u
19
−
1
2
u
18
+ ··· − u + 1
u
19
− 4u
18
+ ··· + 4u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
19
+ 14u
18
− 49u
17
+ 118u
16
− 238u
15
+ 405u
14
− 622u
13
+ 886u
12
− 1180u
11
+
1475u
10
−1689u
9
+1761u
8
−1647u
7
+1374u
6
−1015u
5
+655u
4
−363u
3
+170u
2
−66u+12
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
+ 11u
19
+ ··· + 36u + 4
c
2
, c
6
u
20
− 5u
19
+ ··· − 10u + 2
c
3
u
20
+ 5u
19
+ ··· − 10u + 10
c
4
, c
7
, c
10
u
20
+ 15u
18
+ ··· + 2u + 1
c
5
u
20
+ u
19
+ ··· + u + 1
c
8
u
20
+ 11u
19
+ ··· + 10u + 10
c
9
, c
12
u
20
− 3u
19
+ ··· + 3u + 1
c
11
u
20
− 19u
19
+ ··· − 2304u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− y
19
+ ··· − 208y + 16
c
2
, c
6
y
20
+ 11y
19
+ ··· + 36y + 4
c
3
y
20
− 13y
19
+ ··· + 1940y + 100
c
4
, c
7
, c
10
y
20
+ 30y
19
+ ··· + 4y + 1
c
5
y
20
− 19y
19
+ ··· + 7y + 1
c
8
y
20
− 3y
19
+ ··· + 1460y + 100
c
9
, c
12
y
20
− 11y
19
+ ··· + 11y + 1
c
11
y
20
− 9y
19
+ ··· + 524288y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.988466 + 0.164208I
a = 0.083650 − 0.252088I
b = −1.31829 − 0.86406I
3.16459 − 7.53851I −1.81526 + 4.10532I
u = 0.988466 − 0.164208I
a = 0.083650 + 0.252088I
b = −1.31829 + 0.86406I
3.16459 + 7.53851I −1.81526 − 4.10532I
u = −0.230979 + 0.893127I
a = −1.51428 + 0.24987I
b = 0.618322 + 1.140400I
−0.82008 − 3.37374I −7.04529 + 0.08324I
u = −0.230979 − 0.893127I
a = −1.51428 − 0.24987I
b = 0.618322 − 1.140400I
−0.82008 + 3.37374I −7.04529 − 0.08324I
u = 0.743178 + 0.313816I
a = 0.040715 + 0.499230I
b = 0.715480 − 0.112619I
−0.854263 + 0.828569I −4.29561 − 2.11881I
u = 0.743178 − 0.313816I
a = 0.040715 − 0.499230I
b = 0.715480 + 0.112619I
−0.854263 − 0.828569I −4.29561 + 2.11881I
u = 0.348476 + 1.207610I
a = −1.77185 − 0.05613I
b = 1.221280 − 0.316490I
−5.09486 + 4.27767I −6.93870 − 3.93528I
u = 0.348476 − 1.207610I
a = −1.77185 + 0.05613I
b = 1.221280 + 0.316490I
−5.09486 − 4.27767I −6.93870 + 3.93528I
u = −0.904379 + 0.906046I
a = −0.071879 − 0.437712I
b = −0.847385 − 0.116530I
8.73338 − 3.30325I −7.62069 + 4.42366I
u = −0.904379 − 0.906046I
a = −0.071879 + 0.437712I
b = −0.847385 + 0.116530I
8.73338 + 3.30325I −7.62069 − 4.42366I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.130781 + 0.697014I
a = 1.214520 + 0.459557I
b = 0.132234 − 0.751539I
−0.259969 + 1.114940I −6.76006 − 5.17901I
u = −0.130781 − 0.697014I
a = 1.214520 − 0.459557I
b = 0.132234 + 0.751539I
−0.259969 − 1.114940I −6.76006 + 5.17901I
u = 0.590387 + 1.171510I
a = −0.831475 − 0.979178I
b = 0.850680 − 0.233951I
−3.33496 + 4.34846I −6.57341 − 3.74600I
u = 0.590387 − 1.171510I
a = −0.831475 + 0.979178I
b = 0.850680 + 0.233951I
−3.33496 − 4.34846I −6.57341 + 3.74600I
u = 0.181642 + 0.634443I
a = 0.754937 + 0.401077I
b = 0.044656 − 0.325945I
−0.338993 + 1.073370I −4.95066 − 6.25444I
u = 0.181642 − 0.634443I
a = 0.754937 − 0.401077I
b = 0.044656 + 0.325945I
−0.338993 − 1.073370I −4.95066 + 6.25444I
u = 0.564854 + 1.265020I
a = 1.91175 + 0.60844I
b = −1.44189 + 1.06169I
−0.23167 + 13.11790I −4.38679 − 6.82889I
u = 0.564854 − 1.265020I
a = 1.91175 − 0.60844I
b = −1.44189 − 1.06169I
−0.23167 − 13.11790I −4.38679 + 6.82889I
u = 0.349135 + 1.341000I
a = 1.18393 + 0.98393I
b = −1.47508 − 0.55967I
−1.78563 − 2.89136I −6.11353 + 1.76882I
u = 0.349135 − 1.341000I
a = 1.18393 − 0.98393I
b = −1.47508 + 0.55967I
−1.78563 + 2.89136I −6.11353 − 1.76882I
6
II.
I
u
2
= hu
9
+2u
8
+· · · +b+1, −u
10
−4u
9
+· · · +2a−4, u
11
+2u
10
+· · · +2u+2i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
1
2
u
10
+ 2u
9
+ ··· +
3
2
u + 2
−u
9
− 2u
8
− 4u
7
− 4u
6
− 5u
5
− 4u
4
− 4u
3
− 2u
2
− u − 1
a
5
=
−
5
2
u
10
− 4u
9
+ ··· −
11
2
u + 1
u
10
+ 2u
9
+ 4u
8
+ 5u
7
+ 6u
6
+ 7u
5
+ 6u
4
+ 5u
3
+ 3u
2
+ 3u + 1
a
12
=
−
1
2
u
10
− 2u
9
+ ··· −
5
2
u − 3
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
a
10
=
u
10
+ 5u
9
+ 9u
8
+ 15u
7
+ 15u
6
+ 19u
5
+ 17u
4
+ 15u
3
+ 9u
2
+ 6u + 6
−u
9
− 2u
8
− 4u
7
− 4u
6
− 5u
5
− 4u
4
− 4u
3
− 2u
2
− u − 2
a
11
=
−
1
2
u
10
− 2u
9
+ ··· −
7
2
u − 4
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
a
8
=
3
2
u
10
+ 7u
9
+ ··· +
19
2
u + 11
−u
9
− 2u
8
− 4u
7
− 4u
6
− 6u
5
− 5u
4
− 6u
3
− 3u
2
− 2u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
10
− 6u
9
− 12u
8
− 23u
7
− 27u
6
− 31u
5
− 30u
4
− 25u
3
− 20u
2
− 10u − 12
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 6u
10
+ ··· − 16u + 4
c
2
u
11
− 2u
10
+ 5u
9
− 6u
8
+ 9u
7
− 9u
6
+ 10u
5
− 8u
4
+ 6u
3
− 5u
2
+ 2u − 2
c
3
u
11
+ 2u
10
+ u
9
− 3u
8
− 15u
7
− 6u
6
+ u
5
− 17u
4
+ 8u
3
− 7u
2
− 6u − 2
c
4
, c
7
u
11
+ 5u
9
− u
8
+ u
7
− 4u
6
− 14u
5
− u
4
+ 4u
3
+ 7u
2
+ 3u + 1
c
5
u
11
+ u
10
+ u
9
+ 5u
8
− 4u
7
− 14u
6
+ u
5
− 11u
4
+ u
3
+ 2u
2
+ 2u − 1
c
6
u
11
+ 2u
10
+ 5u
9
+ 6u
8
+ 9u
7
+ 9u
6
+ 10u
5
+ 8u
4
+ 6u
3
+ 5u
2
+ 2u + 2
c
8
u
11
+ 8u
10
+ ··· + 2u − 2
c
9
u
11
− 3u
10
+ u
9
+ 5u
8
− 7u
7
+ 2u
6
+ 7u
5
− 7u
4
+ 2u
2
− 2u − 1
c
10
u
11
+ 5u
9
+ u
8
+ u
7
+ 4u
6
− 14u
5
+ u
4
+ 4u
3
− 7u
2
+ 3u − 1
c
11
u
11
+ 2u
10
− 2u
9
+ 7u
7
− 7u
6
− 2u
5
+ 7u
4
− 5u
3
− u
2
+ 3u − 1
c
12
u
11
+ 3u
10
+ u
9
− 5u
8
− 7u
7
− 2u
6
+ 7u
5
+ 7u
4
− 2u
2
− 2u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
+ 2y
10
+ ··· − 8y −16
c
2
, c
6
y
11
+ 6y
10
+ ··· − 16y −4
c
3
y
11
− 2y
10
+ ··· + 8y −4
c
4
, c
7
, c
10
y
11
+ 10y
10
+ ··· − 5y −1
c
5
y
11
+ y
10
+ ··· + 8y −1
c
8
y
11
− 12y
10
+ ··· + 40y −4
c
9
, c
12
y
11
− 7y
10
+ ··· + 8y −1
c
11
y
11
− 8y
10
+ ··· + 7y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.952070
a = −0.0720390
b = 1.36568
−4.80947 −8.08890
u = 0.403355 + 0.969097I
a = −0.951198 − 0.161815I
b = 0.426727 − 1.018660I
−0.52666 + 4.17339I −3.41102 − 8.36050I
u = 0.403355 − 0.969097I
a = −0.951198 + 0.161815I
b = 0.426727 + 1.018660I
−0.52666 − 4.17339I −3.41102 + 8.36050I
u = −0.186482 + 0.923547I
a = 2.30424 + 1.12564I
b = −1.117110 + 0.211347I
5.27605 − 0.83166I −7.37066 − 0.42439I
u = −0.186482 − 0.923547I
a = 2.30424 − 1.12564I
b = −1.117110 − 0.211347I
5.27605 + 0.83166I −7.37066 + 0.42439I
u = 0.525451 + 0.714735I
a = 0.807343 − 0.228094I
b = 0.412616 + 0.757804I
0.321119 − 0.386062I −0.453787 − 0.883807I
u = 0.525451 − 0.714735I
a = 0.807343 + 0.228094I
b = 0.412616 − 0.757804I
0.321119 + 0.386062I −0.453787 + 0.883807I
u = −0.794887 + 0.904829I
a = −0.518512 − 0.481273I
b = −0.484466 − 0.075834I
9.44423 − 2.99337I 2.32422 + 0.94995I
u = −0.794887 − 0.904829I
a = −0.518512 + 0.481273I
b = −0.484466 + 0.075834I
9.44423 + 2.99337I 2.32422 − 0.94995I
u = −0.471402 + 1.288100I
a = −1.60586 + 0.79965I
b = 1.57940 + 0.31572I
−8.82013 − 5.04219I −10.54429 + 3.49363I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.471402 − 1.288100I
a = −1.60586 − 0.79965I
b = 1.57940 − 0.31572I
−8.82013 + 5.04219I −10.54429 − 3.49363I
11
III. I
u
3
= h−u
7
a − u
6
+ · · · + a + 1, −2u
7
a + 5u
7
+ · · · − a − 4, u
8
+ u
7
+
3u
6
+ 2u
5
+ 3u
4
+ 2u
3
− 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
a
u
7
a + u
6
+ ··· − a − 1
a
5
=
−u
7
a + 4u
7
+ ··· − 5u + 2
−u
7
a − 2u
5
a + u
4
a − 2u
3
a + u
2
a + u
3
+ a + u − 1
a
12
=
−u
6
a + u
6
− 2u
4
a + u
3
a + u
4
− u
2
a − u
3
+ au + a − 2
−1
a
10
=
−2u
7
a − 2u
6
a + ··· + 4a − 5
u
6
+ 2u
4
+ u
2
− 2
a
11
=
−u
6
a + u
6
− 2u
4
a + u
3
a + u
4
− u
2
a − u
3
+ au + a − 1
−1
a
8
=
−u
7
a − 2u
6
a + ··· + 4a − 2
u
7
a + 2u
6
+ ··· − a − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 8u
5
− 4u
4
− 4u
3
− 4u
2
+ 4u + 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 5u
7
+ 11u
6
+ 10u
5
− u
4
− 10u
3
− 6u
2
+ 1)
2
c
2
, c
6
(u
8
+ u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
− 1)
2
c
3
(u
8
− u
7
− 5u
6
+ 4u
5
+ 7u
4
− 4u
3
− 2u
2
+ 2u − 1)
2
c
4
, c
7
, c
10
u
16
− u
15
+ ··· + 8u + 1
c
5
u
16
+ u
15
+ ··· − 550u − 131
c
8
(u
8
− 5u
7
+ 5u
6
+ 10u
5
− 17u
4
− 6u
3
+ 18u
2
− 7)
2
c
9
, c
12
u
16
− 5u
15
+ ··· + 290u − 41
c
11
(u + 1)
16
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
− 3y
7
+ 19y
6
− 34y
5
+ 71y
4
− 66y
3
+ 34y
2
− 12y + 1)
2
c
2
, c
6
(y
8
+ 5y
7
+ 11y
6
+ 10y
5
− y
4
− 10y
3
− 6y
2
+ 1)
2
c
3
(y
8
− 11y
7
+ 47y
6
− 98y
5
+ 103y
4
− 50y
3
+ 6y
2
+ 1)
2
c
4
, c
7
, c
10
y
16
+ 15y
15
+ ··· + 36y + 1
c
5
y
16
− 5y
15
+ ··· − 254292y + 17161
c
8
(y
8
− 15y
7
+ 91y
6
− 294y
5
+ 575y
4
− 718y
3
+ 562y
2
− 252y + 49)
2
c
9
, c
12
y
16
− 9y
15
+ ··· − 2920y + 1681
c
11
(y −1)
16
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.914675
a = 0.436222
b = −0.809231
−3.59615 0.177900
u = −0.914675
a = 0.189279
b = 1.63136
−3.59615 0.177900
u = −0.252896 + 0.819281I
a = 2.65515 − 0.52400I
b = −1.80316 + 0.56016I
6.08846 − 1.27532I 2.81947 + 5.08518I
u = −0.252896 + 0.819281I
a = −2.35083 − 2.13459I
b = −0.321107 − 0.355262I
6.08846 − 1.27532I 2.81947 + 5.08518I
u = −0.252896 − 0.819281I
a = 2.65515 + 0.52400I
b = −1.80316 − 0.56016I
6.08846 + 1.27532I 2.81947 − 5.08518I
u = −0.252896 − 0.819281I
a = −2.35083 + 2.13459I
b = −0.321107 + 0.355262I
6.08846 + 1.27532I 2.81947 − 5.08518I
u = 0.394459 + 1.112500I
a = −0.171959 + 1.373110I
b = −0.63430 − 1.69466I
2.23454 + 3.63283I −2.42240 − 4.51802I
u = 0.394459 + 1.112500I
a = 1.74900 + 0.37851I
b = −0.413053 + 1.180340I
2.23454 + 3.63283I −2.42240 − 4.51802I
u = 0.394459 − 1.112500I
a = −0.171959 − 1.373110I
b = −0.63430 + 1.69466I
2.23454 − 3.63283I −2.42240 + 4.51802I
u = 0.394459 − 1.112500I
a = 1.74900 − 0.37851I
b = −0.413053 − 1.180340I
2.23454 − 3.63283I −2.42240 + 4.51802I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.473514 + 1.273020I
a = 1.39433 − 0.52484I
b = −0.980224 − 0.230007I
−7.49271 − 4.93524I −2.98443 + 2.99422I
u = −0.473514 + 1.273020I
a = −1.76444 + 0.96072I
b = 1.94259 + 0.45832I
−7.49271 − 4.93524I −2.98443 + 2.99422I
u = −0.473514 − 1.273020I
a = 1.39433 + 0.52484I
b = −0.980224 + 0.230007I
−7.49271 + 4.93524I −2.98443 − 2.99422I
u = −0.473514 − 1.273020I
a = −1.76444 − 0.96072I
b = 1.94259 − 0.45832I
−7.49271 + 4.93524I −2.98443 − 2.99422I
u = 0.578577
a = 0.67601 + 1.65350I
b = −0.701810 + 1.159550I
5.22545 0.996810
u = 0.578577
a = 0.67601 − 1.65350I
b = −0.701810 − 1.159550I
5.22545 0.996810
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 5u
7
+ 11u
6
+ 10u
5
− u
4
− 10u
3
− 6u
2
+ 1)
2
· (u
11
− 6u
10
+ ··· − 16u + 4)(u
20
+ 11u
19
+ ··· + 36u + 4)
c
2
(u
8
+ u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
− 1)
2
· (u
11
− 2u
10
+ 5u
9
− 6u
8
+ 9u
7
− 9u
6
+ 10u
5
− 8u
4
+ 6u
3
− 5u
2
+ 2u − 2)
· (u
20
− 5u
19
+ ··· − 10u + 2)
c
3
(u
8
− u
7
− 5u
6
+ 4u
5
+ 7u
4
− 4u
3
− 2u
2
+ 2u − 1)
2
· (u
11
+ 2u
10
+ u
9
− 3u
8
− 15u
7
− 6u
6
+ u
5
− 17u
4
+ 8u
3
− 7u
2
− 6u − 2)
· (u
20
+ 5u
19
+ ··· − 10u + 10)
c
4
, c
7
(u
11
+ 5u
9
− u
8
+ u
7
− 4u
6
− 14u
5
− u
4
+ 4u
3
+ 7u
2
+ 3u + 1)
· (u
16
− u
15
+ ··· + 8u + 1)(u
20
+ 15u
18
+ ··· + 2u + 1)
c
5
(u
11
+ u
10
+ u
9
+ 5u
8
− 4u
7
− 14u
6
+ u
5
− 11u
4
+ u
3
+ 2u
2
+ 2u − 1)
· (u
16
+ u
15
+ ··· − 550u − 131)(u
20
+ u
19
+ ··· + u + 1)
c
6
(u
8
+ u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
− 1)
2
· (u
11
+ 2u
10
+ 5u
9
+ 6u
8
+ 9u
7
+ 9u
6
+ 10u
5
+ 8u
4
+ 6u
3
+ 5u
2
+ 2u + 2)
· (u
20
− 5u
19
+ ··· − 10u + 2)
c
8
(u
8
− 5u
7
+ 5u
6
+ 10u
5
− 17u
4
− 6u
3
+ 18u
2
− 7)
2
· (u
11
+ 8u
10
+ ··· + 2u − 2)(u
20
+ 11u
19
+ ··· + 10u + 10)
c
9
(u
11
− 3u
10
+ u
9
+ 5u
8
− 7u
7
+ 2u
6
+ 7u
5
− 7u
4
+ 2u
2
− 2u − 1)
· (u
16
− 5u
15
+ ··· + 290u − 41)(u
20
− 3u
19
+ ··· + 3u + 1)
c
10
(u
11
+ 5u
9
+ u
8
+ u
7
+ 4u
6
− 14u
5
+ u
4
+ 4u
3
− 7u
2
+ 3u − 1)
· (u
16
− u
15
+ ··· + 8u + 1)(u
20
+ 15u
18
+ ··· + 2u + 1)
c
11
((u + 1)
16
)(u
11
+ 2u
10
+ ··· + 3u − 1)
· (u
20
− 19u
19
+ ··· − 2304u + 256)
c
12
(u
11
+ 3u
10
+ u
9
− 5u
8
− 7u
7
− 2u
6
+ 7u
5
+ 7u
4
− 2u
2
− 2u + 1)
· (u
16
− 5u
15
+ ··· + 290u − 41)(u
20
− 3u
19
+ ··· + 3u + 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
8
− 3y
7
+ 19y
6
− 34y
5
+ 71y
4
− 66y
3
+ 34y
2
− 12y + 1)
2
· (y
11
+ 2y
10
+ ··· − 8y −16)(y
20
− y
19
+ ··· − 208y + 16)
c
2
, c
6
(y
8
+ 5y
7
+ 11y
6
+ 10y
5
− y
4
− 10y
3
− 6y
2
+ 1)
2
· (y
11
+ 6y
10
+ ··· − 16y −4)(y
20
+ 11y
19
+ ··· + 36y + 4)
c
3
(y
8
− 11y
7
+ 47y
6
− 98y
5
+ 103y
4
− 50y
3
+ 6y
2
+ 1)
2
· (y
11
− 2y
10
+ ··· + 8y −4)(y
20
− 13y
19
+ ··· + 1940y + 100)
c
4
, c
7
, c
10
(y
11
+ 10y
10
+ ··· − 5y −1)(y
16
+ 15y
15
+ ··· + 36y + 1)
· (y
20
+ 30y
19
+ ··· + 4y + 1)
c
5
(y
11
+ y
10
+ ··· + 8y −1)(y
16
− 5y
15
+ ··· − 254292y + 17161)
· (y
20
− 19y
19
+ ··· + 7y + 1)
c
8
(y
8
− 15y
7
+ 91y
6
− 294y
5
+ 575y
4
− 718y
3
+ 562y
2
− 252y + 49)
2
· (y
11
− 12y
10
+ ··· + 40y −4)(y
20
− 3y
19
+ ··· + 1460y + 100)
c
9
, c
12
(y
11
− 7y
10
+ ··· + 8y −1)(y
16
− 9y
15
+ ··· − 2920y + 1681)
· (y
20
− 11y
19
+ ··· + 11y + 1)
c
11
((y −1)
16
)(y
11
− 8y
10
+ ··· + 7y −1)
· (y
20
− 9y
19
+ ··· + 524288y + 65536)
18
