12a
0093
(K12a
0093
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 4 12 1 6 7 9
Solving Sequence
5,10
6 11
3,7
2 1 4 8 9 12
c
5
c
10
c
6
c
2
c
1
c
4
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.70075 × 10
79
u
71
− 3.81232 × 10
79
u
70
+ ··· + 7.87156 × 10
79
b + 2.01580 × 10
80
,
− 2.44050 × 10
79
u
71
+ 6.22842 × 10
79
u
70
+ ··· + 1.57431 × 10
80
a − 3.01318 × 10
80
,
u
72
− 2u
71
+ ··· + 24u + 8i
I
u
2
= h−4a
2
u + 2a
2
+ 4au + 7b + 12a − 6u − 4, 4a
3
− 6a
2
u − 8a
2
+ 2au + 8a − u − 2, u
2
− 2i
I
u
3
= hb + 1, −u
2
+ a + u + 2, u
3
− u
2
− 2u + 1i
I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 84 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
= h3.70 × 10
79
u
71
− 3.81 × 10
79
u
70
+ · · · + 7.87 × 10
79
b + 2.02 ×
10
80
, −2.44 × 10
79
u
71
+ 6.23 × 10
79
u
70
+ · · · + 1.57 × 10
80
a − 3.01 ×
10
80
, u
72
− 2u
71
+ · · · + 24u + 8i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
11
=
−u
−u
3
+ u
a
3
=
0.155020u
71
− 0.395628u
70
+ ··· − 37.7884u + 1.91396
−0.470142u
71
+ 0.484315u
70
+ ··· + 4.00972u − 2.56087
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−0.315123u
71
+ 0.0886872u
70
+ ··· − 33.7787u − 0.646903
−0.470142u
71
+ 0.484315u
70
+ ··· + 4.00972u − 2.56087
a
1
=
1.73551u
71
− 3.17752u
70
+ ··· − 2.59470u + 17.5888
−2.40461u
71
+ 2.78349u
70
+ ··· + 14.3590u − 6.88864
a
4
=
0.485716u
71
− 1.14719u
70
+ ··· − 26.7644u + 3.00194
−0.981957u
71
+ 1.07115u
70
+ ··· + 3.98093u − 0.323764
a
8
=
−0.556973u
71
+ 1.35772u
70
+ ··· − 20.8031u − 10.0464
−0.333969u
71
− 1.38159u
70
+ ··· + 31.1725u + 18.7963
a
9
=
0.363304u
71
− 1.99774u
70
+ ··· + 35.4662u + 20.3509
0.618338u
71
+ 1.54449u
70
+ ··· − 40.5582u − 23.2300
a
12
=
u
3
− 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.63154u
71
− 8.59389u
70
+ ··· − 116.925u − 7.71745
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
72
+ 37u
71
+ ··· + 107u + 1
c
2
, c
4
u
72
− 7u
71
+ ··· + 5u + 1
c
3
, c
7
u
72
+ 2u
71
+ ··· + 36u − 8
c
5
, c
6
, c
10
c
11
u
72
− 2u
71
+ ··· + 24u + 8
c
8
, c
9
, c
12
u
72
+ 5u
71
+ ··· + 41u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
72
+ 3y
71
+ ··· − 8427y + 1
c
2
, c
4
y
72
− 37y
71
+ ··· − 107y + 1
c
3
, c
7
y
72
+ 30y
71
+ ··· − 3280y + 64
c
5
, c
6
, c
10
c
11
y
72
− 88y
71
+ ··· − 2752y + 64
c
8
, c
9
, c
12
y
72
− 73y
71
+ ··· + 1707y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.875758 + 0.429272I
a = 0.262678 + 0.101583I
b = −1.287090 − 0.279824I
−8.31181 + 2.46798I 0
u = −0.875758 − 0.429272I
a = 0.262678 − 0.101583I
b = −1.287090 + 0.279824I
−8.31181 − 2.46798I 0
u = 0.827261 + 0.504621I
a = 0.09772 + 2.12500I
b = −1.121890 − 0.521031I
−7.76669 − 5.28143I 0
u = 0.827261 − 0.504621I
a = 0.09772 − 2.12500I
b = −1.121890 + 0.521031I
−7.76669 + 5.28143I 0
u = −0.799643 + 0.671253I
a = 0.06752 + 1.80494I
b = 1.205120 − 0.572281I
−6.25612 + 11.79520I 0
u = −0.799643 − 0.671253I
a = 0.06752 − 1.80494I
b = 1.205120 + 0.572281I
−6.25612 − 11.79520I 0
u = −0.744414 + 0.572251I
a = −0.652228 − 1.062510I
b = 0.233482 + 0.906675I
−3.31502 + 6.41563I 0
u = −0.744414 − 0.572251I
a = −0.652228 + 1.062510I
b = 0.233482 − 0.906675I
−3.31502 − 6.41563I 0
u = 0.786461 + 0.477851I
a = 0.68942 − 1.66417I
b = 1.084140 + 0.564418I
0.01076 − 7.70106I 0
u = 0.786461 − 0.477851I
a = 0.68942 + 1.66417I
b = 1.084140 − 0.564418I
0.01076 + 7.70106I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.857434 + 0.264670I
a = 1.02566 − 1.10598I
b = −0.327725 + 0.634372I
−5.42751 − 0.70274I 0
u = 0.857434 − 0.264670I
a = 1.02566 + 1.10598I
b = −0.327725 − 0.634372I
−5.42751 + 0.70274I 0
u = −0.879575 + 0.163473I
a = 1.027390 + 0.651113I
b = 0.950405 − 0.535597I
−0.97750 + 2.84413I 0
u = −0.879575 − 0.163473I
a = 1.027390 − 0.651113I
b = 0.950405 + 0.535597I
−0.97750 − 2.84413I 0
u = −0.199773 + 0.851046I
a = −0.996478 − 0.881875I
b = 1.147690 + 0.510260I
−4.44972 − 6.76334I −12.00000 + 0.I
u = −0.199773 − 0.851046I
a = −0.996478 + 0.881875I
b = 1.147690 − 0.510260I
−4.44972 + 6.76334I −12.00000 + 0.I
u = 0.626406 + 0.476151I
a = −0.717312 + 0.408958I
b = 0.380216 − 0.718908I
2.05866 − 2.81348I −9.50002 + 4.98668I
u = 0.626406 − 0.476151I
a = −0.717312 − 0.408958I
b = 0.380216 + 0.718908I
2.05866 + 2.81348I −9.50002 − 4.98668I
u = 1.181710 + 0.470204I
a = −0.1216000 − 0.0229142I
b = 1.094920 − 0.394215I
−8.72689 + 2.18989I 0
u = 1.181710 − 0.470204I
a = −0.1216000 + 0.0229142I
b = 1.094920 + 0.394215I
−8.72689 − 2.18989I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.611935 + 0.376277I
a = −0.283350 + 0.621830I
b = 0.649429 + 0.513270I
−0.07524 − 1.41658I −12.97255 + 1.10740I
u = −0.611935 − 0.376277I
a = −0.283350 − 0.621830I
b = 0.649429 − 0.513270I
−0.07524 + 1.41658I −12.97255 − 1.10740I
u = −0.214744 + 0.682258I
a = 0.40025 + 1.69752I
b = 0.197456 − 0.697303I
−1.72777 − 2.16585I −11.52549 + 1.08940I
u = −0.214744 − 0.682258I
a = 0.40025 − 1.69752I
b = 0.197456 + 0.697303I
−1.72777 + 2.16585I −11.52549 − 1.08940I
u = 0.054234 + 0.691316I
a = 1.57683 − 1.56133I
b = −1.142460 + 0.370676I
−5.43584 + 1.26277I −16.3916 − 0.1881I
u = 0.054234 − 0.691316I
a = 1.57683 + 1.56133I
b = −1.142460 − 0.370676I
−5.43584 − 1.26277I −16.3916 + 0.1881I
u = −0.617110 + 0.307371I
a = −0.59785 − 2.50870I
b = −0.986315 + 0.384932I
−2.03116 + 2.58391I −16.3746 − 6.6287I
u = −0.617110 − 0.307371I
a = −0.59785 + 2.50870I
b = −0.986315 − 0.384932I
−2.03116 − 2.58391I −16.3746 + 6.6287I
u = 0.276521 + 0.561410I
a = −0.19398 − 1.44729I
b = 0.600878 + 0.650005I
3.08581 − 0.76384I −6.34873 + 2.59077I
u = 0.276521 − 0.561410I
a = −0.19398 + 1.44729I
b = 0.600878 − 0.650005I
3.08581 + 0.76384I −6.34873 − 2.59077I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.396880 + 0.035985I
a = 0.186911 + 0.763642I
b = 0.831473 − 0.725123I
−1.87165 + 2.75314I 0
u = −1.396880 − 0.035985I
a = 0.186911 − 0.763642I
b = 0.831473 + 0.725123I
−1.87165 − 2.75314I 0
u = −1.40156
a = 11.4734
b = −0.988970
−8.19953 0
u = 0.092090 + 0.573260I
a = −0.770057 + 1.161670I
b = 0.953023 − 0.598994I
2.06822 + 4.08017I −7.94616 − 5.26935I
u = 0.092090 − 0.573260I
a = −0.770057 − 1.161670I
b = 0.953023 + 0.598994I
2.06822 − 4.08017I −7.94616 + 5.26935I
u = 0.550545 + 0.163361I
a = −1.57695 + 0.17909I
b = −1.110070 + 0.163246I
−2.56966 − 0.57818I −16.8714 + 8.9218I
u = 0.550545 − 0.163361I
a = −1.57695 − 0.17909I
b = −1.110070 − 0.163246I
−2.56966 + 0.57818I −16.8714 − 8.9218I
u = 1.42095 + 0.21273I
a = 0.542378 − 0.597190I
b = 0.590617 + 0.161261I
−6.67741 − 0.58823I 0
u = 1.42095 − 0.21273I
a = 0.542378 + 0.597190I
b = 0.590617 − 0.161261I
−6.67741 + 0.58823I 0
u = 1.47025
a = 0.911193
b = −0.327218
−6.78796 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.481111 + 0.095743I
a = −0.79648 + 1.70877I
b = 0.865855 − 0.831513I
0.90495 + 3.07172I −20.6395 − 5.9253I
u = −0.481111 − 0.095743I
a = −0.79648 − 1.70877I
b = 0.865855 + 0.831513I
0.90495 − 3.07172I −20.6395 + 5.9253I
u = 1.53498 + 0.03198I
a = 0.438335 + 0.164331I
b = −0.058233 − 0.496424I
−6.93072 − 0.11771I 0
u = 1.53498 − 0.03198I
a = 0.438335 − 0.164331I
b = −0.058233 + 0.496424I
−6.93072 + 0.11771I 0
u = 1.58385 + 0.02369I
a = −0.055937 − 0.975650I
b = 0.910185 + 0.970380I
−6.39453 − 3.47846I 0
u = 1.58385 − 0.02369I
a = −0.055937 + 0.975650I
b = 0.910185 − 0.970380I
−6.39453 + 3.47846I 0
u = −1.58359 + 0.12100I
a = −0.233603 − 0.250046I
b = 0.219437 + 0.848024I
−5.41979 + 4.93889I 0
u = −1.58359 − 0.12100I
a = −0.233603 + 0.250046I
b = 0.219437 − 0.848024I
−5.41979 − 4.93889I 0
u = −1.58812 + 0.03042I
a = −1.228490 + 0.430142I
b = −1.230760 − 0.307392I
−10.01110 + 1.19025I 0
u = −1.58812 − 0.03042I
a = −1.228490 − 0.430142I
b = −1.230760 + 0.307392I
−10.01110 − 1.19025I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59443 + 0.07004I
a = −0.95915 + 1.33782I
b = −1.126480 − 0.469683I
−9.64311 − 3.88422I 0
u = 1.59443 − 0.07004I
a = −0.95915 − 1.33782I
b = −1.126480 + 0.469683I
−9.64311 + 3.88422I 0
u = −0.395087
a = 0.927031
b = −0.104752
−0.588530 −16.7510
u = −0.221019 + 0.289419I
a = 2.12036 + 0.93378I
b = −0.778490 − 0.216174I
−0.944244 − 0.257791I −11.16562 − 1.59535I
u = −0.221019 − 0.289419I
a = 2.12036 − 0.93378I
b = −0.778490 + 0.216174I
−0.944244 + 0.257791I −11.16562 + 1.59535I
u = 1.62768 + 0.17150I
a = −0.431502 + 0.570990I
b = 0.243814 − 1.044500I
−11.3658 − 9.2318I 0
u = 1.62768 − 0.17150I
a = −0.431502 − 0.570990I
b = 0.243814 + 1.044500I
−11.3658 + 9.2318I 0
u = −1.64174 + 0.14153I
a = 0.96072 + 1.05427I
b = 1.188910 − 0.551097I
−8.31688 + 10.07720I 0
u = −1.64174 − 0.14153I
a = 0.96072 − 1.05427I
b = 1.188910 + 0.551097I
−8.31688 − 10.07720I 0
u = −1.64839 + 0.08124I
a = 0.477835 + 0.762351I
b = −0.442405 − 0.890711I
−14.0714 + 2.0898I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.64839 − 0.08124I
a = 0.477835 − 0.762351I
b = −0.442405 + 0.890711I
−14.0714 − 2.0898I 0
u = −1.65163 + 0.14342I
a = −0.41603 − 1.43600I
b = −1.153970 + 0.638956I
−16.2646 + 7.7641I 0
u = −1.65163 − 0.14342I
a = −0.41603 + 1.43600I
b = −1.153970 − 0.638956I
−16.2646 − 7.7641I 0
u = 1.64915 + 0.20871I
a = 0.65126 − 1.32967I
b = 1.260260 + 0.616858I
−14.5211 − 15.1783I 0
u = 1.64915 − 0.20871I
a = 0.65126 + 1.32967I
b = 1.260260 − 0.616858I
−14.5211 + 15.1783I 0
u = 1.65979 + 0.11678I
a = −0.486333 − 0.039718I
b = −1.41864 + 0.27823I
−17.0477 − 4.5612I 0
u = 1.65979 − 0.11678I
a = −0.486333 + 0.039718I
b = −1.41864 − 0.27823I
−17.0477 + 4.5612I 0
u = 1.66435 + 0.06433I
a = 1.010600 − 0.515375I
b = 1.126480 + 0.439828I
−9.85240 − 3.84777I 0
u = 1.66435 − 0.06433I
a = 1.010600 + 0.515375I
b = 1.126480 − 0.439828I
−9.85240 + 3.84777I 0
u = 0.229806
a = −13.4178
b = −0.871083
−2.90601 −61.9330
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.78412 + 0.04723I
a = 0.534525 − 0.028315I
b = 1.096760 + 0.161668I
−19.6154 − 0.2070I 0
u = −1.78412 − 0.04723I
a = 0.534525 + 0.028315I
b = 1.096760 − 0.161668I
−19.6154 + 0.2070I 0
12
II. I
u
2
=
h−4a
2
u+2a
2
+4au+7b+12a−6u−4, 4a
3
−6a
2
u−8a
2
+2au+8a−u−2, u
2
−2i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
2
a
11
=
−u
−u
a
3
=
a
4
7
a
2
u −
4
7
au + ··· −
12
7
a +
4
7
a
7
=
−1
0
a
2
=
4
7
a
2
u −
4
7
au + ··· −
5
7
a +
4
7
4
7
a
2
u −
4
7
au + ··· −
12
7
a +
4
7
a
1
=
1
2
u
2
7
a
2
u +
5
7
au + ··· +
8
7
a +
2
7
a
4
=
−
3
7
a
2
u +
10
7
au + ··· +
16
7
a −
3
7
−
2
7
a
2
u +
9
7
au + ··· +
20
7
a −
9
7
a
8
=
1
2
u
2
7
a
2
u +
5
7
au + ··· +
8
7
a +
2
7
a
9
=
1
2
u
2
7
a
2
u +
5
7
au + ··· +
8
7
a +
2
7
a
12
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16
7
a
2
u −
8
7
a
2
−
16
7
au −
48
7
a +
24
7
u −
124
7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
(u
3
+ u
2
+ 2u + 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
10
c
11
(u
2
− 2)
3
c
8
, c
9
(u + 1)
6
c
12
(u − 1)
6
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
10
c
11
(y −2)
6
c
8
, c
9
, c
12
(y −1)
6
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 0.361309 + 0.347270I
b = 0.877439 − 0.744862I
−3.55561 + 2.82812I −16.4902 − 2.9794I
u = 1.41421
a = 0.361309 − 0.347270I
b = 0.877439 + 0.744862I
−3.55561 − 2.82812I −16.4902 + 2.9794I
u = 1.41421
a = 3.39870
b = −0.754878
−7.69319 −23.0200
u = −1.41421
a = −0.116187 + 1.142450I
b = 0.877439 − 0.744862I
−3.55561 + 2.82812I −16.4902 − 2.9794I
u = −1.41421
a = −0.116187 − 1.142450I
b = 0.877439 + 0.744862I
−3.55561 − 2.82812I −16.4902 + 2.9794I
u = −1.41421
a = 0.111054
b = −0.754878
−7.69319 −23.0200
16
III. I
u
3
= hb + 1, −u
2
+ a + u + 2, u
3
− u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
11
=
−u
−u
2
− u + 1
a
3
=
u
2
− u − 2
−1
a
7
=
−u
2
+ 1
−u
2
− u + 1
a
2
=
u
2
− u − 3
−1
a
1
=
−1
0
a
4
=
u
2
− u − 2
−1
a
8
=
−u
2
+ 1
−u
2
− u + 1
a
9
=
u
u
a
12
=
u
2
− 1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
2
+ 4u − 16
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
8
c
9
u
3
− u
2
− 2u + 1
c
10
, c
11
, c
12
u
3
+ u
2
− 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
8
c
9
, c
10
, c
11
c
12
y
3
− 5y
2
+ 6y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24698
a = 0.801938
b = −1.00000
−7.98968 −19.4330
u = 0.445042
a = −2.24698
b = −1.00000
−2.34991 −14.0220
u = 1.80194
a = −0.554958
b = −1.00000
−19.2692 −5.54530
20
IV. I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
6
=
1
0
a
11
=
v
0
a
3
=
0
v
2
+ 3v − 1
a
7
=
1
0
a
2
=
v
2
+ 3v − 1
v
2
+ 3v − 1
a
1
=
v
2
+ 3v − 1
−v
2
− 2v + 3
a
4
=
−2v
2
− 5v + 4
−2v
2
− 5v + 3
a
8
=
−v
2
− 3v + 1
v
2
+ 2v − 3
a
9
=
−v
2
− 2v + 1
v
2
+ 2v − 3
a
12
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2v − 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
, c
10
c
11
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
(u − 1)
3
c
12
(u + 1)
3
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
y
3
− y
2
+ 2y − 1
c
5
, c
6
, c
10
c
11
y
3
c
8
, c
9
, c
12
(y − 1)
3
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.539798 + 0.182582I
a = 0
b = 0.877439 + 0.744862I
1.37919 − 2.82812I −7.07960 − 0.36516I
v = 0.539798 − 0.182582I
a = 0
b = 0.877439 − 0.744862I
1.37919 + 2.82812I −7.07960 + 0.36516I
v = −3.07960
a = 0
b = −0.754878
−2.75839 0.159190
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
3
− u
2
+ 2u − 1)
3
(u
72
+ 37u
71
+ ··· + 107u + 1)
c
2
((u − 1)
3
)(u
3
+ u
2
− 1)
3
(u
72
− 7u
71
+ ··· + 5u + 1)
c
3
u
3
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
72
+ 2u
71
+ ··· + 36u − 8)
c
4
((u + 1)
3
)(u
3
− u
2
+ 1)
3
(u
72
− 7u
71
+ ··· + 5u + 1)
c
5
, c
6
u
3
(u
2
− 2)
3
(u
3
− u
2
− 2u + 1)(u
72
− 2u
71
+ ··· + 24u + 8)
c
7
u
3
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
72
+ 2u
71
+ ··· + 36u − 8)
c
8
, c
9
((u − 1)
3
)(u + 1)
6
(u
3
− u
2
− 2u + 1)(u
72
+ 5u
71
+ ··· + 41u + 7)
c
10
, c
11
u
3
(u
2
− 2)
3
(u
3
+ u
2
− 2u − 1)(u
72
− 2u
71
+ ··· + 24u + 8)
c
12
((u − 1)
6
)(u + 1)
3
(u
3
+ u
2
− 2u − 1)(u
72
+ 5u
71
+ ··· + 41u + 7)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
3
)(y
3
+ 3y
2
+ 2y − 1)
3
(y
72
+ 3y
71
+ ··· − 8427y + 1)
c
2
, c
4
((y − 1)
3
)(y
3
− y
2
+ 2y − 1)
3
(y
72
− 37y
71
+ ··· − 107y + 1)
c
3
, c
7
y
3
(y
3
+ 3y
2
+ 2y − 1)
3
(y
72
+ 30y
71
+ ··· − 3280y + 64)
c
5
, c
6
, c
10
c
11
y
3
(y − 2)
6
(y
3
− 5y
2
+ 6y − 1)(y
72
− 88y
71
+ ··· − 2752y + 64)
c
8
, c
9
, c
12
((y − 1)
9
)(y
3
− 5y
2
+ 6y − 1)(y
72
− 73y
71
+ ··· + 1707y + 49)
26
