11n
162
(K11n
162
)
A knot diagram
1
Linearized knot diagam
10 5 1 7 10 3 11 5 3 8 4
Solving Sequence
4,11
1
3,8
7 5 2 6 10 9
c
11
c
3
c
7
c
4
c
2
c
6
c
10
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, −3u
12
− 15u
11
+ ··· + 11a − 20,
u
13
+ u
12
+ 7u
11
+ 6u
10
+ 19u
9
+ 15u
8
+ 22u
7
+ 18u
6
+ 7u
5
+ 10u
4
+ 2u
2
+ 4u − 1i
I
u
2
= h−62903946761724u
25
− 381362114178501u
24
+ ··· + 640188464864309b − 1417634446440228,
911334568428454u
25
+ 2453993677512419u
24
+ ··· + 640188464864309a − 843495134320420,
u
26
+ 3u
25
+ ··· + 9u + 1i
I
u
3
= hb + u, −u
5
+ u
4
− 3u
3
+ u
2
+ a − 3u + 1, u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
− 2u + 1i
I
u
4
= h−u
3
+ u
2
+ b − 2u + 2, −u
5
+ 2u
4
− u
3
+ 3a + 3u − 4, u
6
− 2u
5
+ 4u
4
− 6u
3
+ 6u
2
− 5u + 3i
* 4 irreducible components of dim
C
= 0, with total 51 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
= hb + u, −3u
12
− 15u
11
+ · · · + 11a − 20, u
13
+ u
12
+ · · · + 4u − 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
0.272727u
12
+ 1.36364u
11
+ ··· + 5.18182u + 1.81818
−u
a
7
=
0.272727u
12
+ 1.36364u
11
+ ··· + 4.18182u + 1.81818
−u
a
5
=
−0.545455u
12
+ 2.27273u
11
+ ··· + 7.63636u − 3.63636
0.363636u
12
− 1.18182u
11
+ ··· − 3.09091u + 1.09091
a
2
=
4.81818u
12
+ 4.09091u
11
+ ··· − 4.45455u + 1.45455
−2.27273u
12
− 2.36364u
11
+ ··· + 0.818182u + 0.181818
a
6
=
0.0909091u
12
+ 0.454545u
11
+ ··· + 1.72727u + 2.27273
−0.0909091u
12
+ 0.545455u
11
+ ··· − 0.727273u − 0.272727
a
10
=
1.09091u
12
+ 1.45455u
11
+ ··· + 0.727273u + 1.27273
−u
2
a
9
=
1.81818u
12
+ 2.09091u
11
+ ··· − 0.454545u + 1.45455
−0.636364u
12
− 0.181818u
11
+ ··· − 0.0909091u + 0.0909091
a
9
=
1.81818u
12
+ 2.09091u
11
+ ··· − 0.454545u + 1.45455
−0.636364u
12
− 0.181818u
11
+ ··· − 0.0909091u + 0.0909091
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
4
11
u
12
−
42
11
u
11
−
75
11
u
10
−
247
11
u
9
−
294
11
u
8
−
543
11
u
7
−
478
11
u
6
−
433
11
u
5
− 23u
4
−
29
11
u
3
−
28
11
u
2
−
32
11
u −
89
11
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
+ 16u
12
+ ··· + 384u + 32
c
2
, c
5
u
13
+ 12u
11
+ ··· + 7u
2
+ 1
c
3
, c
7
, c
10
c
11
u
13
− u
12
+ ··· + 4u + 1
c
4
u
13
− 11u
12
+ ··· − 40u + 4
c
6
, c
8
u
13
− u
12
+ ··· − 11u + 3
c
9
u
13
− 8u
12
+ ··· + 6u + 12
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 12y
12
+ ··· + 59904y −1024
c
2
, c
5
y
13
+ 24y
12
+ ··· − 14y −1
c
3
, c
7
, c
10
c
11
y
13
+ 13y
12
+ ··· + 20y −1
c
4
y
13
− 3y
12
+ ··· + 456y −16
c
6
, c
8
y
13
+ 11y
12
+ ··· − 35y −9
c
9
y
13
− 14y
12
+ ··· + 732y −144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.809423 + 0.117584I
a = 0.348533 − 0.706548I
b = 0.809423 − 0.117584I
5.36911 + 2.95494I −7.16291 − 2.81901I
u = −0.809423 − 0.117584I
a = 0.348533 + 0.706548I
b = 0.809423 + 0.117584I
5.36911 − 2.95494I −7.16291 + 2.81901I
u = −0.046196 + 1.261130I
a = −1.11366 + 3.26926I
b = 0.046196 − 1.261130I
12.31700 + 2.15873I 3.13107 − 3.07256I
u = −0.046196 − 1.261130I
a = −1.11366 − 3.26926I
b = 0.046196 + 1.261130I
12.31700 − 2.15873I 3.13107 + 3.07256I
u = −0.151527 + 1.292460I
a = 0.71662 + 1.73016I
b = 0.151527 − 1.292460I
6.35965 − 0.39707I −2.26484 + 2.21487I
u = −0.151527 − 1.292460I
a = 0.71662 − 1.73016I
b = 0.151527 + 1.292460I
6.35965 + 0.39707I −2.26484 − 2.21487I
u = 0.479303 + 0.472811I
a = 0.182244 + 0.741863I
b = −0.479303 − 0.472811I
−0.52618 − 1.43256I −3.73519 + 6.28375I
u = 0.479303 − 0.472811I
a = 0.182244 − 0.741863I
b = −0.479303 + 0.472811I
−0.52618 + 1.43256I −3.73519 − 6.28375I
u = 0.40436 + 1.44082I
a = −0.36627 + 1.65681I
b = −0.40436 − 1.44082I
6.52797 − 5.89125I −0.30193 + 3.39089I
u = 0.40436 − 1.44082I
a = −0.36627 − 1.65681I
b = −0.40436 + 1.44082I
6.52797 + 5.89125I −0.30193 − 3.39089I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.48592 + 1.50310I
a = 0.64061 + 1.74510I
b = 0.48592 − 1.50310I
15.6748 + 13.1069I −1.18846 − 5.87531I
u = −0.48592 − 1.50310I
a = 0.64061 − 1.74510I
b = 0.48592 + 1.50310I
15.6748 − 13.1069I −1.18846 + 5.87531I
u = 0.218803
a = 3.18385
b = −0.218803
−0.973187 −8.95550
6
II.
I
u
2
= h−6.29×10
13
u
25
−3.81×10
14
u
24
+· · ·+6.40×10
14
b−1.42×10
15
, 9.11×
10
14
u
25
+2.45×10
15
u
24
+· · ·+6.40×10
14
a−8.43×10
14
, u
26
+3u
25
+· · ·+9u+1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
−1.42354u
25
− 3.83324u
24
+ ··· − 30.3254u + 1.31757
0.0982585u
25
+ 0.595703u
24
+ ··· + 12.7692u + 2.21440
a
7
=
−1.32528u
25
− 3.23753u
24
+ ··· − 17.5562u + 3.53197
0.0982585u
25
+ 0.595703u
24
+ ··· + 12.7692u + 2.21440
a
5
=
−3.59109u
25
− 10.1484u
24
+ ··· − 88.3953u − 7.10835
0.279522u
25
+ 0.762410u
24
+ ··· + 8.19857u + 2.54254
a
2
=
1.43267u
25
+ 5.14988u
24
+ ··· + 85.8161u + 25.6973
1.45570u
25
+ 4.17786u
24
+ ··· + 43.0260u + 4.92495
a
6
=
−1.11476u
25
− 2.66132u
24
+ ··· − 13.3210u + 4.20145
0.383189u
25
+ 1.21076u
24
+ ··· + 17.2921u + 2.93923
a
10
=
−1.85007u
25
− 5.49107u
24
+ ··· − 77.2940u − 14.2016
−0.692471u
25
− 1.85702u
24
+ ··· − 12.8116u − 0.482676
a
9
=
−1.71634u
25
− 5.14621u
24
+ ··· − 73.8523u − 13.9762
−0.513166u
25
− 1.32858u
24
+ ··· − 8.99682u − 0.200919
a
9
=
−1.71634u
25
− 5.14621u
24
+ ··· − 73.8523u − 13.9762
−0.513166u
25
− 1.32858u
24
+ ··· − 8.99682u − 0.200919
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
835837455787153
640188464864309
u
25
+
1938384712386284
640188464864309
u
24
+ ··· +
13509636668298897
640188464864309
u −
455441820193168
640188464864309
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
13
− 4u
12
+ ··· + 47u + 1)
2
c
2
, c
5
u
26
− u
25
+ ··· + 193u + 61
c
3
, c
7
, c
10
c
11
u
26
− 3u
25
+ ··· − 9u + 1
c
4
(u
13
+ u
12
+ ··· + 8u + 5)
2
c
6
, c
8
u
26
+ 4u
25
+ ··· + 2400u + 1353
c
9
(u
13
+ 3u
12
+ ··· + 2u + 3)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
13
− 16y
12
+ ··· + 2493y −1)
2
c
2
, c
5
y
26
+ 33y
25
+ ··· + 38147y + 3721
c
3
, c
7
, c
10
c
11
y
26
+ 19y
25
+ ··· − y + 1
c
4
(y
13
+ 9y
12
+ ··· − 136y −25)
2
c
6
, c
8
y
26
+ 20y
25
+ ··· + 9336774y + 1830609
c
9
(y
13
− 19y
12
+ ··· + 124y −9)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.067900 + 1.180330I
a = 0.517992 − 0.149968I
b = −1.207500 − 0.051879I
1.265650 − 0.287296I −2.88954 − 0.89161I
u = 0.067900 − 1.180330I
a = 0.517992 + 0.149968I
b = −1.207500 + 0.051879I
1.265650 + 0.287296I −2.88954 + 0.89161I
u = 0.247316 + 1.177340I
a = 0.311935 − 0.046135I
b = 0.524618 − 0.069053I
2.03958 − 2.67289I −1.48191 + 5.19592I
u = 0.247316 − 1.177340I
a = 0.311935 + 0.046135I
b = 0.524618 + 0.069053I
2.03958 + 2.67289I −1.48191 − 5.19592I
u = 1.207500 + 0.051879I
a = 0.196751 + 0.489452I
b = −0.067900 − 1.180330I
1.265650 − 0.287296I −2.88954 − 0.89161I
u = 1.207500 − 0.051879I
a = 0.196751 − 0.489452I
b = −0.067900 + 1.180330I
1.265650 + 0.287296I −2.88954 + 0.89161I
u = −0.216549 + 1.266240I
a = −0.86731 − 1.86678I
b = −0.45644 + 1.36303I
5.76658 + 5.41588I −0.94009 − 2.54727I
u = −0.216549 − 1.266240I
a = −0.86731 + 1.86678I
b = −0.45644 − 1.36303I
5.76658 − 5.41588I −0.94009 + 2.54727I
u = −1.274900 + 0.275508I
a = 0.251587 + 0.623600I
b = 0.326804 − 1.347110I
10.00280 + 7.01304I −2.38090 − 4.98186I
u = −1.274900 − 0.275508I
a = 0.251587 − 0.623600I
b = 0.326804 + 1.347110I
10.00280 − 7.01304I −2.38090 + 4.98186I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.394224 + 1.245000I
a = −0.638079 + 0.785356I
b = 0.160428 + 0.147487I
8.78740 + 1.45996I −3.65650 − 0.27682I
u = −0.394224 − 1.245000I
a = −0.638079 − 0.785356I
b = 0.160428 − 0.147487I
8.78740 − 1.45996I −3.65650 + 0.27682I
u = −0.052461 + 1.357580I
a = −0.07916 − 1.70109I
b = 0.78161 + 1.55425I
13.70610 − 0.67900I 1.58151 + 0.47574I
u = −0.052461 − 1.357580I
a = −0.07916 + 1.70109I
b = 0.78161 − 1.55425I
13.70610 + 0.67900I 1.58151 − 0.47574I
u = −0.326804 + 1.347110I
a = −0.425005 + 0.468743I
b = 1.274900 − 0.275508I
10.00280 + 7.01304I −2.38090 − 4.98186I
u = −0.326804 − 1.347110I
a = −0.425005 − 0.468743I
b = 1.274900 + 0.275508I
10.00280 − 7.01304I −2.38090 + 4.98186I
u = 0.45644 + 1.36303I
a = 1.02148 − 1.52994I
b = 0.216549 + 1.266240I
5.76658 − 5.41588I −0.94009 + 2.54727I
u = 0.45644 − 1.36303I
a = 1.02148 + 1.52994I
b = 0.216549 − 1.266240I
5.76658 + 5.41588I −0.94009 − 2.54727I
u = −0.524618 + 0.069053I
a = −0.158561 − 0.699160I
b = −0.247316 − 1.177340I
2.03958 − 2.67289I −1.48191 + 5.19592I
u = −0.524618 − 0.069053I
a = −0.158561 + 0.699160I
b = −0.247316 + 1.177340I
2.03958 + 2.67289I −1.48191 − 5.19592I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.252433 + 0.419434I
a = 1.07447 − 1.78530I
b = −0.252433 + 0.419434I
−0.889471 −5.46516 + 0.I
u = 0.252433 − 0.419434I
a = 1.07447 + 1.78530I
b = −0.252433 − 0.419434I
−0.889471 −5.46516 + 0.I
u = −0.78161 + 1.55425I
a = −0.588096 − 1.192760I
b = 0.052461 + 1.357580I
13.70610 + 0.67900I 1.58151 + 0.I
u = −0.78161 − 1.55425I
a = −0.588096 + 1.192760I
b = 0.052461 − 1.357580I
13.70610 − 0.67900I 1.58151 + 0.I
u = −0.160428 + 0.147487I
a = 5.88200 − 1.47414I
b = 0.394224 + 1.245000I
8.78740 − 1.45996I −3.65650 + 0.27682I
u = −0.160428 − 0.147487I
a = 5.88200 + 1.47414I
b = 0.394224 − 1.245000I
8.78740 + 1.45996I −3.65650 − 0.27682I
12
III.
I
u
3
= hb+u, −u
5
+u
4
−3u
3
+u
2
+a−3u+1, u
6
−u
5
+3u
4
−2u
3
+3u
2
−2u+1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
u
5
− u
4
+ 3u
3
− u
2
+ 3u − 1
−u
a
7
=
u
5
− u
4
+ 3u
3
− u
2
+ 2u − 1
−u
a
5
=
u
4
+ 2u
2
u
4
− u
3
+ u
2
a
2
=
u
2
− u + 1
u
5
+ u
3
+ 2u
2
− u + 1
a
6
=
u
5
+ 2u
3
+ u
2
+ u
0
a
10
=
u
3
+ u
−u
2
a
9
=
u
3
− u
2
+ 2u − 1
−u
4
+ u
3
− 3u
2
+ u − 1
a
9
=
u
3
− u
2
+ 2u − 1
−u
4
+ u
3
− 3u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
5
− 9u
4
+ 19u
3
− 13u
2
+ 14u − 15
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− u
5
+ 8u
3
+ 3u
2
− u + 3
c
2
, c
5
u
6
+ 2u
4
+ 3u
3
− 2u
2
− 2u + 1
c
3
, c
10
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ 2u + 1
c
4
u
6
− 2u
5
+ 3u
4
− 2u
3
+ 5u
2
− 7u + 3
c
6
, c
8
u
6
+ u
5
+ 2u
4
+ 2u
3
+ u
2
+ u + 1
c
7
, c
11
u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
− 2u + 1
c
9
u
6
− 3u
5
+ 2u
4
+ u
2
− u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− y
5
+ 22y
4
− 60y
3
+ 25y
2
+ 17y + 9
c
2
, c
5
y
6
+ 4y
5
− 15y
3
+ 20y
2
− 8y + 1
c
3
, c
7
, c
10
c
11
y
6
+ 5y
5
+ 11y
4
+ 12y
3
+ 7y
2
+ 2y + 1
c
4
y
6
+ 2y
5
+ 11y
4
+ 4y
3
+ 15y
2
− 19y + 9
c
6
, c
8
y
6
+ 3y
5
+ 2y
4
+ y
2
+ y + 1
c
9
y
6
− 5y
5
+ 6y
4
+ 5y
2
+ y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.368622 + 1.044700I
a = 0.344849 + 0.081037I
b = 0.368622 − 1.044700I
9.91965 + 2.91185I −0.22592 − 3.63955I
u = −0.368622 − 1.044700I
a = 0.344849 − 0.081037I
b = 0.368622 + 1.044700I
9.91965 − 2.91185I −0.22592 + 3.63955I
u = 0.474902 + 0.458521I
a = −0.07450 + 1.48771I
b = −0.474902 − 0.458521I
−1.33814 − 0.90202I −11.17385 + 4.13696I
u = 0.474902 − 0.458521I
a = −0.07450 − 1.48771I
b = −0.474902 + 0.458521I
−1.33814 + 0.90202I −11.17385 − 4.13696I
u = 0.393720 + 1.309500I
a = −0.77035 + 1.73149I
b = −0.393720 − 1.309500I
4.57797 − 6.62522I −5.60023 + 6.47362I
u = 0.393720 − 1.309500I
a = −0.77035 − 1.73149I
b = −0.393720 + 1.309500I
4.57797 + 6.62522I −5.60023 − 6.47362I
16
IV. I
u
4
= h−u
3
+ u
2
+ b − 2u + 2, −u
5
+ 2u
4
− u
3
+ 3a + 3u − 4, u
6
− 2u
5
+
4u
4
− 6u
3
+ 6u
2
− 5u + 3i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
1
3
u
5
−
2
3
u
4
+
1
3
u
3
− u +
4
3
u
3
− u
2
+ 2u − 2
a
7
=
1
3
u
5
−
2
3
u
4
+ ··· + u −
2
3
u
3
− u
2
+ 2u − 2
a
5
=
−
2
3
u
5
+
4
3
u
4
+ ··· − u +
1
3
u
2
+ 1
a
2
=
−
1
3
u
5
+
5
3
u
4
+ ··· − 3u +
5
3
−u
4
+ 2u
3
− 2u
2
+ 2u − 1
a
6
=
1
3
u
5
+
1
3
u
4
+ ··· − 3u +
7
3
u
3
− u
2
+ 3u − 2
a
10
=
−
1
3
u
5
+
5
3
u
4
+ ··· − 4u +
8
3
−u
4
+ 2u
3
− 2u
2
+ 3u − 1
a
9
=
−
1
3
u
5
+
2
3
u
4
+ ··· − 3u +
8
3
−u
5
+ u
4
− 2u
3
+ 3u
2
− u + 2
a
9
=
−
1
3
u
5
+
2
3
u
4
+ ··· − 3u +
8
3
−u
5
+ u
4
− 2u
3
+ 3u
2
− u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
4
+ 3u
3
− 6u
2
+ 6u − 6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 2u + 1)
2
c
2
, c
5
u
6
+ 3u
4
− 3u
3
− u + 3
c
3
, c
10
u
6
+ 2u
5
+ 4u
4
+ 6u
3
+ 6u
2
+ 5u + 3
c
4
, c
9
(u
3
+ u
2
+ 1)
2
c
6
, c
8
u
6
− 3u
5
+ 5u
4
− 2u
3
− u
2
+ 2u + 1
c
7
, c
11
u
6
− 2u
5
+ 4u
4
− 6u
3
+ 6u
2
− 5u + 3
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 5y
2
+ 2y − 1)
2
c
2
, c
5
y
6
+ 6y
5
+ 9y
4
− 3y
3
+ 12y
2
− y + 9
c
3
, c
7
, c
10
c
11
y
6
+ 4y
5
+ 4y
4
− 2y
3
+ 11y + 9
c
4
, c
9
(y
3
− y
2
− 2y − 1)
2
c
6
, c
8
y
6
+ y
5
+ 11y
4
+ 19y
2
− 6y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.044140 + 0.390425I
a = 0.242056 − 0.443900I
b = −0.188646 + 1.182980I
1.07850 + 1.58317I −4.02349 − 3.48462I
u = 1.044140 − 0.390425I
a = 0.242056 + 0.443900I
b = −0.188646 − 1.182980I
1.07850 − 1.58317I −4.02349 + 3.48462I
u = 0.188646 + 1.182980I
a = 0.360189 − 0.302713I
b = −1.044140 + 0.390425I
1.07850 − 1.58317I −4.02349 + 3.48462I
u = 0.188646 − 1.182980I
a = 0.360189 + 0.302713I
b = −1.044140 − 0.390425I
1.07850 + 1.58317I −4.02349 − 3.48462I
u = −0.232786 + 1.275990I
a = −0.43558 − 2.38757I
b = 0.232786 + 1.275990I
11.0025 −6 − 0.953017 + 0.10I
u = −0.232786 − 1.275990I
a = −0.43558 + 2.38757I
b = 0.232786 − 1.275990I
11.0025 −6 − 0.953017 + 0.10I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 2u + 1)
2
(u
6
− u
5
+ 8u
3
+ 3u
2
− u + 3)
· ((u
13
− 4u
12
+ ··· + 47u + 1)
2
)(u
13
+ 16u
12
+ ··· + 384u + 32)
c
2
, c
5
(u
6
+ 2u
4
+ 3u
3
− 2u
2
− 2u + 1)(u
6
+ 3u
4
− 3u
3
− u + 3)
· (u
13
+ 12u
11
+ ··· + 7u
2
+ 1)(u
26
− u
25
+ ··· + 193u + 61)
c
3
, c
10
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ 2u + 1)
· (u
6
+ 2u
5
+ ··· + 5u + 3)(u
13
− u
12
+ ··· + 4u + 1)
· (u
26
− 3u
25
+ ··· − 9u + 1)
c
4
(u
3
+ u
2
+ 1)
2
(u
6
− 2u
5
+ 3u
4
− 2u
3
+ 5u
2
− 7u + 3)
· (u
13
− 11u
12
+ ··· − 40u + 4)(u
13
+ u
12
+ ··· + 8u + 5)
2
c
6
, c
8
(u
6
− 3u
5
+ 5u
4
− 2u
3
− u
2
+ 2u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ u
2
+ u + 1)
· (u
13
− u
12
+ ··· − 11u + 3)(u
26
+ 4u
25
+ ··· + 2400u + 1353)
c
7
, c
11
(u
6
− 2u
5
+ 4u
4
− 6u
3
+ 6u
2
− 5u + 3)
· (u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
− 2u + 1)(u
13
− u
12
+ ··· + 4u + 1)
· (u
26
− 3u
25
+ ··· − 9u + 1)
c
9
((u
3
+ u
2
+ 1)
2
)(u
6
− 3u
5
+ ··· − u + 1)(u
13
− 8u
12
+ ··· + 6u + 12)
· (u
13
+ 3u
12
+ ··· + 2u + 3)
2
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 5y
2
+ 2y − 1)
2
(y
6
− y
5
+ 22y
4
− 60y
3
+ 25y
2
+ 17y + 9)
· (y
13
− 16y
12
+ ··· + 2493y − 1)
2
· (y
13
− 12y
12
+ ··· + 59904y − 1024)
c
2
, c
5
(y
6
+ 4y
5
− 15y
3
+ 20y
2
− 8y + 1)(y
6
+ 6y
5
+ ··· − y + 9)
· (y
13
+ 24y
12
+ ··· − 14y − 1)(y
26
+ 33y
25
+ ··· + 38147y + 3721)
c
3
, c
7
, c
10
c
11
(y
6
+ 4y
5
+ 4y
4
− 2y
3
+ 11y + 9)(y
6
+ 5y
5
+ ··· + 2y + 1)
· (y
13
+ 13y
12
+ ··· + 20y − 1)(y
26
+ 19y
25
+ ··· − y + 1)
c
4
(y
3
− y
2
− 2y − 1)
2
(y
6
+ 2y
5
+ 11y
4
+ 4y
3
+ 15y
2
− 19y + 9)
· (y
13
− 3y
12
+ ··· + 456y − 16)(y
13
+ 9y
12
+ ··· − 136y − 25)
2
c
6
, c
8
(y
6
+ y
5
+ 11y
4
+ 19y
2
− 6y + 1)(y
6
+ 3y
5
+ 2y
4
+ y
2
+ y + 1)
· (y
13
+ 11y
12
+ ··· − 35y − 9)
· (y
26
+ 20y
25
+ ··· + 9336774y + 1830609)
c
9
(y
3
− y
2
− 2y − 1)
2
(y
6
− 5y
5
+ 6y
4
+ 5y
2
+ y + 1)
· ((y
13
− 19y
12
+ ··· + 124y − 9)
2
)(y
13
− 14y
12
+ ··· + 732y − 144)
22
