12a
0462
(K12a
0462
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 8 2 5 12 1 4 10 9
Solving Sequence
3,11 4,6
2 7 5 1 10 12 9 8
c
3
c
2
c
6
c
4
c
1
c
10
c
11
c
9
c
8
c
5
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.55777 × 10
154
u
87
+ 1.33040 × 10
154
u
86
+ ··· + 1.37278 × 10
154
b − 6.08647 × 10
155
,
4.05262 × 10
155
u
87
+ 2.19316 × 10
156
u
86
+ ··· + 3.02011 × 10
155
a + 5.78829 × 10
157
,
u
88
+ 2u
87
+ ··· + 128u + 32i
I
u
2
= hb, u
4
+ u
2
+ a + u, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
v
1
= ha, −2v
4
+ v
3
+ 3v
2
+ b − 6v + 2, v
5
− v
4
− v
3
+ 4v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 98 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
= h2.56 × 10
154
u
87
+ 1.33 × 10
154
u
86
+ · · · + 1.37 × 10
154
b − 6.09 ×
10
155
, 4.05 × 10
155
u
87
+ 2.19 × 10
156
u
86
+ · · · + 3.02 × 10
155
a + 5.79 ×
10
157
, u
88
+ 2u
87
+ · · · + 128u + 32i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
−1.34188u
87
− 7.26185u
86
+ ··· − 648.536u − 191.658
−1.86321u
87
− 0.969132u
86
+ ··· + 62.2360u + 44.3369
a
2
=
3.04936u
87
+ 5.94300u
86
+ ··· + 329.238u + 75.2429
−1.43574u
87
− 2.17821u
86
+ ··· − 23.2178u + 6.62152
a
7
=
−4.53882u
87
− 7.84119u
86
+ ··· − 388.579u − 74.4637
1.02928u
87
− 2.25200u
86
+ ··· − 369.905u − 130.560
a
5
=
−0.0781229u
87
+ 1.92398u
86
+ ··· + 185.114u + 62.4308
−0.503789u
87
− 3.88549u
86
+ ··· − 424.089u − 133.649
a
1
=
1.61362u
87
+ 3.76479u
86
+ ··· + 306.020u + 81.8645
−1.43574u
87
− 2.17821u
86
+ ··· − 23.2178u + 6.62152
a
10
=
u
u
3
+ u
a
12
=
u
3
u
5
+ u
3
+ u
a
9
=
−1.55260u
87
− 6.01547u
86
+ ··· − 445.753u − 125.053
1.59435u
87
+ 2.04652u
86
+ ··· + 133.630u + 23.9040
a
8
=
−3.04936u
87
− 5.94300u
86
+ ··· − 329.238u − 75.2429
1.61315u
87
+ 1.25714u
86
+ ··· + 54.4288u + 1.63829
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.28609u
87
+ 5.01107u
86
+ ··· + 173.927u + 44.2883
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 36u
87
+ ··· + 3584u + 1024
c
2
, c
6
u
88
− 2u
87
+ ··· − 128u + 32
c
3
, c
10
u
88
+ 2u
87
+ ··· + 128u + 32
c
4
, c
5
, c
7
u
88
− 7u
87
+ ··· + 9u − 1
c
8
, c
9
, c
12
u
88
+ 7u
87
+ ··· − 9u − 1
c
11
u
88
− 36u
87
+ ··· − 3584u + 1024
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
88
+ 24y
87
+ ··· − 66715648y + 1048576
c
2
, c
3
, c
6
c
10
y
88
+ 36y
87
+ ··· + 3584y + 1024
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
88
− 77y
87
+ ··· − 57y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395995 + 0.919848I
a = 2.65099 − 0.04295I
b = −0.586527 − 0.945687I
2.26153 + 3.00983I 0
u = −0.395995 − 0.919848I
a = 2.65099 + 0.04295I
b = −0.586527 + 0.945687I
2.26153 − 3.00983I 0
u = −0.404116 + 0.907512I
a = −0.395066 − 0.612626I
b = 0.361388 − 1.098660I
2.25457 + 0.19023I 0
u = −0.404116 − 0.907512I
a = −0.395066 + 0.612626I
b = 0.361388 + 1.098660I
2.25457 − 0.19023I 0
u = −0.886787 + 0.438676I
a = 0.282546 + 1.241530I
b = −0.415238 + 0.812588I
0.69474 − 1.25403I 0
u = −0.886787 − 0.438676I
a = 0.282546 − 1.241530I
b = −0.415238 − 0.812588I
0.69474 + 1.25403I 0
u = 0.812254 + 0.547196I
a = 0.436136 − 0.137542I
b = −0.616284 − 1.184160I
−6.80158 + 6.33791I 0
u = 0.812254 − 0.547196I
a = 0.436136 + 0.137542I
b = −0.616284 + 1.184160I
−6.80158 − 6.33791I 0
u = 0.474341 + 0.926493I
a = 1.015950 + 0.235751I
b = −1.123980 + 0.220654I
−0.22584 − 2.46461I 0
u = 0.474341 − 0.926493I
a = 1.015950 − 0.235751I
b = −1.123980 − 0.220654I
−0.22584 + 2.46461I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.625512 + 0.717766I
a = −0.175517 − 1.114280I
b = −0.159287 − 0.924776I
−2.96877 − 1.76029I 0
u = 0.625512 − 0.717766I
a = −0.175517 + 1.114280I
b = −0.159287 + 0.924776I
−2.96877 + 1.76029I 0
u = 0.995359 + 0.339245I
a = −0.580860 − 0.374909I
b = 0.678568 − 0.640826I
4.14234 + 0.58263I 0
u = 0.995359 − 0.339245I
a = −0.580860 + 0.374909I
b = 0.678568 + 0.640826I
4.14234 − 0.58263I 0
u = 0.159287 + 0.924776I
a = 1.36498 + 1.59127I
b = −0.625512 − 0.717766I
2.96877 + 1.76029I 0
u = 0.159287 − 0.924776I
a = 1.36498 − 1.59127I
b = −0.625512 + 0.717766I
2.96877 − 1.76029I 0
u = −0.678568 + 0.640826I
a = 1.063540 − 0.436699I
b = −0.995359 − 0.339245I
−4.14234 − 0.58263I 0
u = −0.678568 − 0.640826I
a = 1.063540 + 0.436699I
b = −0.995359 + 0.339245I
−4.14234 + 0.58263I 0
u = 0.073976 + 1.077970I
a = −1.08508 − 1.73052I
b = 0.521667 + 0.977886I
−1.30307 + 4.99629I 0
u = 0.073976 − 1.077970I
a = −1.08508 + 1.73052I
b = 0.521667 − 0.977886I
−1.30307 − 4.99629I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.958984 + 0.503942I
a = 0.926029 + 0.597774I
b = −0.958984 + 0.503942I
3.72374I 0
u = 0.958984 − 0.503942I
a = 0.926029 − 0.597774I
b = −0.958984 − 0.503942I
− 3.72374I 0
u = 0.415238 + 0.812588I
a = −1.44367 − 1.70184I
b = 0.886787 + 0.438676I
−0.69474 − 1.25403I 0
u = 0.415238 − 0.812588I
a = −1.44367 + 1.70184I
b = 0.886787 − 0.438676I
−0.69474 + 1.25403I 0
u = 0.702985 + 0.565831I
a = −0.460163 + 0.540285I
b = 0.495675 + 0.994508I
−1.40784 + 2.54267I −3.45686 − 3.29238I
u = 0.702985 − 0.565831I
a = −0.460163 − 0.540285I
b = 0.495675 − 0.994508I
−1.40784 − 2.54267I −3.45686 + 3.29238I
u = −0.521667 + 0.977886I
a = −0.200965 + 0.894250I
b = −0.073976 + 1.077970I
1.30307 + 4.99629I 0
u = −0.521667 − 0.977886I
a = −0.200965 − 0.894250I
b = −0.073976 − 1.077970I
1.30307 − 4.99629I 0
u = −0.495675 + 0.994508I
a = 0.546599 − 1.120560I
b = −0.702985 + 0.565831I
1.40784 + 2.54267I 0
u = −0.495675 − 0.994508I
a = 0.546599 + 1.120560I
b = −0.702985 − 0.565831I
1.40784 − 2.54267I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.798601 + 0.772998I
a = 1.096920 − 0.166790I
b = 0.033875 − 1.258740I
−6.87603 − 1.37349I 0
u = −0.798601 − 0.772998I
a = 1.096920 + 0.166790I
b = 0.033875 + 1.258740I
−6.87603 + 1.37349I 0
u = 0.586527 + 0.945687I
a = −1.79270 − 1.01470I
b = 0.395995 − 0.919848I
−2.26153 − 3.00983I 0
u = 0.586527 − 0.945687I
a = −1.79270 + 1.01470I
b = 0.395995 + 0.919848I
−2.26153 + 3.00983I 0
u = −0.471722 + 1.010740I
a = −2.48364 − 0.23893I
b = 0.651889 + 1.129260I
−2.77315 + 6.92377I 0
u = −0.471722 − 1.010740I
a = −2.48364 + 0.23893I
b = 0.651889 − 1.129260I
−2.77315 − 6.92377I 0
u = −1.021560 + 0.502568I
a = −0.452502 − 0.480269I
b = 0.617119 − 0.992602I
3.07312 − 5.61606I 0
u = −1.021560 − 0.502568I
a = −0.452502 + 0.480269I
b = 0.617119 + 0.992602I
3.07312 + 5.61606I 0
u = 1.123980 + 0.220654I
a = 0.425729 + 0.019981I
b = −0.474341 + 0.926493I
0.22584 − 2.46461I 0
u = 1.123980 − 0.220654I
a = 0.425729 − 0.019981I
b = −0.474341 − 0.926493I
0.22584 + 2.46461I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.769853 + 0.852318I
a = 0.864593 + 0.257379I
b = −0.066555 + 1.321620I
−10.45800 − 2.88090I 0
u = 0.769853 − 0.852318I
a = 0.864593 − 0.257379I
b = −0.066555 − 1.321620I
−10.45800 + 2.88090I 0
u = −0.361388 + 1.098660I
a = −0.11965 + 1.46530I
b = 0.404116 − 0.907512I
−2.25457 − 0.19023I 0
u = −0.361388 − 1.098660I
a = −0.11965 − 1.46530I
b = 0.404116 + 0.907512I
−2.25457 + 0.19023I 0
u = −0.358618 + 0.763180I
a = 0.471283 + 0.174177I
b = −0.537085 + 1.290420I
−3.83566 − 3.43814I 0.61318 − 1.44912I
u = −0.358618 − 0.763180I
a = 0.471283 − 0.174177I
b = −0.537085 − 1.290420I
−3.83566 + 3.43814I 0.61318 + 1.44912I
u = −0.684043 + 0.947304I
a = 0.721420 − 0.287781I
b = −0.157119 − 1.376880I
−6.29574 + 6.95849I 0
u = −0.684043 − 0.947304I
a = 0.721420 + 0.287781I
b = −0.157119 + 1.376880I
−6.29574 − 6.95849I 0
u = −0.617119 + 0.992602I
a = −0.89496 + 1.13273I
b = 1.021560 − 0.502568I
−3.07312 + 5.61606I 0
u = −0.617119 − 0.992602I
a = −0.89496 − 1.13273I
b = 1.021560 + 0.502568I
−3.07312 − 5.61606I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.443550 + 1.114320I
a = −0.636408 − 0.138775I
b = 0.637561 − 0.134384I
5.24580 − 3.85196I 0
u = 0.443550 − 1.114320I
a = −0.636408 + 0.138775I
b = 0.637561 + 0.134384I
5.24580 + 3.85196I 0
u = 0.613830 + 1.034560I
a = 2.09577 + 0.54409I
b = −0.613830 + 1.034560I
− 7.63074I 0
u = 0.613830 − 1.034560I
a = 2.09577 − 0.54409I
b = −0.613830 − 1.034560I
7.63074I 0
u = −0.365401 + 0.697232I
a = −0.790767 + 0.184744I
b = 0.430621 + 0.240473I
0.192499 + 1.200880I 3.44276 − 4.83413I
u = −0.365401 − 0.697232I
a = −0.790767 − 0.184744I
b = 0.430621 − 0.240473I
0.192499 − 1.200880I 3.44276 + 4.83413I
u = −1.078720 + 0.561603I
a = 0.410171 + 0.130932I
b = −0.687566 + 1.140520I
−1.99246 − 9.73563I 0
u = −1.078720 − 0.561603I
a = 0.410171 − 0.130932I
b = −0.687566 − 1.140520I
−1.99246 + 9.73563I 0
u = −0.033875 + 1.258740I
a = −1.59344 + 0.20088I
b = 0.798601 − 0.772998I
6.87603 + 1.37349I 0
u = −0.033875 − 1.258740I
a = −1.59344 − 0.20088I
b = 0.798601 + 0.772998I
6.87603 − 1.37349I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.655409 + 1.077200I
a = −2.11903 − 0.25132I
b = 0.703968 − 1.167180I
−5.18587 − 11.86060I 0
u = 0.655409 − 1.077200I
a = −2.11903 + 0.25132I
b = 0.703968 + 1.167180I
−5.18587 + 11.86060I 0
u = −0.119816 + 0.724230I
a = −3.31363 + 0.21378I
b = 0.496811 + 0.533389I
−0.110831 − 0.799402I 3.78510 − 2.23405I
u = −0.119816 − 0.724230I
a = −3.31363 − 0.21378I
b = 0.496811 − 0.533389I
−0.110831 + 0.799402I 3.78510 + 2.23405I
u = −0.496811 + 0.533389I
a = −2.32822 + 1.78680I
b = 0.119816 + 0.724230I
0.110831 − 0.799402I −3.78510 − 2.23405I
u = −0.496811 − 0.533389I
a = −2.32822 − 1.78680I
b = 0.119816 − 0.724230I
0.110831 + 0.799402I −3.78510 + 2.23405I
u = −0.651889 + 1.129260I
a = −1.52240 + 0.84713I
b = 0.471722 + 1.010740I
2.77315 + 6.92377I 0
u = −0.651889 − 1.129260I
a = −1.52240 − 0.84713I
b = 0.471722 − 1.010740I
2.77315 − 6.92377I 0
u = 0.066555 + 1.321620I
a = 1.45861 − 0.47999I
b = −0.769853 + 0.852318I
10.45800 − 2.88090I 0
u = 0.066555 − 1.321620I
a = 1.45861 + 0.47999I
b = −0.769853 − 0.852318I
10.45800 + 2.88090I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.687566 + 1.140520I
a = −0.821367 − 0.858877I
b = 1.078720 + 0.561603I
1.99246 − 9.73563I 0
u = 0.687566 − 1.140520I
a = −0.821367 + 0.858877I
b = 1.078720 − 0.561603I
1.99246 + 9.73563I 0
u = 0.616284 + 1.184160I
a = 0.579368 + 0.788710I
b = −0.812254 − 0.547196I
6.80158 − 6.33791I 0
u = 0.616284 − 1.184160I
a = 0.579368 − 0.788710I
b = −0.812254 + 0.547196I
6.80158 + 6.33791I 0
u = −0.637561 + 0.134384I
a = 0.495827 − 0.083510I
b = −0.443550 − 1.114320I
−5.24580 + 3.85196I −8.95635 − 3.01207I
u = −0.637561 − 0.134384I
a = 0.495827 + 0.083510I
b = −0.443550 + 1.114320I
−5.24580 − 3.85196I −8.95635 + 3.01207I
u = 0.645090
a = −0.735762
b = −0.330483
2.22439 4.34230
u = −0.703968 + 1.167180I
a = 1.76924 − 0.55256I
b = −0.655409 − 1.077200I
5.18587 + 11.86060I 0
u = −0.703968 − 1.167180I
a = 1.76924 + 0.55256I
b = −0.655409 + 1.077200I
5.18587 − 11.86060I 0
u = 0.157119 + 1.376880I
a = −1.29707 + 0.71694I
b = 0.684043 − 0.947304I
6.29574 − 6.95849I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157119 − 1.376880I
a = −1.29707 − 0.71694I
b = 0.684043 + 0.947304I
6.29574 + 6.95849I 0
u = −0.748964 + 1.177590I
a = −1.81834 + 0.32952I
b = 0.748964 + 1.177590I
16.3231I 0
u = −0.748964 − 1.177590I
a = −1.81834 − 0.32952I
b = 0.748964 − 1.177590I
− 16.3231I 0
u = 0.537085 + 1.290420I
a = −0.079296 − 0.880909I
b = 0.358618 + 0.763180I
3.83566 − 3.43814I 0
u = 0.537085 − 1.290420I
a = −0.079296 + 0.880909I
b = 0.358618 − 0.763180I
3.83566 + 3.43814I 0
u = −0.430621 + 0.240473I
a = −0.693685 + 0.556563I
b = 0.365401 + 0.697232I
−0.192499 + 1.200880I −3.44276 − 4.83413I
u = −0.430621 − 0.240473I
a = −0.693685 − 0.556563I
b = 0.365401 − 0.697232I
−0.192499 − 1.200880I −3.44276 + 4.83413I
u = 0.330483
a = 2.08127
b = −0.645090
−2.22439 −4.34230
13
II. I
u
2
= hb, u
4
+ u
2
+ a + u, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
−u
4
− u
2
− u
0
a
2
=
1
0
a
7
=
−u
4
− u
2
− u
0
a
5
=
−u
4
− u
2
− u + 1
u
2
a
1
=
1
0
a
10
=
u
u
3
+ u
a
12
=
u
3
u
4
− u
3
+ u
2
+ 1
a
9
=
−u
3
u
3
+ u
a
8
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
− 3u
3
+ u
2
− 3u
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
5
c
3
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
4
, c
5
(u − 1)
5
c
7
(u + 1)
5
c
8
, c
9
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
10
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
11
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
12
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
5
c
3
, c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
4
, c
5
, c
7
(y −1)
5
c
8
, c
9
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
11
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.896438 − 0.890762I
b = 0
−1.31583 + 1.53058I −1.49901 − 3.45976I
u = −0.339110 − 0.822375I
a = 0.896438 + 0.890762I
b = 0
−1.31583 − 1.53058I −1.49901 + 3.45976I
u = 0.766826
a = −1.70062
b = 0
0.756147 −3.75670
u = 0.455697 + 1.200150I
a = 0.453870 + 0.402731I
b = 0
4.22763 − 4.40083I 2.37737 + 5.82971I
u = 0.455697 − 1.200150I
a = 0.453870 − 0.402731I
b = 0
4.22763 + 4.40083I 2.37737 − 5.82971I
17
III. I
v
1
= ha, −2v
4
+ v
3
+ 3v
2
+ b − 6v + 2, v
5
− v
4
− v
3
+ 4v
2
− 3v + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
v
0
a
4
=
1
0
a
6
=
0
2v
4
− v
3
− 3v
2
+ 6v − 2
a
2
=
1
v
4
− v
3
− v
2
+ 4v − 3
a
7
=
2v
4
− v
3
− 3v
2
+ 6v − 2
−v
3
+ v − 2
a
5
=
−2v
4
+ v
3
+ 3v
2
− 7v + 3
v
3
− 2v + 3
a
1
=
v
4
− v
3
− v
2
+ 4v − 2
v
4
− v
3
− v
2
+ 4v − 3
a
10
=
v
0
a
12
=
v
0
a
9
=
−v
4
+ v
3
+ v
2
− 3v + 2
−v
4
+ v
3
+ v
2
− 4v + 3
a
8
=
−v
4
+ v
3
+ v
2
− 4v + 2
−v
4
+ v
3
+ v
2
− 4v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7v
4
+ 2v
3
+ 9v
2
− 23v + 7
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
10
, c
11
u
5
c
4
, c
5
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
, c
9
(u + 1)
5
c
12
(u − 1)
5
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
c
2
, c
6
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
3
, c
10
, c
11
y
5
c
4
, c
5
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
8
, c
9
, c
12
(y − 1)
5
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.896438 + 0.890762I
a = 0
b = −0.339110 − 0.822375I
1.31583 + 1.53058I 1.49901 − 3.45976I
v = 0.896438 − 0.890762I
a = 0
b = −0.339110 + 0.822375I
1.31583 − 1.53058I 1.49901 + 3.45976I
v = 0.453870 + 0.402731I
a = 0
b = 0.455697 + 1.200150I
−4.22763 + 4.40083I −2.37737 − 5.82971I
v = 0.453870 − 0.402731I
a = 0
b = 0.455697 − 1.200150I
−4.22763 − 4.40083I −2.37737 + 5.82971I
v = −1.70062
a = 0
b = 0.766826
−0.756147 3.75670
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
5
(u
5
− 3u
4
+ ··· − u + 1)(u
88
+ 36u
87
+ ··· + 3584u + 1024)
c
2
u
5
(u
5
− u
4
+ ··· + u − 1)(u
88
− 2u
87
+ ··· − 128u + 32)
c
3
u
5
(u
5
− u
4
+ ··· + u − 1)(u
88
+ 2u
87
+ ··· + 128u + 32)
c
4
, c
5
((u − 1)
5
)(u
5
+ u
4
+ ··· + u − 1)(u
88
− 7u
87
+ ··· + 9u − 1)
c
6
u
5
(u
5
+ u
4
+ ··· + u + 1)(u
88
− 2u
87
+ ··· − 128u + 32)
c
7
((u + 1)
5
)(u
5
− u
4
+ ··· + u + 1)(u
88
− 7u
87
+ ··· + 9u − 1)
c
8
, c
9
((u + 1)
5
)(u
5
− u
4
+ ··· + u + 1)(u
88
+ 7u
87
+ ··· − 9u − 1)
c
10
u
5
(u
5
+ u
4
+ ··· + u + 1)(u
88
+ 2u
87
+ ··· + 128u + 32)
c
11
u
5
(u
5
− 3u
4
+ ··· − u + 1)(u
88
− 36u
87
+ ··· − 3584u + 1024)
c
12
((u − 1)
5
)(u
5
+ u
4
+ ··· + u − 1)(u
88
+ 7u
87
+ ··· − 9u − 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
88
+ 24y
87
+ ··· − 66715648y + 1048576)
c
2
, c
3
, c
6
c
10
y
5
(y
5
+ 3y
4
+ ··· − y − 1)(y
88
+ 36y
87
+ ··· + 3584y + 1024)
c
4
, c
5
, c
7
c
8
, c
9
, c
12
((y − 1)
5
)(y
5
− 5y
4
+ ··· − y − 1)(y
88
− 77y
87
+ ··· − 57y + 1)
23
