11a
275
(K11a
275
)
A knot diagram
1
Linearized knot diagam
5 7 1 10 2 9 3 11 6 4 8
Solving Sequence
6,9 2,7
3 10 5 1 4 11 8
c
6
c
2
c
9
c
5
c
1
c
4
c
10
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.60406 × 10
219
u
79
− 7.17243 × 10
219
u
78
+ ··· + 4.34238 × 10
220
b − 5.34167 × 10
220
,
1.16482 × 10
219
u
79
+ 3.98757 × 10
219
u
78
+ ··· + 4.34238 × 10
220
a − 4.56749 × 10
220
,
u
80
+ 4u
79
+ ··· − 27u + 34i
I
u
2
= h−6630u
15
+ 14537u
14
+ ··· + 13613b − 33108, 5953u
15
− 4661u
14
+ ··· + 13613a + 59873,
u
16
− 3u
15
+ ··· + u + 1i
* 2 irreducible components of dim
C
= 0, with total 96 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
= h−1.60 × 10
219
u
79
− 7.17 × 10
219
u
78
+ · · · + 4.34 × 10
220
b − 5.34 ×
10
220
, 1.16 × 10
219
u
79
+ 3.99 × 10
219
u
78
+ · · · + 4.34 × 10
220
a − 4.57 ×
10
220
, u
80
+ 4u
79
+ · · · − 27u + 34i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
2
=
−0.0268244u
79
− 0.0918292u
78
+ ··· − 5.38213u + 1.05184
0.0369397u
79
+ 0.165173u
78
+ ··· + 0.512746u + 1.23013
a
7
=
1
u
2
a
3
=
−0.0588440u
79
− 0.241530u
78
+ ··· − 4.56519u − 0.704217
0.0522405u
79
+ 0.236004u
78
+ ··· + 1.01761u + 1.96528
a
10
=
−u
u
a
5
=
0.0188852u
79
+ 0.0877304u
78
+ ··· + 10.3791u + 0.440251
−0.0179480u
79
− 0.0787893u
78
+ ··· − 0.984862u − 1.15735
a
1
=
0.00943403u
79
+ 0.0573905u
78
+ ··· − 1.31883u + 0.270591
−0.0530260u
79
− 0.228362u
78
+ ··· − 1.09682u − 1.74483
a
4
=
0.0236248u
79
+ 0.0987805u
78
+ ··· + 10.4875u + 0.263710
−0.0226876u
79
− 0.0898394u
78
+ ··· − 1.09319u − 0.980806
a
11
=
−0.00299351u
79
− 0.0183881u
78
+ ··· + 8.20270u − 3.09923
0.0297591u
79
+ 0.156515u
78
+ ··· − 0.945183u + 1.83821
a
8
=
−0.0233526u
79
− 0.108117u
78
+ ··· − 10.4317u − 0.210530
0.0379355u
79
+ 0.146692u
78
+ ··· + 2.16096u + 0.319527
a
8
=
−0.0233526u
79
− 0.108117u
78
+ ··· − 10.4317u − 0.210530
0.0379355u
79
+ 0.146692u
78
+ ··· + 2.16096u + 0.319527
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0374310u
79
+ 0.158984u
78
+ ··· − 4.27920u − 10.1108
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
80
+ u
79
+ ··· − 6u − 1
c
2
, c
7
u
80
− u
79
+ ··· + 3416u − 3721
c
3
u
80
− 3u
79
+ ··· + 35212u − 5777
c
4
, c
10
u
80
+ 5u
79
+ ··· − 306u − 527
c
6
, c
9
u
80
− 4u
79
+ ··· + 27u + 34
c
8
, c
11
u
80
+ 2u
79
+ ··· − 181u + 31
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
80
− 43y
79
+ ··· − 4y + 1
c
2
, c
7
y
80
− 47y
79
+ ··· − 72209726y + 13845841
c
3
y
80
− 25y
79
+ ··· − 1723258088y + 33373729
c
4
, c
10
y
80
+ 37y
79
+ ··· + 5061478y + 277729
c
6
, c
9
y
80
+ 46y
79
+ ··· − 6577y + 1156
c
8
, c
11
y
80
+ 46y
79
+ ··· − 21229y + 961
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.106386 + 1.004750I
a = 1.30657 − 3.48011I
b = −0.934597 + 0.108810I
−1.54698 + 0.32425I 0. + 43.4640I
u = −0.106386 − 1.004750I
a = 1.30657 + 3.48011I
b = −0.934597 − 0.108810I
−1.54698 − 0.32425I 0. − 43.4640I
u = −0.949052 + 0.351718I
a = 0.026470 − 0.205607I
b = 1.365600 + 0.175084I
−10.27100 − 4.13973I −15.7867 + 0.I
u = −0.949052 − 0.351718I
a = 0.026470 + 0.205607I
b = 1.365600 − 0.175084I
−10.27100 + 4.13973I −15.7867 + 0.I
u = 0.962671
a = 0.0366403
b = 1.32951
−6.48924 −14.1030
u = 0.937397 + 0.161665I
a = 0.920463 − 0.400431I
b = 0.967920 + 0.489832I
−2.35882 − 5.51067I −9.84350 + 5.87992I
u = 0.937397 − 0.161665I
a = 0.920463 + 0.400431I
b = 0.967920 − 0.489832I
−2.35882 + 5.51067I −9.84350 − 5.87992I
u = −0.793127 + 0.690281I
a = 0.518674 + 0.094068I
b = −1.273860 − 0.525082I
−6.89106 + 0.74404I 0
u = −0.793127 − 0.690281I
a = 0.518674 − 0.094068I
b = −1.273860 + 0.525082I
−6.89106 − 0.74404I 0
u = −0.659363 + 0.854056I
a = −0.57349 − 1.44928I
b = −0.199019 + 0.681360I
−3.86467 + 5.85230I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.659363 − 0.854056I
a = −0.57349 + 1.44928I
b = −0.199019 − 0.681360I
−3.86467 − 5.85230I 0
u = −0.805203 + 0.426514I
a = −1.28132 − 1.16225I
b = −0.252459 − 0.114986I
−3.58794 + 6.02169I −10.86973 − 2.67201I
u = −0.805203 − 0.426514I
a = −1.28132 + 1.16225I
b = −0.252459 + 0.114986I
−3.58794 − 6.02169I −10.86973 + 2.67201I
u = 0.387429 + 1.022610I
a = 0.54036 − 1.44386I
b = −0.59005 + 1.44645I
3.03457 − 2.75755I 0
u = 0.387429 − 1.022610I
a = 0.54036 + 1.44386I
b = −0.59005 − 1.44645I
3.03457 + 2.75755I 0
u = 0.498626 + 0.991215I
a = 0.201073 + 1.385690I
b = −0.651728 − 0.201624I
0.84491 − 2.13326I 0
u = 0.498626 − 0.991215I
a = 0.201073 − 1.385690I
b = −0.651728 + 0.201624I
0.84491 + 2.13326I 0
u = 0.775066 + 0.803905I
a = 0.351470 − 0.336348I
b = 0.684548 − 0.092570I
−0.81827 − 2.05131I 0
u = 0.775066 − 0.803905I
a = 0.351470 + 0.336348I
b = 0.684548 + 0.092570I
−0.81827 + 2.05131I 0
u = −0.598911 + 0.644725I
a = 0.666718 + 0.938431I
b = −0.468858 − 0.776453I
−4.43027 − 1.02077I −11.34703 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598911 − 0.644725I
a = 0.666718 − 0.938431I
b = −0.468858 + 0.776453I
−4.43027 + 1.02077I −11.34703 + 0.I
u = −0.132414 + 0.853219I
a = 0.07134 − 1.57906I
b = −0.966164 + 0.359794I
−0.328167 + 0.843678I −6.69440 − 1.81465I
u = −0.132414 − 0.853219I
a = 0.07134 + 1.57906I
b = −0.966164 − 0.359794I
−0.328167 − 0.843678I −6.69440 + 1.81465I
u = 1.116250 + 0.229412I
a = 0.099344 + 0.155243I
b = −1.214420 + 0.397022I
−2.84331 + 4.24599I 0
u = 1.116250 − 0.229412I
a = 0.099344 − 0.155243I
b = −1.214420 − 0.397022I
−2.84331 − 4.24599I 0
u = −0.431362 + 1.068660I
a = 0.215285 + 1.394890I
b = 1.208240 − 0.650185I
3.92912 + 5.75666I 0
u = −0.431362 − 1.068660I
a = 0.215285 − 1.394890I
b = 1.208240 + 0.650185I
3.92912 − 5.75666I 0
u = 0.205171 + 0.782039I
a = 0.45788 + 1.43880I
b = 0.046673 − 0.232573I
1.09182 − 1.88602I −3.93284 + 6.84227I
u = 0.205171 − 0.782039I
a = 0.45788 − 1.43880I
b = 0.046673 + 0.232573I
1.09182 + 1.88602I −3.93284 − 6.84227I
u = −0.395238 + 1.125030I
a = −1.09528 + 1.30675I
b = 1.221700 − 0.524298I
−5.77402 − 0.98954I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395238 − 1.125030I
a = −1.09528 − 1.30675I
b = 1.221700 + 0.524298I
−5.77402 + 0.98954I 0
u = −0.679537 + 1.008540I
a = 0.05788 − 1.67451I
b = −1.111850 + 0.790562I
−5.89450 + 4.83270I 0
u = −0.679537 − 1.008540I
a = 0.05788 + 1.67451I
b = −1.111850 − 0.790562I
−5.89450 − 4.83270I 0
u = −0.085610 + 1.213650I
a = −0.506285 − 0.982225I
b = 0.400724 + 1.016080I
6.51711 − 0.28172I 0
u = −0.085610 − 1.213650I
a = −0.506285 + 0.982225I
b = 0.400724 − 1.016080I
6.51711 + 0.28172I 0
u = 0.317123 + 0.711899I
a = −0.51685 + 2.64573I
b = 0.038672 − 1.233930I
1.84806 − 0.31109I −8.59302 − 2.40672I
u = 0.317123 − 0.711899I
a = −0.51685 − 2.64573I
b = 0.038672 + 1.233930I
1.84806 + 0.31109I −8.59302 + 2.40672I
u = 0.067213 + 0.764941I
a = −1.80505 + 1.83294I
b = −1.099080 − 0.188046I
−2.33888 − 0.32984I −8.07472 − 4.98162I
u = 0.067213 − 0.764941I
a = −1.80505 − 1.83294I
b = −1.099080 + 0.188046I
−2.33888 + 0.32984I −8.07472 + 4.98162I
u = 0.607844 + 0.450538I
a = 0.522201 + 0.024471I
b = 0.220687 − 0.347615I
−0.75850 − 1.84706I −5.49749 + 3.01488I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.607844 − 0.450538I
a = 0.522201 − 0.024471I
b = 0.220687 + 0.347615I
−0.75850 + 1.84706I −5.49749 − 3.01488I
u = −0.482232 + 1.167990I
a = 0.278937 + 1.270480I
b = −0.306276 − 1.309440I
−0.18620 + 9.95806I 0
u = −0.482232 − 1.167990I
a = 0.278937 − 1.270480I
b = −0.306276 + 1.309440I
−0.18620 − 9.95806I 0
u = −0.145194 + 0.718422I
a = −0.718273 − 0.325939I
b = 1.86404 + 0.21206I
−7.72237 + 3.39581I −2.62157 − 5.42993I
u = −0.145194 − 0.718422I
a = −0.718273 + 0.325939I
b = 1.86404 − 0.21206I
−7.72237 − 3.39581I −2.62157 + 5.42993I
u = −0.284742 + 1.290950I
a = −0.049100 − 0.733204I
b = −1.200570 + 0.409251I
0.524621 − 0.718329I 0
u = −0.284742 − 1.290950I
a = −0.049100 + 0.733204I
b = −1.200570 − 0.409251I
0.524621 + 0.718329I 0
u = 0.484484 + 1.248630I
a = 0.139134 − 1.321260I
b = 1.244740 + 0.562971I
1.63511 − 10.27850I 0
u = 0.484484 − 1.248630I
a = 0.139134 + 1.321260I
b = 1.244740 − 0.562971I
1.63511 + 10.27850I 0
u = 0.693014 + 1.153210I
a = −0.233591 + 0.433958I
b = −1.209870 − 0.311520I
1.00831 − 3.62362I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.693014 − 1.153210I
a = −0.233591 − 0.433958I
b = −1.209870 + 0.311520I
1.00831 + 3.62362I 0
u = 0.505678 + 1.267990I
a = −0.627794 − 1.192600I
b = 1.219070 + 0.431198I
−2.57891 − 5.15325I 0
u = 0.505678 − 1.267990I
a = −0.627794 + 1.192600I
b = 1.219070 − 0.431198I
−2.57891 + 5.15325I 0
u = −0.610191 + 1.221500I
a = −0.43570 + 1.51047I
b = 1.199520 − 0.436737I
−7.51244 + 9.85286I 0
u = −0.610191 − 1.221500I
a = −0.43570 − 1.51047I
b = 1.199520 + 0.436737I
−7.51244 − 9.85286I 0
u = 0.204953 + 1.350040I
a = −0.308819 + 0.965842I
b = 0.190591 − 0.919605I
4.86269 − 4.86500I 0
u = 0.204953 − 1.350040I
a = −0.308819 − 0.965842I
b = 0.190591 + 0.919605I
4.86269 + 4.86500I 0
u = −0.502245 + 0.337110I
a = 0.626882 + 0.952788I
b = 0.728847 + 0.455431I
1.91146 − 1.96925I −2.72689 + 3.92118I
u = −0.502245 − 0.337110I
a = 0.626882 − 0.952788I
b = 0.728847 − 0.455431I
1.91146 + 1.96925I −2.72689 − 3.92118I
u = 0.66119 + 1.26252I
a = 0.23631 + 1.39596I
b = −1.33184 − 0.78181I
0.29094 − 10.51250I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.66119 − 1.26252I
a = 0.23631 − 1.39596I
b = −1.33184 + 0.78181I
0.29094 + 10.51250I 0
u = −0.59203 + 1.31115I
a = −0.021584 − 0.482843I
b = 0.440321 + 0.673105I
2.09582 + 1.45533I 0
u = −0.59203 − 1.31115I
a = −0.021584 + 0.482843I
b = 0.440321 − 0.673105I
2.09582 − 1.45533I 0
u = 0.30134 + 1.42505I
a = 0.013198 + 0.631788I
b = 0.442076 − 0.614277I
2.20909 − 0.33519I 0
u = 0.30134 − 1.42505I
a = 0.013198 − 0.631788I
b = 0.442076 + 0.614277I
2.20909 + 0.33519I 0
u = −1.44394 + 0.42259I
a = 0.0637499 + 0.0240536I
b = −1.152850 − 0.428505I
−6.52297 − 9.40235I 0
u = −1.44394 − 0.42259I
a = 0.0637499 − 0.0240536I
b = −1.152850 + 0.428505I
−6.52297 + 9.40235I 0
u = −0.76723 + 1.33457I
a = 0.124143 − 1.294850I
b = −1.32553 + 0.70779I
−3.4640 + 16.9486I 0
u = −0.76723 − 1.33457I
a = 0.124143 + 1.294850I
b = −1.32553 − 0.70779I
−3.4640 − 16.9486I 0
u = 0.85727 + 1.29795I
a = 0.154855 − 0.913546I
b = 1.074300 + 0.512049I
0.33774 − 4.80042I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.85727 − 1.29795I
a = 0.154855 + 0.913546I
b = 1.074300 − 0.512049I
0.33774 + 4.80042I 0
u = −1.13250 + 1.08347I
a = 0.357811 + 0.825069I
b = 1.059500 − 0.561243I
0.29351 + 6.24678I 0
u = −1.13250 − 1.08347I
a = 0.357811 − 0.825069I
b = 1.059500 + 0.561243I
0.29351 − 6.24678I 0
u = 0.311983 + 0.229233I
a = 0.21073 + 3.18354I
b = −0.957483 − 0.269471I
−3.66318 − 0.26666I −14.9328 + 0.9814I
u = 0.311983 − 0.229233I
a = 0.21073 − 3.18354I
b = −0.957483 + 0.269471I
−3.66318 + 0.26666I −14.9328 − 0.9814I
u = −0.242211 + 0.227257I
a = −2.94710 − 4.83050I
b = 0.447980 + 0.630904I
−3.20065 − 6.05158I −6.61264 + 3.93826I
u = −0.242211 − 0.227257I
a = −2.94710 + 4.83050I
b = 0.447980 − 0.630904I
−3.20065 + 6.05158I −6.61264 − 3.93826I
u = 0.217813
a = 1.63753
b = −0.452023
−0.718352 −14.2620
u = 0.31645 + 1.94342I
a = 0.401083 + 0.176751I
b = −0.757995 + 0.007392I
3.44325 − 2.33828I 0
u = 0.31645 − 1.94342I
a = 0.401083 − 0.176751I
b = −0.757995 − 0.007392I
3.44325 + 2.33828I 0
12
II. I
u
2
= h−6630u
15
+ 14537u
14
+ · · · + 13613b − 33108, 5953u
15
− 4661u
14
+
· · · + 13613a + 59873, u
16
− 3u
15
+ · · · + u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
2
=
−0.437303u
15
+ 0.342393u
14
+ ··· − 5.84493u − 4.39822
0.487034u
15
− 1.06788u
14
+ ··· + 3.44362u + 2.43209
a
7
=
1
u
2
a
3
=
−1.56564u
15
+ 3.28245u
14
+ ··· − 7.88173u − 5.86079
0.919195u
15
− 1.81679u
14
+ ··· + 5.01690u + 2.87703
a
10
=
−u
u
a
5
=
3.20929u
15
− 9.05451u
14
+ ··· + 6.85624u + 3.49849
−2.08095u
15
+ 6.11445u
14
+ ··· − 4.81944u − 2.03592
a
1
=
2.36590u
15
− 9.75869u
14
+ ··· + 0.387130u − 0.295894
−1.18784u
15
+ 5.09315u
14
+ ··· − 1.75163u − 0.207669
a
4
=
2.77712u
15
− 8.30559u
14
+ ··· + 5.28296u + 3.05355
−1.64879u
15
+ 5.36553u
14
+ ··· − 3.24616u − 1.59098
a
11
=
−0.342761u
15
+ 0.588041u
14
+ ··· − 7.16470u + 1.08565
0.783002u
15
− 2.55528u
14
+ ··· + 4.73628u − 1.42841
a
8
=
−1.48182u
15
+ 5.50878u
14
+ ··· + 0.746198u − 2.02233
0.481819u
15
− 2.50878u
14
+ ··· + 0.253802u + 1.02233
a
8
=
−1.48182u
15
+ 5.50878u
14
+ ··· + 0.746198u − 2.02233
0.481819u
15
− 2.50878u
14
+ ··· + 0.253802u + 1.02233
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
126196
13613
u
15
+
361017
13613
u
14
+ ··· −
176076
13613
u −
182048
13613
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 4u
15
+ ··· + 4u + 1
c
2
u
16
+ 6u
13
+ ··· − 2u + 1
c
3
u
16
+ 6u
15
+ ··· + 12u + 1
c
4
u
16
− 4u
15
+ ··· + 4u + 1
c
5
u
16
− 4u
15
+ ··· − 4u + 1
c
6
u
16
− 3u
15
+ ··· + u + 1
c
7
u
16
− 6u
13
+ ··· + 2u + 1
c
8
u
16
+ 3u
15
+ ··· − u + 1
c
9
u
16
+ 3u
15
+ ··· − u + 1
c
10
u
16
+ 4u
15
+ ··· − 4u + 1
c
11
u
16
− 3u
15
+ ··· + u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
16
− 8y
15
+ ··· − 8y + 1
c
2
, c
7
y
16
− 36y
14
+ ··· − 2y + 1
c
3
y
16
− 2y
15
+ ··· − 16y + 1
c
4
, c
10
y
16
− 40y
14
+ ··· + 2y + 1
c
6
, c
9
y
16
+ 13y
15
+ ··· + 13y + 1
c
8
, c
11
y
16
+ 5y
15
+ ··· + 7y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.101294 + 0.981672I
a = 0.12047 − 2.74164I
b = −1.002360 + 0.178823I
−1.67108 + 0.41329I −23.4089 + 3.7817I
u = −0.101294 − 0.981672I
a = 0.12047 + 2.74164I
b = −1.002360 − 0.178823I
−1.67108 − 0.41329I −23.4089 − 3.7817I
u = 0.623315 + 0.892744I
a = −0.203916 + 0.768996I
b = −0.933085 − 0.164926I
−1.48457 − 2.42366I −12.58854 + 4.41901I
u = 0.623315 − 0.892744I
a = −0.203916 − 0.768996I
b = −0.933085 + 0.164926I
−1.48457 + 2.42366I −12.58854 − 4.41901I
u = −0.699739 + 0.517450I
a = 1.75573 + 1.74837I
b = 0.606505 − 0.489801I
−3.58696 + 6.81151I −11.0601 − 13.1790I
u = −0.699739 − 0.517450I
a = 1.75573 − 1.74837I
b = 0.606505 + 0.489801I
−3.58696 − 6.81151I −11.0601 + 13.1790I
u = 0.310572 + 1.172820I
a = −0.010870 + 1.004540I
b = 0.252552 − 1.034960I
4.17484 − 1.01269I −2.56085 + 0.73282I
u = 0.310572 − 1.172820I
a = −0.010870 − 1.004540I
b = 0.252552 + 1.034960I
4.17484 + 1.01269I −2.56085 − 0.73282I
u = 0.183037 + 0.692134I
a = 0.04599 − 2.88279I
b = −0.260836 + 1.037800I
2.13903 − 1.01254I −1.87145 + 5.73964I
u = 0.183037 − 0.692134I
a = 0.04599 + 2.88279I
b = −0.260836 − 1.037800I
2.13903 + 1.01254I −1.87145 − 5.73964I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00338 + 1.15887I
a = 0.264250 − 0.814168I
b = 1.114260 + 0.514050I
1.36811 − 5.87068I −3.73603 + 6.05900I
u = 1.00338 − 1.15887I
a = 0.264250 + 0.814168I
b = 1.114260 − 0.514050I
1.36811 + 5.87068I −3.73603 − 6.05900I
u = −0.203694 + 0.378381I
a = −1.98850 − 0.07556I
b = 1.70034 + 0.18352I
−8.21157 + 3.18915I −16.8553 − 0.1010I
u = −0.203694 − 0.378381I
a = −1.98850 + 0.07556I
b = 1.70034 − 0.18352I
−8.21157 − 3.18915I −16.8553 + 0.1010I
u = 0.38442 + 1.82901I
a = 0.0168503 + 0.1111360I
b = 0.522619 − 0.189004I
3.98234 − 2.11939I 1.081156 + 0.586483I
u = 0.38442 − 1.82901I
a = 0.0168503 − 0.1111360I
b = 0.522619 + 0.189004I
3.98234 + 2.11939I 1.081156 − 0.586483I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
+ 4u
15
+ ··· + 4u + 1)(u
80
+ u
79
+ ··· − 6u − 1)
c
2
(u
16
+ 6u
13
+ ··· − 2u + 1)(u
80
− u
79
+ ··· + 3416u − 3721)
c
3
(u
16
+ 6u
15
+ ··· + 12u + 1)(u
80
− 3u
79
+ ··· + 35212u − 5777)
c
4
(u
16
− 4u
15
+ ··· + 4u + 1)(u
80
+ 5u
79
+ ··· − 306u − 527)
c
5
(u
16
− 4u
15
+ ··· − 4u + 1)(u
80
+ u
79
+ ··· − 6u − 1)
c
6
(u
16
− 3u
15
+ ··· + u + 1)(u
80
− 4u
79
+ ··· + 27u + 34)
c
7
(u
16
− 6u
13
+ ··· + 2u + 1)(u
80
− u
79
+ ··· + 3416u − 3721)
c
8
(u
16
+ 3u
15
+ ··· − u + 1)(u
80
+ 2u
79
+ ··· − 181u + 31)
c
9
(u
16
+ 3u
15
+ ··· − u + 1)(u
80
− 4u
79
+ ··· + 27u + 34)
c
10
(u
16
+ 4u
15
+ ··· − 4u + 1)(u
80
+ 5u
79
+ ··· − 306u − 527)
c
11
(u
16
− 3u
15
+ ··· + u + 1)(u
80
+ 2u
79
+ ··· − 181u + 31)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
16
− 8y
15
+ ··· − 8y + 1)(y
80
− 43y
79
+ ··· − 4y + 1)
c
2
, c
7
(y
16
− 36y
14
+ ··· − 2y + 1)
· (y
80
− 47y
79
+ ··· − 72209726y + 13845841)
c
3
(y
16
− 2y
15
+ ··· − 16y + 1)
· (y
80
− 25y
79
+ ··· − 1723258088y + 33373729)
c
4
, c
10
(y
16
− 40y
14
+ ··· + 2y + 1)(y
80
+ 37y
79
+ ··· + 5061478y + 277729)
c
6
, c
9
(y
16
+ 13y
15
+ ··· + 13y + 1)(y
80
+ 46y
79
+ ··· − 6577y + 1156)
c
8
, c
11
(y
16
+ 5y
15
+ ··· + 7y + 1)(y
80
+ 46y
79
+ ··· − 21229y + 961)
19
