12a
0024
(K12a
0024
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 11 12 4 1 8 7 10
Solving Sequence
7,12 4,8
9 5 11 6 3 2 10 1
c
7
c
8
c
4
c
11
c
6
c
3
c
2
c
10
c
12
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h17u
89
− 27u
88
+ ··· + 2b + 10, 11u
89
− 17u
88
+ ··· + 2a + 9, u
90
− 3u
89
+ ··· − 2u − 1i
I
u
2
= h−u
2
a + b, u
4
a + u
3
a − u
2
a + a
2
− au + u
2
+ u − 1, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 100 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
=
h17u
89
−27u
88
+· · ·+2b+10, 11u
89
−17u
88
+· · ·+2a+9, u
90
−3u
89
+· · ·−2u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
−
11
2
u
89
+
17
2
u
88
+ ··· −
13
2
u −
9
2
−
17
2
u
89
+
27
2
u
88
+ ··· −
27
2
u − 5
a
8
=
1
u
2
a
9
=
−u
11
+ 6u
9
− 12u
7
+ 8u
5
− u
3
+ 2u
−u
13
+ 5u
11
− 7u
9
+ 2u
5
+ 3u
3
+ u
a
5
=
3
2
u
89
−
1
2
u
88
+ ··· +
15
2
u +
1
2
9
2
u
89
−
9
2
u
88
+ ··· +
15
2
u + 3
a
11
=
u
u
a
6
=
−u
2
+ 1
−u
2
a
3
=
−2u
89
+ 4u
88
+ ··· + 2u −
3
2
−2u
89
+ 4u
88
+ ··· −
5
2
u − 1
a
2
=
1
2
u
86
−
1
2
u
85
+ ··· + 5u −
3
2
−u
89
+ 2u
88
+ ··· −
1
2
u − 1
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
1
=
u
7
− 4u
5
+ 4u
3
u
9
− 3u
7
+ u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
5
2
u
89
−
7
2
u
88
+ ··· +
35
2
u +
3
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
90
+ 46u
89
+ ··· + 5u + 1
c
2
, c
5
u
90
+ 6u
89
+ ··· + 7u + 1
c
3
u
90
− 6u
89
+ ··· − 21049u + 2857
c
4
, c
8
u
90
− u
89
+ ··· − 1024u − 1024
c
6
, c
7
, c
11
u
90
+ 3u
89
+ ··· + 2u − 1
c
9
, c
12
u
90
+ 13u
89
+ ··· + 250u − 7
c
10
u
90
− 9u
89
+ ··· − 5322u + 1237
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
90
+ 2y
89
+ ··· − 19y + 1
c
2
, c
5
y
90
+ 46y
89
+ ··· + 5y + 1
c
3
y
90
− 42y
89
+ ··· + 178045685y + 8162449
c
4
, c
8
y
90
− 55y
89
+ ··· − 16777216y + 1048576
c
6
, c
7
, c
11
y
90
− 85y
89
+ ··· − 2y + 1
c
9
, c
12
y
90
+ 79y
89
+ ··· − 113894y + 49
c
10
y
90
− 33y
89
+ ··· − 33961930y + 1530169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.035540 + 0.147829I
a = −1.178990 + 0.129145I
b = −2.35944 + 0.04325I
−4.04276 + 3.69637I 0
u = 1.035540 − 0.147829I
a = −1.178990 − 0.129145I
b = −2.35944 − 0.04325I
−4.04276 − 3.69637I 0
u = 1.159310 + 0.090200I
a = 0.799616 − 0.379304I
b = 1.82834 − 0.69618I
−1.75007 − 0.25828I 0
u = 1.159310 − 0.090200I
a = 0.799616 + 0.379304I
b = 1.82834 + 0.69618I
−1.75007 + 0.25828I 0
u = −0.437999 + 0.686714I
a = 0.33190 − 1.91263I
b = 0.196118 − 0.060111I
−9.70066 + 3.66881I −11.15932 − 3.34519I
u = −0.437999 − 0.686714I
a = 0.33190 + 1.91263I
b = 0.196118 + 0.060111I
−9.70066 − 3.66881I −11.15932 + 3.34519I
u = −0.408798 + 0.704111I
a = 0.19713 − 2.43169I
b = −0.1107110 + 0.0409626I
−7.6515 + 12.5202I −8.50844 − 9.24171I
u = −0.408798 − 0.704111I
a = 0.19713 + 2.43169I
b = −0.1107110 − 0.0409626I
−7.6515 − 12.5202I −8.50844 + 9.24171I
u = −0.519185 + 0.621006I
a = −0.639891 + 0.342871I
b = −1.157860 + 0.042784I
−10.00680 + 0.68806I −11.88470 − 2.78683I
u = −0.519185 − 0.621006I
a = −0.639891 − 0.342871I
b = −1.157860 − 0.042784I
−10.00680 − 0.68806I −11.88470 + 2.78683I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.551816 + 0.587844I
a = −0.721885 − 0.251112I
b = −1.50250 − 0.11783I
−8.18869 − 8.18776I −9.87272 + 3.39708I
u = −0.551816 − 0.587844I
a = −0.721885 + 0.251112I
b = −1.50250 + 0.11783I
−8.18869 + 8.18776I −9.87272 − 3.39708I
u = −0.411438 + 0.688379I
a = −0.04849 + 2.23057I
b = −0.0163093 − 0.1154220I
−4.87794 + 7.26864I −5.96969 − 5.95912I
u = −0.411438 − 0.688379I
a = −0.04849 − 2.23057I
b = −0.0163093 + 0.1154220I
−4.87794 − 7.26864I −5.96969 + 5.95912I
u = −0.527543 + 0.586369I
a = 0.466491 + 0.096694I
b = 1.329780 + 0.182524I
−5.33184 − 3.01556I −7.21234 − 0.07113I
u = −0.527543 − 0.586369I
a = 0.466491 − 0.096694I
b = 1.329780 − 0.182524I
−5.33184 + 3.01556I −7.21234 + 0.07113I
u = 0.426107 + 0.647594I
a = 1.24151 − 1.36025I
b = 0.698493 − 0.178607I
−4.09139 − 5.96624I −8.21287 + 6.74869I
u = 0.426107 − 0.647594I
a = 1.24151 + 1.36025I
b = 0.698493 + 0.178607I
−4.09139 + 5.96624I −8.21287 − 6.74869I
u = 0.469022 + 0.601759I
a = 0.73660 − 1.53917I
b = 0.609093 − 0.543821I
−4.28017 + 1.86136I −8.94738 − 0.21875I
u = 0.469022 − 0.601759I
a = 0.73660 + 1.53917I
b = 0.609093 + 0.543821I
−4.28017 − 1.86136I −8.94738 + 0.21875I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.730493 + 0.189798I
a = −0.774454 − 0.466152I
b = −1.39580 − 0.61388I
−4.18196 − 3.80025I −10.98096 + 4.73672I
u = 0.730493 − 0.189798I
a = −0.774454 + 0.466152I
b = −1.39580 + 0.61388I
−4.18196 + 3.80025I −10.98096 − 4.73672I
u = −0.413257 + 0.622880I
a = 0.73526 + 1.38556I
b = −0.463774 − 0.507608I
−1.76351 + 4.66487I −7.53917 − 7.21944I
u = −0.413257 − 0.622880I
a = 0.73526 − 1.38556I
b = −0.463774 + 0.507608I
−1.76351 − 4.66487I −7.53917 + 7.21944I
u = −0.433709 + 0.592654I
a = −0.735605 − 0.677095I
b = 0.768130 + 0.537666I
−1.87712 − 0.73957I −8.41694 − 0.27201I
u = −0.433709 − 0.592654I
a = −0.735605 + 0.677095I
b = 0.768130 − 0.537666I
−1.87712 + 0.73957I −8.41694 + 0.27201I
u = 1.261540 + 0.134061I
a = 0.602278 − 0.940882I
b = 1.76416 − 1.98860I
−1.67033 − 1.06008I 0
u = 1.261540 − 0.134061I
a = 0.602278 + 0.940882I
b = 1.76416 + 1.98860I
−1.67033 + 1.06008I 0
u = 0.409031 + 0.601690I
a = −0.89429 + 1.09608I
b = −0.448688 + 0.262318I
−1.22702 − 1.91248I −3.96230 + 3.55807I
u = 0.409031 − 0.601690I
a = −0.89429 − 1.09608I
b = −0.448688 − 0.262318I
−1.22702 + 1.91248I −3.96230 − 3.55807I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.276300 + 0.096082I
a = 1.40005 + 1.66428I
b = 2.00156 + 2.73492I
−2.65099 − 0.98383I 0
u = −1.276300 − 0.096082I
a = 1.40005 − 1.66428I
b = 2.00156 − 2.73492I
−2.65099 + 0.98383I 0
u = −1.274020 + 0.144176I
a = −0.82202 − 1.79830I
b = −1.22136 − 3.06947I
−1.80283 + 3.89148I 0
u = −1.274020 − 0.144176I
a = −0.82202 + 1.79830I
b = −1.22136 + 3.06947I
−1.80283 − 3.89148I 0
u = 0.203863 + 0.668626I
a = 1.87283 + 0.93707I
b = 0.0335509 + 0.1254080I
−2.25258 + 0.41899I −7.65968 + 0.68972I
u = 0.203863 − 0.668626I
a = 1.87283 − 0.93707I
b = 0.0335509 − 0.1254080I
−2.25258 − 0.41899I −7.65968 − 0.68972I
u = 0.119191 + 0.683033I
a = 1.96671 + 1.78497I
b = −0.0552694 − 0.0778810I
−1.33539 − 7.02339I −4.65258 + 7.68511I
u = 0.119191 − 0.683033I
a = 1.96671 − 1.78497I
b = −0.0552694 + 0.0778810I
−1.33539 + 7.02339I −4.65258 − 7.68511I
u = 0.308931 + 0.619062I
a = −1.193670 + 0.120245I
b = −0.235643 − 0.064548I
−0.48363 − 2.34563I −5.80863 + 1.86911I
u = 0.308931 − 0.619062I
a = −1.193670 − 0.120245I
b = −0.235643 + 0.064548I
−0.48363 + 2.34563I −5.80863 − 1.86911I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307800 + 0.159281I
a = −0.482256 + 1.274220I
b = −1.78724 + 2.77159I
−3.40681 − 5.45128I 0
u = 1.307800 − 0.159281I
a = −0.482256 − 1.274220I
b = −1.78724 − 2.77159I
−3.40681 + 5.45128I 0
u = −1.299790 + 0.224911I
a = −0.01884 − 1.71554I
b = −0.02023 − 3.28053I
−3.29956 + 5.65949I 0
u = −1.299790 − 0.224911I
a = −0.01884 + 1.71554I
b = −0.02023 + 3.28053I
−3.29956 − 5.65949I 0
u = −1.297930 + 0.254453I
a = −0.23628 + 1.82699I
b = −0.33307 + 3.61523I
−5.74518 + 10.42230I 0
u = −1.297930 − 0.254453I
a = −0.23628 − 1.82699I
b = −0.33307 − 3.61523I
−5.74518 − 10.42230I 0
u = 1.343220 + 0.065105I
a = −0.086124 + 0.903621I
b = −0.56348 + 2.46276I
−5.00570 + 0.83074I 0
u = 1.343220 − 0.065105I
a = −0.086124 − 0.903621I
b = −0.56348 − 2.46276I
−5.00570 − 0.83074I 0
u = 0.114121 + 0.632819I
a = −1.51121 − 1.76847I
b = −0.0735512 + 0.0732549I
1.09432 − 2.53863I −0.39286 + 4.64184I
u = 0.114121 − 0.632819I
a = −1.51121 + 1.76847I
b = −0.0735512 − 0.0732549I
1.09432 + 2.53863I −0.39286 − 4.64184I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.360390 + 0.243110I
a = −0.350565 + 1.164240I
b = −0.87333 + 2.45780I
−7.18925 + 2.87956I 0
u = −1.360390 − 0.243110I
a = −0.350565 − 1.164240I
b = −0.87333 − 2.45780I
−7.18925 − 2.87956I 0
u = −1.41779
a = 0.815249
b = 0.429776
−7.33492 0
u = 0.398019 + 0.418448I
a = −0.083964 + 1.026110I
b = 0.176209 + 0.457399I
−1.15580 − 0.94935I −8.91971 + 4.56142I
u = 0.398019 − 0.418448I
a = −0.083964 − 1.026110I
b = 0.176209 − 0.457399I
−1.15580 + 0.94935I −8.91971 − 4.56142I
u = −1.41162 + 0.17588I
a = 0.399227 + 0.654735I
b = 0.45610 + 1.60564I
−6.84094 + 3.22476I 0
u = −1.41162 − 0.17588I
a = 0.399227 − 0.654735I
b = 0.45610 − 1.60564I
−6.84094 − 3.22476I 0
u = −1.41987 + 0.23861I
a = 0.560750 − 0.298797I
b = 1.43017 − 0.55315I
−6.02002 + 5.49310I 0
u = −1.41987 − 0.23861I
a = 0.560750 + 0.298797I
b = 1.43017 + 0.55315I
−6.02002 − 5.49310I 0
u = 0.559261
a = 0.232713
b = 0.959638
−1.28839 −8.06550
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44510 + 0.02573I
a = −0.626593 − 0.164956I
b = 0.040468 − 0.468518I
−10.78930 + 4.28605I 0
u = −1.44510 − 0.02573I
a = −0.626593 + 0.164956I
b = 0.040468 + 0.468518I
−10.78930 − 4.28605I 0
u = 0.009036 + 0.549222I
a = −0.76604 − 2.41165I
b = −0.340171 + 0.150886I
2.08637 − 1.40419I 2.94065 + 3.79757I
u = 0.009036 − 0.549222I
a = −0.76604 + 2.41165I
b = −0.340171 − 0.150886I
2.08637 + 1.40419I 2.94065 − 3.79757I
u = −1.45603 + 0.22571I
a = 0.786694 + 0.252582I
b = 1.90775 + 1.02183I
−7.22826 + 4.96225I 0
u = −1.45603 − 0.22571I
a = 0.786694 − 0.252582I
b = 1.90775 − 1.02183I
−7.22826 − 4.96225I 0
u = 1.46085 + 0.21961I
a = 1.51400 − 0.77409I
b = 2.57466 − 0.64144I
−7.96927 − 2.24977I 0
u = 1.46085 − 0.21961I
a = 1.51400 + 0.77409I
b = 2.57466 + 0.64144I
−7.96927 + 2.24977I 0
u = 1.45954 + 0.23127I
a = −1.53208 + 1.18300I
b = −2.88668 + 1.62021I
−7.79425 − 7.80059I 0
u = 1.45954 − 0.23127I
a = −1.53208 − 1.18300I
b = −2.88668 − 1.62021I
−7.79425 + 7.80059I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.077839 + 0.509254I
a = 0.35241 + 2.82775I
b = 0.559949 − 0.149409I
0.90059 + 3.01272I 0.99662 − 2.60175I
u = −0.077839 − 0.509254I
a = 0.35241 − 2.82775I
b = 0.559949 + 0.149409I
0.90059 − 3.01272I 0.99662 + 2.60175I
u = −1.46697 + 0.23745I
a = −0.974601 − 0.264270I
b = −2.50201 − 1.11654I
−10.19580 + 9.20433I 0
u = −1.46697 − 0.23745I
a = −0.974601 + 0.264270I
b = −2.50201 + 1.11654I
−10.19580 − 9.20433I 0
u = −1.47202 + 0.21480I
a = −0.814653 − 0.449704I
b = −1.89943 − 1.68245I
−10.53570 + 1.12123I 0
u = −1.47202 − 0.21480I
a = −0.814653 + 0.449704I
b = −1.89943 + 1.68245I
−10.53570 − 1.12123I 0
u = 1.46760 + 0.25488I
a = −1.12234 + 1.71367I
b = −2.30620 + 3.30911I
−10.9366 − 10.7133I 0
u = 1.46760 − 0.25488I
a = −1.12234 − 1.71367I
b = −2.30620 − 3.30911I
−10.9366 + 10.7133I 0
u = 1.46890 + 0.26154I
a = 1.04664 − 1.82928I
b = 2.22403 − 3.69552I
−13.7057 − 16.0444I 0
u = 1.46890 − 0.26154I
a = 1.04664 + 1.82928I
b = 2.22403 + 3.69552I
−13.7057 + 16.0444I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48501 + 0.19499I
a = 0.705338 − 0.300694I
b = 0.343196 + 0.209852I
−11.83800 + 0.20054I 0
u = 1.48501 − 0.19499I
a = 0.705338 + 0.300694I
b = 0.343196 − 0.209852I
−11.83800 − 0.20054I 0
u = 1.47754 + 0.24955I
a = 0.95232 − 1.53885I
b = 1.68583 − 2.99988I
−15.8899 − 7.0859I 0
u = 1.47754 − 0.24955I
a = 0.95232 + 1.53885I
b = 1.68583 + 2.99988I
−15.8899 + 7.0859I 0
u = 1.49233 + 0.18793I
a = −0.522585 + 0.225682I
b = 0.153616 − 0.382005I
−14.8163 + 5.4132I 0
u = 1.49233 − 0.18793I
a = −0.522585 − 0.225682I
b = 0.153616 + 0.382005I
−14.8163 − 5.4132I 0
u = 1.49184 + 0.20747I
a = −0.642233 + 0.591756I
b = −0.252785 + 0.589048I
−16.5297 − 3.6839I 0
u = 1.49184 − 0.20747I
a = −0.642233 − 0.591756I
b = −0.252785 − 0.589048I
−16.5297 + 3.6839I 0
u = −0.207923 + 0.145493I
a = −0.41209 + 2.80249I
b = 0.329617 + 0.565743I
−0.31997 − 1.73362I −2.68908 + 4.51513I
u = −0.207923 − 0.145493I
a = −0.41209 − 2.80249I
b = 0.329617 − 0.565743I
−0.31997 + 1.73362I −2.68908 − 4.51513I
13
II.
I
u
2
= h−u
2
a+b, u
4
a+u
3
a−u
2
a+a
2
−au+u
2
+u−1, u
5
+u
4
−2u
3
−u
2
+u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
a
u
2
a
a
8
=
1
u
2
a
9
=
1
u
2
a
5
=
a
u
2
a
a
11
=
u
u
a
6
=
−u
2
+ 1
−u
2
a
3
=
−u
3
a + 2au
u
4
a − u
3
a − u
2
a + 2au − a
a
2
=
−u
3
a + u
4
+ u
3
+ 2au − u
2
− u
u
4
a − u
3
a + u
4
− u
2
a + 2au − u
2
− a + u
a
10
=
−u
3
+ 2u
u
4
− u
3
− u
2
+ 2u − 1
a
1
=
u
2
− 1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
a − u
3
a − 9u
2
a − 4u
3
+ 2au − u
2
+ 7u − 9
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
8
u
10
c
6
, c
7
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
9
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
10
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
12
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
8
y
10
c
6
, c
7
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
9
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = −0.652039 + 1.129360I
b = −0.96690 + 1.67471I
−2.40108 + 2.02988I −6.62546 − 4.42764I
u = 1.21774
a = −0.652039 − 1.129360I
b = −0.96690 − 1.67471I
−2.40108 − 2.02988I −6.62546 + 4.42764I
u = 0.309916 + 0.549911I
a = 1.114310 + 0.148503I
b = −0.280560 + 0.349171I
−0.32910 − 3.56046I −5.04069 + 7.43801I
u = 0.309916 + 0.549911I
a = −0.685764 + 0.890773I
b = −0.162111 − 0.417558I
−0.329100 + 0.499304I −2.53179 + 1.09027I
u = 0.309916 − 0.549911I
a = 1.114310 − 0.148503I
b = −0.280560 − 0.349171I
−0.32910 + 3.56046I −5.04069 − 7.43801I
u = 0.309916 − 0.549911I
a = −0.685764 − 0.890773I
b = −0.162111 + 0.417558I
−0.329100 − 0.499304I −2.53179 − 1.09027I
u = −1.41878 + 0.21917I
a = 0.492416 + 0.603584I
b = 1.34292 + 0.87976I
−5.87256 + 6.43072I −9.19707 − 7.98272I
u = −1.41878 + 0.21917I
a = −0.768927 + 0.124653I
b = −1.43335 + 0.72312I
−5.87256 + 2.37095I −6.60498 + 0.29447I
u = −1.41878 − 0.21917I
a = 0.492416 − 0.603584I
b = 1.34292 − 0.87976I
−5.87256 − 6.43072I −9.19707 + 7.98272I
u = −1.41878 − 0.21917I
a = −0.768927 − 0.124653I
b = −1.43335 − 0.72312I
−5.87256 − 2.37095I −6.60498 − 0.29447I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
90
+ 46u
89
+ ··· + 5u + 1)
c
2
((u
2
+ u + 1)
5
)(u
90
+ 6u
89
+ ··· + 7u + 1)
c
3
((u
2
− u + 1)
5
)(u
90
− 6u
89
+ ··· − 21049u + 2857)
c
4
, c
8
u
10
(u
90
− u
89
+ ··· − 1024u − 1024)
c
5
((u
2
− u + 1)
5
)(u
90
+ 6u
89
+ ··· + 7u + 1)
c
6
, c
7
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
90
+ 3u
89
+ ··· + 2u − 1)
c
9
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
90
+ 13u
89
+ ··· + 250u − 7)
c
10
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
)(u
90
− 9u
89
+ ··· − 5322u + 1237)
c
11
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
90
+ 3u
89
+ ··· + 2u − 1)
c
12
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
90
+ 13u
89
+ ··· + 250u − 7)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
90
+ 2y
89
+ ··· − 19y + 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
90
+ 46y
89
+ ··· + 5y + 1)
c
3
((y
2
+ y + 1)
5
)(y
90
− 42y
89
+ ··· + 1.78046 × 10
8
y + 8162449)
c
4
, c
8
y
10
(y
90
− 55y
89
+ ··· − 1.67772 × 10
7
y + 1048576)
c
6
, c
7
, c
11
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
90
− 85y
89
+ ··· − 2y + 1)
c
9
, c
12
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
90
+ 79y
89
+ ··· − 113894y + 49)
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
· (y
90
− 33y
89
+ ··· − 33961930y + 1530169)
19
