12n
0207
(K12n
0207
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 9 4 11 5 8 6 10
Solving Sequence
8,11 4,9
3 7 6 12 5 2 10 1
c
8
c
3
c
7
c
6
c
11
c
5
c
2
c
10
c
12
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
17
+ 6u
16
+ ··· + b − u, u
15
+ 6u
14
+ ··· + a − 2u, u
18
+ 7u
17
+ ··· + u + 1i
I
u
2
= hb, u
8
+ 2u
7
− u
6
− 4u
5
− u
4
+ 2u
3
+ 2u
2
+ a + 2u + 1, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
I
u
3
= h−2652a
8
+ 26713b + ··· − 65147a + 3162, a
9
+ a
8
+ 2a
7
+ 19a
6
− 5a
5
+ 15a
4
− 6a
3
+ 4a
2
− a + 1,
u − 1i
I
u
4
= h87u
17
+ 355u
16
+ ··· + 256b + 153, 33u
17
+ 85u
16
+ ··· + 256a + 111, u
18
+ 4u
17
+ ··· − 9u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 54 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
= hu
17
+6u
16
+· · ·+b −u, u
15
+6u
14
+· · ·+a −2u, u
18
+7u
17
+· · ·+u +1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
4
=
−u
15
− 6u
14
+ ··· − 2u
2
+ 2u
−u
17
− 6u
16
+ ··· + 4u
3
+ u
a
9
=
1
u
2
a
3
=
−u
17
− 6u
16
+ ··· − 2u
2
+ 3u
−u
17
− 6u
16
+ ··· + 4u
3
+ u
a
7
=
−u
3
− 2u
2
+ 2
u
3
− u
a
6
=
u
5
+ 2u
4
− 4u
2
− u + 2
u
7
+ 2u
6
+ u
5
− 2u
4
− u
a
12
=
u
11
+ 4u
10
+ 4u
9
− 8u
8
− 18u
7
+ 24u
5
+ 8u
4
− 15u
3
− 4u
2
+ 4u
u
13
+ 4u
12
+ ··· − 2u
2
+ u
a
5
=
u
17
+ 6u
16
+ ··· − u + 2
u
17
+ 7u
16
+ ··· − u + 1
a
2
=
−2u
17
− 13u
16
+ ··· + 4u − 1
−u
17
− 7u
16
+ ··· + u − 1
a
10
=
u
u
a
1
=
−u
15
− 4u
14
+ ··· − 4u
2
+ 4u
−u
15
− 4u
14
+ ··· − 2u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
17
− 56u
16
− 160u
15
− 168u
14
+ 176u
13
+ 660u
12
+ 460u
11
−
492u
10
− 880u
9
− 108u
8
+ 496u
7
+ 224u
6
− 96u
5
− 88u
4
− 52u
3
− 4u
2
+ 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 11u
17
+ ··· + 3u + 1
c
2
, c
4
, c
8
c
10
u
18
− 7u
17
+ ··· − u + 1
c
3
, c
7
, c
9
u
18
+ u
17
+ ··· + u − 1
c
5
, c
11
u
18
+ u
17
+ ··· + 3u − 1
c
6
u
18
− 5u
17
+ ··· + 77u − 23
c
12
u
18
− 3u
17
+ ··· + 517u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 41y
17
+ ··· − 47y + 1
c
2
, c
4
, c
8
c
10
y
18
− 11y
17
+ ··· − 3y + 1
c
3
, c
7
, c
9
y
18
+ 21y
17
+ ··· − 7y + 1
c
5
, c
11
y
18
+ 13y
17
+ ··· − 43y + 1
c
6
y
18
+ y
17
+ ··· − 5331y + 529
c
12
y
18
+ 29y
17
+ ··· − 268915y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.944628
a = −5.10321
b = −0.318928
−3.03100 −72.2820
u = 1.090030 + 0.138340I
a = 0.85982 + 4.45023I
b = 0.344494 − 0.511075I
−5.78192 − 0.83339I −4.3200 − 13.4737I
u = 1.090030 − 0.138340I
a = 0.85982 − 4.45023I
b = 0.344494 + 0.511075I
−5.78192 + 0.83339I −4.3200 + 13.4737I
u = −1.074780 + 0.345327I
a = −0.427778 + 0.032515I
b = −0.557323 + 0.726879I
−5.49927 + 7.93492I −11.8455 − 13.1993I
u = −1.074780 − 0.345327I
a = −0.427778 − 0.032515I
b = −0.557323 − 0.726879I
−5.49927 − 7.93492I −11.8455 + 13.1993I
u = −0.771241 + 0.273342I
a = 0.446361 − 0.431948I
b = 0.136626 − 0.709955I
0.64686 + 2.83787I 0.86568 − 9.86296I
u = −0.771241 − 0.273342I
a = 0.446361 + 0.431948I
b = 0.136626 + 0.709955I
0.64686 − 2.83787I 0.86568 + 9.86296I
u = 0.681784 + 0.343900I
a = 0.43124 − 1.72853I
b = −0.781322 + 0.060789I
−3.91966 − 2.10303I −13.59813 + 2.08848I
u = 0.681784 − 0.343900I
a = 0.43124 + 1.72853I
b = −0.781322 − 0.060789I
−3.91966 + 2.10303I −13.59813 − 2.08848I
u = 0.466479
a = −0.766868
b = 0.604129
−1.09450 −7.23730
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.123110 + 0.372790I
a = −1.26837 + 1.31989I
b = 0.367491 + 0.554636I
−0.53975 − 1.77290I −3.88757 + 3.00933I
u = −0.123110 − 0.372790I
a = −1.26837 − 1.31989I
b = 0.367491 − 0.554636I
−0.53975 + 1.77290I −3.88757 − 3.00933I
u = −1.28135 + 1.04067I
a = 0.956293 + 0.739630I
b = 0.74883 − 1.97520I
9.51613 + 3.71804I −9.22156 − 1.51475I
u = −1.28135 − 1.04067I
a = 0.956293 − 0.739630I
b = 0.74883 + 1.97520I
9.51613 − 3.71804I −9.22156 + 1.51475I
u = −1.33771 + 1.06945I
a = −0.924080 − 0.832513I
b = −0.83783 + 2.05810I
13.3797 + 9.0997I −6.48039 − 4.12934I
u = −1.33771 − 1.06945I
a = −0.924080 + 0.832513I
b = −0.83783 − 2.05810I
13.3797 − 9.0997I −6.48039 + 4.12934I
u = −1.38917 + 1.06637I
a = 0.861553 + 0.883276I
b = 0.93643 − 2.07951I
9.0651 + 14.3484I −9.75296 − 6.52825I
u = −1.38917 − 1.06637I
a = 0.861553 − 0.883276I
b = 0.93643 + 2.07951I
9.0651 − 14.3484I −9.75296 + 6.52825I
6
II.
I
u
2
= hb, u
8
+ 2u
7
+ · · · + a + 1, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
4
=
−u
8
− 2u
7
+ u
6
+ 4u
5
+ u
4
− 2u
3
− 2u
2
− 2u − 1
0
a
9
=
1
u
2
a
3
=
−u
8
− 2u
7
+ u
6
+ 4u
5
+ u
4
− 2u
3
− 2u
2
− 2u − 1
0
a
7
=
1
0
a
6
=
−u
2
+ 1
−u
4
a
12
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
5
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
− u
7
+ 3u
6
+ 2u
5
− 3u
4
− 2u
3
+ 1
a
2
=
−2u
7
− 2u
6
+ 4u
5
+ 4u
4
− 2u
3
− 2u
2
− 2u − 2
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u
3
− 1
a
10
=
u
u
a
1
=
u
8
− 3u
6
+ 3u
4
− 1
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u
3
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
8
+ u
7
+ 2u
6
+ u
5
− 3u
4
− 5u
3
+ 2u
2
+ 3u − 5
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
8
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
9
, c
12
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
10
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
11
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
8
, c
10
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
9
, c
12
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 0.483566 − 0.305056I
b = 0
0.13850 + 2.09337I −6.02684 − 1.69698I
u = −0.772920 − 0.510351I
a = 0.483566 + 0.305056I
b = 0
0.13850 − 2.09337I −6.02684 + 1.69698I
u = 0.825933
a = −3.56378
b = 0
−2.84338 −3.87310
u = 1.173910 + 0.391555I
a = 1.23246 + 1.62704I
b = 0
−6.01628 − 1.33617I −16.4774 + 4.4812I
u = 1.173910 − 0.391555I
a = 1.23246 − 1.62704I
b = 0
−6.01628 + 1.33617I −16.4774 − 4.4812I
u = −0.141484 + 0.739668I
a = −1.022450 + 0.246780I
b = 0
−2.26187 − 2.45442I −8.53903 + 2.82066I
u = −0.141484 − 0.739668I
a = −1.022450 − 0.246780I
b = 0
−2.26187 + 2.45442I −8.53903 − 2.82066I
u = −1.172470 + 0.500383I
a = −0.411691 + 0.129409I
b = 0
−5.24306 + 7.08493I −9.02021 − 2.94778I
u = −1.172470 − 0.500383I
a = −0.411691 − 0.129409I
b = 0
−5.24306 − 7.08493I −9.02021 + 2.94778I
10
III.
I
u
3
= h−2652a
8
+ 26713b + · · · − 65147a + 3162, a
9
+ a
8
+ · · · − a + 1, u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
1
a
4
=
a
0.0992775a
8
− 0.0110059a
7
+ ··· + 2.43878a − 0.118369
a
9
=
1
1
a
3
=
0.0992775a
8
− 0.0110059a
7
+ ··· + 3.43878a − 0.118369
0.0992775a
8
− 0.0110059a
7
+ ··· + 2.43878a − 0.118369
a
7
=
0.110283a
8
+ 0.0737469a
7
+ ··· + 0.0190918a + 1.09928
0.235690a
8
+ 0.0462696a
7
+ ··· − 0.0895444a + 0.334369
a
6
=
0.235690a
8
+ 0.0462696a
7
+ ··· − 0.0895444a + 0.334369
0.361098a
8
+ 0.0187923a
7
+ ··· − 0.198181a − 0.430539
a
12
=
0.895893a
8
+ 0.647288a
7
+ ··· + 0.918841a − 1.22203
1.03171a
8
+ 0.767978a
7
+ ··· + 1.14806a − 1.23011
a
5
=
1.32041a
8
+ 1.20204a
7
+ ··· + 3.01677a − 1.11279
1.32041a
8
+ 1.20204a
7
+ ··· + 3.01677a − 1.11279
a
2
=
1.32041a
8
+ 1.20204a
7
+ ··· + 4.01677a − 1.11279
1.32041a
8
+ 1.20204a
7
+ ··· + 3.01677a − 1.11279
a
10
=
1
1
a
1
=
0.760079a
8
+ 0.526598a
7
+ ··· + 0.689627a − 1.21394
0.895893a
8
+ 0.647288a
7
+ ··· + 0.918841a − 1.22203
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
20687
26713
a
8
+
30282
26713
a
7
+
57293
26713
a
6
+
423871
26713
a
5
+
90930
26713
a
4
+
389154
26713
a
3
+
110924
26713
a
2
−
5178
26713
a −
181861
26713
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
6
u
9
− 2u
8
+ 5u
7
− 22u
6
+ 52u
5
− 63u
4
+ 41u
3
− 10u
2
− 2u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
(u − 1)
9
c
9
u
9
c
10
(u + 1)
9
c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
12
u
9
− 3u
8
+ 3u
7
+ 2u
6
+ u
5
+ 9u
4
+ 3u
3
+ 2u + 1
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1
c
2
, c
4
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
c
3
, c
7
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1
c
5
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1
c
6
y
9
+ 6y
8
+ ··· + 24y − 1
c
8
, c
10
(y − 1)
9
c
9
y
9
c
12
y
9
− 3y
8
+ 23y
7
+ 62y
6
− 13y
5
− 57y
4
+ 9y
3
− 6y
2
+ 4y − 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.037875 + 0.791187I
b = −0.628449 + 0.875112I
−2.26187 + 2.45442I −8.53903 − 2.82066I
u = 1.00000
a = −0.037875 − 0.791187I
b = −0.628449 − 0.875112I
−2.26187 − 2.45442I −8.53903 + 2.82066I
u = 1.00000
a = 0.417942 + 0.357732I
b = 0.728966 + 0.986295I
−5.24306 − 7.08493I −9.02021 + 2.94778I
u = 1.00000
a = 0.417942 − 0.357732I
b = 0.728966 − 0.986295I
−5.24306 + 7.08493I −9.02021 − 2.94778I
u = 1.00000
a = −0.218072 + 0.482572I
b = −0.140343 + 0.966856I
0.13850 + 2.09337I −6.02684 − 1.69698I
u = 1.00000
a = −0.218072 − 0.482572I
b = −0.140343 − 0.966856I
0.13850 − 2.09337I −6.02684 + 1.69698I
u = 1.00000
a = 0.80973 + 2.39258I
b = 0.796005 − 0.733148I
−6.01628 − 1.33617I −16.4774 + 4.4812I
u = 1.00000
a = 0.80973 − 2.39258I
b = 0.796005 + 0.733148I
−6.01628 + 1.33617I −16.4774 − 4.4812I
u = 1.00000
a = −2.94345
b = −0.512358
−2.84338 −3.87310
16
IV. I
u
4
= h87u
17
+ 355u
16
+ · · · + 256b + 153, 33u
17
+ 85u
16
+ · · · + 256a +
111, u
18
+ 4u
17
+ · · · − 9u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
4
=
−0.128906u
17
− 0.332031u
16
+ ··· − 8.87109u − 0.433594
−0.339844u
17
− 1.38672u
16
+ ··· + 1.46484u − 0.597656
a
9
=
1
u
2
a
3
=
−0.468750u
17
− 1.71875u
16
+ ··· − 7.40625u − 1.03125
−0.339844u
17
− 1.38672u
16
+ ··· + 1.46484u − 0.597656
a
7
=
−0.0507813u
17
− 0.160156u
16
+ ··· − 5.93359u + 2.94141
−0.226563u
17
− 0.765625u
16
+ ··· − 3.55469u − 0.328125
a
6
=
−0.242188u
17
− 0.812500u
16
+ ··· − 9.53906u + 2.65625
−0.277344u
17
− 0.964844u
16
+ ··· − 3.36328u − 0.441406
a
12
=
0.812500u
17
+ 3.19531u
16
+ ··· − 0.437500u + 3.36719
0.0351563u
17
+ 0.121094u
16
+ ··· − 4.28516u + 1.14453
a
5
=
0.128906u
17
+ 0.332031u
16
+ ··· + 8.87109u + 0.433594
0.183594u
17
+ 0.667969u
16
+ ··· − 0.433594u + 0.128906
a
2
=
0
−0.183594u
17
− 0.667969u
16
+ ··· + 0.433594u − 0.128906
a
10
=
u
u
a
1
=
0.714844u
17
+ 2.70703u
16
+ ··· − 1.21484u + 3.40234
−0.0625000u
17
− 0.367188u
16
+ ··· − 5.06250u + 1.17969
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
43
128
u
17
−
91
64
u
16
+ ··· +
75
128
u −
619
64
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 10u
17
+ ··· + 18u + 1
c
2
, c
4
, c
8
c
10
u
18
− 4u
17
+ ··· − 9u
2
+ 1
c
3
, c
7
, c
9
u
18
+ u
17
+ ··· + 1024u + 512
c
5
, c
11
(u
9
+ u
8
+ 4u
7
+ 3u
6
+ 5u
5
+ 3u
4
− 3u − 1)
2
c
6
u
18
− 3u
17
+ ··· + 3241u + 1303
c
12
u
18
+ 4u
17
+ ··· + 1179u − 199
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 38y
17
+ ··· − 206y + 1
c
2
, c
4
, c
8
c
10
y
18
+ 10y
17
+ ··· − 18y + 1
c
3
, c
7
, c
9
y
18
+ 39y
17
+ ··· − 262144y + 262144
c
5
, c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ y
5
− 31y
4
− 24y
3
+ 6y
2
+ 9y − 1)
2
c
6
y
18
+ 33y
17
+ ··· − 7027677y + 1697809
c
12
y
18
+ 40y
17
+ ··· − 5352529y + 39601
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.292342 + 0.889650I
a = 0.150415 + 1.204670I
b = 1.52260 − 1.29705I
0.11314 + 3.86354I −7.87583 − 4.20503I
u = −0.292342 − 0.889650I
a = 0.150415 − 1.204670I
b = 1.52260 + 1.29705I
0.11314 − 3.86354I −7.87583 + 4.20503I
u = −0.167320 + 1.143090I
a = −0.144832 − 0.989456I
b = −0.96197 + 1.32057I
3.85626 −3.50861 + 0.I
u = −0.167320 − 1.143090I
a = −0.144832 + 0.989456I
b = −0.96197 − 1.32057I
3.85626 −3.50861 + 0.I
u = 0.673526
a = −0.538185
b = 0.433195
−1.08370 −8.12940
u = 1.255930 + 0.512460I
a = 0.105046 − 0.414131I
b = −0.200843 + 0.459012I
−4.49282 − 1.55423I −10.08319 + 1.78109I
u = 1.255930 − 0.512460I
a = 0.105046 + 0.414131I
b = −0.200843 − 0.459012I
−4.49282 + 1.55423I −10.08319 − 1.78109I
u = 0.095228 + 1.376890I
a = 0.102057 + 0.817363I
b = 0.595275 − 1.147110I
0.11314 − 3.86354I −7.87583 + 4.20503I
u = 0.095228 − 1.376890I
a = 0.102057 − 0.817363I
b = 0.595275 + 1.147110I
0.11314 + 3.86354I −7.87583 − 4.20503I
u = −1.04620 + 1.32365I
a = −0.622785 − 0.838280I
b = 0.01330 + 2.66058I
10.52390 + 4.99486I −8.55415 − 3.07435I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04620 − 1.32365I
a = −0.622785 + 0.838280I
b = 0.01330 − 2.66058I
10.52390 − 4.99486I −8.55415 + 3.07435I
u = −0.156952 + 0.191508I
a = 0.57547 − 2.26873I
b = −1.015350 − 0.875548I
−4.49282 + 1.55423I −10.08319 − 1.78109I
u = −0.156952 − 0.191508I
a = 0.57547 + 2.26873I
b = −1.015350 + 0.875548I
−4.49282 − 1.55423I −10.08319 + 1.78109I
u = −1.06998 + 1.41248I
a = 0.603827 + 0.797115I
b = −0.12400 − 2.50290I
14.5478 −5.33565 + 0.I
u = −1.06998 − 1.41248I
a = 0.603827 − 0.797115I
b = −0.12400 + 2.50290I
14.5478 −5.33565 + 0.I
u = 0.195082
a = −1.85810
b = 0.606622
−1.08370 −8.12940
u = −1.05267 + 1.50913I
a = −0.571061 − 0.768659I
b = 0.15107 + 2.32872I
10.52390 − 4.99486I −8.55415 + 3.07435I
u = −1.05267 − 1.50913I
a = −0.571061 + 0.768659I
b = 0.15107 − 2.32872I
10.52390 + 4.99486I −8.55415 − 3.07435I
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
18
− 10u
17
+ ··· + 18u + 1)(u
18
+ 11u
17
+ ··· + 3u + 1)
c
2
, c
8
(u − 1)
9
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
18
− 7u
17
+ ··· − u + 1)(u
18
− 4u
17
+ ··· − 9u
2
+ 1)
c
3
u
9
(u
9
+ u
8
+ ··· + u − 1)(u
18
+ u
17
+ ··· + u − 1)
· (u
18
+ u
17
+ ··· + 1024u + 512)
c
4
, c
10
(u + 1)
9
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
18
− 7u
17
+ ··· − u + 1)(u
18
− 4u
17
+ ··· − 9u
2
+ 1)
c
5
, c
11
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
9
+ u
8
+ 4u
7
+ 3u
6
+ 5u
5
+ 3u
4
− 3u − 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
18
+ u
17
+ ··· + 3u − 1)
c
6
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
9
− 2u
8
+ 5u
7
− 22u
6
+ 52u
5
− 63u
4
+ 41u
3
− 10u
2
− 2u + 1)
· (u
18
− 5u
17
+ ··· + 77u − 23)(u
18
− 3u
17
+ ··· + 3241u + 1303)
c
7
, c
9
u
9
(u
9
− u
8
+ ··· + u + 1)(u
18
+ u
17
+ ··· + u − 1)
· (u
18
+ u
17
+ ··· + 1024u + 512)
c
12
(u
9
− 3u
8
+ 3u
7
+ 2u
6
+ u
5
+ 9u
4
+ 3u
3
+ 2u + 1)
· (u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
18
− 3u
17
+ ··· + 517u − 1)(u
18
+ 4u
17
+ ··· + 1179u − 199)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
9
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
18
+ 38y
17
+ ··· − 206y + 1)(y
18
+ 41y
17
+ ··· − 47y + 1)
c
2
, c
4
, c
8
c
10
(y − 1)
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
18
− 11y
17
+ ··· − 3y + 1)(y
18
+ 10y
17
+ ··· − 18y + 1)
c
3
, c
7
, c
9
y
9
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
18
+ 21y
17
+ ··· − 7y + 1)(y
18
+ 39y
17
+ ··· − 262144y + 262144)
c
5
, c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ y
5
− 31y
4
− 24y
3
+ 6y
2
+ 9y − 1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
2
· (y
18
+ 13y
17
+ ··· − 43y + 1)
c
6
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
9
+ 6y
8
+ ··· + 24y − 1)(y
18
+ y
17
+ ··· − 5331y + 529)
· (y
18
+ 33y
17
+ ··· − 7027677y + 1697809)
c
12
(y
9
− 3y
8
+ 23y
7
+ 62y
6
− 13y
5
− 57y
4
+ 9y
3
− 6y
2
+ 4y − 1)
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
18
+ 29y
17
+ ··· − 268915y + 1)
· (y
18
+ 40y
17
+ ··· − 5352529y + 39601)
23
