12a
1223
(K12a
1223
)
A knot diagram
1
Linearized knot diagam
5 6 8 10 2 11 12 4 1 3 7 9
Solving Sequence
6,11
7 12
3,8
2 5 1 10 4 9
c
6
c
11
c
7
c
2
c
5
c
1
c
10
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3.57598 × 10
170
u
85
+ 1.01646 × 10
170
u
84
+ ··· + 2.31147 × 10
171
b − 4.59337 × 10
171
,
8.19062 × 10
171
u
85
+ 1.94837 × 10
172
u
84
+ ··· + 1.61803 × 10
172
a − 2.37902 × 10
173
, u
86
+ 2u
85
+ ··· − 43u − 7i
I
u
2
= hu
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ b + 1,
u
15
− 9u
13
+ 2u
12
+ 31u
11
− 14u
10
− 48u
9
+ 36u
8
+ 26u
7
− 40u
6
+ 8u
5
+ 16u
4
− 8u
3
+ a,
u
18
− u
17
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 104 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
= h3.58 × 10
170
u
85
+ 1.02 × 10
170
u
84
+ · · · + 2.31 × 10
171
b − 4.59 ×
10
171
, 8.19 × 10
171
u
85
+ 1.95 × 10
172
u
84
+ · · · + 1.62 × 10
172
a − 2.38 ×
10
173
, u
86
+ 2u
85
+ · · · − 43u − 7i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
−0.506210u
85
− 1.20416u
84
+ ··· + 19.3397u + 14.7032
−0.154706u
85
− 0.0439746u
84
+ ··· + 0.0924782u + 1.98721
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−0.660916u
85
− 1.24814u
84
+ ··· + 19.4322u + 16.6904
−0.154706u
85
− 0.0439746u
84
+ ··· + 0.0924782u + 1.98721
a
5
=
0.0356140u
85
+ 0.948982u
84
+ ··· − 85.0217u − 27.4994
−1.04716u
85
− 0.439822u
84
+ ··· + 37.0962u + 3.37904
a
1
=
3.18148u
85
+ 2.79945u
84
+ ··· − 96.9770u − 29.8437
2.86152u
85
+ 1.39695u
84
+ ··· − 91.4443u − 18.0567
a
10
=
−0.994047u
85
− 1.13219u
84
+ ··· + 98.6363u + 6.28721
−0.776751u
85
− 0.662827u
84
+ ··· + 15.6810u + 7.57944
a
4
=
−1.04225u
85
− 1.40402u
84
+ ··· + 33.9514u + 17.8765
−0.397611u
85
− 0.156340u
84
+ ··· + 6.69560u + 3.09603
a
9
=
2.45518u
85
+ 1.64740u
84
+ ··· − 104.010u − 27.7858
2.48561u
85
+ 1.37154u
84
+ ··· − 43.7893u − 10.0526
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.959329u
85
− 0.908484u
84
+ ··· − 101.771u − 16.8438
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
86
+ 6u
85
+ ··· − 158u + 47
c
3
, c
8
u
86
− 24u
84
+ ··· + 2u + 1
c
4
u
86
− u
85
+ ··· − 33283u + 13877
c
6
, c
7
, c
11
u
86
− 2u
85
+ ··· + 43u − 7
c
9
, c
12
u
86
− 2u
85
+ ··· + 46u − 1
c
10
u
86
+ 3u
85
+ ··· + 1643283u + 1221183
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
86
− 100y
85
+ ··· − 128552y + 2209
c
3
, c
8
y
86
− 48y
85
+ ··· − 36y + 1
c
4
y
86
+ 33y
85
+ ··· − 67871217y + 192571129
c
6
, c
7
, c
11
y
86
− 92y
85
+ ··· − 3039y + 49
c
9
, c
12
y
86
− 72y
85
+ ··· − 8784y + 1
c
10
y
86
+ 45y
85
+ ··· + 22828629889629y + 1491287919489
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.789217 + 0.531072I
a = −0.333546 + 1.319880I
b = 1.57228 − 0.20818I
−10.78230 + 6.15211I 0
u = −0.789217 − 0.531072I
a = −0.333546 − 1.319880I
b = 1.57228 + 0.20818I
−10.78230 − 6.15211I 0
u = 0.504496 + 0.785795I
a = −0.224964 − 1.153010I
b = 0.630992 + 0.646745I
−0.62218 − 8.31784I 0
u = 0.504496 − 0.785795I
a = −0.224964 + 1.153010I
b = 0.630992 − 0.646745I
−0.62218 + 8.31784I 0
u = 0.693135 + 0.815814I
a = −0.560371 + 0.113537I
b = 0.469055 − 0.386035I
−1.03113 + 2.97558I 0
u = 0.693135 − 0.815814I
a = −0.560371 − 0.113537I
b = 0.469055 + 0.386035I
−1.03113 − 2.97558I 0
u = −0.555192 + 0.689225I
a = 0.52969 − 1.71387I
b = −1.48386 + 0.12467I
−3.00766 + 5.60382I 0
u = −0.555192 − 0.689225I
a = 0.52969 + 1.71387I
b = −1.48386 − 0.12467I
−3.00766 − 5.60382I 0
u = 0.796633 + 0.316728I
a = 1.116010 − 0.334984I
b = 0.528452 + 0.300147I
−1.225560 + 0.382406I 0
u = 0.796633 − 0.316728I
a = 1.116010 + 0.334984I
b = 0.528452 − 0.300147I
−1.225560 − 0.382406I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.555636 + 0.644693I
a = 0.736530 − 0.444696I
b = −1.44874 − 0.02658I
−2.96973 − 0.99166I 0
u = −0.555636 − 0.644693I
a = 0.736530 + 0.444696I
b = −1.44874 + 0.02658I
−2.96973 + 0.99166I 0
u = −0.213002 + 1.133890I
a = −0.989144 + 0.204843I
b = 1.53849 + 0.08270I
−8.25387 − 0.91603I 0
u = −0.213002 − 1.133890I
a = −0.989144 − 0.204843I
b = 1.53849 − 0.08270I
−8.25387 + 0.91603I 0
u = 0.666006 + 0.942281I
a = 0.480118 + 1.083050I
b = −1.56944 − 0.19659I
−7.92614 − 11.41240I 0
u = 0.666006 − 0.942281I
a = 0.480118 − 1.083050I
b = −1.56944 + 0.19659I
−7.92614 + 11.41240I 0
u = −1.17555
a = 1.35986
b = 1.06692
0.921670 0
u = −0.152567 + 0.809303I
a = 1.006560 + 0.126524I
b = −0.479008 − 0.309869I
−1.40654 + 0.45091I 0
u = −0.152567 − 0.809303I
a = 1.006560 − 0.126524I
b = −0.479008 + 0.309869I
−1.40654 − 0.45091I 0
u = 0.794490 + 0.120729I
a = −1.35076 + 1.02036I
b = −1.49966 + 0.07263I
−7.85799 + 0.61029I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.794490 − 0.120729I
a = −1.35076 − 1.02036I
b = −1.49966 − 0.07263I
−7.85799 − 0.61029I 0
u = 0.455465 + 0.649631I
a = −1.08140 − 1.18633I
b = 1.48458 + 0.06927I
−6.18326 − 2.15194I 0
u = 0.455465 − 0.649631I
a = −1.08140 + 1.18633I
b = 1.48458 − 0.06927I
−6.18326 + 2.15194I 0
u = −0.447792 + 0.591674I
a = 0.03198 + 1.54449I
b = 0.422429 − 0.502306I
3.23618 + 3.43219I 0. − 7.59193I
u = −0.447792 − 0.591674I
a = 0.03198 − 1.54449I
b = 0.422429 + 0.502306I
3.23618 − 3.43219I 0. + 7.59193I
u = 0.728943
a = 0.704489
b = 0.348138
−1.42668 −5.68360
u = 0.732516 + 1.109930I
a = 0.518848 + 0.350147I
b = −1.53688 + 0.10163I
−7.82387 + 4.66675I 0
u = 0.732516 − 1.109930I
a = 0.518848 − 0.350147I
b = −1.53688 − 0.10163I
−7.82387 − 4.66675I 0
u = −0.639962
a = −1.66888
b = 0.425683
3.24162 7.90500
u = −0.448279 + 0.438995I
a = −0.814157 − 0.936435I
b = 0.463919 + 0.389009I
3.01283 + 0.20437I 1.047842 + 0.913639I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.448279 − 0.438995I
a = −0.814157 + 0.936435I
b = 0.463919 − 0.389009I
3.01283 − 0.20437I 1.047842 − 0.913639I
u = 0.301148 + 0.545313I
a = 0.049969 + 1.231930I
b = 0.351841 − 0.788610I
0.23561 − 3.61201I −3.68648 + 6.73668I
u = 0.301148 − 0.545313I
a = 0.049969 − 1.231930I
b = 0.351841 + 0.788610I
0.23561 + 3.61201I −3.68648 − 6.73668I
u = −1.378730 + 0.010185I
a = −0.225333 − 0.989484I
b = −0.532361 + 0.659791I
−5.07390 + 2.06341I 0
u = −1.378730 − 0.010185I
a = −0.225333 + 0.989484I
b = −0.532361 − 0.659791I
−5.07390 − 2.06341I 0
u = −0.550593 + 0.279146I
a = 0.050258 − 1.209990I
b = −0.657179 + 0.743375I
−3.42725 + 2.76216I −11.9294 − 7.8140I
u = −0.550593 − 0.279146I
a = 0.050258 + 1.209990I
b = −0.657179 − 0.743375I
−3.42725 − 2.76216I −11.9294 + 7.8140I
u = −1.378290 + 0.151019I
a = −0.051213 − 0.853728I
b = −0.555720 + 0.673304I
−5.10950 + 2.50442I 0
u = −1.378290 − 0.151019I
a = −0.051213 + 0.853728I
b = −0.555720 − 0.673304I
−5.10950 − 2.50442I 0
u = −1.42209 + 0.12454I
a = 0.33476 + 1.43001I
b = 1.53896 − 0.19132I
−11.92440 + 5.10845I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42209 − 0.12454I
a = 0.33476 − 1.43001I
b = 1.53896 + 0.19132I
−11.92440 − 5.10845I 0
u = 1.43671 + 0.10420I
a = −0.841755 − 1.016560I
b = −0.489916 + 0.093972I
−6.58825 − 4.01957I 0
u = 1.43671 − 0.10420I
a = −0.841755 + 1.016560I
b = −0.489916 − 0.093972I
−6.58825 + 4.01957I 0
u = −0.550897
a = −0.646774
b = −1.15486
−2.44460 4.14310
u = 1.44643 + 0.10189I
a = −0.039747 + 0.577367I
b = 0.474440 − 0.652725I
−2.94499 − 2.06223I 0
u = 1.44643 − 0.10189I
a = −0.039747 − 0.577367I
b = 0.474440 + 0.652725I
−2.94499 + 2.06223I 0
u = −1.44932 + 0.15031I
a = −0.055491 − 0.603649I
b = 0.262382 + 1.153010I
−5.46589 + 6.01776I 0
u = −1.44932 − 0.15031I
a = −0.055491 + 0.603649I
b = 0.262382 − 1.153010I
−5.46589 − 6.01776I 0
u = 1.47482 + 0.01278I
a = 1.39413 − 1.35914I
b = 1.55105 + 0.02316I
−13.62500 + 3.61708I 0
u = 1.47482 − 0.01278I
a = 1.39413 + 1.35914I
b = 1.55105 − 0.02316I
−13.62500 − 3.61708I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48243 + 0.00101I
a = −0.547223 + 0.505995I
b = −1.84865 − 0.43880I
−12.06140 − 1.11145I 0
u = −1.48243 − 0.00101I
a = −0.547223 − 0.505995I
b = −1.84865 + 0.43880I
−12.06140 + 1.11145I 0
u = 1.49657 + 0.10349I
a = −0.577335 + 0.591255I
b = −1.58583 − 0.20548I
−9.77886 − 1.28438I 0
u = 1.49657 − 0.10349I
a = −0.577335 − 0.591255I
b = −1.58583 + 0.20548I
−9.77886 + 1.28438I 0
u = 1.50078 + 0.07624I
a = −0.287601 + 0.644186I
b = −0.938000 − 1.046720I
−10.10640 − 4.04965I 0
u = 1.50078 − 0.07624I
a = −0.287601 − 0.644186I
b = −0.938000 + 1.046720I
−10.10640 + 4.04965I 0
u = 1.49571 + 0.18966I
a = 0.442239 − 0.965539I
b = 0.528911 + 0.591680I
−3.13918 − 6.25627I 0
u = 1.49571 − 0.18966I
a = 0.442239 + 0.965539I
b = 0.528911 − 0.591680I
−3.13918 + 6.25627I 0
u = −1.47770 + 0.31519I
a = 0.241795 + 1.031910I
b = 1.55911 − 0.19231I
−12.16490 + 5.62093I 0
u = −1.47770 − 0.31519I
a = 0.241795 − 1.031910I
b = 1.55911 + 0.19231I
−12.16490 − 5.62093I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48644 + 0.31043I
a = 0.194147 + 0.776740I
b = −0.565736 − 0.086897I
−6.86869 − 4.70358I 0
u = 1.48644 − 0.31043I
a = 0.194147 − 0.776740I
b = −0.565736 + 0.086897I
−6.86869 + 4.70358I 0
u = −1.51990 + 0.26159I
a = 0.360201 + 0.874167I
b = 0.806729 − 0.781995I
−7.21157 + 12.10600I 0
u = −1.51990 − 0.26159I
a = 0.360201 − 0.874167I
b = 0.806729 + 0.781995I
−7.21157 − 12.10600I 0
u = 1.55340 + 0.22517I
a = −0.70812 + 1.46505I
b = −1.53653 − 0.16703I
−9.98549 − 8.95683I 0
u = 1.55340 − 0.22517I
a = −0.70812 − 1.46505I
b = −1.53653 + 0.16703I
−9.98549 + 8.95683I 0
u = 1.59072 + 0.16952I
a = 0.556696 − 0.964732I
b = 1.67598 + 0.27758I
−18.6620 − 8.8164I 0
u = 1.59072 − 0.16952I
a = 0.556696 + 0.964732I
b = 1.67598 − 0.27758I
−18.6620 + 8.8164I 0
u = 0.231835 + 0.323647I
a = 0.69062 + 1.23900I
b = −0.301055 − 0.322396I
−0.206463 − 0.876909I −4.71593 + 7.65224I
u = 0.231835 − 0.323647I
a = 0.69062 − 1.23900I
b = −0.301055 + 0.322396I
−0.206463 + 0.876909I −4.71593 − 7.65224I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60372 + 0.06660I
a = 0.307257 + 0.415115I
b = 0.536103 − 0.041755I
−9.65329 + 0.15213I 0
u = −1.60372 − 0.06660I
a = 0.307257 − 0.415115I
b = 0.536103 + 0.041755I
−9.65329 − 0.15213I 0
u = −1.63067
a = 0.612409
b = 0.508496
−9.66712 0
u = −1.60323 + 0.30921I
a = −0.502737 − 1.166510I
b = −1.63933 + 0.24572I
−15.3320 + 16.0041I 0
u = −1.60323 − 0.30921I
a = −0.502737 + 1.166510I
b = −1.63933 − 0.24572I
−15.3320 − 16.0041I 0
u = 1.60103 + 0.45329I
a = 0.161139 − 0.880209I
b = 1.56979 + 0.01972I
−14.2347 − 5.0655I 0
u = 1.60103 − 0.45329I
a = 0.161139 + 0.880209I
b = 1.56979 − 0.01972I
−14.2347 + 5.0655I 0
u = −1.67558
a = −1.40435
b = −1.55197
−16.7542 0
u = −0.140424 + 0.272759I
a = −3.81925 − 0.22914I
b = −0.428162 + 0.296323I
−1.27530 + 2.62216I −8.64557 − 11.14295I
u = −0.140424 − 0.272759I
a = −3.81925 + 0.22914I
b = −0.428162 − 0.296323I
−1.27530 − 2.62216I −8.64557 + 11.14295I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70594 + 0.15407I
a = −0.733525 − 0.538845I
b = −1.56345 + 0.01074I
−16.9023 + 0.3370I 0
u = −1.70594 − 0.15407I
a = −0.733525 + 0.538845I
b = −1.56345 − 0.01074I
−16.9023 − 0.3370I 0
u = 0.274418 + 0.016499I
a = 0.11655 + 2.14778I
b = −1.64428 − 0.30370I
−6.03987 − 1.09293I −21.9287 + 6.9762I
u = 0.274418 − 0.016499I
a = 0.11655 − 2.14778I
b = −1.64428 + 0.30370I
−6.03987 + 1.09293I −21.9287 − 6.9762I
u = −0.186864 + 0.089463I
a = 0.37438 + 9.46767I
b = 1.51710 + 0.07808I
−7.83183 − 3.89836I −12.6530 + 7.2106I
u = −0.186864 − 0.089463I
a = 0.37438 − 9.46767I
b = 1.51710 − 0.07808I
−7.83183 + 3.89836I −12.6530 − 7.2106I
13
II. I
u
2
=
hu
7
−4u
5
+u
4
+4u
3
−2u
2
+b+1, u
15
−9u
13
+· · ·−8u
3
+a, u
18
−u
17
+· · ·−u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
−u
15
+ 9u
13
+ ··· − 16u
4
+ 8u
3
−u
7
+ 4u
5
− u
4
− 4u
3
+ 2u
2
− 1
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−u
15
+ 9u
13
+ ··· + 2u
2
− 1
−u
7
+ 4u
5
− u
4
− 4u
3
+ 2u
2
− 1
a
5
=
−u
14
+ 8u
12
+ ··· − 2u + 1
−u
14
+ 8u
12
+ ··· + 4u
2
− 1
a
1
=
u
17
− 10u
15
+ ··· + 3u − 2
u
17
− 10u
15
+ ··· − 6u
2
+ u
a
10
=
−u
7
+ 4u
5
− u
4
− 4u
3
+ 2u
2
−u
9
+ 5u
7
− u
6
− 7u
5
+ 3u
4
+ u
3
− 2u
2
+ 2u
a
4
=
−u
15
− u
14
+ ··· − 22u
4
+ 4u
2
−u
16
+ 9u
14
+ ··· + 2u
2
− 1
a
9
=
u
16
− 9u
14
+ ··· − 3u + 1
u
16
− 9u
14
+ ··· + u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
17
− 12u
15
+ 59u
13
− 7u
12
− 149u
11
+ 53u
10
+ 187u
9
− 146u
8
−
72u
7
+ 168u
6
− 52u
5
− 57u
4
+ 33u
3
− 14u
2
− 3u − 10
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
18
− u
17
+ ··· + 4u − 1
c
3
u
18
+ u
17
+ ··· + 4u − 1
c
4
u
18
+ 2u
16
+ ··· + 5u + 1
c
5
u
18
+ u
17
+ ··· − 4u − 1
c
6
, c
7
u
18
− u
17
+ ··· − u + 1
c
8
u
18
− u
17
+ ··· − 4u − 1
c
9
u
18
+ 3u
17
+ ··· + 8u + 1
c
10
u
18
+ 2u
16
+ ··· − 3u + 1
c
11
u
18
+ u
17
+ ··· + u + 1
c
12
u
18
− 3u
17
+ ··· − 8u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
18
− 25y
17
+ ··· − 6y + 1
c
3
, c
8
y
18
− 17y
17
+ ··· − 30y + 1
c
4
y
18
+ 4y
17
+ ··· − 11y + 1
c
6
, c
7
, c
11
y
18
− 21y
17
+ ··· + 3y + 1
c
9
, c
12
y
18
− 21y
17
+ ··· − 126y + 1
c
10
y
18
+ 4y
17
+ ··· − 17y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04652
a = 1.35774
b = 0.929235
1.68470 −2.89640
u = 0.421317 + 0.719343I
a = −0.88354 − 1.48981I
b = 1.49998 − 0.07412I
−7.24260 + 3.06692I −6.84701 − 0.28152I
u = 0.421317 − 0.719343I
a = −0.88354 + 1.48981I
b = 1.49998 + 0.07412I
−7.24260 − 3.06692I −6.84701 + 0.28152I
u = 0.736639
a = −0.280998
b = −1.05817
−2.80594 −18.8820
u = −0.710637
a = −1.48023
b = 0.557070
2.91571 −17.3300
u = 0.335739 + 0.515313I
a = 0.362599 + 1.098660I
b = −0.228311 + 0.286762I
−1.19486 + 1.88580I −7.38603 − 0.40266I
u = 0.335739 − 0.515313I
a = 0.362599 − 1.098660I
b = −0.228311 − 0.286762I
−1.19486 − 1.88580I −7.38603 + 0.40266I
u = 1.41202 + 0.17279I
a = 0.303163 + 0.821591I
b = −0.090569 − 0.602651I
−5.33102 − 4.37921I −7.08751 + 4.02776I
u = 1.41202 − 0.17279I
a = 0.303163 − 0.821591I
b = −0.090569 + 0.602651I
−5.33102 + 4.37921I −7.08751 − 4.02776I
u = 1.41693 + 0.30832I
a = −0.098754 − 1.309610I
b = 1.49607 + 0.15929I
−11.01080 − 6.88296I −10.04016 + 5.97512I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41693 − 0.30832I
a = −0.098754 + 1.309610I
b = 1.49607 − 0.15929I
−11.01080 + 6.88296I −10.04016 − 5.97512I
u = −1.46458 + 0.10051I
a = −0.235538 − 0.626928I
b = −1.46470 + 0.46646I
−10.68550 + 2.64083I −13.65203 − 2.66841I
u = −1.46458 − 0.10051I
a = −0.235538 + 0.626928I
b = −1.46470 − 0.46646I
−10.68550 − 2.64083I −13.65203 + 2.66841I
u = 1.50471
a = −0.745312
b = −1.83585
−12.2233 −14.9920
u = −0.161184 + 0.384390I
a = 0.814554 − 0.868946I
b = −1.55890 − 0.19298I
−5.66306 − 0.87639I −4.20175 − 2.57088I
u = −0.161184 − 0.384390I
a = 0.814554 + 0.868946I
b = −1.55890 + 0.19298I
−5.66306 + 0.87639I −4.20175 + 2.57088I
u = −1.66215
a = −0.582630
b = −0.435772
−9.48097 16.0990
u = −1.74253
a = 1.20647
b = 1.53636
−16.2697 −2.56890
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
18
− u
17
+ ··· + 4u − 1)(u
86
+ 6u
85
+ ··· − 158u + 47)
c
3
(u
18
+ u
17
+ ··· + 4u − 1)(u
86
− 24u
84
+ ··· + 2u + 1)
c
4
(u
18
+ 2u
16
+ ··· + 5u + 1)(u
86
− u
85
+ ··· − 33283u + 13877)
c
5
(u
18
+ u
17
+ ··· − 4u − 1)(u
86
+ 6u
85
+ ··· − 158u + 47)
c
6
, c
7
(u
18
− u
17
+ ··· − u + 1)(u
86
− 2u
85
+ ··· + 43u − 7)
c
8
(u
18
− u
17
+ ··· − 4u − 1)(u
86
− 24u
84
+ ··· + 2u + 1)
c
9
(u
18
+ 3u
17
+ ··· + 8u + 1)(u
86
− 2u
85
+ ··· + 46u − 1)
c
10
(u
18
+ 2u
16
+ ··· − 3u + 1)(u
86
+ 3u
85
+ ··· + 1643283u + 1221183)
c
11
(u
18
+ u
17
+ ··· + u + 1)(u
86
− 2u
85
+ ··· + 43u − 7)
c
12
(u
18
− 3u
17
+ ··· − 8u + 1)(u
86
− 2u
85
+ ··· + 46u − 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
18
− 25y
17
+ ··· − 6y + 1)(y
86
− 100y
85
+ ··· − 128552y + 2209)
c
3
, c
8
(y
18
− 17y
17
+ ··· − 30y + 1)(y
86
− 48y
85
+ ··· − 36y + 1)
c
4
(y
18
+ 4y
17
+ ··· − 11y + 1)
· (y
86
+ 33y
85
+ ··· − 67871217y + 192571129)
c
6
, c
7
, c
11
(y
18
− 21y
17
+ ··· + 3y + 1)(y
86
− 92y
85
+ ··· − 3039y + 49)
c
9
, c
12
(y
18
− 21y
17
+ ··· − 126y + 1)(y
86
− 72y
85
+ ··· − 8784y + 1)
c
10
(y
18
+ 4y
17
+ ··· − 17y + 1)
· (y
86
+ 45y
85
+ ··· + 22828629889629y + 1491287919489)
20
