12a
0882
(K12a
0882
)
A knot diagram
1
Linearized knot diagam
4 6 7 10 3 2 11 12 1 5 9 8
Solving Sequence
8,12
9
1,4
2 10 5 11 7 3 6
c
8
c
12
c
1
c
9
c
4
c
11
c
7
c
3
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4u
74
− 16u
73
+ ··· + 4b − 5, −u
74
+ 8u
73
+ ··· + 4a + 13, u
75
− 4u
74
+ ··· − 6u + 1i
I
u
2
= hu
2
a + b + a, u
2
a + a
2
+ u
2
+ a + u + 1, u
3
+ u
2
+ 2u + 1i
I
u
3
= h−u
3
+ b − u, a + u, u
7
+ 3u
5
+ 2u
3
− u − 1i
I
u
4
= hu
2
+ b + u + 1, a + u, u
3
+ u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 91 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
=
h4u
74
−16u
73
+· · ·+4b−5, −u
74
+8u
73
+· · ·+4a+13, u
75
−4u
74
+· · ·−6u+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
4
=
1
4
u
74
− 2u
73
+ ··· +
65
4
u −
13
4
−u
74
+ 4u
73
+ ··· − 4u +
5
4
a
2
=
1
4
u
74
−
3
4
u
73
+ ··· + 7u +
3
4
−
1
4
u
74
+ u
73
+ ··· −
9
4
u +
1
2
a
10
=
−u
4
− u
2
+ 1
−u
4
− 2u
2
a
5
=
15
4
u
74
− 10u
73
+ ··· +
23
4
u −
3
4
2u
74
− u
73
+ ··· − 8u +
7
4
a
11
=
−u
u
3
+ u
a
7
=
−u
4
− u
2
+ 1
u
6
+ 2u
4
+ u
2
a
3
=
13
4
u
74
−
55
4
u
73
+ ··· +
53
2
u −
17
4
u
74
−
15
4
u
73
+ ··· −
11
4
u +
5
4
a
6
=
−u
74
+
19
4
u
73
+ ··· −
7
4
u +
3
4
−
3
4
u
74
+ 3u
73
+ ··· +
9
4
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
9
2
u
74
+
19
2
u
73
+ ··· −
39
2
u −
9
4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
75
− 14u
74
+ ··· + 204u + 801
c
2
, c
5
, c
6
u
75
− 4u
74
+ ··· + 10u − 1
c
3
u
75
+ 4u
74
+ ··· + 2274u − 153
c
4
, c
10
u
75
+ 6u
74
+ ··· − 3072u − 512
c
7
, c
9
u
75
− 4u
74
+ ··· − 750u − 153
c
8
, c
11
, c
12
u
75
+ 4u
74
+ ··· − 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
75
+ 42y
74
+ ··· + 136940526y −641601
c
2
, c
5
, c
6
y
75
+ 70y
74
+ ··· + 34y −1
c
3
y
75
+ 14y
74
+ ··· + 593622y −23409
c
4
, c
10
y
75
− 42y
74
+ ··· + 3276800y −262144
c
7
, c
9
y
75
− 58y
74
+ ··· − 431082y −23409
c
8
, c
11
, c
12
y
75
+ 62y
74
+ ··· − 14y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.129331 + 1.117110I
a = 0.29237 − 1.85419I
b = 0.11903 − 1.46059I
1.67101 − 2.28476I 0
u = −0.129331 − 1.117110I
a = 0.29237 + 1.85419I
b = 0.11903 + 1.46059I
1.67101 + 2.28476I 0
u = 0.864283 + 0.073603I
a = −0.630215 − 0.318792I
b = −0.46463 − 1.50057I
14.07080 + 0.97614I 11.89444 − 0.69772I
u = 0.864283 − 0.073603I
a = −0.630215 + 0.318792I
b = −0.46463 + 1.50057I
14.07080 − 0.97614I 11.89444 + 0.69772I
u = 0.851962 + 0.130511I
a = 0.189706 + 0.407751I
b = −0.20536 + 2.41576I
12.0915 + 11.1738I 9.92293 − 6.69276I
u = 0.851962 − 0.130511I
a = 0.189706 − 0.407751I
b = −0.20536 − 2.41576I
12.0915 − 11.1738I 9.92293 + 6.69276I
u = 0.838542 + 0.118303I
a = −0.263667 − 0.275157I
b = 0.30731 − 2.10324I
6.28260 + 7.50607I 6.31085 − 6.58507I
u = 0.838542 − 0.118303I
a = −0.263667 + 0.275157I
b = 0.30731 + 2.10324I
6.28260 − 7.50607I 6.31085 + 6.58507I
u = 0.834761 + 0.091281I
a = 0.443254 + 0.200964I
b = −0.17545 + 1.64029I
7.24740 + 3.22206I 8.45543 − 0.86065I
u = 0.834761 − 0.091281I
a = 0.443254 − 0.200964I
b = −0.17545 − 1.64029I
7.24740 − 3.22206I 8.45543 + 0.86065I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.806243 + 0.042985I
a = 0.254905 + 0.770452I
b = 0.64512 + 2.35548I
8.28866 − 4.61277I 9.57496 + 3.37665I
u = −0.806243 − 0.042985I
a = 0.254905 − 0.770452I
b = 0.64512 − 2.35548I
8.28866 + 4.61277I 9.57496 − 3.37665I
u = 0.417667 + 1.122760I
a = 2.24416 − 1.33147I
b = 0.82696 − 1.40165I
9.05288 − 6.61172I 0
u = 0.417667 − 1.122760I
a = 2.24416 + 1.33147I
b = 0.82696 + 1.40165I
9.05288 + 6.61172I 0
u = 0.394262 + 1.136570I
a = −1.88247 + 1.23446I
b = −0.590542 + 1.186780I
3.16758 − 3.06037I 0
u = 0.394262 − 1.136570I
a = −1.88247 − 1.23446I
b = −0.590542 − 1.186780I
3.16758 + 3.06037I 0
u = −0.767081 + 0.032918I
a = −0.147823 − 0.586406I
b = −0.41161 − 1.84908I
2.54564 − 1.71234I 5.68970 + 3.98160I
u = −0.767081 − 0.032918I
a = −0.147823 + 0.586406I
b = −0.41161 + 1.84908I
2.54564 + 1.71234I 5.68970 − 3.98160I
u = 0.387354 + 1.172960I
a = 1.54778 − 0.81015I
b = 0.496497 − 0.735271I
3.93329 + 1.17961I 0
u = 0.387354 − 1.172960I
a = 1.54778 + 0.81015I
b = 0.496497 + 0.735271I
3.93329 − 1.17961I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.761899 + 0.044601I
a = 0.670042 − 0.120108I
b = −1.140900 + 0.673722I
5.34357 + 3.86193I 9.73760 − 4.61433I
u = 0.761899 − 0.044601I
a = 0.670042 + 0.120108I
b = −1.140900 − 0.673722I
5.34357 − 3.86193I 9.73760 + 4.61433I
u = −0.502648 + 0.555980I
a = 1.35292 − 0.76273I
b = 0.424196 + 0.870841I
6.99841 − 6.56505I 7.94758 + 6.80228I
u = −0.502648 − 0.555980I
a = 1.35292 + 0.76273I
b = 0.424196 − 0.870841I
6.99841 + 6.56505I 7.94758 − 6.80228I
u = 0.417996 + 1.195510I
a = −1.81445 + 0.17291I
b = −0.943590 + 0.346371I
10.62020 + 3.61647I 0
u = 0.417996 − 1.195510I
a = −1.81445 − 0.17291I
b = −0.943590 − 0.346371I
10.62020 − 3.61647I 0
u = −0.586451 + 0.420780I
a = −0.745096 − 0.020246I
b = 0.568271 − 1.084970I
7.43119 + 2.66733I 9.42694 + 0.01688I
u = −0.586451 − 0.420780I
a = −0.745096 + 0.020246I
b = 0.568271 + 1.084970I
7.43119 − 2.66733I 9.42694 − 0.01688I
u = −0.352653 + 1.230150I
a = −2.08694 − 2.25380I
b = −1.15302 − 2.28427I
4.63286 + 0.43633I 0
u = −0.352653 − 1.230150I
a = −2.08694 + 2.25380I
b = −1.15302 + 2.28427I
4.63286 − 0.43633I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.316269 + 1.249700I
a = 1.82642 + 1.56645I
b = 1.16268 + 1.70863I
−1.20445 − 2.19229I 0
u = −0.316269 − 1.249700I
a = 1.82642 − 1.56645I
b = 1.16268 − 1.70863I
−1.20445 + 2.19229I 0
u = 0.053632 + 1.289800I
a = −1.55559 + 0.97168I
b = −0.72624 + 1.73649I
−0.99866 + 4.23513I 0
u = 0.053632 − 1.289800I
a = −1.55559 − 0.97168I
b = −0.72624 − 1.73649I
−0.99866 − 4.23513I 0
u = 0.016620 + 1.304390I
a = 1.194330 − 0.735726I
b = 0.69581 − 1.49341I
−5.82265 + 0.81095I 0
u = 0.016620 − 1.304390I
a = 1.194330 + 0.735726I
b = 0.69581 + 1.49341I
−5.82265 − 0.81095I 0
u = −0.667774 + 0.163365I
a = 0.235125 + 0.105097I
b = 1.132700 + 0.443466I
4.25302 − 0.78723I 8.08019 + 0.69488I
u = −0.667774 − 0.163365I
a = 0.235125 − 0.105097I
b = 1.132700 − 0.443466I
4.25302 + 0.78723I 8.08019 − 0.69488I
u = 0.321229 + 1.276340I
a = 0.975526 + 0.758046I
b = 1.38917 − 0.31193I
−2.32532 + 3.88876I 0
u = 0.321229 − 1.276340I
a = 0.975526 − 0.758046I
b = 1.38917 + 0.31193I
−2.32532 − 3.88876I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.099287 + 1.314930I
a = −0.318472 + 0.820675I
b = −0.439087 + 1.148180I
−3.46404 − 2.05434I 0
u = −0.099287 − 1.314930I
a = −0.318472 − 0.820675I
b = −0.439087 − 1.148180I
−3.46404 + 2.05434I 0
u = −0.450416 + 0.509884I
a = −0.960127 + 0.859309I
b = −0.166013 − 0.591858I
1.28106 − 3.47044I 3.88375 + 7.68592I
u = −0.450416 − 0.509884I
a = −0.960127 − 0.859309I
b = −0.166013 + 0.591858I
1.28106 + 3.47044I 3.88375 − 7.68592I
u = −0.332166 + 1.293110I
a = −2.54722 − 1.00893I
b = −1.85697 − 1.49469I
−1.59371 − 5.68239I 0
u = −0.332166 − 1.293110I
a = −2.54722 + 1.00893I
b = −1.85697 + 1.49469I
−1.59371 + 5.68239I 0
u = 0.331305 + 1.302290I
a = −1.56104 − 0.14984I
b = −1.55504 + 0.97937I
1.12844 + 7.81474I 0
u = 0.331305 − 1.302290I
a = −1.56104 + 0.14984I
b = −1.55504 − 0.97937I
1.12844 − 7.81474I 0
u = −0.355420 + 1.298670I
a = 3.07198 + 1.18787I
b = 2.20157 + 1.78185I
4.10044 − 8.79609I 0
u = −0.355420 − 1.298670I
a = 3.07198 − 1.18787I
b = 2.20157 − 1.78185I
4.10044 + 8.79609I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.036427 + 1.346260I
a = −0.607791 + 0.422715I
b = −0.629673 + 1.192930I
−3.35604 − 2.35859I 0
u = −0.036427 − 1.346260I
a = −0.607791 − 0.422715I
b = −0.629673 − 1.192930I
−3.35604 + 2.35859I 0
u = −0.204057 + 1.350880I
a = −0.508818 + 0.849448I
b = −0.815090 + 0.663922I
−3.59967 − 2.38098I 0
u = −0.204057 − 1.350880I
a = −0.508818 − 0.849448I
b = −0.815090 − 0.663922I
−3.59967 + 2.38098I 0
u = −0.269785 + 1.347060I
a = 1.64477 − 0.56880I
b = 1.62647 + 0.01247I
−0.50518 − 4.19710I 0
u = −0.269785 − 1.347060I
a = 1.64477 + 0.56880I
b = 1.62647 − 0.01247I
−0.50518 + 4.19710I 0
u = 0.391046 + 1.322010I
a = 1.06116 − 1.80811I
b = 0.48619 − 2.18356I
9.70536 + 5.47983I 0
u = 0.391046 − 1.322010I
a = 1.06116 + 1.80811I
b = 0.48619 + 2.18356I
9.70536 − 5.47983I 0
u = 0.368532 + 1.330510I
a = −1.73222 + 1.34594I
b = −1.12286 + 2.08477I
2.78873 + 7.54981I 0
u = 0.368532 − 1.330510I
a = −1.73222 − 1.34594I
b = −1.12286 − 2.08477I
2.78873 − 7.54981I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.368054 + 1.347150I
a = 2.22544 − 1.63294I
b = 1.36977 − 2.45177I
1.67578 + 11.84830I 0
u = 0.368054 − 1.347150I
a = 2.22544 + 1.63294I
b = 1.36977 + 2.45177I
1.67578 − 11.84830I 0
u = −0.103421 + 1.398990I
a = −0.156439 − 0.588353I
b = 0.497683 − 1.119190I
−4.75437 − 5.19853I 0
u = −0.103421 − 1.398990I
a = −0.156439 + 0.588353I
b = 0.497683 + 1.119190I
−4.75437 + 5.19853I 0
u = 0.373793 + 1.356110I
a = −2.39427 + 1.96966I
b = −1.37738 + 2.74063I
7.4137 + 15.5822I 0
u = 0.373793 − 1.356110I
a = −2.39427 − 1.96966I
b = −1.37738 − 2.74063I
7.4137 − 15.5822I 0
u = −0.11241 + 1.42300I
a = 0.455015 + 0.662998I
b = −0.434609 + 1.177910I
0.66003 − 8.48529I 0
u = −0.11241 − 1.42300I
a = 0.455015 − 0.662998I
b = −0.434609 − 1.177910I
0.66003 + 8.48529I 0
u = −0.484381
a = −0.253063
b = −0.395089
0.828246 12.7290
u = −0.040668 + 0.478942I
a = 0.06428 − 2.03562I
b = −0.380831 − 0.239183I
2.10140 − 1.97255I 1.62971 + 4.07824I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.040668 − 0.478942I
a = 0.06428 + 2.03562I
b = −0.380831 + 0.239183I
2.10140 + 1.97255I 1.62971 − 4.07824I
u = 0.268652 + 0.175360I
a = −0.22486 − 2.74712I
b = −0.722155 + 0.751154I
3.41208 + 3.23701I −0.51319 − 4.60923I
u = 0.268652 − 0.175360I
a = −0.22486 + 2.74712I
b = −0.722155 − 0.751154I
3.41208 − 3.23701I −0.51319 + 4.60923I
u = 0.113105 + 0.236302I
a = 0.51485 + 2.54920I
b = 0.559155 − 0.256506I
−1.187190 + 0.455593I −6.24430 − 1.84121I
u = 0.113105 − 0.236302I
a = 0.51485 − 2.54920I
b = 0.559155 + 0.256506I
−1.187190 − 0.455593I −6.24430 + 1.84121I
12
II. I
u
2
= hu
2
a + b + a, u
2
a + a
2
+ u
2
+ a + u + 1, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
4
=
a
−u
2
a − a
a
2
=
−u
2
a − au − 2a + u − 1
u
2
a + u
2
+ 2a + u + 1
a
10
=
−u
−u
2
− u − 1
a
5
=
a
−u
2
a − a
a
11
=
−u
−u
2
− u − 1
a
7
=
−u
−u
a
3
=
−u
2
a − au
−2u
2
a − au − 2a
a
6
=
−au − u − 1
u
2
a + 2u
2
+ 2a + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
2
a + 5u
2
− a + 5u + 8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
+ u
2
− 1)
2
c
2
, c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
4
, c
10
u
6
c
5
, c
6
, c
8
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
9
(u
3
− u
2
+ 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
(y
3
− y
2
+ 2y −1)
2
c
2
, c
5
, c
6
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
4
, c
10
y
6
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.662359 + 0.562280I
b = −0.754878
−4.13758 − 2.82812I −4.97655 + 4.84887I
u = −0.215080 + 1.307140I
a = 1.32472
b = 0.877439 + 0.744862I
− 5.65624I 3.89456 + 5.95889I
u = −0.215080 − 1.307140I
a = −0.662359 − 0.562280I
b = −0.754878
−4.13758 + 2.82812I −4.97655 − 4.84887I
u = −0.215080 − 1.307140I
a = 1.32472
b = 0.877439 − 0.744862I
5.65624I 3.89456 − 5.95889I
u = −0.569840
a = −0.662359 + 0.562280I
b = 0.877439 − 0.744862I
4.13758 + 2.82812I 8.08199 − 1.11003I
u = −0.569840
a = −0.662359 − 0.562280I
b = 0.877439 + 0.744862I
4.13758 − 2.82812I 8.08199 + 1.11003I
16
III. I
u
3
= h−u
3
+ b − u, a + u, u
7
+ 3u
5
+ 2u
3
− u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
4
=
−u
u
3
+ u
a
2
=
−u
5
− 2u
3
+ u
2u + 1
a
10
=
−u
4
− u
2
+ 1
−u
4
− 2u
2
a
5
=
u
4
+ u
2
− u − 1
u
4
+ u
3
+ 2u
2
+ u
a
11
=
−u
u
3
+ u
a
7
=
−u
4
− u
2
+ 1
u
6
+ 2u
4
+ u
2
a
3
=
u
5
+ 2u
3
− u − 1
u
5
+ 3u
3
+ u
2
+ u
a
6
=
u
6
+ u
4
− 2u
2
+ 1
u
6
+ 2u
4
− u
2
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
− 2u
6
+ u
5
+ 2u
4
− 4u
3
+ 6u
2
− 3u + 3
c
2
, c
5
, c
6
c
8
, c
11
, c
12
u
7
+ 3u
5
+ 2u
3
− u + 1
c
3
, c
7
, c
9
u
7
− u
5
− 2u
4
+ 2u
3
+ 2u
2
− 3u + 2
c
4
, c
10
(u − 1)
7
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
7
− 2y
6
+ y
5
+ 6y
4
− 2y
3
− 24y
2
− 27y −9
c
2
, c
5
, c
6
c
8
, c
11
, c
12
y
7
+ 6y
6
+ 13y
5
+ 10y
4
− 2y
3
− 4y
2
+ y −1
c
3
, c
7
, c
9
y
7
− 2y
6
+ 5y
5
− 14y
4
+ 18y
3
− 8y
2
+ y −4
c
4
, c
10
(y −1)
7
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.757137
a = −0.757137
b = 1.19117
1.64493 6.00000
u = 0.311114 + 1.246820I
a = −0.311114 − 1.246820I
b = −1.109710 − 0.329390I
1.64493 6.00000
u = 0.311114 − 1.246820I
a = −0.311114 + 1.246820I
b = −1.109710 + 0.329390I
1.64493 6.00000
u = −0.501027 + 0.385135I
a = 0.501027 − 0.385135I
b = −0.403848 + 0.618048I
1.64493 6.00000
u = −0.501027 − 0.385135I
a = 0.501027 + 0.385135I
b = −0.403848 − 0.618048I
1.64493 6.00000
u = −0.18866 + 1.40255I
a = 0.18866 − 1.40255I
b = 0.91797 − 1.20672I
1.64493 6.00000
u = −0.18866 − 1.40255I
a = 0.18866 + 1.40255I
b = 0.91797 + 1.20672I
1.64493 6.00000
20
IV. I
u
4
= hu
2
+ b + u + 1, a + u, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
4
=
−u
−u
2
− u − 1
a
2
=
2u + 1
2u
a
10
=
−u
−u
2
− u − 1
a
5
=
−u
−u
2
− u − 1
a
11
=
−u
−u
2
− u − 1
a
7
=
−u
−u
a
3
=
−2u − 1
−u
2
− 2u − 2
a
6
=
−2u
2
− 2u
−2u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
+ u
2
− 1
c
2
, c
11
, c
12
u
3
− u
2
+ 2u − 1
c
4
, c
10
u
3
c
5
, c
6
, c
8
u
3
+ u
2
+ 2u + 1
c
7
, c
9
u
3
− u
2
+ 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
y
3
− y
2
+ 2y −1
c
2
, c
5
, c
6
c
8
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
c
4
, c
10
y
3
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.215080 − 1.307140I
b = 0.877439 − 0.744862I
0 0
u = −0.215080 − 1.307140I
a = 0.215080 + 1.307140I
b = 0.877439 + 0.744862I
0 0
u = −0.569840
a = 0.569840
b = −0.754878
0 0
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
3
(u
7
− 2u
6
+ u
5
+ 2u
4
− 4u
3
+ 6u
2
− 3u + 3)
· (u
75
− 14u
74
+ ··· + 204u + 801)
c
2
((u
3
− u
2
+ 2u − 1)
3
)(u
7
+ 3u
5
+ 2u
3
− u + 1)(u
75
− 4u
74
+ ··· + 10u − 1)
c
3
(u
3
+ u
2
− 1)
3
(u
7
− u
5
− 2u
4
+ 2u
3
+ 2u
2
− 3u + 2)
· (u
75
+ 4u
74
+ ··· + 2274u − 153)
c
4
, c
10
u
9
(u − 1)
7
(u
75
+ 6u
74
+ ··· − 3072u − 512)
c
5
, c
6
((u
3
+ u
2
+ 2u + 1)
3
)(u
7
+ 3u
5
+ 2u
3
− u + 1)(u
75
− 4u
74
+ ··· + 10u − 1)
c
7
, c
9
(u
3
− u
2
+ 1)
3
(u
7
− u
5
− 2u
4
+ 2u
3
+ 2u
2
− 3u + 2)
· (u
75
− 4u
74
+ ··· − 750u − 153)
c
8
((u
3
+ u
2
+ 2u + 1)
3
)(u
7
+ 3u
5
+ 2u
3
− u + 1)(u
75
+ 4u
74
+ ··· − 6u − 1)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
3
)(u
7
+ 3u
5
+ 2u
3
− u + 1)(u
75
+ 4u
74
+ ··· − 6u − 1)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
3
(y
7
− 2y
6
+ y
5
+ 6y
4
− 2y
3
− 24y
2
− 27y −9)
· (y
75
+ 42y
74
+ ··· + 136940526y −641601)
c
2
, c
5
, c
6
(y
3
+ 3y
2
+ 2y −1)
3
(y
7
+ 6y
6
+ 13y
5
+ 10y
4
− 2y
3
− 4y
2
+ y −1)
· (y
75
+ 70y
74
+ ··· + 34y −1)
c
3
(y
3
− y
2
+ 2y −1)
3
(y
7
− 2y
6
+ 5y
5
− 14y
4
+ 18y
3
− 8y
2
+ y −4)
· (y
75
+ 14y
74
+ ··· + 593622y −23409)
c
4
, c
10
y
9
(y −1)
7
(y
75
− 42y
74
+ ··· + 3276800y −262144)
c
7
, c
9
(y
3
− y
2
+ 2y −1)
3
(y
7
− 2y
6
+ 5y
5
− 14y
4
+ 18y
3
− 8y
2
+ y −4)
· (y
75
− 58y
74
+ ··· − 431082y −23409)
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
3
(y
7
+ 6y
6
+ 13y
5
+ 10y
4
− 2y
3
− 4y
2
+ y −1)
· (y
75
+ 62y
74
+ ··· − 14y −1)
26
