12n
0131
(K12n
0131
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 12 3 9 11 1 8 6 10
Solving Sequence
3,5
2 1
4,10
9 12 6 7 11 8
c
2
c
1
c
4
c
9
c
12
c
5
c
6
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.86219 × 10
101
u
65
+ 3.04230 × 10
102
u
64
+ ··· + 1.07604 × 10
101
b − 6.59997 × 10
101
,
1.26922 × 10
102
u
65
+ 1.35759 × 10
103
u
64
+ ··· + 2.15207 × 10
101
a − 2.45951 × 10
103
,
u
66
+ 11u
65
+ ··· − 184u − 1i
I
u
2
= h−2a
8
+ 3a
7
− 6a
6
+ 5a
5
− 9a
4
+ 6a
3
− 8a
2
+ b + 3a − 4, a
9
− a
8
+ 2a
7
− a
6
+ 3a
5
− a
4
+ 2a
3
+ a + 1, u − 1i
I
u
3
= hu
4
+ u
3
− u
2
+ b − 2u − 1, −u
5
− u
4
+ u
3
+ u
2
+ a − u − 1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 81 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
= h2.86 × 10
101
u
65
+ 3.04 × 10
102
u
64
+ · · · + 1.08 × 10
101
b − 6.60 ×
10
101
, 1.27 × 10
102
u
65
+ 1.36 × 10
103
u
64
+ · · · + 2.15 × 10
101
a − 2.46 ×
10
103
, u
66
+ 11u
65
+ · · · − 184u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
−5.89768u
65
− 63.0828u
64
+ ··· + 2827.10u + 114.286
−2.65994u
65
− 28.2732u
64
+ ··· + 1025.61u + 6.13360
a
9
=
−8.52453u
65
− 90.7723u
64
+ ··· + 3834.57u + 120.324
−2.57433u
65
− 27.0269u
64
+ ··· + 862.488u + 5.23234
a
12
=
−8.72655u
65
− 89.2240u
64
+ ··· + 1798.25u − 38.9602
−5.28403u
65
− 54.4051u
64
+ ··· + 1316.97u + 6.95585
a
6
=
−3.83893u
65
− 41.0224u
64
+ ··· + 1345.05u − 6.03327
−1.51701u
65
− 16.1400u
64
+ ··· + 494.366u + 2.63312
a
7
=
−5.35594u
65
− 57.1624u
64
+ ··· + 1839.41u − 3.40015
−1.51701u
65
− 16.1400u
64
+ ··· + 494.366u + 2.63312
a
11
=
13.7708u
65
+ 144.182u
64
+ ··· − 4481.24u − 77.0429
0.429501u
65
+ 4.69148u
64
+ ··· − 219.153u − 1.47738
a
8
=
−7.65340u
65
− 81.3957u
64
+ ··· + 3054.18u + 72.2685
−5.10197u
65
− 53.2822u
64
+ ··· + 1553.54u + 8.78813
(ii) Obstruction class = −1
(iii) Cusp Shapes = 7.00145u
65
+ 70.4042u
64
+ ··· − 636.383u − 12.3310
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 21u
65
+ ··· + 31524u + 1
c
2
, c
4
u
66
− 11u
65
+ ··· + 184u − 1
c
3
, c
6
u
66
+ 8u
65
+ ··· − 7168u + 512
c
5
, c
11
u
66
+ 3u
65
+ ··· − 2u − 1
c
7
u
66
+ 28u
65
+ ··· − 143u + 1
c
8
, c
10
u
66
− 8u
65
+ ··· − 11u + 1
c
9
, c
12
u
66
− 2u
65
+ ··· + 192u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 59y
65
+ ··· − 992297680y + 1
c
2
, c
4
y
66
− 21y
65
+ ··· − 31524y + 1
c
3
, c
6
y
66
− 60y
65
+ ··· − 76021760y + 262144
c
5
, c
11
y
66
+ 15y
65
+ ··· − 20y + 1
c
7
y
66
+ 28y
65
+ ··· − 12229y + 1
c
8
, c
10
y
66
− 28y
65
+ ··· + 143y + 1
c
9
, c
12
y
66
+ 42y
65
+ ··· + 77824y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00537
a = 0.406767
b = −11.0855
−2.82917 365.350
u = 0.687723 + 0.687263I
a = −1.353200 − 0.228510I
b = −1.300520 + 0.290425I
−2.23471 − 2.98196I 0
u = 0.687723 − 0.687263I
a = −1.353200 + 0.228510I
b = −1.300520 − 0.290425I
−2.23471 + 2.98196I 0
u = 1.028820 + 0.216167I
a = 0.012733 + 0.445672I
b = 0.438763 + 0.902849I
−1.91057 − 0.79816I 0
u = 1.028820 − 0.216167I
a = 0.012733 − 0.445672I
b = 0.438763 − 0.902849I
−1.91057 + 0.79816I 0
u = 0.783333 + 0.429567I
a = 2.12816 + 1.63033I
b = 2.36643 − 1.94607I
−3.21013 − 1.26950I −4.00000 + 7.64083I
u = 0.783333 − 0.429567I
a = 2.12816 − 1.63033I
b = 2.36643 + 1.94607I
−3.21013 + 1.26950I −4.00000 − 7.64083I
u = 1.125970 + 0.056995I
a = 0.023922 − 0.599547I
b = 0.36398 + 1.57344I
0.81136 + 2.64313I 0
u = 1.125970 − 0.056995I
a = 0.023922 + 0.599547I
b = 0.36398 − 1.57344I
0.81136 − 2.64313I 0
u = −0.824004 + 0.171548I
a = −1.143160 + 0.689270I
b = −0.151706 + 0.583718I
−4.86194 + 7.45999I −0.96246 − 11.41011I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.824004 − 0.171548I
a = −1.143160 − 0.689270I
b = −0.151706 − 0.583718I
−4.86194 − 7.45999I −0.96246 + 11.41011I
u = 0.515278 + 1.048940I
a = −1.36638 − 1.36297I
b = −1.375720 + 0.022642I
2.19847 − 2.32521I 0
u = 0.515278 − 1.048940I
a = −1.36638 + 1.36297I
b = −1.375720 − 0.022642I
2.19847 + 2.32521I 0
u = −0.745847 + 0.910266I
a = −1.20178 + 2.28035I
b = −2.03130 + 0.52431I
2.17496 − 0.19887I 0
u = −0.745847 − 0.910266I
a = −1.20178 − 2.28035I
b = −2.03130 − 0.52431I
2.17496 + 0.19887I 0
u = −0.760288 + 0.928501I
a = 1.67368 − 0.06126I
b = 1.88450 + 0.90427I
7.72304 − 2.79945I 0
u = −0.760288 − 0.928501I
a = 1.67368 + 0.06126I
b = 1.88450 − 0.90427I
7.72304 + 2.79945I 0
u = 0.668448 + 0.397576I
a = 0.003744 − 1.234270I
b = −1.38255 + 1.28759I
2.07274 − 4.10478I −2.27198 − 0.09641I
u = 0.668448 − 0.397576I
a = 0.003744 + 1.234270I
b = −1.38255 − 1.28759I
2.07274 + 4.10478I −2.27198 + 0.09641I
u = −0.856203 + 0.882898I
a = 0.290557 + 1.073450I
b = 0.231042 + 0.438928I
3.57906 + 2.47635I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856203 − 0.882898I
a = 0.290557 − 1.073450I
b = 0.231042 − 0.438928I
3.57906 − 2.47635I 0
u = −1.118290 + 0.517016I
a = 0.122393 − 0.353509I
b = −0.055274 − 0.183449I
−1.20228 + 5.48361I 0
u = −1.118290 − 0.517016I
a = 0.122393 + 0.353509I
b = −0.055274 + 0.183449I
−1.20228 − 5.48361I 0
u = −0.690354 + 1.028160I
a = −0.438411 − 1.018090I
b = −0.341152 − 0.391855I
4.03833 − 2.66127I 0
u = −0.690354 − 1.028160I
a = −0.438411 + 1.018090I
b = −0.341152 + 0.391855I
4.03833 + 2.66127I 0
u = 1.274370 + 0.103527I
a = 0.09874 + 1.51084I
b = 1.63942 + 2.71558I
−4.31795 − 0.78820I 0
u = 1.274370 − 0.103527I
a = 0.09874 − 1.51084I
b = 1.63942 − 2.71558I
−4.31795 + 0.78820I 0
u = −0.983683 + 0.830782I
a = 0.570504 + 0.494511I
b = 0.437347 + 0.006156I
3.17239 + 3.89822I 0
u = −0.983683 − 0.830782I
a = 0.570504 − 0.494511I
b = 0.437347 − 0.006156I
3.17239 − 3.89822I 0
u = −0.894353 + 0.951169I
a = −1.78516 + 0.28107I
b = −2.14588 − 0.82546I
9.29382 + 3.78649I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.894353 − 0.951169I
a = −1.78516 − 0.28107I
b = −2.14588 + 0.82546I
9.29382 − 3.78649I 0
u = −1.062290 + 0.802217I
a = 2.22217 − 0.70557I
b = 2.85845 + 0.87099I
1.18870 + 6.56344I 0
u = −1.062290 − 0.802217I
a = 2.22217 + 0.70557I
b = 2.85845 − 0.87099I
1.18870 − 6.56344I 0
u = −1.057290 + 0.809211I
a = −0.51219 + 1.44953I
b = −1.79007 + 0.34040I
6.78475 + 9.23321I 0
u = −1.057290 − 0.809211I
a = −0.51219 − 1.44953I
b = −1.79007 − 0.34040I
6.78475 − 9.23321I 0
u = −0.620743 + 0.209791I
a = 1.51472 − 0.44133I
b = 0.351541 − 0.610430I
−1.43375 + 2.91518I 0.46506 − 4.85019I
u = −0.620743 − 0.209791I
a = 1.51472 + 0.44133I
b = 0.351541 + 0.610430I
−1.43375 − 2.91518I 0.46506 + 4.85019I
u = −0.597235 + 0.259408I
a = −0.28543 + 1.39421I
b = −0.011224 + 0.406559I
1.17931 − 1.63015I 3.12613 + 3.30141I
u = −0.597235 − 0.259408I
a = −0.28543 − 1.39421I
b = −0.011224 − 0.406559I
1.17931 + 1.63015I 3.12613 − 3.30141I
u = −0.994697 + 0.913978I
a = 0.79592 − 1.57410I
b = 1.87674 − 0.36992I
8.98485 + 3.05406I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.994697 − 0.913978I
a = 0.79592 + 1.57410I
b = 1.87674 + 0.36992I
8.98485 − 3.05406I 0
u = 0.784334 + 1.103720I
a = 1.32414 + 1.54204I
b = 1.68117 + 0.18497I
1.02644 − 7.74901I 0
u = 0.784334 − 1.103720I
a = 1.32414 − 1.54204I
b = 1.68117 − 0.18497I
1.02644 + 7.74901I 0
u = −0.634943 + 0.050863I
a = −1.58118 − 0.94089I
b = −0.349515 − 0.878817I
−5.23148 + 1.44469I −2.19147 − 1.36304I
u = −0.634943 − 0.050863I
a = −1.58118 + 0.94089I
b = −0.349515 + 0.878817I
−5.23148 − 1.44469I −2.19147 + 1.36304I
u = 0.601289 + 0.105594I
a = 0.258323 + 0.970497I
b = 1.215100 − 0.178401I
−1.82059 + 0.01526I −7.87182 − 0.48568I
u = 0.601289 − 0.105594I
a = 0.258323 − 0.970497I
b = 1.215100 + 0.178401I
−1.82059 − 0.01526I −7.87182 + 0.48568I
u = −1.127320 + 0.826259I
a = −0.431491 − 0.571092I
b = −0.399530 − 0.114576I
2.66554 + 9.42263I 0
u = −1.127320 − 0.826259I
a = −0.431491 + 0.571092I
b = −0.399530 + 0.114576I
2.66554 − 9.42263I 0
u = −0.147109 + 0.577451I
a = −1.41532 − 0.01491I
b = −0.366040 + 0.326712I
1.31523 − 1.27199I 3.06090 + 2.68907I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.147109 − 0.577451I
a = −1.41532 + 0.01491I
b = −0.366040 − 0.326712I
1.31523 + 1.27199I 3.06090 − 2.68907I
u = −0.723739 + 1.209940I
a = 1.67771 − 1.53567I
b = 2.06140 − 0.32997I
9.83371 − 2.67210I 0
u = −0.723739 − 1.209940I
a = 1.67771 + 1.53567I
b = 2.06140 + 0.32997I
9.83371 + 2.67210I 0
u = 0.411231 + 0.411306I
a = 0.32779 + 1.74947I
b = 0.97919 − 1.06319I
2.74552 + 1.51786I −0.89722 − 4.70084I
u = 0.411231 − 0.411306I
a = 0.32779 − 1.74947I
b = 0.97919 + 1.06319I
2.74552 − 1.51786I −0.89722 + 4.70084I
u = −0.60092 + 1.28586I
a = −1.89989 + 1.40726I
b = −2.07450 + 0.29742I
8.19227 − 8.99833I 0
u = −0.60092 − 1.28586I
a = −1.89989 − 1.40726I
b = −2.07450 − 0.29742I
8.19227 + 8.99833I 0
u = −1.19778 + 0.88601I
a = −1.78025 + 0.89840I
b = −2.69078 − 0.32973I
8.24876 + 10.14770I 0
u = −1.19778 − 0.88601I
a = −1.78025 − 0.89840I
b = −2.69078 + 0.32973I
8.24876 − 10.14770I 0
u = −1.26526 + 0.84227I
a = 1.68547 − 1.04922I
b = 2.75955 + 0.13511I
5.9981 + 16.5072I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.26526 − 0.84227I
a = 1.68547 + 1.04922I
b = 2.75955 − 0.13511I
5.9981 − 16.5072I 0
u = 1.42330 + 0.57117I
a = −0.920325 + 0.724904I
b = −1.27403 + 1.04616I
−1.42259 + 0.46359I 0
u = 1.42330 − 0.57117I
a = −0.920325 − 0.724904I
b = −1.27403 − 1.04616I
−1.42259 − 0.46359I 0
u = 1.59839 + 0.34758I
a = 0.832676 − 0.993612I
b = 1.38737 − 1.32476I
−1.87995 − 4.31692I 0
u = 1.59839 − 0.34758I
a = 0.832676 + 0.993612I
b = 1.38737 + 1.32476I
−1.87995 + 4.31692I 0
u = −0.00563429
a = 98.6949
b = 0.501097
−1.20362 −8.91660
11
II.
I
u
2
= h−2a
8
+b +· · · +3a −4, a
9
−a
8
+2a
7
−a
6
+3a
5
−a
4
+2a
3
+a +1, u −1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
4
=
1
0
a
10
=
a
2a
8
− 3a
7
+ 6a
6
− 5a
5
+ 9a
4
− 6a
3
+ 8a
2
− 3a + 4
a
9
=
a
2a
8
− 3a
7
+ 6a
6
− 5a
5
+ 9a
4
− 6a
3
+ 8a
2
− 4a + 4
a
12
=
−a
2
a
8
− 2a
7
+ 3a
6
− 3a
5
+ 4a
4
− 4a
3
+ 3a
2
− 2a + 1
a
6
=
a
4
0
a
7
=
a
4
0
a
11
=
−a
6
− a
2
a
8
− 2a
7
+ 3a
6
− 3a
5
+ 4a
4
− 4a
3
+ 3a
2
− 2a + 1
a
8
=
−a
6
− a
2
a
8
− 2a
7
+ 4a
6
− 3a
5
+ 6a
4
− 4a
3
+ 6a
2
− 2a + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −45a
8
+ 71a
7
−127a
6
+ 112a
5
−192a
4
+ 149a
3
−165a
2
+ 83a −97
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
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
7
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
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
c
12
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
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
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.140343 + 0.966856I
b = −0.302374 + 0.039314I
0.13850 + 2.09337I −4.31028 − 3.82038I
u = 1.00000
a = −0.140343 − 0.966856I
b = −0.302374 − 0.039314I
0.13850 − 2.09337I −4.31028 + 3.82038I
u = 1.00000
a = −0.628449 + 0.875112I
b = −0.223063 + 0.988364I
−2.26187 + 2.45442I −6.95900 − 1.69416I
u = 1.00000
a = −0.628449 − 0.875112I
b = −0.223063 − 0.988364I
−2.26187 − 2.45442I −6.95900 + 1.69416I
u = 1.00000
a = 0.796005 + 0.733148I
b = −0.194585 + 1.248300I
−6.01628 + 1.33617I −13.56769 − 0.26615I
u = 1.00000
a = 0.796005 − 0.733148I
b = −0.194585 − 1.248300I
−6.01628 − 1.33617I −13.56769 + 0.26615I
u = 1.00000
a = 0.728966 + 0.986295I
b = 0.026651 + 0.835796I
−5.24306 − 7.08493I −11.54551 + 1.34000I
u = 1.00000
a = 0.728966 − 0.986295I
b = 0.026651 − 0.835796I
−5.24306 + 7.08493I −11.54551 − 1.34000I
u = 1.00000
a = −0.512358
b = 9.38674
−2.84338 −223.240
15
III. I
u
3
=
hu
4
+u
3
−u
2
+b−2u−1, −u
5
−u
4
+u
3
+u
2
+a−u−1, u
6
+u
5
−u
4
−2u
3
+u+1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
u
5
+ u
4
− u
3
− u
2
+ u + 1
−u
4
− u
3
+ u
2
+ 2u + 1
a
9
=
u
5
+ u
4
− u
3
− u
2
+ u + 1
−u
4
− u
3
+ u
2
+ 2u + 1
a
12
=
−u
2
+ 1
−u
2
a
6
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
7
=
2u
5
− 3u
3
+ 2u
u
5
− u
3
+ u
a
11
=
−2u
5
+ 3u
3
− 2u
−u
5
+ u
3
− u
a
8
=
3u
5
+ u
4
− 4u
3
− u
2
+ 3u + 1
u
5
− u
4
− 2u
3
+ u
2
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
5
+ u
4
− u
3
− 2u
2
− 3u − 7
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
6
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
7
, c
8
(u − 1)
6
c
9
, c
12
u
6
c
10
(u + 1)
6
c
11
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
6
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
7
, c
8
, c
10
(y −1)
6
c
9
, c
12
y
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 1.00126 + 1.15863I
b = 2.68739 − 0.76772I
−3.53554 − 0.92430I −12.60470 − 5.55069I
u = 1.002190 − 0.295542I
a = 1.00126 − 1.15863I
b = 2.68739 + 0.76772I
−3.53554 + 0.92430I −12.60470 + 5.55069I
u = −0.428243 + 0.664531I
a = −0.001257 + 1.158630I
b = −0.346225 + 0.393823I
0.245672 − 0.924305I −5.68949 + 0.25702I
u = −0.428243 − 0.664531I
a = −0.001257 − 1.158630I
b = −0.346225 − 0.393823I
0.245672 + 0.924305I −5.68949 − 0.25702I
u = −1.073950 + 0.558752I
a = 0.500000 − 0.260139I
b = 0.658836 + 0.177500I
−1.64493 + 5.69302I −11.7058 − 8.3306I
u = −1.073950 − 0.558752I
a = 0.500000 + 0.260139I
b = 0.658836 − 0.177500I
−1.64493 − 5.69302I −11.7058 + 8.3306I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
66
+ 21u
65
+ ··· + 31524u + 1)
c
2
((u − 1)
9
)(u
6
+ u
5
+ ··· + u + 1)(u
66
− 11u
65
+ ··· + 184u − 1)
c
3
u
9
(u
6
− u
5
+ ··· − u + 1)(u
66
+ 8u
65
+ ··· − 7168u + 512)
c
4
((u + 1)
9
)(u
6
− u
5
+ ··· − u + 1)(u
66
− 11u
65
+ ··· + 184u − 1)
c
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
66
+ 3u
65
+ ··· − 2u − 1)
c
6
u
9
(u
6
+ u
5
+ ··· + u + 1)(u
66
+ 8u
65
+ ··· − 7168u + 512)
c
7
(u − 1)
6
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
66
+ 28u
65
+ ··· − 143u + 1)
c
8
(u − 1)
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
66
− 8u
65
+ ··· − 11u + 1)
c
9
u
6
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
66
− 2u
65
+ ··· + 192u + 64)
c
10
(u + 1)
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
66
− 8u
65
+ ··· − 11u + 1)
c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
66
+ 3u
65
+ ··· − 2u − 1)
c
12
u
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
66
− 2u
65
+ ··· + 192u + 64)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
66
+ 59y
65
+ ··· − 992297680y + 1)
c
2
, c
4
(y −1)
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
66
− 21y
65
+ ··· − 31524y + 1)
c
3
, c
6
y
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
66
− 60y
65
+ ··· − 76021760y + 262144)
c
5
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
66
+ 15y
65
+ ··· − 20y + 1)
c
7
(y −1)
6
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
66
+ 28y
65
+ ··· − 12229y + 1)
c
8
, c
10
(y −1)
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
66
− 28y
65
+ ··· + 143y + 1)
c
9
, c
12
y
6
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
66
+ 42y
65
+ ··· + 77824y + 4096)
21
