11a
217
(K11a
217
)
A knot diagram
1
Linearized knot diagam
7 1 10 8 11 2 4 6 3 5 9
Solving Sequence
1,7
2
3,9
10 4 6 8 11 5
c
1
c
2
c
9
c
3
c
6
c
8
c
11
c
5
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.17366 × 10
130
u
87
− 2.47035 × 10
130
u
86
+ ··· + 1.30550 × 10
131
b + 1.73562 × 10
131
,
− 1.20844 × 10
131
u
87
− 1.95249 × 10
131
u
86
+ ··· + 3.91650 × 10
131
a + 2.77458 × 10
132
,
u
88
+ u
87
+ ··· − 15u − 9i
I
u
2
= h−u
18
+ u
17
+ ··· + b − 1, 2u
18
− 3u
17
+ ··· + a + 7, u
19
+ 6u
17
+ ··· + 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 107 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
= h1.17 × 10
130
u
87
− 2.47 × 10
130
u
86
+ · · · + 1.31 × 10
131
b + 1.74 ×
10
131
, −1.21 × 10
131
u
87
− 1.95 × 10
131
u
86
+ · · · + 3.92 × 10
131
a + 2.77 ×
10
132
, u
88
+ u
87
+ · · · − 15u − 9i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
9
=
0.308550u
87
+ 0.498528u
86
+ ··· + 7.54550u − 7.08434
−0.0899012u
87
+ 0.189226u
86
+ ··· − 2.55127u − 1.32947
a
10
=
−0.386032u
87
− 0.283155u
86
+ ··· + 12.0176u − 0.729770
−0.256563u
87
+ 0.494342u
86
+ ··· − 0.570209u − 4.79156
a
4
=
0.317057u
87
− 0.164745u
86
+ ··· − 15.3332u + 2.84818
−0.127635u
87
+ 0.423062u
86
+ ··· + 4.82042u − 0.610035
a
6
=
−u
u
3
+ u
a
8
=
−0.244942u
87
− 0.153358u
86
+ ··· + 12.6279u − 2.44254
−0.265588u
87
+ 0.498825u
86
+ ··· − 1.17630u − 5.08573
a
11
=
−0.728320u
87
− 0.445892u
86
+ ··· + 23.4775u + 5.97101
0.299986u
87
+ 0.213630u
86
+ ··· − 6.17882u − 4.63479
a
5
=
−0.566401u
87
+ 0.182126u
86
+ ··· + 13.2863u + 1.44734
0.921798u
87
+ 0.106995u
86
+ ··· − 9.79027u − 4.16570
a
5
=
−0.566401u
87
+ 0.182126u
86
+ ··· + 13.2863u + 1.44734
0.921798u
87
+ 0.106995u
86
+ ··· − 9.79027u − 4.16570
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.34526u
87
− 2.29597u
86
+ ··· + 57.3933u + 23.8601
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
88
+ u
87
+ ··· − 15u − 9
c
2
u
88
+ 39u
87
+ ··· + 1917u + 81
c
3
, c
9
u
88
− 2u
87
+ ··· − 1806u − 5669
c
4
, c
7
u
88
+ 2u
87
+ ··· − 4u − 1
c
5
, c
10
u
88
+ u
87
+ ··· + 369u + 73
c
8
u
88
− 2u
87
+ ··· + 116u − 29
c
11
u
88
+ 4u
87
+ ··· − 84596u − 23303
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
88
+ 39y
87
+ ··· + 1917y + 81
c
2
y
88
+ 31y
87
+ ··· + 1377y + 6561
c
3
, c
9
y
88
− 68y
87
+ ··· − 295181122y + 32137561
c
4
, c
7
y
88
− 48y
87
+ ··· − 78y + 1
c
5
, c
10
y
88
− 57y
87
+ ··· − 140103y + 5329
c
8
y
88
+ 8y
87
+ ··· − 160080y + 841
c
11
y
88
− 32y
87
+ ··· − 13342637414y + 543029809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.672994 + 0.730216I
a = −1.10735 − 1.07414I
b = 0.991137 + 0.532051I
3.40131 + 0.63657I 0
u = −0.672994 − 0.730216I
a = −1.10735 + 1.07414I
b = 0.991137 − 0.532051I
3.40131 − 0.63657I 0
u = 0.549677 + 0.855702I
a = 1.280460 − 0.488061I
b = −0.644430 − 0.292848I
0.34598 + 2.20232I 0
u = 0.549677 − 0.855702I
a = 1.280460 + 0.488061I
b = −0.644430 + 0.292848I
0.34598 − 2.20232I 0
u = 0.828880 + 0.513872I
a = 1.43498 − 1.02467I
b = −1.62216 + 0.64715I
8.90367 − 4.46822I 0
u = 0.828880 − 0.513872I
a = 1.43498 + 1.02467I
b = −1.62216 − 0.64715I
8.90367 + 4.46822I 0
u = −0.288083 + 0.930672I
a = 2.01211 + 0.27156I
b = −0.75665 + 1.25554I
−0.95666 + 2.66976I 0
u = −0.288083 − 0.930672I
a = 2.01211 − 0.27156I
b = −0.75665 − 1.25554I
−0.95666 − 2.66976I 0
u = 0.525827 + 0.813502I
a = −1.17367 + 0.85281I
b = 0.498338 + 1.251820I
−0.090444 + 1.045920I 0
u = 0.525827 − 0.813502I
a = −1.17367 − 0.85281I
b = 0.498338 − 1.251820I
−0.090444 − 1.045920I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.532741 + 0.803423I
a = 1.41185 − 0.72781I
b = −0.993775 − 0.272407I
6.59048 − 1.60100I 0
u = −0.532741 − 0.803423I
a = 1.41185 + 0.72781I
b = −0.993775 + 0.272407I
6.59048 + 1.60100I 0
u = 0.539664 + 0.896196I
a = −0.042642 + 0.542138I
b = 1.06395 − 1.25945I
−0.37079 + 3.25945I 0
u = 0.539664 − 0.896196I
a = −0.042642 − 0.542138I
b = 1.06395 + 1.25945I
−0.37079 − 3.25945I 0
u = −0.743273 + 0.736993I
a = −0.943024 − 0.750996I
b = 1.073520 + 0.651963I
3.60538 + 0.57994I 0
u = −0.743273 − 0.736993I
a = −0.943024 + 0.750996I
b = 1.073520 − 0.651963I
3.60538 − 0.57994I 0
u = 0.418994 + 0.851230I
a = −1.92662 + 0.69990I
b = 1.49127 + 0.27379I
−1.16615 + 0.99172I 0
u = 0.418994 − 0.851230I
a = −1.92662 − 0.69990I
b = 1.49127 − 0.27379I
−1.16615 − 0.99172I 0
u = 0.157375 + 1.064390I
a = −0.001733 − 0.538652I
b = 0.730790 − 0.971384I
−3.08031 − 3.58796I 0
u = 0.157375 − 1.064390I
a = −0.001733 + 0.538652I
b = 0.730790 + 0.971384I
−3.08031 + 3.58796I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.424583 + 0.989136I
a = −0.85380 + 1.41030I
b = 1.229640 + 0.518489I
−1.60218 + 2.32473I 0
u = 0.424583 − 0.989136I
a = −0.85380 − 1.41030I
b = 1.229640 − 0.518489I
−1.60218 − 2.32473I 0
u = −0.954150 + 0.504375I
a = 1.27641 + 0.78432I
b = −1.41629 − 0.70913I
6.30173 + 11.20680I 0
u = −0.954150 − 0.504375I
a = 1.27641 − 0.78432I
b = −1.41629 + 0.70913I
6.30173 − 11.20680I 0
u = −0.570950 + 0.920505I
a = 0.35854 + 1.78146I
b = −0.648133 + 0.346156I
6.17225 − 2.81909I 0
u = −0.570950 − 0.920505I
a = 0.35854 − 1.78146I
b = −0.648133 − 0.346156I
6.17225 + 2.81909I 0
u = −0.825409 + 0.389965I
a = 0.744459 − 0.263975I
b = −1.099570 − 0.053538I
8.37441 − 1.00046I 0
u = −0.825409 − 0.389965I
a = 0.744459 + 0.263975I
b = −1.099570 + 0.053538I
8.37441 + 1.00046I 0
u = −0.864107 + 0.670402I
a = −0.795663 − 0.661817I
b = 1.117810 + 0.571773I
3.99640 + 0.52623I 0
u = −0.864107 − 0.670402I
a = −0.795663 + 0.661817I
b = 1.117810 − 0.571773I
3.99640 − 0.52623I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.987316 + 0.473726I
a = −0.821517 + 0.527676I
b = 1.091220 − 0.562324I
2.36912 − 4.77643I 0
u = 0.987316 − 0.473726I
a = −0.821517 − 0.527676I
b = 1.091220 + 0.562324I
2.36912 + 4.77643I 0
u = 0.748244 + 0.800032I
a = 1.42273 + 0.31582I
b = −0.926866 + 0.143704I
5.12945 − 1.10437I 0
u = 0.748244 − 0.800032I
a = 1.42273 − 0.31582I
b = −0.926866 − 0.143704I
5.12945 + 1.10437I 0
u = −0.521304 + 0.736352I
a = 1.41976 − 0.43169I
b = 0.29104 + 1.85754I
1.35988 + 3.41417I 0
u = −0.521304 − 0.736352I
a = 1.41976 + 0.43169I
b = 0.29104 − 1.85754I
1.35988 − 3.41417I 0
u = −0.558781 + 0.949859I
a = −1.159030 + 0.427247I
b = −0.19983 − 2.03307I
0.64622 − 7.81246I 0
u = −0.558781 − 0.949859I
a = −1.159030 − 0.427247I
b = −0.19983 + 2.03307I
0.64622 + 7.81246I 0
u = 0.020883 + 1.113770I
a = −0.786207 − 0.139160I
b = −0.892118 + 0.756600I
3.07957 − 2.82800I 0
u = 0.020883 − 1.113770I
a = −0.786207 + 0.139160I
b = −0.892118 − 0.756600I
3.07957 + 2.82800I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.068391 + 0.882123I
a = 0.289943 + 0.967539I
b = 0.361809 + 0.714360I
−1.62956 + 1.49672I −2.18266 − 4.73494I
u = 0.068391 − 0.882123I
a = 0.289943 − 0.967539I
b = 0.361809 − 0.714360I
−1.62956 − 1.49672I −2.18266 + 4.73494I
u = −0.652582 + 0.904482I
a = −1.87179 − 0.49715I
b = 1.140730 − 0.831300I
2.89016 − 5.77549I 0
u = −0.652582 − 0.904482I
a = −1.87179 + 0.49715I
b = 1.140730 + 0.831300I
2.89016 + 5.77549I 0
u = 0.999619 + 0.565212I
a = 0.889970 + 0.066196I
b = −1.045120 + 0.006616I
6.55539 + 5.69360I 0
u = 0.999619 − 0.565212I
a = 0.889970 − 0.066196I
b = −1.045120 − 0.006616I
6.55539 − 5.69360I 0
u = 0.711121 + 0.909996I
a = 1.12820 − 1.52674I
b = −0.681383 − 0.228321I
4.78905 + 6.64535I 0
u = 0.711121 − 0.909996I
a = 1.12820 + 1.52674I
b = −0.681383 + 0.228321I
4.78905 − 6.64535I 0
u = 0.617819 + 0.541637I
a = −1.94871 + 1.12700I
b = 0.745025 − 0.523421I
1.17276 − 5.12018I 5.98234 + 4.87453I
u = 0.617819 − 0.541637I
a = −1.94871 − 1.12700I
b = 0.745025 + 0.523421I
1.17276 + 5.12018I 5.98234 − 4.87453I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699347 + 0.964380I
a = −1.65613 − 0.72307I
b = 1.011390 − 0.874674I
2.91455 − 6.08125I 0
u = −0.699347 − 0.964380I
a = −1.65613 + 0.72307I
b = 1.011390 + 0.874674I
2.91455 + 6.08125I 0
u = 0.603972 + 1.028600I
a = −2.00103 + 0.72468I
b = 1.041580 + 0.628310I
−0.23970 + 9.99743I 0
u = 0.603972 − 1.028600I
a = −2.00103 − 0.72468I
b = 1.041580 − 0.628310I
−0.23970 − 9.99743I 0
u = 0.452174 + 1.105960I
a = 0.538003 + 0.865414I
b = 0.776965 − 0.935888I
−1.27582 + 4.49844I 0
u = 0.452174 − 1.105960I
a = 0.538003 − 0.865414I
b = 0.776965 + 0.935888I
−1.27582 − 4.49844I 0
u = −0.550712 + 1.074730I
a = 1.29204 + 0.62612I
b = −0.877930 + 0.444608I
−4.17850 − 5.69977I 0
u = −0.550712 − 1.074730I
a = 1.29204 − 0.62612I
b = −0.877930 − 0.444608I
−4.17850 + 5.69977I 0
u = −0.418001 + 1.139750I
a = 0.30516 + 1.43036I
b = −1.74406 − 0.38088I
−2.54284 − 4.00372I 0
u = −0.418001 − 1.139750I
a = 0.30516 − 1.43036I
b = −1.74406 + 0.38088I
−2.54284 + 4.00372I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.235896 + 1.191590I
a = 0.047892 − 0.136256I
b = −0.292908 − 0.768153I
−6.26061 − 1.83587I 0
u = −0.235896 − 1.191590I
a = 0.047892 + 0.136256I
b = −0.292908 + 0.768153I
−6.26061 + 1.83587I 0
u = −0.697556 + 1.017660I
a = −1.40280 − 0.71129I
b = 1.08357 − 0.92479I
2.90972 − 6.30768I 0
u = −0.697556 − 1.017660I
a = −1.40280 + 0.71129I
b = 1.08357 + 0.92479I
2.90972 + 6.30768I 0
u = 0.008092 + 0.764905I
a = 1.14418 + 1.17371I
b = 0.210534 + 0.328300I
−1.42460 + 1.54545I −1.14589 − 4.93438I
u = 0.008092 − 0.764905I
a = 1.14418 − 1.17371I
b = 0.210534 − 0.328300I
−1.42460 − 1.54545I −1.14589 + 4.93438I
u = −0.737322
a = 2.19967
b = −1.48738
0.805893 8.65370
u = 0.655494 + 1.088190I
a = 1.60130 − 1.13359I
b = −1.73234 − 0.92925I
7.17217 + 10.01930I 0
u = 0.655494 − 1.088190I
a = 1.60130 + 1.13359I
b = −1.73234 + 0.92925I
7.17217 − 10.01930I 0
u = −0.628107 + 0.256489I
a = 1.34336 + 0.46833I
b = −0.423109 − 0.347668I
−2.03705 + 1.14331I −0.66173 − 1.29864I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.628107 − 0.256489I
a = 1.34336 − 0.46833I
b = −0.423109 + 0.347668I
−2.03705 − 1.14331I −0.66173 + 1.29864I
u = 0.024501 + 1.333540I
a = −0.231763 − 0.033800I
b = −0.900322 − 0.607173I
−0.68113 + 8.56435I 0
u = 0.024501 − 1.333540I
a = −0.231763 + 0.033800I
b = −0.900322 + 0.607173I
−0.68113 − 8.56435I 0
u = −0.699704 + 1.136130I
a = 1.52044 + 0.94432I
b = −1.47465 + 0.92567I
4.3565 − 17.2462I 0
u = −0.699704 − 1.136130I
a = 1.52044 − 0.94432I
b = −1.47465 − 0.92567I
4.3565 + 17.2462I 0
u = −0.619798 + 1.190130I
a = 0.321227 + 0.830580I
b = −0.831881 + 0.388008I
5.93694 − 4.42882I 0
u = −0.619798 − 1.190130I
a = 0.321227 − 0.830580I
b = −0.831881 − 0.388008I
5.93694 + 4.42882I 0
u = 0.702911 + 1.150830I
a = −1.147340 + 0.666605I
b = 1.10356 + 0.88760I
0.29144 + 10.89830I 0
u = 0.702911 − 1.150830I
a = −1.147340 − 0.666605I
b = 1.10356 − 0.88760I
0.29144 − 10.89830I 0
u = 0.603081 + 0.191254I
a = −1.061460 − 0.858322I
b = 0.699506 + 0.668876I
1.312400 − 0.427135I 7.68860 + 0.03322I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.603081 − 0.191254I
a = −1.061460 + 0.858322I
b = 0.699506 − 0.668876I
1.312400 + 0.427135I 7.68860 − 0.03322I
u = 0.782309 + 1.124420I
a = 0.659480 − 0.750725I
b = −0.859534 − 0.291051I
4.85892 + 0.75021I 0
u = 0.782309 − 1.124420I
a = 0.659480 + 0.750725I
b = −0.859534 + 0.291051I
4.85892 − 0.75021I 0
u = 0.09795 + 1.48857I
a = 0.198655 + 0.067322I
b = 0.552268 − 0.131033I
−4.69267 − 1.22369I 0
u = 0.09795 − 1.48857I
a = 0.198655 − 0.067322I
b = 0.552268 + 0.131033I
−4.69267 + 1.22369I 0
u = 0.396189
a = −0.357439
b = 0.603577
0.888455 11.7580
u = −0.124814 + 0.274497I
a = −3.46331 + 3.55911I
b = 0.199334 − 0.805485I
0.79049 − 4.65679I 5.10183 + 7.14957I
u = −0.124814 − 0.274497I
a = −3.46331 − 3.55911I
b = 0.199334 + 0.805485I
0.79049 + 4.65679I 5.10183 − 7.14957I
13
II.
I
u
2
= h−u
18
+u
17
+· · ·+b−1, 2u
18
−3u
17
+· · ·+a+7, u
19
+6u
17
+· · ·+2u−1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
9
=
−2u
18
+ 3u
17
+ ··· + 16u − 7
u
18
− u
17
+ ··· + 4u
2
+ 1
a
10
=
−2u
18
+ 2u
17
+ ··· + 13u − 5
u
18
− u
17
+ ··· − 2u + 2
a
4
=
3u
18
+ 16u
16
+ ··· − 5u + 2
u
18
+ u
17
+ ··· − u
2
− 1
a
6
=
−u
u
3
+ u
a
8
=
−2u
18
+ 3u
17
+ ··· + 13u − 6
u
18
+ 5u
16
+ ··· − 2u
2
+ 3u
a
11
=
2u
18
+ u
17
+ ··· + 5u − 5
−u
18
− u
17
+ ··· + 5u
2
+ 1
a
5
=
4u
18
+ u
17
+ ··· − 4u
2
− 4
−u
18
− 2u
17
+ ··· − 2u + 2
a
5
=
4u
18
+ u
17
+ ··· − 4u
2
− 4
−u
18
− 2u
17
+ ··· − 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
18
+ 2u
17
−30u
16
+ 8u
15
−72u
14
+ 23u
13
−117u
12
+ 56u
11
−
133u
10
+ 81u
9
− 113u
8
+ 80u
7
− 76u
6
+ 46u
5
− 37u
4
+ 16u
3
− 4u
2
+ 3
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 6u
17
+ ··· + 2u − 1
c
2
u
19
+ 12u
18
+ ··· − 8u − 1
c
3
u
19
+ u
18
+ ··· − u − 1
c
4
u
19
+ u
18
+ ··· − u − 1
c
5
u
19
− 6u
17
+ ··· + 2u − 1
c
6
u
19
+ 6u
17
+ ··· + 2u + 1
c
7
u
19
− u
18
+ ··· − u + 1
c
8
u
19
+ 3u
18
+ ··· − 5u + 1
c
9
u
19
− u
18
+ ··· − u + 1
c
10
u
19
− 6u
17
+ ··· + 2u + 1
c
11
u
19
− 7u
18
+ ··· + 7u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
19
+ 12y
18
+ ··· − 8y −1
c
2
y
19
− 12y
17
+ ··· + 12y −1
c
3
, c
9
y
19
− 19y
18
+ ··· + 15y −1
c
4
, c
7
y
19
− 15y
18
+ ··· + 19y −1
c
5
, c
10
y
19
− 12y
18
+ ··· + 20y −1
c
8
y
19
− 3y
18
+ ··· + 21y −1
c
11
y
19
− 3y
18
+ ··· + 19y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.300339 + 1.028100I
a = −0.710824 + 0.912612I
b = −0.164956 − 1.062830I
−0.80374 − 5.96566I 2.56814 + 7.23829I
u = −0.300339 − 1.028100I
a = −0.710824 − 0.912612I
b = −0.164956 + 1.062830I
−0.80374 + 5.96566I 2.56814 − 7.23829I
u = −0.769769 + 0.810412I
a = −0.639951 − 0.518424I
b = 0.811253 + 0.714824I
3.17953 + 1.36019I 3.92371 − 4.81231I
u = −0.769769 − 0.810412I
a = −0.639951 + 0.518424I
b = 0.811253 − 0.714824I
3.17953 − 1.36019I 3.92371 + 4.81231I
u = 0.562434 + 0.668186I
a = 1.08875 + 1.00323I
b = −0.926740 + 0.221997I
6.76547 + 0.96312I 8.25509 + 3.80362I
u = 0.562434 − 0.668186I
a = 1.08875 − 1.00323I
b = −0.926740 − 0.221997I
6.76547 − 0.96312I 8.25509 − 3.80362I
u = −0.706602 + 0.910457I
a = −1.67700 − 0.51030I
b = 0.753084 − 1.044950I
2.86959 − 6.94689I 4.90485 + 11.31459I
u = −0.706602 − 0.910457I
a = −1.67700 + 0.51030I
b = 0.753084 + 1.044950I
2.86959 + 6.94689I 4.90485 − 11.31459I
u = −0.273008 + 0.799953I
a = 2.28416 + 0.16634I
b = 0.142356 + 1.370340I
0.06532 + 3.52454I 1.23723 − 4.17495I
u = −0.273008 − 0.799953I
a = 2.28416 − 0.16634I
b = 0.142356 − 1.370340I
0.06532 − 3.52454I 1.23723 + 4.17495I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.448828 + 1.089750I
a = −0.38006 + 1.45167I
b = 1.72088 − 0.46919I
−3.15207 + 3.62872I −4.99993 − 0.96458I
u = 0.448828 − 1.089750I
a = −0.38006 − 1.45167I
b = 1.72088 + 0.46919I
−3.15207 − 3.62872I −4.99993 + 0.96458I
u = 0.612086 + 1.067960I
a = 0.254962 − 1.118410I
b = −0.614195 − 0.372988I
5.42685 + 3.75788I 2.42054 − 2.81140I
u = 0.612086 − 1.067960I
a = 0.254962 + 1.118410I
b = −0.614195 + 0.372988I
5.42685 − 3.75788I 2.42054 + 2.81140I
u = 0.181011 + 0.621059I
a = −1.96932 + 1.56059I
b = 0.890170 + 0.697260I
−0.988482 − 0.416067I 1.322447 + 0.053453I
u = 0.181011 − 0.621059I
a = −1.96932 − 1.56059I
b = 0.890170 − 0.697260I
−0.988482 + 0.416067I 1.322447 − 0.053453I
u = −0.029408 + 1.410930I
a = 0.338962 + 0.132093I
b = 0.319721 − 0.077815I
−4.90569 + 0.94743I −3.91857 + 6.41242I
u = −0.029408 − 1.410930I
a = 0.338962 − 0.132093I
b = 0.319721 + 0.077815I
−4.90569 − 0.94743I −3.91857 − 6.41242I
u = 0.549531
a = −2.17935
b = 1.13686
−0.464251 1.57300
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
19
+ 6u
17
+ ··· + 2u − 1)(u
88
+ u
87
+ ··· − 15u − 9)
c
2
(u
19
+ 12u
18
+ ··· − 8u − 1)(u
88
+ 39u
87
+ ··· + 1917u + 81)
c
3
(u
19
+ u
18
+ ··· − u − 1)(u
88
− 2u
87
+ ··· − 1806u − 5669)
c
4
(u
19
+ u
18
+ ··· − u − 1)(u
88
+ 2u
87
+ ··· − 4u − 1)
c
5
(u
19
− 6u
17
+ ··· + 2u − 1)(u
88
+ u
87
+ ··· + 369u + 73)
c
6
(u
19
+ 6u
17
+ ··· + 2u + 1)(u
88
+ u
87
+ ··· − 15u − 9)
c
7
(u
19
− u
18
+ ··· − u + 1)(u
88
+ 2u
87
+ ··· − 4u − 1)
c
8
(u
19
+ 3u
18
+ ··· − 5u + 1)(u
88
− 2u
87
+ ··· + 116u − 29)
c
9
(u
19
− u
18
+ ··· − u + 1)(u
88
− 2u
87
+ ··· − 1806u − 5669)
c
10
(u
19
− 6u
17
+ ··· + 2u + 1)(u
88
+ u
87
+ ··· + 369u + 73)
c
11
(u
19
− 7u
18
+ ··· + 7u − 1)(u
88
+ 4u
87
+ ··· − 84596u − 23303)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
19
+ 12y
18
+ ··· − 8y −1)(y
88
+ 39y
87
+ ··· + 1917y + 81)
c
2
(y
19
− 12y
17
+ ··· + 12y −1)(y
88
+ 31y
87
+ ··· + 1377y + 6561)
c
3
, c
9
(y
19
− 19y
18
+ ··· + 15y −1)
· (y
88
− 68y
87
+ ··· − 295181122y + 32137561)
c
4
, c
7
(y
19
− 15y
18
+ ··· + 19y −1)(y
88
− 48y
87
+ ··· − 78y + 1)
c
5
, c
10
(y
19
− 12y
18
+ ··· + 20y −1)(y
88
− 57y
87
+ ··· − 140103y + 5329)
c
8
(y
19
− 3y
18
+ ··· + 21y −1)(y
88
+ 8y
87
+ ··· − 160080y + 841)
c
11
(y
19
− 3y
18
+ ··· + 19y −1)
· (y
88
− 32y
87
+ ··· − 13342637414y + 543029809)
20
