12a
0069
(K12a
0069
)
A knot diagram
1
Linearized knot diagam
3 5 7 9 2 10 11 12 6 4 1 8
Solving Sequence
6,9
10
2,7
5 3 1 4 11 12 8
c
9
c
6
c
5
c
2
c
1
c
4
c
10
c
11
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.65770 × 10
416
u
118
− 1.62086 × 10
417
u
117
+ ··· + 7.02397 × 10
415
b − 9.50919 × 10
416
,
− 7.94572 × 10
415
u
118
+ 1.92807 × 10
416
u
117
+ ··· + 7.02397 × 10
415
a + 1.46155 × 10
416
,
u
119
− u
118
+ ··· − 10u
3
− 1i
* 1 irreducible components of dim
C
= 0, with total 119 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
= h7.66 × 10
416
u
118
− 1.62 × 10
417
u
117
+ · · · + 7.02 × 10
415
b − 9.51 ×
10
416
, −7.95 × 10
415
u
118
+ 1.93 × 10
416
u
117
+ · · · + 7.02 × 10
415
a + 1.46 ×
10
416
, u
119
− u
118
+ · · · − 10u
3
− 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
2
=
1.13123u
118
− 2.74499u
117
+ ··· − 0.679206u − 2.08080
−10.9022u
118
+ 23.0761u
117
+ ··· − 11.1828u + 13.5382
a
7
=
u
−u
3
+ u
a
5
=
0.947849u
118
− 3.85311u
117
+ ··· − 3.86697u − 3.09518
−14.8208u
118
+ 24.3819u
117
+ ··· − 16.3486u + 11.6263
a
3
=
0.869184u
118
− 4.24063u
117
+ ··· − 4.92860u − 3.11758
−15.6125u
118
+ 27.9535u
117
+ ··· − 18.8594u + 14.1353
a
1
=
−0.700733u
118
− 0.837427u
117
+ ··· + 2.27817u − 0.562810
0.130477u
118
+ 1.80102u
117
+ ··· − 2.77571u + 1.78291
a
4
=
15.7687u
118
− 28.2350u
117
+ ··· + 12.4817u − 14.7215
−14.8208u
118
+ 24.3819u
117
+ ··· − 16.3486u + 11.6263
a
11
=
0.244750u
118
− 1.71369u
117
+ ··· − 1.10194u − 3.47644
−1.42573u
118
+ 1.50735u
117
+ ··· − 0.807561u + 0.768205
a
12
=
0.683348u
118
− 1.40205u
117
+ ··· − 0.666971u − 2.50037
2.26430u
118
− 3.52278u
117
+ ··· + 2.98299u − 1.11611
a
8
=
−3.44836u
118
+ 3.50134u
117
+ ··· − 5.29495u + 0.898973
3.52208u
118
− 3.23364u
117
+ ··· + 4.70691u − 0.312411
(ii) Obstruction class = −1
(iii) Cusp Shapes = −91.5861u
118
+ 200.489u
117
+ ··· − 97.6537u + 125.725
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
119
+ 47u
118
+ ··· + 76u − 1
c
2
, c
5
u
119
+ u
118
+ ··· + 4u − 1
c
3
u
119
− 11u
118
+ ··· − 44u − 41
c
4
u
119
+ 17u
118
+ ··· − 9590288u − 2011573
c
6
, c
9
u
119
− u
118
+ ··· − 10u
3
− 1
c
7
u
119
+ 5u
118
+ ··· − 2541506u − 300233
c
8
, c
12
u
119
− 5u
118
+ ··· + 2u − 1
c
10
u
119
− 3u
118
+ ··· − 4u + 1
c
11
u
119
+ 59u
118
+ ··· − 10u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
119
+ 51y
118
+ ··· + 3612y −1
c
2
, c
5
y
119
+ 47y
118
+ ··· + 76y −1
c
3
y
119
− 29y
118
+ ··· − 1094568y −1681
c
4
y
119
− 97y
118
+ ··· + 36045891989112y −4046425934329
c
6
, c
9
y
119
− 85y
118
+ ··· + 10y
2
− 1
c
7
y
119
− 53y
118
+ ··· − 333755460568y −90139854289
c
8
, c
12
y
119
+ 59y
118
+ ··· − 10y
2
− 1
c
10
y
119
− 5y
118
+ ··· + 36y −1
c
11
y
119
+ 3y
118
+ ··· − 20y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.035610 + 0.034259I
a = 0.442668 + 0.851761I
b = −3.97968 + 9.10996I
−0.86467 − 1.64898I 0
u = −1.035610 − 0.034259I
a = 0.442668 − 0.851761I
b = −3.97968 − 9.10996I
−0.86467 + 1.64898I 0
u = −0.153531 + 0.943119I
a = 0.329336 − 0.874707I
b = 0.612984 − 0.109115I
−2.01394 − 8.29603I 0
u = −0.153531 − 0.943119I
a = 0.329336 + 0.874707I
b = 0.612984 + 0.109115I
−2.01394 + 8.29603I 0
u = 0.195630 + 0.932978I
a = −0.333343 − 0.813020I
b = −0.621938 + 0.026733I
0.44663 + 3.21872I 0
u = 0.195630 − 0.932978I
a = −0.333343 + 0.813020I
b = −0.621938 − 0.026733I
0.44663 − 3.21872I 0
u = 1.052800 + 0.041861I
a = −0.530406 − 0.799447I
b = −5.59734 − 1.83768I
1.78369 + 2.11474I 0
u = 1.052800 − 0.041861I
a = −0.530406 + 0.799447I
b = −5.59734 + 1.83768I
1.78369 − 2.11474I 0
u = −0.931249 + 0.000665I
a = 0.536962 − 0.910284I
b = −4.83863 + 6.77336I
−0.80226 − 5.64486I 0
u = −0.931249 − 0.000665I
a = 0.536962 + 0.910284I
b = −4.83863 − 6.77336I
−0.80226 + 5.64486I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.060990 + 0.301097I
a = 0.546458 − 0.953653I
b = 1.06405 + 1.45475I
0.30758 − 5.30584I 0
u = −1.060990 − 0.301097I
a = 0.546458 + 0.953653I
b = 1.06405 − 1.45475I
0.30758 + 5.30584I 0
u = 0.267796 + 0.851309I
a = 1.278180 + 0.154070I
b = 1.75621 + 0.23838I
−8.34950 + 2.40655I 0
u = 0.267796 − 0.851309I
a = 1.278180 − 0.154070I
b = 1.75621 − 0.23838I
−8.34950 − 2.40655I 0
u = −0.074330 + 1.125290I
a = −0.997873 − 0.486870I
b = −1.79400 + 0.03937I
−3.88873 − 13.56350I 0
u = −0.074330 − 1.125290I
a = −0.997873 + 0.486870I
b = −1.79400 − 0.03937I
−3.88873 + 13.56350I 0
u = 1.13014
a = −0.111440
b = 0.759054
1.93584 0
u = −1.121190 + 0.188539I
a = −0.145641 − 0.105682I
b = −0.989741 − 0.222670I
−1.05597 − 3.63117I 0
u = −1.121190 − 0.188539I
a = −0.145641 + 0.105682I
b = −0.989741 + 0.222670I
−1.05597 + 3.63117I 0
u = −0.132272 + 0.843702I
a = 0.195416 − 0.810399I
b = 0.328272 − 0.000696I
−4.11006 − 0.27210I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.132272 − 0.843702I
a = 0.195416 + 0.810399I
b = 0.328272 + 0.000696I
−4.11006 + 0.27210I 0
u = −0.147996 + 1.139970I
a = −0.981418 − 0.346599I
b = −1.82266 + 0.10584I
−6.26033 − 4.80404I 0
u = −0.147996 − 1.139970I
a = −0.981418 + 0.346599I
b = −1.82266 − 0.10584I
−6.26033 + 4.80404I 0
u = 0.081715 + 1.152440I
a = 0.948415 − 0.459935I
b = 1.77493 + 0.07000I
−1.22644 + 8.24609I 0
u = 0.081715 − 1.152440I
a = 0.948415 + 0.459935I
b = 1.77493 − 0.07000I
−1.22644 − 8.24609I 0
u = 1.158970 + 0.018063I
a = −0.479317 − 0.521293I
b = −0.258759 − 1.112910I
2.16234 + 1.39239I 0
u = 1.158970 − 0.018063I
a = −0.479317 + 0.521293I
b = −0.258759 + 1.112910I
2.16234 − 1.39239I 0
u = 1.143840 + 0.215265I
a = −0.705485 − 0.961559I
b = −1.26062 + 1.12141I
−0.39199 + 2.55993I 0
u = 1.143840 − 0.215265I
a = −0.705485 + 0.961559I
b = −1.26062 − 1.12141I
−0.39199 − 2.55993I 0
u = 0.801969 + 0.209169I
a = −0.607950 − 0.823356I
b = 0.16247 + 2.03835I
1.10471 + 1.87596I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.801969 − 0.209169I
a = −0.607950 + 0.823356I
b = 0.16247 − 2.03835I
1.10471 − 1.87596I 0
u = −0.281744 + 0.773549I
a = −1.307150 + 0.320885I
b = −1.66811 + 0.26788I
−4.34747 + 1.40844I 0
u = −0.281744 − 0.773549I
a = −1.307150 − 0.320885I
b = −1.66811 − 0.26788I
−4.34747 − 1.40844I 0
u = −1.172220 + 0.136967I
a = 0.807474 − 0.803851I
b = 1.175190 + 0.567020I
3.94124 − 4.31721I 0
u = −1.172220 − 0.136967I
a = 0.807474 + 0.803851I
b = 1.175190 − 0.567020I
3.94124 + 4.31721I 0
u = −1.167230 + 0.178565I
a = 0.781709 − 0.909729I
b = 1.20647 + 0.89400I
3.04776 − 5.27945I 0
u = −1.167230 − 0.178565I
a = 0.781709 + 0.909729I
b = 1.20647 − 0.89400I
3.04776 + 5.27945I 0
u = −1.112690 + 0.397752I
a = 0.429494 − 1.022980I
b = 0.94831 + 1.23748I
−1.79609 − 5.72361I 0
u = −1.112690 − 0.397752I
a = 0.429494 + 1.022980I
b = 0.94831 − 1.23748I
−1.79609 + 5.72361I 0
u = −0.976273 + 0.682780I
a = 0.287128 − 0.765903I
b = 0.620309 + 1.052770I
−3.68701 − 1.75662I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.976273 − 0.682780I
a = 0.287128 + 0.765903I
b = 0.620309 − 1.052770I
−3.68701 + 1.75662I 0
u = 1.178780 + 0.192982I
a = −0.796177 − 0.953278I
b = −1.13146 + 0.97080I
0.72920 + 9.76423I 0
u = 1.178780 − 0.192982I
a = −0.796177 + 0.953278I
b = −1.13146 − 0.97080I
0.72920 − 9.76423I 0
u = 0.227268 + 0.769683I
a = 1.43240 + 0.29302I
b = 1.69375 + 0.33844I
−7.32116 − 6.11305I 0
u = 0.227268 − 0.769683I
a = 1.43240 − 0.29302I
b = 1.69375 − 0.33844I
−7.32116 + 6.11305I 0
u = 1.192600 + 0.108357I
a = −0.864274 − 0.703004I
b = −0.913943 + 0.343127I
2.62468 + 0.41803I 0
u = 1.192600 − 0.108357I
a = −0.864274 + 0.703004I
b = −0.913943 − 0.343127I
2.62468 − 0.41803I 0
u = 1.117730 + 0.438448I
a = −0.371372 − 1.011530I
b = −0.90305 + 1.17790I
−5.72733 + 2.25424I 0
u = 1.117730 − 0.438448I
a = −0.371372 + 1.011530I
b = −0.90305 − 1.17790I
−5.72733 − 2.25424I 0
u = 1.137120 + 0.397553I
a = −0.421645 − 1.060100I
b = −0.97948 + 1.20682I
−4.54003 + 10.40590I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.137120 − 0.397553I
a = −0.421645 + 1.060100I
b = −0.97948 − 1.20682I
−4.54003 − 10.40590I 0
u = −1.211580 + 0.058016I
a = 0.891343 − 0.447261I
b = 0.461806 + 0.041016I
5.32038 − 2.42918I 0
u = −1.211580 − 0.058016I
a = 0.891343 + 0.447261I
b = 0.461806 − 0.041016I
5.32038 + 2.42918I 0
u = −1.216590 + 0.032056I
a = 0.875980 − 0.267951I
b = 0.254703 − 0.026118I
5.57248 − 1.21411I 0
u = −1.216590 − 0.032056I
a = 0.875980 + 0.267951I
b = 0.254703 + 0.026118I
5.57248 + 1.21411I 0
u = 1.217680 + 0.072944I
a = −0.945939 − 0.521474I
b = −0.520719 + 0.178092I
3.35181 + 6.81145I 0
u = 1.217680 − 0.072944I
a = −0.945939 + 0.521474I
b = −0.520719 − 0.178092I
3.35181 − 6.81145I 0
u = 1.225940 + 0.017958I
a = −0.929497 − 0.146641I
b = −0.173944 + 0.003829I
3.90070 − 3.03494I 0
u = 1.225940 − 0.017958I
a = −0.929497 + 0.146641I
b = −0.173944 − 0.003829I
3.90070 + 3.03494I 0
u = 0.331299 + 1.228400I
a = −0.469326 − 0.596666I
b = −1.180590 + 0.461415I
2.25963 + 0.51321I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.331299 − 1.228400I
a = −0.469326 + 0.596666I
b = −1.180590 − 0.461415I
2.25963 − 0.51321I 0
u = −0.070400 + 1.338550I
a = 0.640915 − 0.478369I
b = 1.58846 + 0.31260I
1.89300 + 5.19696I 0
u = −0.070400 − 1.338550I
a = 0.640915 + 0.478369I
b = 1.58846 − 0.31260I
1.89300 − 5.19696I 0
u = −0.618966 + 0.213699I
a = 0.289041 + 0.890207I
b = −1.50194 − 0.12865I
−0.81399 − 3.20969I 4.00000 + 3.78505I
u = −0.618966 − 0.213699I
a = 0.289041 − 0.890207I
b = −1.50194 + 0.12865I
−0.81399 + 3.20969I 4.00000 − 3.78505I
u = 1.36081 + 0.41935I
a = 0.504075 − 0.490516I
b = 0.335719 − 0.339804I
0.57021 + 4.89518I 0
u = 1.36081 − 0.41935I
a = 0.504075 + 0.490516I
b = 0.335719 + 0.339804I
0.57021 − 4.89518I 0
u = −0.548066 + 0.171348I
a = 0.622984 + 0.047785I
b = −0.920128 + 0.468198I
−0.74082 + 3.28237I 3.06985 − 2.32334I
u = −0.548066 − 0.171348I
a = 0.622984 − 0.047785I
b = −0.920128 − 0.468198I
−0.74082 − 3.28237I 3.06985 + 2.32334I
u = 1.36388 + 0.43901I
a = 0.543618 − 0.540469I
b = 0.202526 − 0.389545I
2.69460 + 13.23130I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36388 − 0.43901I
a = 0.543618 + 0.540469I
b = 0.202526 + 0.389545I
2.69460 − 13.23130I 0
u = −1.36970 + 0.43404I
a = −0.516877 − 0.541045I
b = −0.218373 − 0.331413I
5.26875 − 8.10776I 0
u = −1.36970 − 0.43404I
a = −0.516877 + 0.541045I
b = −0.218373 + 0.331413I
5.26875 + 8.10776I 0
u = 0.493931 + 0.252338I
a = −0.609440 − 0.306431I
b = 0.494472 + 0.702216I
1.054520 + 0.810570I 7.06407 − 4.23502I
u = 0.493931 − 0.252338I
a = −0.609440 + 0.306431I
b = 0.494472 − 0.702216I
1.054520 − 0.810570I 7.06407 + 4.23502I
u = 0.534128 + 0.145589I
a = −0.396428 + 1.301490I
b = 1.318260 − 0.418949I
1.040460 − 0.925928I 6.71411 + 2.60230I
u = 0.534128 − 0.145589I
a = −0.396428 − 1.301490I
b = 1.318260 + 0.418949I
1.040460 + 0.925928I 6.71411 − 2.60230I
u = −1.40175 + 0.43210I
a = −0.433268 − 0.579226I
b = −0.187091 − 0.112631I
7.65450 − 5.79278I 0
u = −1.40175 − 0.43210I
a = −0.433268 + 0.579226I
b = −0.187091 + 0.112631I
7.65450 + 5.79278I 0
u = 1.38862 + 0.52166I
a = 0.715613 + 0.556426I
b = 2.22954 − 1.14573I
0.6898 + 19.3458I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38862 − 0.52166I
a = 0.715613 − 0.556426I
b = 2.22954 + 1.14573I
0.6898 − 19.3458I 0
u = −1.39430 + 0.52630I
a = −0.705322 + 0.541088I
b = −2.20450 − 1.12922I
3.3933 − 14.1115I 0
u = −1.39430 − 0.52630I
a = −0.705322 − 0.541088I
b = −2.20450 + 1.12922I
3.3933 + 14.1115I 0
u = 1.42662 + 0.43230I
a = 0.380839 − 0.589100I
b = 0.196843 + 0.029715I
7.34633 + 0.64079I 0
u = 1.42662 − 0.43230I
a = 0.380839 + 0.589100I
b = 0.196843 − 0.029715I
7.34633 − 0.64079I 0
u = −0.265452 + 0.428627I
a = −1.32488 + 1.37649I
b = −1.153860 + 0.239152I
−1.83128 + 2.21574I −1.91021 − 3.90777I
u = −0.265452 − 0.428627I
a = −1.32488 − 1.37649I
b = −1.153860 − 0.239152I
−1.83128 − 2.21574I −1.91021 + 3.90777I
u = 1.40600 + 0.51747I
a = 0.673518 + 0.551712I
b = 2.21991 − 1.07852I
−1.44520 + 10.61230I 0
u = 1.40600 − 0.51747I
a = 0.673518 − 0.551712I
b = 2.21991 + 1.07852I
−1.44520 − 10.61230I 0
u = −1.40565 + 0.55799I
a = −0.688502 + 0.469329I
b = −2.09567 − 1.09859I
6.36962 − 11.59910I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40565 − 0.55799I
a = −0.688502 − 0.469329I
b = −2.09567 + 1.09859I
6.36962 + 11.59910I 0
u = −1.24582 + 0.86613I
a = −0.587834 + 0.208633I
b = −1.88360 − 0.64005I
0.68393 + 2.45853I 0
u = −1.24582 − 0.86613I
a = −0.587834 − 0.208633I
b = −1.88360 + 0.64005I
0.68393 − 2.45853I 0
u = 1.41588 + 0.58047I
a = 0.666124 + 0.431988I
b = 2.04803 − 1.05914I
6.35756 + 6.24409I 0
u = 1.41588 − 0.58047I
a = 0.666124 − 0.431988I
b = 2.04803 + 1.05914I
6.35756 − 6.24409I 0
u = 0.020033 + 0.427434I
a = 2.49913 + 1.14547I
b = 0.895052 + 0.739664I
−3.53579 − 0.04474I −2.46644 − 0.41353I
u = 0.020033 − 0.427434I
a = 2.49913 − 1.14547I
b = 0.895052 − 0.739664I
−3.53579 + 0.04474I −2.46644 + 0.41353I
u = −0.373614 + 0.197542I
a = 2.11982 − 0.74278I
b = −0.520379 + 1.023180I
−0.96055 − 5.90753I −0.24664 + 9.37993I
u = −0.373614 − 0.197542I
a = 2.11982 + 0.74278I
b = −0.520379 − 1.023180I
−0.96055 + 5.90753I −0.24664 − 9.37993I
u = 0.407927 + 0.082101I
a = −1.57057 − 1.37925I
b = 0.722910 + 0.807246I
1.04244 + 1.79312I 5.29922 − 6.16096I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.407927 − 0.082101I
a = −1.57057 + 1.37925I
b = 0.722910 − 0.807246I
1.04244 − 1.79312I 5.29922 + 6.16096I
u = −0.063587 + 0.405526I
a = 2.82339 + 0.89838I
b = 0.703723 + 0.928875I
−2.78311 − 7.47461I −1.05463 + 6.66610I
u = −0.063587 − 0.405526I
a = 2.82339 − 0.89838I
b = 0.703723 − 0.928875I
−2.78311 + 7.47461I −1.05463 − 6.66610I
u = −1.59847 + 0.13072I
a = −0.228524 − 0.483802I
b = −1.103600 + 0.448792I
−1.19670 − 3.16016I 0
u = −1.59847 − 0.13072I
a = −0.228524 + 0.483802I
b = −1.103600 − 0.448792I
−1.19670 + 3.16016I 0
u = 0.042672 + 0.353002I
a = −3.04504 + 1.11704I
b = −0.605859 + 0.777493I
−0.32076 + 3.17904I 3.12260 − 2.64536I
u = 0.042672 − 0.353002I
a = −3.04504 − 1.11704I
b = −0.605859 − 0.777493I
−0.32076 − 3.17904I 3.12260 + 2.64536I
u = −0.252617 + 0.244076I
a = 3.02079 − 0.42092I
b = −0.129014 + 0.983795I
−1.30633 + 0.86062I −2.81438 − 0.47339I
u = −0.252617 − 0.244076I
a = 3.02079 + 0.42092I
b = −0.129014 − 0.983795I
−1.30633 − 0.86062I −2.81438 + 0.47339I
u = −1.58209 + 0.54345I
a = −0.490657 + 0.442532I
b = −2.05705 − 0.90475I
−2.07281 − 7.24639I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58209 − 0.54345I
a = −0.490657 − 0.442532I
b = −2.05705 + 0.90475I
−2.07281 + 7.24639I 0
u = 1.48865 + 0.78475I
a = 0.545170 + 0.294464I
b = 2.02388 − 0.85427I
3.14356 + 3.22083I 0
u = 1.48865 − 0.78475I
a = 0.545170 − 0.294464I
b = 2.02388 + 0.85427I
3.14356 − 3.22083I 0
u = −1.56146 + 0.69154I
a = −0.089957 − 0.621770I
b = 0.092627 + 0.952473I
0.23657 + 6.97702I 0
u = −1.56146 − 0.69154I
a = −0.089957 + 0.621770I
b = 0.092627 − 0.952473I
0.23657 − 6.97702I 0
u = 0.132835 + 0.246557I
a = −3.88097 + 0.27662I
b = −0.175037 + 0.757890I
0.41339 + 2.76637I 0.999591 − 0.880383I
u = 0.132835 − 0.246557I
a = −3.88097 − 0.27662I
b = −0.175037 − 0.757890I
0.41339 − 2.76637I 0.999591 + 0.880383I
u = 1.66926 + 0.48655I
a = 0.182810 − 0.545721I
b = 0.379844 + 0.808584I
3.28885 − 1.37430I 0
u = 1.66926 − 0.48655I
a = 0.182810 + 0.545721I
b = 0.379844 − 0.808584I
3.28885 + 1.37430I 0
16
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
119
+ 47u
118
+ ··· + 76u − 1
c
2
, c
5
u
119
+ u
118
+ ··· + 4u − 1
c
3
u
119
− 11u
118
+ ··· − 44u − 41
c
4
u
119
+ 17u
118
+ ··· − 9590288u − 2011573
c
6
, c
9
u
119
− u
118
+ ··· − 10u
3
− 1
c
7
u
119
+ 5u
118
+ ··· − 2541506u − 300233
c
8
, c
12
u
119
− 5u
118
+ ··· + 2u − 1
c
10
u
119
− 3u
118
+ ··· − 4u + 1
c
11
u
119
+ 59u
118
+ ··· − 10u
2
− 1
17
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
119
+ 51y
118
+ ··· + 3612y −1
c
2
, c
5
y
119
+ 47y
118
+ ··· + 76y −1
c
3
y
119
− 29y
118
+ ··· − 1094568y −1681
c
4
y
119
− 97y
118
+ ··· + 36045891989112y −4046425934329
c
6
, c
9
y
119
− 85y
118
+ ··· + 10y
2
− 1
c
7
y
119
− 53y
118
+ ··· − 333755460568y −90139854289
c
8
, c
12
y
119
+ 59y
118
+ ··· − 10y
2
− 1
c
10
y
119
− 5y
118
+ ··· + 36y −1
c
11
y
119
+ 3y
118
+ ··· − 20y −1
18
