12n
0436
(K12n
0436
)
A knot diagram
1
Linearized knot diagam
3 5 8 10 2 12 3 12 5 9 6 4
Solving Sequence
3,5
2 6
1,10
4 9 11 12 7 8
c
2
c
5
c
1
c
4
c
9
c
10
c
12
c
6
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−37827406u
18
+ 29757877u
17
+ ··· + 120133473b + 294183386, a − 1, u
19
+ 6u
17
+ ··· + 2u + 1i
I
u
2
= h−u
4
− u
3
− 2u
2
+ b − 2u + 2, a + 1, u
5
+ u
4
+ 2u
3
+ 3u
2
+ u + 1i
I
u
3
= hb − 1, 19u
11
− 5u
10
+ 80u
9
− 30u
8
+ 158u
7
− 42u
6
+ 229u
5
− 4u
4
+ 188u
3
+ 17u
2
+ 5a + 39u + 21,
u
12
− u
11
+ 5u
10
− 5u
9
+ 12u
8
− 10u
7
+ 19u
6
− 12u
5
+ 18u
4
− 9u
3
+ 8u
2
− 2u + 1i
I
u
4
= hb + 1, 858366437u
13
+ 13303924407u
12
+ ··· + 198592491933a − 215876970671,
u
14
− 5u
12
+ u
11
+ 20u
10
− 3u
9
− 41u
8
+ 3u
7
+ 27u
6
+ 15u
5
+ 23u
4
− 53u
3
− 33u
2
+ 71u − 27i
I
u
5
= hb − 1, a + u, u
2
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 52 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−3.78 × 10
7
u
18
+ 2.98 × 10
7
u
17
+ · · · + 1.20 × 10
8
b + 2.94 × 10
8
, a −
1, u
19
+ 6u
17
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
1
0.314878u
18
− 0.247707u
17
+ ··· − 3.86583u − 2.44880
a
4
=
−u
0.247707u
18
− 0.105766u
17
+ ··· + 4.07856u + 0.314878
a
9
=
1
0.314878u
18
− 0.247707u
17
+ ··· − 3.86583u − 2.44880
a
11
=
u
2
+ 1
0.420645u
18
− 0.371361u
17
+ ··· − 3.68529u − 2.20110
a
12
=
−0.00612192u
18
+ 0.0147829u
17
+ ··· + 0.322078u + 1.37136
0.297103u
18
− 0.361177u
17
+ ··· − 3.38666u − 1.84452
a
7
=
0.648921u
18
+ 0.257817u
17
+ ··· + 6.78287u + 0.742285
−0.744255u
18
+ 0.115009u
17
+ ··· − 1.84764u + 0.485311
a
8
=
0.0953339u
18
− 0.372826u
17
+ ··· − 4.93523u − 1.22760
0.744255u
18
− 0.115009u
17
+ ··· + 1.84764u − 0.485311
(ii) Obstruction class = −1
(iii) Cusp Shapes =
42941320
40044491
u
18
+
84579765
40044491
u
17
+ ··· +
1067191176
40044491
u +
715529589
40044491
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
19
+ 12u
18
+ ··· − 12u − 1
c
2
, c
4
, c
5
c
9
u
19
+ 6u
17
+ ··· + 2u − 1
c
3
, c
7
u
19
+ 5u
18
+ ··· − 5u − 3
c
6
, c
11
, c
12
u
19
+ u
18
+ ··· + u − 3
c
8
u
19
− u
18
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
19
+ 32y
18
+ ··· + 116y −1
c
2
, c
4
, c
5
c
9
y
19
+ 12y
18
+ ··· − 12y −1
c
3
, c
7
y
19
− 3y
18
+ ··· + 103y −9
c
6
, c
11
, c
12
y
19
− 17y
18
+ ··· + 73y −9
c
8
y
19
+ 11y
18
+ ··· + 44y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.581330 + 0.811360I
a = 1.00000
b = 1.79148 + 0.06667I
1.93762 + 6.06371I 8.03507 − 11.60220I
u = 0.581330 − 0.811360I
a = 1.00000
b = 1.79148 − 0.06667I
1.93762 − 6.06371I 8.03507 + 11.60220I
u = −0.052078 + 1.011790I
a = 1.00000
b = −0.842437 + 0.221761I
−5.84256 − 3.61662I −2.20671 + 4.58081I
u = −0.052078 − 1.011790I
a = 1.00000
b = −0.842437 − 0.221761I
−5.84256 + 3.61662I −2.20671 − 4.58081I
u = −0.565597 + 0.850482I
a = 1.00000
b = 1.102220 − 0.467413I
1.71886 − 3.11685I 6.74582 + 2.04810I
u = −0.565597 − 0.850482I
a = 1.00000
b = 1.102220 + 0.467413I
1.71886 + 3.11685I 6.74582 − 2.04810I
u = −0.435881 + 0.933169I
a = 1.00000
b = 0.557982 + 0.070489I
1.42719 − 4.85166I 4.33736 + 8.70146I
u = −0.435881 − 0.933169I
a = 1.00000
b = 0.557982 − 0.070489I
1.42719 + 4.85166I 4.33736 − 8.70146I
u = 0.372674 + 0.734435I
a = 1.00000
b = 0.950589 − 1.042440I
2.83649 + 2.15459I 8.45889 − 1.98320I
u = 0.372674 − 0.734435I
a = 1.00000
b = 0.950589 + 1.042440I
2.83649 − 2.15459I 8.45889 + 1.98320I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23610 + 1.41105I
a = 1.00000
b = 3.07117 + 0.59581I
−8.40212 + 4.72676I 11.67641 + 3.78763I
u = 0.23610 − 1.41105I
a = 1.00000
b = 3.07117 − 0.59581I
−8.40212 − 4.72676I 11.67641 − 3.78763I
u = 0.010555 + 0.413321I
a = 1.00000
b = −1.95315 − 0.78032I
−2.02437 − 2.68122I 11.08292 + 6.93097I
u = 0.010555 − 0.413321I
a = 1.00000
b = −1.95315 + 0.78032I
−2.02437 + 2.68122I 11.08292 − 6.93097I
u = −0.374990
a = 1.00000
b = 0.313865
0.679468 14.8670
u = 1.15639 + 1.32365I
a = 1.00000
b = 2.04850 + 0.73446I
12.4777 + 13.4078I 7.73596 − 5.99135I
u = 1.15639 − 1.32365I
a = 1.00000
b = 2.04850 − 0.73446I
12.4777 − 13.4078I 7.73596 + 5.99135I
u = −1.11599 + 1.40313I
a = 1.00000
b = 2.11672 − 0.67442I
11.98080 − 5.53483I 7.70079 + 2.32699I
u = −1.11599 − 1.40313I
a = 1.00000
b = 2.11672 + 0.67442I
11.98080 + 5.53483I 7.70079 − 2.32699I
6
II. I
u
2
= h−u
4
− u
3
− 2u
2
+ b − 2u + 2, a + 1, u
5
+ u
4
+ 2u
3
+ 3u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
−1
u
4
+ u
3
+ 2u
2
+ 2u − 2
a
4
=
−u
−u
2
− 2u − 1
a
9
=
−1
u
4
+ u
3
+ u
2
+ 2u − 2
a
11
=
−u
2
− 1
−u
2
+ u − 2
a
12
=
0
u
4
+ u
2
+ u − 1
a
7
=
u
−u − 1
a
8
=
−1
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
4
+ 6u
3
+ 10u
2
+ 5u − 2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 7u
2
− 5u + 1
c
2
, c
4
u
5
+ u
4
+ 2u
3
+ 3u
2
+ u + 1
c
3
u
5
+ 4u
4
+ 8u
3
+ 7u
2
+ 2u − 1
c
5
, c
9
u
5
− u
4
+ 2u
3
− 3u
2
+ u − 1
c
6
, c
12
u
5
+ 2u
4
+ u
3
+ 2u
2
+ 1
c
7
u
5
− 4u
4
+ 8u
3
− 7u
2
+ 2u + 1
c
8
u
5
− 3u
3
+ u
2
+ 3u + 1
c
10
u
5
+ 3u
4
− 7u
2
− 5u − 1
c
11
u
5
− 2u
4
+ u
3
− 2u
2
− 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
5
− 9y
4
+ 32y
3
− 43y
2
+ 11y −1
c
2
, c
4
, c
5
c
9
y
5
+ 3y
4
− 7y
2
− 5y −1
c
3
, c
7
y
5
+ 12y
3
− 9y
2
+ 18y −1
c
6
, c
11
, c
12
y
5
− 2y
4
− 7y
3
− 8y
2
− 4y −1
c
8
y
5
− 6y
4
+ 15y
3
− 19y
2
+ 7y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.23887
a = −1.00000
b = −0.953942
5.64999 7.52320
u = −0.082938 + 0.638199I
a = −1.00000
b = −2.71682 + 0.90269I
−2.41512 + 2.46056I −5.06862 + 1.07566I
u = −0.082938 − 0.638199I
a = −1.00000
b = −2.71682 − 0.90269I
−2.41512 − 2.46056I −5.06862 − 1.07566I
u = 0.202374 + 1.381280I
a = −1.00000
b = −3.30621 − 0.67253I
−8.63454 + 4.90423I −10.6930 − 12.7347I
u = 0.202374 − 1.381280I
a = −1.00000
b = −3.30621 + 0.67253I
−8.63454 − 4.90423I −10.6930 + 12.7347I
10
III. I
u
3
= hb − 1, 19u
11
− 5u
10
+ · · · + 5a + 21, u
12
− u
11
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
−
19
5
u
11
+ u
10
+ ··· −
39
5
u −
21
5
1
a
4
=
2
5
u
11
+ 2u
10
+ ··· −
53
5
u +
33
5
14
5
u
11
− 3u
10
+ ··· +
64
5
u −
19
5
a
9
=
−
19
5
u
11
+ u
10
+ ··· −
39
5
u −
21
5
1
5
u
11
+ u
10
+ ··· −
9
5
u +
19
5
a
11
=
−
3
5
u
11
− 2u
9
+ ··· +
7
5
u +
8
5
−
11
5
u
11
+ 2u
10
+ ··· −
31
5
u −
4
5
a
12
=
−
3
5
u
11
− 2u
9
+ ··· +
7
5
u +
13
5
−
11
5
u
11
+ 2u
10
+ ··· −
31
5
u +
1
5
a
7
=
16
5
u
11
− 3u
10
+ ··· +
81
5
u −
36
5
2
5
u
11
+ u
10
+ ··· −
18
5
u +
18
5
a
8
=
18
5
u
11
− 2u
10
+ ··· +
63
5
u −
18
5
2
5
u
11
+ u
10
+ ··· −
18
5
u +
18
5
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
28
5
u
11
−10u
10
+27u
9
−46u
8
+
331
5
u
7
−
439
5
u
6
+
513
5
u
5
−
573
5
u
4
+
416
5
u
3
−
466
5
u
2
+
153
5
u−
43
5
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 9u
11
+ ··· − 12u + 1
c
2
, c
4
u
12
− u
11
+ ··· − 2u + 1
c
3
(u
6
− u
5
+ u
4
+ u
3
+ u + 1)
2
c
5
, c
9
u
12
+ u
11
+ ··· + 2u + 1
c
6
, c
12
u
12
− 3u
11
+ 3u
10
+ u
9
− 7u
8
+ 7u
7
+ 2u
6
− 7u
5
+ 6u
4
− 4u
3
+ 4u
2
+ 1
c
7
(u
6
+ u
5
+ u
4
− u
3
− u + 1)
2
c
8
u
12
− 4u
11
+ ··· − 4u + 1
c
10
u
12
+ 9u
11
+ ··· + 12u + 1
c
11
u
12
+ 3u
11
+ 3u
10
− u
9
− 7u
8
− 7u
7
+ 2u
6
+ 7u
5
+ 6u
4
+ 4u
3
+ 4u
2
+ 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
− 3y
11
+ ··· − 16y + 1
c
2
, c
4
, c
5
c
9
y
12
+ 9y
11
+ ··· + 12y + 1
c
3
, c
7
(y
6
+ y
5
+ 3y
4
+ 3y
3
− y + 1)
2
c
6
, c
11
, c
12
y
12
− 3y
11
+ ··· + 8y + 1
c
8
y
12
+ 2y
11
+ ··· + 2y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.692350 + 0.998374I
a = 0.563487 − 0.097097I
b = 1.00000
2.58561 − 4.66235I 13.2371 + 6.7464I
u = −0.692350 − 0.998374I
a = 0.563487 + 0.097097I
b = 1.00000
2.58561 + 4.66235I 13.2371 − 6.7464I
u = −0.132362 + 1.261240I
a = −0.394942 + 0.127357I
b = 1.00000
−4.97366 − 3.43143I 8.85710 + 2.47386I
u = −0.132362 − 1.261240I
a = −0.394942 − 0.127357I
b = 1.00000
−4.97366 + 3.43143I 8.85710 − 2.47386I
u = 0.925178 + 0.902848I
a = 0.743097 + 0.759251I
b = 1.00000
−0.90182 + 3.38184I 5.40576 − 3.42906I
u = 0.925178 − 0.902848I
a = 0.743097 − 0.759251I
b = 1.00000
−0.90182 − 3.38184I 5.40576 + 3.42906I
u = 0.293191 + 0.629796I
a = 1.72349 − 0.29698I
b = 1.00000
2.58561 + 4.66235I 13.2371 − 6.7464I
u = 0.293191 − 0.629796I
a = 1.72349 + 0.29698I
b = 1.00000
2.58561 − 4.66235I 13.2371 + 6.7464I
u = −0.002009 + 1.373350I
a = 0.658392 + 0.672704I
b = 1.00000
−0.90182 − 3.38184I 5.40576 + 3.42906I
u = −0.002009 − 1.373350I
a = 0.658392 − 0.672704I
b = 1.00000
−0.90182 + 3.38184I 5.40576 − 3.42906I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.108352 + 0.514973I
a = −2.29352 − 0.73959I
b = 1.00000
−4.97366 − 3.43143I 8.85710 + 2.47386I
u = 0.108352 − 0.514973I
a = −2.29352 + 0.73959I
b = 1.00000
−4.97366 + 3.43143I 8.85710 − 2.47386I
15
IV. I
u
4
= hb + 1, 8.58 × 10
8
u
13
+ 1.33 × 10
10
u
12
+ · · · + 1.99 × 10
11
a − 2.16 ×
10
11
, u
14
− 5u
12
+ · · · + 71u − 27i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
−0.00432225u
13
− 0.0669911u
12
+ ··· − 1.16044u + 1.08703
−1
a
4
=
−0.230675u
13
− 0.276112u
12
+ ··· + 9.13016u − 2.99354
−0.0669911u
13
− 0.0949882u
12
+ ··· + 2.39391u − 0.116701
a
9
=
−0.00432225u
13
− 0.0669911u
12
+ ··· − 1.16044u + 1.08703
−0.0949882u
13
− 0.112404u
12
+ ··· + 4.63967u − 2.80876
a
11
=
−0.491617u
13
− 0.549779u
12
+ ··· + 22.4159u − 11.7697
−0.708236u
13
− 0.702608u
12
+ ··· + 34.5053u − 20.2635
a
12
=
−0.129369u
13
− 0.179029u
12
+ ··· + 4.92648u − 1.93084
−0.0162597u
13
− 0.0388906u
12
+ ··· + 0.473434u − 0.414339
a
7
=
0.221319u
13
+ 0.290675u
12
+ ··· − 7.66514u + 4.74095
−0.0872540u
13
− 0.0324988u
12
+ ··· + 5.00660u − 3.42430
a
8
=
−0.134065u
13
− 0.258176u
12
+ ··· + 2.65854u − 1.31665
0.0872540u
13
+ 0.0324988u
12
+ ··· − 5.00660u + 3.42430
(ii) Obstruction class = −1
(iii) Cusp Shapes =
28175389
29072243
u
13
+
25539934
29072243
u
12
+ ··· −
1509716152
29072243
u +
1122329736
29072243
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
14
− 10u
13
+ ··· − 3259u + 729
c
2
, c
4
, c
5
c
9
u
14
− 5u
12
+ ··· − 71u − 27
c
3
, c
7
(u
7
− 2u
6
+ 2u
5
+ u
3
− u
2
+ 1)
2
c
6
, c
11
, c
12
u
14
− u
13
+ ··· − 1592u − 389
c
8
u
14
− 3u
13
+ ··· + 359u + 69
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 30y
13
+ ··· + 128753y + 531441
c
2
, c
4
, c
5
c
9
y
14
− 10y
13
+ ··· − 3259y + 729
c
3
, c
7
(y
7
+ 6y
5
+ 5y
3
− y
2
+ 2y − 1)
2
c
6
, c
11
, c
12
y
14
− 33y
13
+ ··· − 366178y + 151321
c
8
y
14
+ 23y
13
+ ··· − 87205y + 4761
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.09942
a = −1.35900
b = −1.00000
6.43854 20.5760
u = −0.223848 + 1.077330I
a = −0.411557 − 0.510160I
b = −1.00000
−2.34758 − 1.80700I 3.91671 + 3.17034I
u = −0.223848 − 1.077330I
a = −0.411557 + 0.510160I
b = −1.00000
−2.34758 + 1.80700I 3.91671 − 3.17034I
u = 1.065070 + 0.315249I
a = −0.970701 + 0.740024I
b = −1.00000
3.95079 − 2.05810I 10.60272 + 4.16307I
u = 1.065070 − 0.315249I
a = −0.970701 − 0.740024I
b = −1.00000
3.95079 + 2.05810I 10.60272 − 4.16307I
u = 0.641734 + 0.329182I
a = −0.95791 − 1.18741I
b = −1.00000
−2.34758 + 1.80700I 3.91671 − 3.17034I
u = 0.641734 − 0.329182I
a = −0.95791 + 1.18741I
b = −1.00000
−2.34758 − 1.80700I 3.91671 + 3.17034I
u = −1.267160 + 0.482164I
a = −0.651522 − 0.496695I
b = −1.00000
3.95079 − 2.05810I 10.60272 + 4.16307I
u = −1.267160 − 0.482164I
a = −0.651522 + 0.496695I
b = −1.00000
3.95079 + 2.05810I 10.60272 − 4.16307I
u = −1.49411
a = −0.735834
b = −1.00000
6.43854 20.5760
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46396 + 1.07750I
a = −0.255519 − 0.994371I
b = −1.00000
13.27180 − 3.91407I 8.69280 + 2.02914I
u = −1.46396 − 1.07750I
a = −0.255519 + 0.994371I
b = −1.00000
13.27180 + 3.91407I 8.69280 − 2.02914I
u = 1.44551 + 1.18040I
a = −0.242413 + 0.943369I
b = −1.00000
13.27180 − 3.91407I 8.69280 + 2.02914I
u = 1.44551 − 1.18040I
a = −0.242413 − 0.943369I
b = −1.00000
13.27180 + 3.91407I 8.69280 − 2.02914I
20
V. I
u
5
= hb − 1, a + u, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u − 1
a
6
=
u
u + 1
a
1
=
−u
−u − 1
a
10
=
−u
1
a
4
=
−1
−1
a
9
=
−u
0
a
11
=
1
1
a
12
=
−u + 1
−u
a
7
=
1
1
a
8
=
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
u
2
− u + 1
c
2
, c
4
, c
8
c
10
u
2
+ u + 1
c
3
, c
11
(u − 1)
2
c
6
, c
7
, c
12
(u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
8
, c
9
c
10
y
2
+ y + 1
c
3
, c
6
, c
7
c
11
, c
12
(y − 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 1.00000
3.28987 12.0000
u = −0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 1.00000
3.28987 12.0000
24
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
5
− 3u
4
+ ··· − 5u + 1)(u
12
− 9u
11
+ ··· − 12u + 1)
· (u
14
− 10u
13
+ ··· − 3259u + 729)(u
19
+ 12u
18
+ ··· − 12u − 1)
c
2
, c
4
(u
2
+ u + 1)(u
5
+ u
4
+ ··· + u + 1)(u
12
− u
11
+ ··· − 2u + 1)
· (u
14
− 5u
12
+ ··· − 71u − 27)(u
19
+ 6u
17
+ ··· + 2u − 1)
c
3
(u − 1)
2
(u
5
+ 4u
4
+ 8u
3
+ 7u
2
+ 2u − 1)(u
6
− u
5
+ u
4
+ u
3
+ u + 1)
2
· ((u
7
− 2u
6
+ 2u
5
+ u
3
− u
2
+ 1)
2
)(u
19
+ 5u
18
+ ··· − 5u − 3)
c
5
, c
9
(u
2
− u + 1)(u
5
− u
4
+ ··· + u − 1)(u
12
+ u
11
+ ··· + 2u + 1)
· (u
14
− 5u
12
+ ··· − 71u − 27)(u
19
+ 6u
17
+ ··· + 2u − 1)
c
6
, c
12
(u + 1)
2
(u
5
+ 2u
4
+ u
3
+ 2u
2
+ 1)
· (u
12
− 3u
11
+ 3u
10
+ u
9
− 7u
8
+ 7u
7
+ 2u
6
− 7u
5
+ 6u
4
− 4u
3
+ 4u
2
+ 1)
· (u
14
− u
13
+ ··· − 1592u − 389)(u
19
+ u
18
+ ··· + u − 3)
c
7
(u + 1)
2
(u
5
− 4u
4
+ 8u
3
− 7u
2
+ 2u + 1)(u
6
+ u
5
+ u
4
− u
3
− u + 1)
2
· ((u
7
− 2u
6
+ 2u
5
+ u
3
− u
2
+ 1)
2
)(u
19
+ 5u
18
+ ··· − 5u − 3)
c
8
(u
2
+ u + 1)(u
5
− 3u
3
+ u
2
+ 3u + 1)(u
12
− 4u
11
+ ··· − 4u + 1)
· (u
14
− 3u
13
+ ··· + 359u + 69)(u
19
− u
18
+ ··· − 2u − 1)
c
10
(u
2
+ u + 1)(u
5
+ 3u
4
+ ··· − 5u − 1)(u
12
+ 9u
11
+ ··· + 12u + 1)
· (u
14
− 10u
13
+ ··· − 3259u + 729)(u
19
+ 12u
18
+ ··· − 12u − 1)
c
11
(u − 1)
2
(u
5
− 2u
4
+ u
3
− 2u
2
− 1)
· (u
12
+ 3u
11
+ 3u
10
− u
9
− 7u
8
− 7u
7
+ 2u
6
+ 7u
5
+ 6u
4
+ 4u
3
+ 4u
2
+ 1)
· (u
14
− u
13
+ ··· − 1592u − 389)(u
19
+ u
18
+ ··· + u − 3)
25
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
2
+ y + 1)(y
5
− 9y
4
+ 32y
3
− 43y
2
+ 11y − 1)
· (y
12
− 3y
11
+ ··· − 16y + 1)(y
14
+ 30y
13
+ ··· + 128753y + 531441)
· (y
19
+ 32y
18
+ ··· + 116y − 1)
c
2
, c
4
, c
5
c
9
(y
2
+ y + 1)(y
5
+ 3y
4
+ ··· − 5y − 1)(y
12
+ 9y
11
+ ··· + 12y + 1)
· (y
14
− 10y
13
+ ··· − 3259y + 729)(y
19
+ 12y
18
+ ··· − 12y − 1)
c
3
, c
7
(y − 1)
2
(y
5
+ 12y
3
− 9y
2
+ 18y − 1)(y
6
+ y
5
+ 3y
4
+ 3y
3
− y + 1)
2
· ((y
7
+ 6y
5
+ 5y
3
− y
2
+ 2y − 1)
2
)(y
19
− 3y
18
+ ··· + 103y − 9)
c
6
, c
11
, c
12
((y − 1)
2
)(y
5
− 2y
4
+ ··· − 4y − 1)(y
12
− 3y
11
+ ··· + 8y + 1)
· (y
14
− 33y
13
+ ··· − 366178y + 151321)(y
19
− 17y
18
+ ··· + 73y − 9)
c
8
(y
2
+ y + 1)(y
5
− 6y
4
+ ··· + 7y − 1)(y
12
+ 2y
11
+ ··· + 2y + 1)
· (y
14
+ 23y
13
+ ··· − 87205y + 4761)(y
19
+ 11y
18
+ ··· + 44y − 1)
26
