12a
0170
(K12a
0170
)
A knot diagram
1
Linearized knot diagam
3 5 9 6 2 10 11 4 1 12 7 8
Solving Sequence
7,11 4,8
9 12 1 3 10 6 5 2
c
7
c
8
c
11
c
12
c
3
c
10
c
6
c
4
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h8u
98
+ 22u
97
+ ··· + 2b − 8u, 8u
98
+ 24u
97
+ ··· + 2a − 11, u
99
+ 3u
98
+ ··· − 5u − 1i
I
u
2
= hu
2
a + b, u
4
+ u
2
a − 2u
3
+ a
2
− au + 3u
2
+ a − 2u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 109 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
=
h8u
98
+22u
97
+· · ·+2b−8u, 8u
98
+24u
97
+· · ·+2a−11, u
99
+3u
98
+· · ·−5u−1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−4u
98
− 12u
97
+ ··· + 27u +
11
2
−4u
98
− 11u
97
+ ··· +
19
2
u
2
+ 4u
a
8
=
1
−u
2
a
9
=
u
11
+ 2u
9
+ 2u
7
+ u
3
−u
13
− 3u
11
− 5u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
12
=
u
u
a
1
=
−u
3
u
5
+ u
3
+ u
a
3
=
4u
97
+ 8u
96
+ ··· − 11u
2
−
1
2
2u
97
+
7
2
u
96
+ ··· −
25
2
u
2
− 2u
a
10
=
u
3
u
3
+ u
a
6
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
5
=
−2u
98
−
9
2
u
97
+ ··· + 13u + 2
−2u
98
−
9
2
u
97
+ ··· − 2u
2
+
1
2
u
a
2
=
−
1
2
u
94
− u
93
+ ··· + 2u −
1
2
1
2
u
96
+ u
95
+ ··· +
3
2
u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
98
−
41
2
u
97
+ ··· + 55u +
15
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
99
+ 32u
98
+ ··· − 28u − 1
c
2
, c
5
u
99
+ 6u
98
+ ··· + 4u + 1
c
3
, c
8
u
99
+ u
98
+ ··· + 3072u + 1024
c
6
, c
12
u
99
+ 3u
98
+ ··· + 1403u + 73
c
7
, c
11
u
99
− 3u
98
+ ··· − 5u + 1
c
9
u
99
− 11u
98
+ ··· + 27259u + 3341
c
10
u
99
+ 53u
98
+ ··· − 13u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
99
+ 76y
98
+ ··· + 624y −1
c
2
, c
5
y
99
+ 32y
98
+ ··· − 28y −1
c
3
, c
8
y
99
+ 55y
98
+ ··· − 17825792y −1048576
c
6
, c
12
y
99
− 75y
98
+ ··· + 237579y −5329
c
7
, c
11
y
99
+ 53y
98
+ ··· − 13y −1
c
9
y
99
+ 25y
98
+ ··· − 762194377y −11162281
c
10
y
99
− 11y
98
+ ··· + 27y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.429848 + 0.885673I
a = −0.153546 − 0.767268I
b = −0.0361333 − 0.0736755I
−1.19873 − 2.05854I 0
u = −0.429848 − 0.885673I
a = −0.153546 + 0.767268I
b = −0.0361333 + 0.0736755I
−1.19873 + 2.05854I 0
u = 0.520030 + 0.825601I
a = 1.59459 + 1.62990I
b = 1.73104 + 0.30568I
0.30032 + 5.50967I 0
u = 0.520030 − 0.825601I
a = 1.59459 − 1.62990I
b = 1.73104 − 0.30568I
0.30032 − 5.50967I 0
u = −0.067585 + 0.970965I
a = 1.71635 + 0.65270I
b = 0.985452 + 0.092942I
−3.46773 − 2.14043I 0
u = −0.067585 − 0.970965I
a = 1.71635 − 0.65270I
b = 0.985452 − 0.092942I
−3.46773 + 2.14043I 0
u = 0.589960 + 0.841124I
a = −1.72526 − 1.03952I
b = −1.192410 − 0.035831I
7.81127 + 4.92186I 0
u = 0.589960 − 0.841124I
a = −1.72526 + 1.03952I
b = −1.192410 + 0.035831I
7.81127 − 4.92186I 0
u = 0.587785 + 0.858222I
a = 1.85438 + 1.06685I
b = 1.239810 − 0.106984I
6.97384 + 11.00210I 0
u = 0.587785 − 0.858222I
a = 1.85438 − 1.06685I
b = 1.239810 + 0.106984I
6.97384 − 11.00210I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.539698 + 0.786920I
a = 0.322917 − 1.006990I
b = −0.159118 + 0.087102I
3.08688 − 4.97900I 0
u = −0.539698 − 0.786920I
a = 0.322917 + 1.006990I
b = −0.159118 − 0.087102I
3.08688 + 4.97900I 0
u = 0.547960 + 0.768863I
a = −1.07630 − 1.33495I
b = −1.38296 − 0.64272I
3.91657 + 2.20363I 0
u = 0.547960 − 0.768863I
a = −1.07630 + 1.33495I
b = −1.38296 + 0.64272I
3.91657 − 2.20363I 0
u = −0.537978 + 0.751303I
a = −0.405247 + 0.942552I
b = 0.237597 − 0.042309I
3.19000 + 0.62409I 0
u = −0.537978 − 0.751303I
a = −0.405247 − 0.942552I
b = 0.237597 + 0.042309I
3.19000 − 0.62409I 0
u = 0.610078 + 0.689564I
a = −0.538676 − 0.708628I
b = −1.03942 − 1.00260I
8.24446 − 0.21969I 0
u = 0.610078 − 0.689564I
a = −0.538676 + 0.708628I
b = −1.03942 + 1.00260I
8.24446 + 0.21969I 0
u = 0.613989 + 0.666989I
a = 0.385176 + 0.652596I
b = 1.05850 + 1.08315I
7.51964 − 6.29705I 0
u = 0.613989 − 0.666989I
a = 0.385176 − 0.652596I
b = 1.05850 − 1.08315I
7.51964 + 6.29705I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.148795 + 1.100110I
a = 1.30891 + 1.51158I
b = 0.641318 + 1.037130I
1.74742 − 6.77346I 0
u = −0.148795 − 1.100110I
a = 1.30891 − 1.51158I
b = 0.641318 − 1.037130I
1.74742 + 6.77346I 0
u = −0.186308 + 1.098120I
a = −1.03578 − 1.47748I
b = −0.333673 − 0.963763I
2.34741 − 1.01757I 0
u = −0.186308 − 1.098120I
a = −1.03578 + 1.47748I
b = −0.333673 + 0.963763I
2.34741 + 1.01757I 0
u = 0.498411 + 0.706670I
a = 0.38383 + 1.60293I
b = 1.42427 + 1.06732I
0.65077 − 1.31271I −0.53545 + 1.30950I
u = 0.498411 − 0.706670I
a = 0.38383 − 1.60293I
b = 1.42427 − 1.06732I
0.65077 + 1.31271I −0.53545 − 1.30950I
u = −0.820785 + 0.171758I
a = 1.304340 + 0.375554I
b = −1.60855 + 1.40861I
3.47980 + 11.99530I −1.53503 − 7.47840I
u = −0.820785 − 0.171758I
a = 1.304340 − 0.375554I
b = −1.60855 − 1.40861I
3.47980 − 11.99530I −1.53503 + 7.47840I
u = 0.833946 + 0.012856I
a = 0.084871 − 0.732326I
b = −0.19316 + 1.42037I
−1.20309 + 2.61578I −0.20305 − 3.89462I
u = 0.833946 − 0.012856I
a = 0.084871 + 0.732326I
b = −0.19316 − 1.42037I
−1.20309 − 2.61578I −0.20305 + 3.89462I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.810571 + 0.181206I
a = −1.195870 − 0.405767I
b = 1.44493 − 1.40454I
4.51727 + 5.99226I 0.25329 − 2.79129I
u = −0.810571 − 0.181206I
a = −1.195870 + 0.405767I
b = 1.44493 + 1.40454I
4.51727 − 5.99226I 0.25329 + 2.79129I
u = 0.116457 + 0.819121I
a = 2.36072 − 0.47151I
b = 0.92714 − 1.16497I
−0.91323 + 2.95442I −9.15892 − 0.78061I
u = 0.116457 − 0.819121I
a = 2.36072 + 0.47151I
b = 0.92714 + 1.16497I
−0.91323 − 2.95442I −9.15892 + 0.78061I
u = −0.278900 + 0.753215I
a = −0.665243 + 0.280196I
b = −0.087537 + 0.193088I
−0.383982 − 1.218840I −4.66040 + 5.43923I
u = −0.278900 − 0.753215I
a = −0.665243 − 0.280196I
b = −0.087537 − 0.193088I
−0.383982 + 1.218840I −4.66040 − 5.43923I
u = −0.521477 + 1.085120I
a = −1.18894 − 0.85234I
b = −0.378212 − 0.754350I
4.02781 − 0.01979I 0
u = −0.521477 − 1.085120I
a = −1.18894 + 0.85234I
b = −0.378212 + 0.754350I
4.02781 + 0.01979I 0
u = −0.780382 + 0.143990I
a = 1.30030 + 0.80184I
b = −1.44582 + 0.86730I
−2.65965 + 5.88729I −5.59627 − 5.93514I
u = −0.780382 − 0.143990I
a = 1.30030 − 0.80184I
b = −1.44582 − 0.86730I
−2.65965 − 5.88729I −5.59627 + 5.93514I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.782638 + 0.077219I
a = 0.512667 − 0.508839I
b = −1.042870 + 0.788319I
−4.26717 − 1.31247I −9.29800 + 0.03301I
u = 0.782638 − 0.077219I
a = 0.512667 + 0.508839I
b = −1.042870 − 0.788319I
−4.26717 + 1.31247I −9.29800 − 0.03301I
u = 0.387534 + 1.152560I
a = 2.31597 + 0.24090I
b = 1.94984 − 1.44963I
−2.70236 + 3.53975I 0
u = 0.387534 − 1.152560I
a = 2.31597 − 0.24090I
b = 1.94984 + 1.44963I
−2.70236 − 3.53975I 0
u = −0.374340 + 1.157870I
a = 0.439971 − 0.718676I
b = 0.791182 + 0.555743I
−2.30156 − 0.62216I 0
u = −0.374340 − 1.157870I
a = 0.439971 + 0.718676I
b = 0.791182 − 0.555743I
−2.30156 + 0.62216I 0
u = −0.524450 + 1.104260I
a = 1.39278 + 0.74600I
b = 0.598909 + 0.920885I
4.36503 − 6.08039I 0
u = −0.524450 − 1.104260I
a = 1.39278 − 0.74600I
b = 0.598909 − 0.920885I
4.36503 + 6.08039I 0
u = 0.754778 + 0.164359I
a = 0.809503 − 0.494638I
b = −1.66362 + 0.41793I
0.49832 − 5.62398I −2.47133 + 4.97773I
u = 0.754778 − 0.164359I
a = 0.809503 + 0.494638I
b = −1.66362 − 0.41793I
0.49832 + 5.62398I −2.47133 − 4.97773I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374341 + 1.174030I
a = −2.42621 + 0.01899I
b = −1.94987 + 1.72785I
−3.38821 − 1.91522I 0
u = 0.374341 − 1.174030I
a = −2.42621 − 0.01899I
b = −1.94987 − 1.72785I
−3.38821 + 1.91522I 0
u = −0.698389 + 0.314322I
a = −0.145640 − 0.527804I
b = 0.057658 − 1.217660I
6.65889 + 1.40997I 2.43753 − 1.73189I
u = −0.698389 − 0.314322I
a = −0.145640 + 0.527804I
b = 0.057658 + 1.217660I
6.65889 − 1.40997I 2.43753 + 1.73189I
u = −0.411903 + 1.165120I
a = −0.540539 − 0.017453I
b = −0.29700 − 1.42113I
−4.64701 − 4.92563I 0
u = −0.411903 − 1.165120I
a = −0.540539 + 0.017453I
b = −0.29700 + 1.42113I
−4.64701 + 4.92563I 0
u = −0.682190 + 0.343573I
a = 0.007635 + 0.534085I
b = 0.102783 + 1.150590I
6.17569 − 4.60385I 1.65384 + 3.69650I
u = −0.682190 − 0.343573I
a = 0.007635 − 0.534085I
b = 0.102783 − 1.150590I
6.17569 + 4.60385I 1.65384 − 3.69650I
u = −0.738443 + 0.176958I
a = −0.862283 − 0.850695I
b = 0.929841 − 0.910793I
1.52040 + 2.97072I 1.42440 − 3.39297I
u = −0.738443 − 0.176958I
a = −0.862283 + 0.850695I
b = 0.929841 + 0.910793I
1.52040 − 2.97072I 1.42440 + 3.39297I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.379010 + 1.195960I
a = −1.13248 + 0.86493I
b = −1.68666 − 0.92984I
−6.62005 + 2.00043I 0
u = −0.379010 − 1.195960I
a = −1.13248 − 0.86493I
b = −1.68666 + 0.92984I
−6.62005 − 2.00043I 0
u = −0.346442 + 1.209000I
a = 0.96703 − 1.51555I
b = 1.98850 + 0.02317I
0.27744 + 2.18746I 0
u = −0.346442 − 1.209000I
a = 0.96703 + 1.51555I
b = 1.98850 − 0.02317I
0.27744 − 2.18746I 0
u = 0.452028 + 1.176960I
a = 1.236010 + 0.526170I
b = 1.34024 − 0.62452I
−5.10216 + 4.23297I 0
u = 0.452028 − 1.176960I
a = 1.236010 − 0.526170I
b = 1.34024 + 0.62452I
−5.10216 − 4.23297I 0
u = 0.719026 + 0.170250I
a = −0.833141 + 0.430733I
b = 1.57941 − 0.21403I
0.993260 − 0.058078I −1.295895 − 0.376120I
u = 0.719026 − 0.170250I
a = −0.833141 − 0.430733I
b = 1.57941 + 0.21403I
0.993260 + 0.058078I −1.295895 + 0.376120I
u = −0.487714 + 1.164570I
a = −1.72264 + 0.58508I
b = −2.39046 − 0.31875I
−4.10280 − 3.36875I 0
u = −0.487714 − 1.164570I
a = −1.72264 − 0.58508I
b = −2.39046 + 0.31875I
−4.10280 + 3.36875I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.503436 + 1.161720I
a = 1.47678 + 1.56908I
b = 2.32069 − 0.26656I
−1.86940 + 4.66794I 0
u = 0.503436 − 1.161720I
a = 1.47678 − 1.56908I
b = 2.32069 + 0.26656I
−1.86940 − 4.66794I 0
u = −0.352655 + 1.218600I
a = −1.16981 + 1.55509I
b = −2.26963 − 0.12608I
−0.77297 + 8.10127I 0
u = −0.352655 − 1.218600I
a = −1.16981 − 1.55509I
b = −2.26963 + 0.12608I
−0.77297 − 8.10127I 0
u = −0.509251 + 1.164960I
a = 2.09954 − 0.12613I
b = 2.14061 + 1.17805I
−1.34809 − 7.65104I 0
u = −0.509251 − 1.164960I
a = 2.09954 + 0.12613I
b = 2.14061 − 1.17805I
−1.34809 + 7.65104I 0
u = 0.416202 + 1.203500I
a = −1.73679 + 0.46421I
b = −1.04501 + 1.75863I
−8.02373 + 2.85549I 0
u = 0.416202 − 1.203500I
a = −1.73679 − 0.46421I
b = −1.04501 − 1.75863I
−8.02373 − 2.85549I 0
u = 0.509764 + 1.172190I
a = −1.35700 − 1.73404I
b = −2.43461 + 0.07894I
−2.43547 + 10.33970I 0
u = 0.509764 − 1.172190I
a = −1.35700 + 1.73404I
b = −2.43461 − 0.07894I
−2.43547 − 10.33970I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.509023 + 1.184160I
a = −2.54283 + 0.34458I
b = −2.80285 − 1.58586I
−5.70404 − 10.65240I 0
u = −0.509023 − 1.184160I
a = −2.54283 − 0.34458I
b = −2.80285 + 1.58586I
−5.70404 + 10.65240I 0
u = 0.710489
a = −0.571018
b = 0.888949
−1.79024 −5.42720
u = 0.484422 + 1.196790I
a = −0.64077 − 1.44346I
b = −1.74928 − 0.47465I
−7.54053 + 5.94143I 0
u = 0.484422 − 1.196790I
a = −0.64077 + 1.44346I
b = −1.74928 + 0.47465I
−7.54053 − 5.94143I 0
u = −0.695291 + 0.114360I
a = 0.77783 + 1.42657I
b = −0.769943 + 0.326838I
−1.12536 − 1.09410I −1.82519 + 0.22936I
u = −0.695291 − 0.114360I
a = 0.77783 − 1.42657I
b = −0.769943 − 0.326838I
−1.12536 + 1.09410I −1.82519 − 0.22936I
u = −0.528378 + 1.185890I
a = 2.72795 + 0.08627I
b = 2.35066 + 2.20158I
1.54708 − 10.92930I 0
u = −0.528378 − 1.185890I
a = 2.72795 − 0.08627I
b = 2.35066 − 2.20158I
1.54708 + 10.92930I 0
u = −0.527736 + 1.192030I
a = −2.85528 − 0.03375I
b = −2.52719 − 2.34386I
0.4566 − 16.9531I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.527736 − 1.192030I
a = −2.85528 + 0.03375I
b = −2.52719 + 2.34386I
0.4566 + 16.9531I 0
u = 0.449018 + 1.228580I
a = −0.98209 + 1.33643I
b = 0.36514 + 1.95200I
−4.92044 + 7.16923I 0
u = 0.449018 − 1.228580I
a = −0.98209 − 1.33643I
b = 0.36514 − 1.95200I
−4.92044 − 7.16923I 0
u = 0.462089 + 1.225950I
a = 0.57144 − 1.48085I
b = −0.86568 − 1.69204I
−4.82712 + 2.01419I 0
u = 0.462089 − 1.225950I
a = 0.57144 + 1.48085I
b = −0.86568 + 1.69204I
−4.82712 − 2.01419I 0
u = 0.081757 + 0.549346I
a = −1.45862 + 1.02333I
b = 0.109324 + 0.863020I
−0.145510 − 1.386820I −3.10450 + 5.15080I
u = 0.081757 − 0.549346I
a = −1.45862 − 1.02333I
b = 0.109324 − 0.863020I
−0.145510 + 1.386820I −3.10450 − 5.15080I
u = −0.263352 + 0.425309I
a = −0.775004 + 1.052880I
b = 0.092361 + 0.476526I
−0.208093 − 1.367100I −1.94407 + 4.53430I
u = −0.263352 − 0.425309I
a = −0.775004 − 1.052880I
b = 0.092361 − 0.476526I
−0.208093 + 1.367100I −1.94407 − 4.53430I
14
II.
I
u
2
= hu
2
a+b, u
4
+u
2
a−2u
3
+a
2
−au+3u
2
+a−2u+1, u
5
−u
4
+2u
3
−u
2
+u−1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
a
−u
2
a
a
8
=
1
−u
2
a
9
=
1
−u
2
a
12
=
u
u
a
1
=
−u
3
u
4
− u
3
+ u
2
+ 1
a
3
=
a
−u
2
a
a
10
=
u
3
u
3
+ u
a
6
=
u
3
−u
4
+ u
3
− u
2
− 1
a
5
=
u
3
a
u
3
a + au
a
2
=
−u
3
+ u
2
+ a − u + 1
−u
2
a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
3
a − u
4
+ 6u
3
− 2au − 7u
2
− a + 6u − 11
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
8
u
10
c
6
, c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
7
(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
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
5
c
3
, c
8
y
10
c
6
, c
9
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
7
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.80632 + 1.36366I
b = −0.307991 + 1.215160I
−0.329100 + 0.499304I −5.91654 + 2.81652I
u = −0.339110 + 0.822375I
a = −1.58413 + 0.01647I
b = −0.898363 − 0.874307I
−0.32910 − 3.56046I −1.60756 + 7.85087I
u = −0.339110 − 0.822375I
a = 0.80632 − 1.36366I
b = −0.307991 − 1.215160I
−0.329100 − 0.499304I −5.91654 − 2.81652I
u = −0.339110 − 0.822375I
a = −1.58413 − 0.01647I
b = −0.898363 + 0.874307I
−0.32910 + 3.56046I −1.60756 − 7.85087I
u = 0.766826
a = −0.410598 + 0.711177I
b = 0.241441 − 0.418187I
−2.40108 + 2.02988I −6.55976 − 2.76390I
u = 0.766826
a = −0.410598 − 0.711177I
b = 0.241441 + 0.418187I
−2.40108 − 2.02988I −6.55976 + 2.76390I
u = 0.455697 + 1.200150I
a = 0.252108 + 0.649344I
b = 1.021040 + 0.524691I
−5.87256 + 2.37095I −10.62344 − 1.09779I
u = 0.455697 + 1.200150I
a = 0.436295 − 0.543004I
b = −0.056121 − 1.146590I
−5.87256 + 6.43072I −9.29269 − 5.42389I
u = 0.455697 − 1.200150I
a = 0.252108 − 0.649344I
b = 1.021040 − 0.524691I
−5.87256 − 2.37095I −10.62344 + 1.09779I
u = 0.455697 − 1.200150I
a = 0.436295 + 0.543004I
b = −0.056121 + 1.146590I
−5.87256 − 6.43072I −9.29269 + 5.42389I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
5
)(u
99
+ 32u
98
+ ··· − 28u − 1)
c
2
((u
2
+ u + 1)
5
)(u
99
+ 6u
98
+ ··· + 4u + 1)
c
3
, c
8
u
10
(u
99
+ u
98
+ ··· + 3072u + 1024)
c
5
((u
2
− u + 1)
5
)(u
99
+ 6u
98
+ ··· + 4u + 1)
c
6
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
99
+ 3u
98
+ ··· + 1403u + 73)
c
7
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
99
− 3u
98
+ ··· − 5u + 1)
c
9
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
99
− 11u
98
+ ··· + 27259u + 3341)
c
10
((u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
)(u
99
+ 53u
98
+ ··· − 13u − 1)
c
11
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
99
− 3u
98
+ ··· − 5u + 1)
c
12
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
99
+ 3u
98
+ ··· + 1403u + 73)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
5
)(y
99
+ 76y
98
+ ··· + 624y −1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
99
+ 32y
98
+ ··· − 28y −1)
c
3
, c
8
y
10
(y
99
+ 55y
98
+ ··· − 1.78258 × 10
7
y −1048576)
c
6
, c
12
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
99
− 75y
98
+ ··· + 237579y −5329)
c
7
, c
11
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
99
+ 53y
98
+ ··· − 13y −1)
c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
99
+ 25y
98
+ ··· − 762194377y −11162281)
c
10
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
99
− 11y
98
+ ··· + 27y −1)
20
