12n
0535
(K12n
0535
)
A knot diagram
1
Linearized knot diagam
3 6 12 9 8 2 11 1 12 8 3 5
Solving Sequence
5,12 1,9
4 3 8 6 2 7 11 10
c
12
c
4
c
3
c
8
c
5
c
2
c
6
c
11
c
10
c
1
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−34964567u
18
− 147929889u
17
+ ··· + 84548050b − 17321241,
− 36305359u
18
− 171870803u
17
+ ··· + 84548050a − 72540507, u
19
+ 4u
18
+ ··· − 3u
3
+ 1i
I
u
2
= hu
5
− u
4
+ 2u
2
+ b − a + 1,
u
6
a − 2u
5
a − u
6
+ u
4
a + u
5
+ 2u
3
a − u
4
− 2u
2
a − 2u
3
+ a
2
+ au + u
2
− a − 3u − 1,
u
7
− 2u
6
+ 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1i
I
u
3
= hu
3
+ 2u
2
+ b + 3u + 2, −u
3
− 3u
2
+ a − 5u − 2, u
4
+ 3u
3
+ 5u
2
+ 3u + 1i
I
u
4
= h−u
5
+ u
4
+ b − a − 2u + 1, u
5
a + a
2
+ 2au + u
2
, u
6
− u
5
+ u
4
+ 2u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 49 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−3.50 × 10
7
u
18
− 1.48 × 10
8
u
17
+ · · · + 8.45 × 10
7
b − 1.73 × 10
7
, −3.63 ×
10
7
u
18
−1.72×10
8
u
17
+· · ·+8.45×10
7
a−7.25×10
7
, u
19
+4u
18
+· · ·−3u
3
+1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
9
=
0.429405u
18
+ 2.03282u
17
+ ··· − 0.972166u + 0.857980
0.413547u
18
+ 1.74965u
17
+ ··· + 0.520629u + 0.204869
a
4
=
−0.658072u
18
− 2.36766u
17
+ ··· − 0.942839u + 0.860317
−0.0707958u
18
+ 0.0522380u
17
+ ··· + 0.273040u + 0.587276
a
3
=
−0.587276u
18
− 2.41990u
17
+ ··· − 1.21588u + 0.273040
−0.0707958u
18
+ 0.0522380u
17
+ ··· + 0.273040u + 0.587276
a
8
=
0.0380189u
18
+ 0.291456u
17
+ ··· − 1.06339u + 0.968309
0.355477u
18
+ 1.40522u
17
+ ··· + 0.129243u + 0.0290509
a
6
=
−0.500327u
18
− 2.21013u
17
+ ··· − 0.556008u + 0.0492471
−0.402635u
18
− 1.32006u
17
+ ··· + 0.181729u + 0.279600
a
2
=
−0.473557u
18
− 1.49737u
17
+ ··· − 2.34644u + 1.18683
0.396856u
18
+ 1.98083u
17
+ ··· + 0.186827u + 0.473557
a
7
=
0.761277u
18
+ 3.01695u
17
+ ··· − 0.400542u + 0.304195
−0.280164u
18
− 1.43418u
17
+ ··· + 1.18128u − 0.688967
a
11
=
−0.484468u
18
− 1.92696u
17
+ ··· − 2.04880u + 0.702358
0.0109112u
18
+ 0.429590u
17
+ ··· − 0.297642u + 0.484468
a
10
=
0.0158583u
18
+ 0.283163u
17
+ ··· − 1.49279u + 0.653111
0.413547u
18
+ 1.74965u
17
+ ··· + 0.520629u + 0.204869
(ii) Obstruction class = −1
(iii) Cusp Shapes =
20137897
8454805
u
18
+
69147964
8454805
u
17
+ ··· +
1296527
8454805
u +
31835641
8454805
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 14u
18
+ ··· − 28u − 4
c
2
, c
4
, c
6
u
19
+ 7u
17
+ ··· − 2u − 2
c
3
, c
11
u
19
+ 2u
18
+ ··· − 11u − 1
c
5
, c
7
, c
10
u
19
− 2u
18
+ ··· + 2u − 1
c
8
u
19
− u
18
+ ··· − 25u − 25
c
9
u
19
− 3u
18
+ ··· + 46u − 11
c
12
u
19
− 4u
18
+ ··· − 3u
3
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 26y
18
+ ··· − 16y −16
c
2
, c
4
, c
6
y
19
+ 14y
18
+ ··· − 28y −4
c
3
, c
11
y
19
− 32y
18
+ ··· + y −1
c
5
, c
7
, c
10
y
19
+ 18y
18
+ ··· + 44y −1
c
8
y
19
+ 3y
18
+ ··· − 1125y −625
c
9
y
19
− 23y
18
+ ··· + 3194y −121
c
12
y
19
− 2y
18
+ ··· + 12y
2
− 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.821475 + 0.594834I
a = 1.075950 + 0.336378I
b = 1.334340 + 0.079123I
1.42522 + 6.81402I 5.23193 − 9.88797I
u = 0.821475 − 0.594834I
a = 1.075950 − 0.336378I
b = 1.334340 − 0.079123I
1.42522 − 6.81402I 5.23193 + 9.88797I
u = −1.173600 + 0.155605I
a = −0.125477 − 0.508306I
b = 0.471294 − 0.636829I
4.32774 + 1.07425I 4.82406 − 6.05931I
u = −1.173600 − 0.155605I
a = −0.125477 + 0.508306I
b = 0.471294 + 0.636829I
4.32774 − 1.07425I 4.82406 + 6.05931I
u = 0.279280 + 0.633920I
a = −0.361697 − 0.610800I
b = −0.662543 + 0.872189I
−1.90560 + 1.10773I −3.54412 − 5.69242I
u = 0.279280 − 0.633920I
a = −0.361697 + 0.610800I
b = −0.662543 − 0.872189I
−1.90560 − 1.10773I −3.54412 + 5.69242I
u = −0.612161
a = 0.732439
b = 0.209228
0.849367 11.9240
u = 0.494731 + 0.181504I
a = −0.30870 + 2.20346I
b = −0.343936 + 0.280922I
0.84702 − 3.36304I 2.65369 + 2.27076I
u = 0.494731 − 0.181504I
a = −0.30870 − 2.20346I
b = −0.343936 − 0.280922I
0.84702 + 3.36304I 2.65369 − 2.27076I
u = −1.04681 + 1.06903I
a = 1.189010 − 0.129598I
b = 2.18978 + 1.06580I
12.2196 − 13.0819I 3.46696 + 5.71029I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04681 − 1.06903I
a = 1.189010 + 0.129598I
b = 2.18978 − 1.06580I
12.2196 + 13.0819I 3.46696 − 5.71029I
u = −0.135208 + 0.466592I
a = 2.29915 − 0.00071I
b = 0.675260 + 1.111080I
0.56206 − 3.63168I 1.44719 + 4.79816I
u = −0.135208 − 0.466592I
a = 2.29915 + 0.00071I
b = 0.675260 − 1.111080I
0.56206 + 3.63168I 1.44719 − 4.79816I
u = −1.09457 + 1.05677I
a = 0.132959 − 1.097140I
b = 1.282940 − 0.166221I
12.33420 + 5.22927I 3.55290 − 2.35688I
u = −1.09457 − 1.05677I
a = 0.132959 + 1.097140I
b = 1.282940 + 0.166221I
12.33420 − 5.22927I 3.55290 + 2.35688I
u = −1.00078 + 1.20924I
a = −0.714217 + 0.472369I
b = −2.07929 − 0.76223I
−8.03695 − 4.24763I 1.64467 − 2.22109I
u = −1.00078 − 1.20924I
a = −0.714217 − 0.472369I
b = −2.07929 + 0.76223I
−8.03695 + 4.24763I 1.64467 + 2.22109I
u = 1.16156 + 1.21360I
a = −0.553206 − 0.397416I
b = −1.47244 + 0.48967I
−6.57114 + 4.42656I −2.73910 − 5.25491I
u = 1.16156 − 1.21360I
a = −0.553206 + 0.397416I
b = −1.47244 − 0.48967I
−6.57114 − 4.42656I −2.73910 + 5.25491I
6
II. I
u
2
= hu
5
− u
4
+ 2u
2
+ b − a + 1, u
6
a − u
6
+ · · · − a − 1, u
7
− 2u
6
+ 2u
5
+
u
4
− 2u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
9
=
a
−u
5
+ u
4
− 2u
2
+ a − 1
a
4
=
−u
5
a − u
6
+ u
4
a + u
5
− u
4
− 2u
2
a − u
3
+ au − a − 3u + 1
u
6
a − u
6
+ ··· − a + 1
a
3
=
−u
6
a + u
5
a − 2u
3
a − au − u
u
6
a − u
6
+ ··· − a + 1
a
8
=
u
5
− u
4
− u
2
a + 2u
2
+ 1
−u
6
+ u
4
a + u
5
+ u
2
a − 2u
3
+ a − 2u
a
6
=
u
6
a − u
6
+ ··· − 2a + 2
−u
6
a + 2u
6
+ ··· + a − 3
a
2
=
−u
6
a + u
5
a + u
6
− u
5
− 2u
3
a + u
4
+ 2u
3
− au − u
2
− a + 2u + 1
u
6
a − u
5
a − 2u
5
+ 2u
3
a + u
4
+ au − 5u
2
+ a − u − 2
a
7
=
−u
5
a + 2u
6
+ u
4
a − 2u
5
+ u
4
− 2u
2
a + 4u
3
− a + 3u − 1
u
6
a − 4u
6
+ 6u
5
+ 3u
3
a − 4u
4
+ 2u
2
a − 7u
3
+ au + 5u
2
+ a − 9u + 2
a
11
=
2u
6
− 2u
5
+ u
4
+ 4u
3
− u
2
+ 4u
u
6
a − u
5
a − u
6
+ 2u
3
a − 2u
3
+ au − u
2
+ a − 3u
a
10
=
u
5
− u
4
+ 2u
2
+ 1
−u
5
+ u
4
− 2u
2
+ a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u
6
+ 12u
5
− 7u
4
− 19u
3
+ 10u
2
− 16u + 7
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 12u
13
+ ··· − 44u + 4
c
2
u
14
+ 6u
12
+ ··· + 11u
2
+ 2
c
3
u
14
+ 2u
13
+ ··· − 2u + 1
c
4
, c
6
u
14
+ 6u
12
+ ··· + 11u
2
+ 2
c
5
, c
7
u
14
− 3u
13
+ ··· − 3u
2
+ 1
c
8
u
14
− 2u
13
+ ··· + u + 1
c
9
u
14
− 6u
13
+ ··· − 80u + 25
c
10
u
14
+ 3u
13
+ ··· − 3u
2
+ 1
c
11
u
14
− 2u
13
+ ··· + 2u + 1
c
12
(u
7
− 2u
6
+ 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 16y
12
+ ··· − 136y + 16
c
2
, c
4
, c
6
y
14
+ 12y
13
+ ··· + 44y + 4
c
3
, c
11
y
14
− 6y
13
+ ··· + 24y + 1
c
5
, c
7
, c
10
y
14
+ 5y
13
+ ··· − 6y + 1
c
8
y
14
+ 4y
13
+ ··· − 19y + 1
c
9
y
14
− 20y
13
+ ··· + 150y + 625
c
12
(y
7
+ 4y
5
− y
4
− 6y
3
− 3y
2
− 2y − 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.17019
a = −0.358738 + 0.564857I
b = −0.028132 + 0.564857I
4.47571 7.29710
u = −1.17019
a = −0.358738 − 0.564857I
b = −0.028132 − 0.564857I
4.47571 7.29710
u = −0.011299 + 0.825523I
a = 1.027240 + 0.770138I
b = 1.88010 + 0.45019I
−0.48483 − 2.53884I −0.79327 + 1.93613I
u = −0.011299 + 0.825523I
a = −1.62561 + 0.25747I
b = −0.772756 − 0.062472I
−0.48483 − 2.53884I −0.79327 + 1.93613I
u = −0.011299 − 0.825523I
a = 1.027240 − 0.770138I
b = 1.88010 − 0.45019I
−0.48483 + 2.53884I −0.79327 − 1.93613I
u = −0.011299 − 0.825523I
a = −1.62561 − 0.25747I
b = −0.772756 + 0.062472I
−0.48483 + 2.53884I −0.79327 − 1.93613I
u = 0.542568 + 0.510771I
a = −1.041010 − 0.581670I
b = −2.22904 − 1.51686I
1.30894 + 4.72329I 3.88706 − 9.04709I
u = 0.542568 + 0.510771I
a = 2.06212 + 0.40264I
b = 0.874091 − 0.532548I
1.30894 + 4.72329I 3.88706 − 9.04709I
u = 0.542568 − 0.510771I
a = −1.041010 + 0.581670I
b = −2.22904 + 1.51686I
1.30894 − 4.72329I 3.88706 + 9.04709I
u = 0.542568 − 0.510771I
a = 2.06212 − 0.40264I
b = 0.874091 + 0.532548I
1.30894 − 4.72329I 3.88706 + 9.04709I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05382 + 1.07114I
a = −0.779358 − 0.521402I
b = −1.60948 + 0.43022I
−5.52936 + 3.91715I 4.75768 − 1.97459I
u = 1.05382 + 1.07114I
a = −0.284648 − 0.316560I
b = −1.114770 + 0.635064I
−5.52936 + 3.91715I 4.75768 − 1.97459I
u = 1.05382 − 1.07114I
a = −0.779358 + 0.521402I
b = −1.60948 − 0.43022I
−5.52936 − 3.91715I 4.75768 + 1.97459I
u = 1.05382 − 1.07114I
a = −0.284648 + 0.316560I
b = −1.114770 − 0.635064I
−5.52936 − 3.91715I 4.75768 + 1.97459I
11
III.
I
u
3
= hu
3
+ 2u
2
+ b + 3u + 2, −u
3
− 3u
2
+ a − 5u − 2, u
4
+ 3u
3
+ 5u
2
+ 3u + 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
9
=
u
3
+ 3u
2
+ 5u + 2
−u
3
− 2u
2
− 3u − 2
a
4
=
u
3
+ 3u
2
+ 4u + 1
−u − 1
a
3
=
u
3
+ 3u
2
+ 5u + 2
−u − 1
a
8
=
2u
3
+ 6u
2
+ 9u + 4
−u
2
− 2u − 2
a
6
=
3u
3
+ 8u
2
+ 12u + 4
−u
3
− 3u
2
− 4u − 3
a
2
=
−u
3
− 2u
2
− 2u + 1
u
3
+ 2u
2
+ 3u + 1
a
7
=
3u
3
+ 7u
2
+ 10u + 2
−u
3
− 3u
2
− 5u − 3
a
11
=
−u
3
− 3u
2
− 4u
u
2
+ 2u + 1
a
10
=
2u
3
+ 5u
2
+ 8u + 4
−u
3
− 2u
2
− 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −10u
3
− 24u
2
− 25u − 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 3u
3
+ 2u
2
+ 1
c
2
, c
11
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
3
, c
4
, c
6
u
4
− u
3
+ 2u
2
− 2u + 1
c
5
, c
7
u
4
− u
3
− u
2
+ u + 1
c
8
(u
2
− u + 1)
2
c
9
u
4
− 6u
3
+ 14u
2
− 15u + 7
c
10
u
4
+ u
3
− u
2
− u + 1
c
12
u
4
+ 3u
3
+ 5u
2
+ 3u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
2
, c
3
, c
4
c
6
, c
11
y
4
+ 3y
3
+ 2y
2
+ 1
c
5
, c
7
, c
10
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
8
(y
2
+ y + 1)
2
c
9
y
4
− 8y
3
+ 30y
2
− 29y + 49
c
12
y
4
+ y
3
+ 9y
2
+ y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.378256 + 0.440597I
a = 0.121744 + 1.306620I
b = −0.929304 − 0.758745I
−1.54288 − 0.56550I 4.01988 − 4.05120I
u = −0.378256 − 0.440597I
a = 0.121744 − 1.306620I
b = −0.929304 + 0.758745I
−1.54288 + 0.56550I 4.01988 + 4.05120I
u = −1.12174 + 1.30662I
a = −0.621744 + 0.440597I
b = −2.07070 − 0.75874I
−8.32672 − 4.62527I −9.5199 + 10.6712I
u = −1.12174 − 1.30662I
a = −0.621744 − 0.440597I
b = −2.07070 + 0.75874I
−8.32672 + 4.62527I −9.5199 − 10.6712I
15
IV.
I
u
4
= h−u
5
+u
4
+b−a−2u+1, u
5
a+a
2
+2au+u
2
, u
6
−u
5
+u
4
+2u
2
−u+1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
9
=
a
u
5
− u
4
+ a + 2u − 1
a
4
=
u
5
a − u
4
a + u
3
+ au − a
u
5
a + u
3
+ au + u
a
3
=
−u
4
a − a − u
u
5
a + u
3
+ au + u
a
8
=
−u
5
+ u
4
− u
2
a − 2u + 1
u
4
a − u
4
+ u
2
a + a + u − 1
a
6
=
u
5
a − u
4
a + u
5
+ u
3
a − u
4
− u
2
a − u
3
+ 2au − a + 2u − 1
u
4
a + u
4
+ u
2
a + u
3
+ 1
a
2
=
u
4
a − 2u
5
+ u
2
− u + 2
−u
4
a + 2u
5
− u
4
− 2u
3
− 3u
2
+ u − 2
a
7
=
3u
5
a − 3u
4
a + 3u
4
− 4u
2
a + 2au + 2u
2
− 3a + u + 1
−u
5
a + 5u
4
a − 4u
5
+ 3u
3
a − 2u
4
+ 4u
2
a − u
3
+ u
2
+ 2a − 3u + 2
a
11
=
u
4
+ 2u
3
+ u
2
+ 2
−u
4
a − u
5
− u
4
− 2u
3
− u
2
− 1
a
10
=
−u
5
+ u
4
− 2u + 1
u
5
− u
4
+ a + 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
5
− 2u
4
+ u
3
− 4u
2
− 7u − 2
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 8u
11
+ ··· − 9u + 1
c
2
, c
4
, c
6
u
12
− 4u
10
+ 16u
8
+ 7u
7
− 20u
6
− 13u
5
+ 14u
4
+ 26u
3
+ 20u
2
+ 7u + 1
c
3
, c
11
u
12
− 16u
10
+ ··· + 10u + 1
c
5
, c
7
, c
10
u
12
− u
11
+ ··· + 606u + 317
c
8
u
12
− 11u
10
+ ··· + 271u + 121
c
9
u
12
− 4u
11
+ ··· − 14u + 11
c
12
(u
6
+ u
5
+ u
4
+ 2u
2
+ u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
+ 32y
11
+ ··· + 47y + 1
c
2
, c
4
, c
6
y
12
− 8y
11
+ ··· − 9y + 1
c
3
, c
11
y
12
− 32y
11
+ ··· + 70y + 1
c
5
, c
7
, c
10
y
12
+ 27y
11
+ ··· − 102224y + 100489
c
8
y
12
− 22y
11
+ ··· + 14163y + 14641
c
9
y
12
− 10y
11
+ ··· − 196y + 121
c
12
(y
6
+ y
5
+ 5y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716019 + 0.809696I
a = −0.440928 − 0.793162I
b = −0.869241 − 0.814613I
2.99789 − 2.65597I 5.23409 + 2.95001I
u = −0.716019 + 0.809696I
a = 1.193290 + 0.483169I
b = 0.764977 + 0.461718I
2.99789 − 2.65597I 5.23409 + 2.95001I
u = −0.716019 − 0.809696I
a = −0.440928 + 0.793162I
b = −0.869241 + 0.814613I
2.99789 + 2.65597I 5.23409 − 2.95001I
u = −0.716019 − 0.809696I
a = 1.193290 − 0.483169I
b = 0.764977 − 0.461718I
2.99789 + 2.65597I 5.23409 − 2.95001I
u = 0.283231 + 0.633899I
a = −0.673606 − 0.685761I
b = −0.942454 + 0.731417I
−1.90302 + 1.10871I −3.38143 − 5.26909I
u = 0.283231 + 0.633899I
a = −0.032040 − 0.500452I
b = −0.300888 + 0.916727I
−1.90302 + 1.10871I −3.38143 − 5.26909I
u = 0.283231 − 0.633899I
a = −0.673606 + 0.685761I
b = −0.942454 − 0.731417I
−1.90302 − 1.10871I −3.38143 + 5.26909I
u = 0.283231 − 0.633899I
a = −0.032040 + 0.500452I
b = −0.300888 − 0.916727I
−1.90302 − 1.10871I −3.38143 + 5.26909I
u = 0.932789 + 0.951611I
a = 1.217360 − 0.202209I
b = 2.41453 − 1.28852I
13.70950 + 3.42721I 4.64734 − 2.54199I
u = 0.932789 + 0.951611I
a = −0.26408 + 1.41445I
b = 0.933081 + 0.328142I
13.70950 + 3.42721I 4.64734 − 2.54199I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932789 − 0.951611I
a = 1.217360 + 0.202209I
b = 2.41453 + 1.28852I
13.70950 − 3.42721I 4.64734 + 2.54199I
u = 0.932789 − 0.951611I
a = −0.26408 − 1.41445I
b = 0.933081 − 0.328142I
13.70950 − 3.42721I 4.64734 + 2.54199I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− 3u
3
+ 2u
2
+ 1)(u
12
− 8u
11
+ ··· − 9u + 1)
· (u
14
− 12u
13
+ ··· − 44u + 4)(u
19
+ 14u
18
+ ··· − 28u − 4)
c
2
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
12
− 4u
10
+ 16u
8
+ 7u
7
− 20u
6
− 13u
5
+ 14u
4
+ 26u
3
+ 20u
2
+ 7u + 1)
· (u
14
+ 6u
12
+ ··· + 11u
2
+ 2)(u
19
+ 7u
17
+ ··· − 2u − 2)
c
3
(u
4
− u
3
+ 2u
2
− 2u + 1)(u
12
− 16u
10
+ ··· + 10u + 1)
· (u
14
+ 2u
13
+ ··· − 2u + 1)(u
19
+ 2u
18
+ ··· − 11u − 1)
c
4
, c
6
(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
12
− 4u
10
+ 16u
8
+ 7u
7
− 20u
6
− 13u
5
+ 14u
4
+ 26u
3
+ 20u
2
+ 7u + 1)
· (u
14
+ 6u
12
+ ··· + 11u
2
+ 2)(u
19
+ 7u
17
+ ··· − 2u − 2)
c
5
, c
7
(u
4
− u
3
− u
2
+ u + 1)(u
12
− u
11
+ ··· + 606u + 317)
· (u
14
− 3u
13
+ ··· − 3u
2
+ 1)(u
19
− 2u
18
+ ··· + 2u − 1)
c
8
((u
2
− u + 1)
2
)(u
12
− 11u
10
+ ··· + 271u + 121)
· (u
14
− 2u
13
+ ··· + u + 1)(u
19
− u
18
+ ··· − 25u − 25)
c
9
(u
4
− 6u
3
+ 14u
2
− 15u + 7)(u
12
− 4u
11
+ ··· − 14u + 11)
· (u
14
− 6u
13
+ ··· − 80u + 25)(u
19
− 3u
18
+ ··· + 46u − 11)
c
10
(u
4
+ u
3
− u
2
− u + 1)(u
12
− u
11
+ ··· + 606u + 317)
· (u
14
+ 3u
13
+ ··· − 3u
2
+ 1)(u
19
− 2u
18
+ ··· + 2u − 1)
c
11
(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
12
− 16u
10
+ ··· + 10u + 1)
· (u
14
− 2u
13
+ ··· + 2u + 1)(u
19
+ 2u
18
+ ··· − 11u − 1)
c
12
(u
4
+ 3u
3
+ 5u
2
+ 3u + 1)(u
6
+ u
5
+ u
4
+ 2u
2
+ u + 1)
2
· ((u
7
− 2u
6
+ ··· − 2u + 1)
2
)(u
19
− 4u
18
+ ··· − 3u
3
− 1)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
− 5y
3
+ 6y
2
+ 4y + 1)(y
12
+ 32y
11
+ ··· + 47y + 1)
· (y
14
− 16y
12
+ ··· − 136y + 16)(y
19
+ 26y
18
+ ··· − 16y − 16)
c
2
, c
4
, c
6
(y
4
+ 3y
3
+ 2y
2
+ 1)(y
12
− 8y
11
+ ··· − 9y + 1)
· (y
14
+ 12y
13
+ ··· + 44y + 4)(y
19
+ 14y
18
+ ··· − 28y − 4)
c
3
, c
11
(y
4
+ 3y
3
+ 2y
2
+ 1)(y
12
− 32y
11
+ ··· + 70y + 1)
· (y
14
− 6y
13
+ ··· + 24y + 1)(y
19
− 32y
18
+ ··· + y − 1)
c
5
, c
7
, c
10
(y
4
− 3y
3
+ 5y
2
− 3y + 1)(y
12
+ 27y
11
+ ··· − 102224y + 100489)
· (y
14
+ 5y
13
+ ··· − 6y + 1)(y
19
+ 18y
18
+ ··· + 44y − 1)
c
8
((y
2
+ y + 1)
2
)(y
12
− 22y
11
+ ··· + 14163y + 14641)
· (y
14
+ 4y
13
+ ··· − 19y + 1)(y
19
+ 3y
18
+ ··· − 1125y − 625)
c
9
(y
4
− 8y
3
+ 30y
2
− 29y + 49)(y
12
− 10y
11
+ ··· − 196y + 121)
· (y
14
− 20y
13
+ ··· + 150y + 625)(y
19
− 23y
18
+ ··· + 3194y − 121)
c
12
(y
4
+ y
3
+ 9y
2
+ y + 1)(y
6
+ y
5
+ 5y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
2
· ((y
7
+ 4y
5
− y
4
− 6y
3
− 3y
2
− 2y − 1)
2
)(y
19
− 2y
18
+ ··· + 12y
2
− 1)
22
