12a
0556
(K12a
0556
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 2 6 4 12 1 5 10
Solving Sequence
2,6
7 3 8
1,11
5 4 9 10 12
c
6
c
2
c
7
c
1
c
5
c
4
c
8
c
10
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.07057 × 10
77
u
84
− 1.50389 × 10
77
u
83
+ ··· + 2.53839 × 10
77
b + 9.88146 × 10
77
,
4.68186 × 10
77
u
84
− 4.98399 × 10
77
u
83
+ ··· + 7.61518 × 10
77
a + 1.56488 × 10
78
, u
85
− 2u
84
+ ··· + 3u − 9i
I
u
2
= hb, u
4
− u
2
+ a − 2u + 1, u
5
+ u
4
− u
2
+ u + 1i
I
u
3
= h−u
3
a − u
2
a + 2u
3
+ au − u
2
+ 2b − u + 1, −2u
3
a + u
2
a + 3u
3
+ a
2
+ au − u
2
− a − 2u, u
4
− u
2
+ 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
= h1.07 × 10
77
u
84
− 1.50 × 10
77
u
83
+ · · · + 2.54 × 10
77
b + 9.88 × 10
77
, 4.68 ×
10
77
u
84
−4.98×10
77
u
83
+· · ·+7.62×10
77
a+1.56×10
78
, u
85
−2u
84
+· · ·+3u−9i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−0.614806u
84
+ 0.654481u
83
+ ··· + 9.36540u − 2.05495
−0.421753u
84
+ 0.592456u
83
+ ··· − 1.27756u − 3.89280
a
5
=
0.681235u
84
− 0.376546u
83
+ ··· − 7.23243u + 7.03410
−0.191650u
84
− 0.675652u
83
+ ··· + 8.48193u + 7.43904
a
4
=
1.86822u
84
− 0.943208u
83
+ ··· − 12.5547u + 7.89357
−0.0907235u
84
− 1.88072u
83
+ ··· + 17.6608u + 14.6758
a
9
=
1.63065u
84
− 3.35202u
83
+ ··· + 13.0436u + 22.5528
−2.79323u
84
+ 3.46800u
83
+ ··· − 2.28892u − 16.8140
a
10
=
0.699998u
84
− 1.53125u
83
+ ··· + 14.4778u + 10.2525
−1.30758u
84
+ 1.53849u
83
+ ··· − 1.30083u − 10.6368
a
12
=
−1.80393u
84
+ 3.41357u
83
+ ··· − 3.48625u − 22.2978
3.09725u
84
− 3.65415u
83
+ ··· + 0.275477u + 18.2000
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.269673u
84
− 0.693788u
83
+ ··· + 4.57663u − 2.13190
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
85
+ 28u
84
+ ··· + 1107u + 81
c
2
, c
6
u
85
− 2u
84
+ ··· + 3u − 9
c
3
, c
4
, c
8
u
85
− 2u
84
+ ··· + 144u − 36
c
5
, c
11
u
85
+ u
84
+ ··· − 96u − 32
c
9
, c
10
, c
12
u
85
− 10u
84
+ ··· + 17u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
85
+ 64y
84
+ ··· + 485595y −6561
c
2
, c
6
y
85
− 28y
84
+ ··· + 1107y −81
c
3
, c
4
, c
8
y
85
+ 80y
84
+ ··· + 16776y −1296
c
5
, c
11
y
85
+ 45y
84
+ ··· + 22016y −1024
c
9
, c
10
, c
12
y
85
− 80y
84
+ ··· − 91y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.998621
a = −0.294335
b = 1.06804
−5.84228 −16.3890
u = −0.806816 + 0.599615I
a = 0.703510 + 0.591628I
b = −0.319657 + 0.693146I
−0.43718 + 2.02855I 0
u = −0.806816 − 0.599615I
a = 0.703510 − 0.591628I
b = −0.319657 − 0.693146I
−0.43718 − 2.02855I 0
u = 0.984839 + 0.081448I
a = 0.48248 + 1.60444I
b = −0.198977 + 1.034500I
−3.82226 − 2.23236I −15.8479 + 4.6950I
u = 0.984839 − 0.081448I
a = 0.48248 − 1.60444I
b = −0.198977 − 1.034500I
−3.82226 + 2.23236I −15.8479 − 4.6950I
u = 1.016480 + 0.146739I
a = 0.131558 − 0.758826I
b = −1.033670 − 0.298635I
−2.02964 − 3.37819I 0
u = 1.016480 − 0.146739I
a = 0.131558 + 0.758826I
b = −1.033670 + 0.298635I
−2.02964 + 3.37819I 0
u = 0.709986 + 0.663321I
a = 2.20996 + 0.27167I
b = −0.850401 + 0.427141I
−1.108310 + 0.109986I −8.00000 + 0.I
u = 0.709986 − 0.663321I
a = 2.20996 − 0.27167I
b = −0.850401 − 0.427141I
−1.108310 − 0.109986I −8.00000 + 0.I
u = −0.900145 + 0.529083I
a = 5.92919 − 1.06315I
b = −0.309938 + 0.046527I
−0.08293 + 2.04372I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.900145 − 0.529083I
a = 5.92919 + 1.06315I
b = −0.309938 − 0.046527I
−0.08293 − 2.04372I 0
u = −0.724002 + 0.754097I
a = −0.922405 + 0.673843I
b = 0.555009 − 0.921380I
1.77796 − 1.79805I 0
u = −0.724002 − 0.754097I
a = −0.922405 − 0.673843I
b = 0.555009 + 0.921380I
1.77796 + 1.79805I 0
u = 0.775319 + 0.522980I
a = −0.458774 + 0.800072I
b = 0.235131 − 0.116553I
1.78078 − 2.10361I 0. + 4.46892I
u = 0.775319 − 0.522980I
a = −0.458774 − 0.800072I
b = 0.235131 + 0.116553I
1.78078 + 2.10361I 0. − 4.46892I
u = 0.268293 + 0.888731I
a = −0.732829 + 0.719131I
b = 0.581673 − 1.021050I
0.28979 − 6.12813I −7.02703 + 5.51860I
u = 0.268293 − 0.888731I
a = −0.732829 − 0.719131I
b = 0.581673 + 1.021050I
0.28979 + 6.12813I −7.02703 − 5.51860I
u = −0.711753 + 0.806285I
a = −1.84218 + 0.24993I
b = 1.26596 + 0.66556I
4.32861 − 2.99556I 0
u = −0.711753 − 0.806285I
a = −1.84218 − 0.24993I
b = 1.26596 − 0.66556I
4.32861 + 2.99556I 0
u = 0.867038 + 0.661822I
a = −1.308520 + 0.434436I
b = −0.06260 − 1.87617I
−5.78886 − 2.56710I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.867038 − 0.661822I
a = −1.308520 − 0.434436I
b = −0.06260 + 1.87617I
−5.78886 + 2.56710I 0
u = 0.759915 + 0.787119I
a = −0.139375 − 0.369733I
b = 0.543133 + 1.290540I
5.21127 − 0.29207I 0
u = 0.759915 − 0.787119I
a = −0.139375 + 0.369733I
b = 0.543133 − 1.290540I
5.21127 + 0.29207I 0
u = −0.674977 + 0.862853I
a = 0.848112 − 1.114180I
b = −0.606952 + 1.131660I
−3.29308 − 5.51174I 0
u = −0.674977 − 0.862853I
a = 0.848112 + 1.114180I
b = −0.606952 − 1.131660I
−3.29308 + 5.51174I 0
u = −0.996557 + 0.465595I
a = 1.127330 + 0.051322I
b = 0.09960 − 1.43805I
−8.63067 + 1.50287I 0
u = −0.996557 − 0.465595I
a = 1.127330 − 0.051322I
b = 0.09960 + 1.43805I
−8.63067 − 1.50287I 0
u = 0.693699 + 0.854594I
a = 0.694895 + 0.626975I
b = −0.729780 − 1.197990I
7.72360 + 5.45340I 0
u = 0.693699 − 0.854594I
a = 0.694895 − 0.626975I
b = −0.729780 + 1.197990I
7.72360 − 5.45340I 0
u = −0.873454 + 0.207048I
a = 1.70854 − 0.67125I
b = −0.20097 − 1.51805I
−8.29116 + 1.11793I −14.9646 + 1.4167I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873454 − 0.207048I
a = 1.70854 + 0.67125I
b = −0.20097 + 1.51805I
−8.29116 − 1.11793I −14.9646 − 1.4167I
u = 0.631492 + 0.905031I
a = −0.944080 − 0.902830I
b = 0.83894 + 1.21192I
2.45406 + 10.41200I 0
u = 0.631492 − 0.905031I
a = −0.944080 + 0.902830I
b = 0.83894 − 1.21192I
2.45406 − 10.41200I 0
u = −0.886138 + 0.123069I
a = −0.92190 − 1.99206I
b = −0.053379 − 0.976140I
−0.667588 + 1.025160I −12.54308 − 0.08033I
u = −0.886138 − 0.123069I
a = −0.92190 + 1.99206I
b = −0.053379 + 0.976140I
−0.667588 − 1.025160I −12.54308 + 0.08033I
u = 0.850775 + 0.712293I
a = 0.798573 + 0.967990I
b = −0.612070 − 0.514601I
2.60791 − 2.73509I 0
u = 0.850775 − 0.712293I
a = 0.798573 − 0.967990I
b = −0.612070 + 0.514601I
2.60791 + 2.73509I 0
u = −1.093410 + 0.191489I
a = −0.21969 + 1.48130I
b = 0.482351 + 1.025410I
0.65643 + 5.42394I 0
u = −1.093410 − 0.191489I
a = −0.21969 − 1.48130I
b = 0.482351 − 1.025410I
0.65643 − 5.42394I 0
u = −0.922652 + 0.626826I
a = −1.48767 + 0.81968I
b = 0.235613 + 0.929059I
−0.82236 + 2.80542I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.922652 − 0.626826I
a = −1.48767 − 0.81968I
b = 0.235613 − 0.929059I
−0.82236 − 2.80542I 0
u = 1.105020 + 0.170837I
a = −0.762252 − 0.928102I
b = 0.412640 − 1.334080I
−10.32480 − 5.23736I 0
u = 1.105020 − 0.170837I
a = −0.762252 + 0.928102I
b = 0.412640 + 1.334080I
−10.32480 + 5.23736I 0
u = 1.034710 + 0.424655I
a = 0.678821 + 0.419020I
b = 0.453832 + 0.596946I
2.03787 − 1.45102I 0
u = 1.034710 − 0.424655I
a = 0.678821 − 0.419020I
b = 0.453832 − 0.596946I
2.03787 + 1.45102I 0
u = 0.887489 + 0.698307I
a = −1.81058 + 0.09319I
b = 0.549211 − 0.690031I
2.49176 − 2.67187I 0
u = 0.887489 − 0.698307I
a = −1.81058 − 0.09319I
b = 0.549211 + 0.690031I
2.49176 + 2.67187I 0
u = 0.759240 + 0.855036I
a = −0.365619 − 1.259310I
b = 0.353657 + 0.964749I
−1.327970 − 0.401840I 0
u = 0.759240 − 0.855036I
a = −0.365619 + 1.259310I
b = 0.353657 − 0.964749I
−1.327970 + 0.401840I 0
u = 0.967500 + 0.663999I
a = −1.16043 − 1.12609I
b = 1.042120 + 0.405267I
−1.88422 − 5.29403I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.967500 − 0.663999I
a = −1.16043 + 1.12609I
b = 1.042120 − 0.405267I
−1.88422 + 5.29403I 0
u = −0.826690 + 0.842297I
a = 1.264590 − 0.276686I
b = −1.032940 − 0.397310I
10.14220 + 0.91099I 0
u = −0.826690 − 0.842297I
a = 1.264590 + 0.276686I
b = −1.032940 + 0.397310I
10.14220 − 0.91099I 0
u = −0.979456 + 0.706863I
a = 1.99453 − 0.39746I
b = −0.548510 − 1.048100I
1.00480 + 7.36064I 0
u = −0.979456 − 0.706863I
a = 1.99453 + 0.39746I
b = −0.548510 + 1.048100I
1.00480 − 7.36064I 0
u = −1.200290 + 0.153170I
a = 0.338551 − 0.939110I
b = −0.631973 − 1.218280I
−4.88195 + 9.31216I 0
u = −1.200290 − 0.153170I
a = 0.338551 + 0.939110I
b = −0.631973 + 1.218280I
−4.88195 − 9.31216I 0
u = 0.967716 + 0.732266I
a = 1.56362 + 0.49238I
b = −0.42587 + 1.36774I
4.57399 − 5.44218I 0
u = 0.967716 − 0.732266I
a = 1.56362 − 0.49238I
b = −0.42587 − 1.36774I
4.57399 + 5.44218I 0
u = −1.000590 + 0.727268I
a = 0.73771 − 1.21462I
b = −1.35820 + 0.57857I
3.44867 + 8.76620I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.000590 − 0.727268I
a = 0.73771 + 1.21462I
b = −1.35820 − 0.57857I
3.44867 − 8.76620I 0
u = −0.946573 + 0.803204I
a = −0.739615 + 0.818673I
b = 1.022410 − 0.261567I
9.77457 + 5.21014I 0
u = −0.946573 − 0.803204I
a = −0.739615 − 0.818673I
b = 1.022410 + 0.261567I
9.77457 − 5.21014I 0
u = 0.995841 + 0.763155I
a = 1.69209 − 0.43161I
b = −0.479759 + 1.044820I
−2.07273 − 5.62883I 0
u = 0.995841 − 0.763155I
a = 1.69209 + 0.43161I
b = −0.479759 − 1.044820I
−2.07273 + 5.62883I 0
u = 0.147072 + 0.728915I
a = 0.683793 − 0.110743I
b = −0.656032 + 0.815272I
4.76220 − 2.53471I −1.46695 + 3.47281I
u = 0.147072 − 0.728915I
a = 0.683793 + 0.110743I
b = −0.656032 − 0.815272I
4.76220 + 2.53471I −1.46695 − 3.47281I
u = −0.150086 + 0.725683I
a = 0.54471 + 1.31256I
b = −0.202918 − 1.187480I
−6.11100 + 2.42065I −11.51467 − 3.42821I
u = −0.150086 − 0.725683I
a = 0.54471 − 1.31256I
b = −0.202918 + 1.187480I
−6.11100 − 2.42065I −11.51467 + 3.42821I
u = 1.027010 + 0.742791I
a = −1.86187 − 0.57547I
b = 0.67693 − 1.27703I
6.70036 − 11.40770I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.027010 − 0.742791I
a = −1.86187 + 0.57547I
b = 0.67693 + 1.27703I
6.70036 + 11.40770I 0
u = −0.730565
a = 0.0171409
b = −0.401918
−1.07739 −9.03050
u = −1.038750 + 0.736760I
a = −2.04598 + 0.10778I
b = 0.672589 + 1.206980I
−4.41235 + 11.46610I 0
u = −1.038750 − 0.736760I
a = −2.04598 − 0.10778I
b = 0.672589 − 1.206980I
−4.41235 − 11.46610I 0
u = 1.166100 + 0.516708I
a = −0.690535 + 0.225074I
b = −0.402473 − 1.048200I
−2.57120 + 1.00877I 0
u = 1.166100 − 0.516708I
a = −0.690535 − 0.225074I
b = −0.402473 + 1.048200I
−2.57120 − 1.00877I 0
u = 1.073740 + 0.736661I
a = 2.00421 + 0.50463I
b = −0.84789 + 1.28835I
1.0897 − 16.4761I 0
u = 1.073740 − 0.736661I
a = 2.00421 − 0.50463I
b = −0.84789 − 1.28835I
1.0897 + 16.4761I 0
u = −0.942740 + 0.934437I
a = −0.350351 − 0.512078I
b = 0.061691 + 0.565881I
8.96196 + 3.42091I 0
u = −0.942740 − 0.934437I
a = −0.350351 + 0.512078I
b = 0.061691 − 0.565881I
8.96196 − 3.42091I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.111200 + 0.545459I
a = −1.08297 − 1.20293I
b = 0.699790 − 0.645759I
1.50806 + 1.20124I −5.48394 − 0.07233I
u = −0.111200 − 0.545459I
a = −1.08297 + 1.20293I
b = 0.699790 + 0.645759I
1.50806 − 1.20124I −5.48394 + 0.07233I
u = −0.193935 + 0.335714I
a = −1.051420 − 0.253121I
b = 0.180316 + 0.662567I
−0.404941 + 0.957173I −6.94345 − 7.00511I
u = −0.193935 − 0.335714I
a = −1.051420 + 0.253121I
b = 0.180316 − 0.662567I
−0.404941 − 0.957173I −6.94345 + 7.00511I
u = 0.311045
a = 3.80168
b = −0.461365
−2.06404 −1.31720
13
II. I
u
2
= hb, u
4
− u
2
+ a − 2u + 1, u
5
+ u
4
− u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
1
=
u
3
−u
4
− u
3
+ u
2
− 1
a
11
=
−u
4
+ u
2
+ 2u − 1
0
a
5
=
1
0
a
4
=
u
4
− u
2
+ 1
−u
4
a
9
=
−u
3
u
4
+ u
3
− u
2
+ 1
a
10
=
−u
4
− u
3
+ u
2
+ 2u − 1
u
4
+ u
3
− u
2
+ 1
a
12
=
−u
4
+ u
2
+ 2u − 1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u
4
− u
3
+ 2u
2
+ 4u − 17
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
2
u
5
− u
4
+ u
2
+ u − 1
c
5
, c
11
u
5
c
6
u
5
+ u
4
− u
2
+ u + 1
c
7
, c
8
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
9
, c
10
(u − 1)
5
c
12
(u + 1)
5
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
8
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
2
, c
6
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
c
5
, c
11
y
5
c
9
, c
10
, c
12
(y −1)
5
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758138 + 0.584034I
a = 1.47956 + 1.63976I
b = 0
0.17487 − 2.21397I −6.59361 − 0.42541I
u = 0.758138 − 0.584034I
a = 1.47956 − 1.63976I
b = 0
0.17487 + 2.21397I −6.59361 + 0.42541I
u = −0.935538 + 0.903908I
a = 0.044146 + 0.313338I
b = 0
9.31336 + 3.33174I 3.61324 + 0.36944I
u = −0.935538 − 0.903908I
a = 0.044146 − 0.313338I
b = 0
9.31336 − 3.33174I 3.61324 − 0.36944I
u = −0.645200
a = −2.04741
b = 0
−2.52712 −20.0390
17
III. I
u
3
= h−u
3
a − u
2
a + 2u
3
+ au − u
2
+ 2b − u + 1, −2u
3
a + u
2
a + 3u
3
+
a
2
+ au − u
2
− a − 2u, u
4
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
1
=
u
3
0
a
11
=
a
1
2
u
3
a − u
3
+ ··· +
1
2
u −
1
2
a
5
=
−
1
2
u
2
a −
1
2
u
3
+ ··· +
1
2
a −
1
2
−
1
2
u
3
a +
1
2
u
2
a + ··· +
1
2
u −
3
2
a
4
=
−
1
2
u
2
a −
1
2
u
3
+ ··· +
1
2
a −
1
2
−
1
2
u
3
a − u
3
+ ··· +
3
2
u −
3
2
a
9
=
1
2
u
2
a −
3
2
u
3
+ ··· −
1
2
a +
1
2
−
1
2
u
3
a + 2u
3
+ ··· −
1
2
u +
1
2
a
10
=
−
1
2
u
3
a + u
3
+ ··· + a +
1
2
1
2
u
3
a − u
3
+ ··· +
1
2
u −
1
2
a
12
=
1
2
u
3
a −
3
2
u
3
+ ··· −
1
2
a +
5
2
u
−
1
2
u
3
a + 2u
3
+ ··· −
1
2
u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
c
2
, c
6
(u
4
− u
2
+ 1)
2
c
3
, c
4
, c
8
(u
2
+ 1)
4
c
5
, c
11
(u
4
+ 3u
2
+ 1)
2
c
7
(u
2
+ u + 1)
4
c
9
, c
10
(u
2
+ u − 1)
4
c
12
(u
2
− u − 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
+ y + 1)
4
c
2
, c
6
(y
2
− y + 1)
4
c
3
, c
4
, c
8
(y + 1)
8
c
5
, c
11
(y
2
+ 3y + 1)
4
c
9
, c
10
, c
12
(y
2
− 3y + 1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 1.344250 − 0.092242I
b = 0.618034I
0.65797 − 2.02988I −10.00000 + 3.46410I
u = 0.866025 + 0.500000I
a = −1.71028 + 0.72622I
b = − 1.61803I
−7.23771 − 2.02988I −10.00000 + 3.46410I
u = 0.866025 − 0.500000I
a = 1.344250 + 0.092242I
b = − 0.618034I
0.65797 + 2.02988I −10.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = −1.71028 − 0.72622I
b = 1.61803I
−7.23771 + 2.02988I −10.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = 1.092240 − 0.344250I
b = − 1.61803I
−7.23771 + 2.02988I −10.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = 0.27378 + 2.71028I
b = 0.618034I
0.65797 + 2.02988I −10.00000 − 3.46410I
u = −0.866025 − 0.500000I
a = 1.092240 + 0.344250I
b = 1.61803I
−7.23771 − 2.02988I −10.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = 0.27378 − 2.71028I
b = − 0.618034I
0.65797 − 2.02988I −10.00000 + 3.46410I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
85
+ 28u
84
+ ··· + 1107u + 81)
c
2
((u
4
− u
2
+ 1)
2
)(u
5
− u
4
+ u
2
+ u − 1)(u
85
− 2u
84
+ ··· + 3u − 9)
c
3
, c
4
((u
2
+ 1)
4
)(u
5
− u
4
+ ··· + 3u − 1)(u
85
− 2u
84
+ ··· + 144u − 36)
c
5
, c
11
u
5
(u
4
+ 3u
2
+ 1)
2
(u
85
+ u
84
+ ··· − 96u − 32)
c
6
((u
4
− u
2
+ 1)
2
)(u
5
+ u
4
− u
2
+ u + 1)(u
85
− 2u
84
+ ··· + 3u − 9)
c
7
(u
2
+ u + 1)
4
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
· (u
85
+ 28u
84
+ ··· + 1107u + 81)
c
8
((u
2
+ 1)
4
)(u
5
+ u
4
+ ··· + 3u + 1)(u
85
− 2u
84
+ ··· + 144u − 36)
c
9
, c
10
((u − 1)
5
)(u
2
+ u − 1)
4
(u
85
− 10u
84
+ ··· + 17u − 1)
c
12
((u + 1)
5
)(u
2
− u − 1)
4
(u
85
− 10u
84
+ ··· + 17u − 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
+ y + 1)
4
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
· (y
85
+ 64y
84
+ ··· + 485595y −6561)
c
2
, c
6
(y
2
− y + 1)
4
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
· (y
85
− 28y
84
+ ··· + 1107y −81)
c
3
, c
4
, c
8
(y + 1)
8
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
· (y
85
+ 80y
84
+ ··· + 16776y −1296)
c
5
, c
11
y
5
(y
2
+ 3y + 1)
4
(y
85
+ 45y
84
+ ··· + 22016y −1024)
c
9
, c
10
, c
12
((y −1)
5
)(y
2
− 3y + 1)
4
(y
85
− 80y
84
+ ··· − 91y −1)
23
