12a
0657
(K12a
0657
)
A knot diagram
1
Linearized knot diagam
3 7 10 12 9 2 6 11 1 8 4 5
Solving Sequence
4,11
12
5,9
6 1 8 7 10 3 2
c
11
c
4
c
5
c
12
c
8
c
7
c
10
c
3
c
2
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.50294 × 10
149
u
95
+ 9.60419 × 10
149
u
94
+ ··· + 5.45085 × 10
150
b + 7.14187 × 10
150
,
5.49450 × 10
151
u
95
+ 1.92581 × 10
152
u
94
+ ··· + 1.25370 × 10
152
a − 2.01529 × 10
152
, u
96
+ 2u
95
+ ··· + 2u
2
+ 1i
I
u
2
= hb + 1, 12u
5
+ 2u
4
− 25u
3
+ 14u
2
+ 23a + 24u − 7, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 102 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
= h2.50 × 10
149
u
95
+ 9.60 × 10
149
u
94
+ · · · + 5.45 × 10
150
b + 7.14 ×
10
150
, 5.49 × 10
151
u
95
+ 1.93 × 10
152
u
94
+ · · · + 1.25 × 10
152
a − 2.02 ×
10
152
, u
96
+ 2u
95
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
5
=
u
−u
3
+ u
a
9
=
−0.438264u
95
− 1.53611u
94
+ ··· − 15.8344u + 1.60748
−0.0459183u
95
− 0.176196u
94
+ ··· − 1.02762u − 1.31023
a
6
=
2.34511u
95
+ 4.53792u
94
+ ··· − 4.30308u + 6.52258
−0.404134u
95
− 0.805885u
94
+ ··· + 3.44265u + 0.468334
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
−0.484182u
95
− 1.71230u
94
+ ··· − 16.8620u + 0.297252
−0.0459183u
95
− 0.176196u
94
+ ··· − 1.02762u − 1.31023
a
7
=
−0.948773u
95
− 2.17227u
94
+ ··· − 8.96234u − 2.40244
0.0561849u
95
− 0.157085u
94
+ ··· − 1.71285u − 1.05821
a
10
=
−0.349694u
95
− 1.34273u
94
+ ··· − 15.8119u + 1.44566
−0.0232900u
95
− 0.115177u
94
+ ··· − 0.862337u − 1.28587
a
3
=
1.33753u
95
+ 2.83107u
94
+ ··· − 9.96316u + 6.91198
−0.555614u
95
− 0.988189u
94
+ ··· + 2.17596u + 0.0933008
a
2
=
−0.0756936u
95
− 0.257581u
94
+ ··· − 8.23068u + 3.42725
0.0319373u
95
+ 0.0106439u
94
+ ··· + 0.274085u − 0.354842
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.54301u
95
+ 5.85152u
94
+ ··· − 26.2365u + 1.81413
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
96
+ 30u
95
+ ··· − 4u + 1
c
2
, c
6
u
96
− 2u
95
+ ··· − 2u + 1
c
3
23(23u
96
− 123u
95
+ ··· − 9356946u + 601141)
c
4
, c
11
, c
12
u
96
− 2u
95
+ ··· + 2u
2
+ 1
c
5
23(23u
96
+ 8u
95
+ ··· − 2521819u + 368999)
c
8
, c
10
u
96
− 7u
95
+ ··· − 4077u + 529
c
9
u
96
− 7u
95
+ ··· − 375360u + 33856
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
96
+ 74y
95
+ ··· + 192y + 1
c
2
, c
6
y
96
− 30y
95
+ ··· + 4y + 1
c
3
529
· (529y
96
− 25893y
95
+ ··· − 85531184791874y + 361370501881)
c
4
, c
11
, c
12
y
96
− 90y
95
+ ··· + 4y + 1
c
5
529
· (529y
96
+ 8354y
95
+ ··· + 6225987047943y + 136160262001)
c
8
, c
10
y
96
− 49y
95
+ ··· − 6810037y + 279841
c
9
y
96
− 39y
95
+ ··· − 23851958272y + 1146228736
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.664093 + 0.724291I
a = −0.152601 + 0.267162I
b = 1.098560 + 0.527969I
2.46810 − 8.40093I 0
u = 0.664093 − 0.724291I
a = −0.152601 − 0.267162I
b = 1.098560 − 0.527969I
2.46810 + 8.40093I 0
u = 0.334101 + 0.923275I
a = 0.687547 + 0.470553I
b = 0.961263 − 0.266335I
−3.49169 − 0.00825I 0
u = 0.334101 − 0.923275I
a = 0.687547 − 0.470553I
b = 0.961263 + 0.266335I
−3.49169 + 0.00825I 0
u = −0.898631 + 0.504886I
a = 0.209912 − 0.192977I
b = 0.686280 − 0.190169I
1.053310 − 0.710227I 0
u = −0.898631 − 0.504886I
a = 0.209912 + 0.192977I
b = 0.686280 + 0.190169I
1.053310 + 0.710227I 0
u = −0.669520 + 0.697805I
a = −0.133986 − 0.212092I
b = 1.017990 − 0.549890I
3.55019 + 2.39774I 0
u = −0.669520 − 0.697805I
a = −0.133986 + 0.212092I
b = 1.017990 + 0.549890I
3.55019 − 2.39774I 0
u = 0.443174 + 0.848605I
a = 0.630015 + 0.813518I
b = 1.171900 − 0.445009I
−4.58322 + 7.44174I 0
u = 0.443174 − 0.848605I
a = 0.630015 − 0.813518I
b = 1.171900 + 0.445009I
−4.58322 − 7.44174I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.463645 + 0.806284I
a = 0.695610 + 1.020350I
b = 1.248500 − 0.622548I
1.86564 + 13.55260I 0
u = 0.463645 − 0.806284I
a = 0.695610 − 1.020350I
b = 1.248500 + 0.622548I
1.86564 − 13.55260I 0
u = −0.452945 + 0.802837I
a = 0.746322 − 0.987694I
b = 1.193980 + 0.629248I
2.88022 − 7.47631I 0
u = −0.452945 − 0.802837I
a = 0.746322 + 0.987694I
b = 1.193980 − 0.629248I
2.88022 + 7.47631I 0
u = −0.384282 + 0.833895I
a = 0.799115 − 0.692769I
b = 0.996785 + 0.458170I
−0.41962 − 4.20352I 0
u = −0.384282 − 0.833895I
a = 0.799115 + 0.692769I
b = 0.996785 − 0.458170I
−0.41962 + 4.20352I 0
u = 0.792963 + 0.739457I
a = 0.028708 + 0.283343I
b = 0.971436 + 0.287560I
−3.61912 − 2.02495I 0
u = 0.792963 − 0.739457I
a = 0.028708 − 0.283343I
b = 0.971436 − 0.287560I
−3.61912 + 2.02495I 0
u = −0.488518 + 0.562688I
a = −0.161461 + 0.365143I
b = 0.306469 − 1.012220I
5.59468 − 1.63818I 2.91885 + 2.68562I
u = −0.488518 − 0.562688I
a = −0.161461 − 0.365143I
b = 0.306469 + 1.012220I
5.59468 + 1.63818I 2.91885 − 2.68562I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.322988 + 0.658130I
a = 1.37204 − 0.52486I
b = 0.498271 + 0.624414I
5.05930 − 2.23755I 2.52582 + 5.05237I
u = −0.322988 − 0.658130I
a = 1.37204 + 0.52486I
b = 0.498271 − 0.624414I
5.05930 + 2.23755I 2.52582 − 5.05237I
u = −1.26745
a = 1.06705
b = −1.64301
−1.61828 0
u = 0.466641 + 0.564477I
a = −0.178245 − 0.425650I
b = 0.225474 + 1.073180I
5.01127 + 7.57568I 1.49767 − 8.14095I
u = 0.466641 − 0.564477I
a = −0.178245 + 0.425650I
b = 0.225474 − 1.073180I
5.01127 − 7.57568I 1.49767 + 8.14095I
u = −1.268200 + 0.059476I
a = 1.18929 + 0.81468I
b = −1.65731 − 0.33248I
2.12370 − 4.56403I 0
u = −1.268200 − 0.059476I
a = 1.18929 − 0.81468I
b = −1.65731 + 0.33248I
2.12370 + 4.56403I 0
u = 1.096330 + 0.643778I
a = 0.158040 + 0.346095I
b = 0.837642 + 0.052188I
−1.26594 + 5.58854I 0
u = 1.096330 − 0.643778I
a = 0.158040 − 0.346095I
b = 0.837642 − 0.052188I
−1.26594 − 5.58854I 0
u = 1.290000 + 0.078493I
a = 1.01584 − 1.13931I
b = −1.53554 + 0.46369I
2.40735 − 0.56323I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.290000 − 0.078493I
a = 1.01584 + 1.13931I
b = −1.53554 − 0.46369I
2.40735 + 0.56323I 0
u = −0.609114 + 0.334240I
a = 0.318331 + 0.157551I
b = 0.287889 − 0.332864I
1.146790 − 0.591982I 6.49485 + 1.54474I
u = −0.609114 − 0.334240I
a = 0.318331 − 0.157551I
b = 0.287889 + 0.332864I
1.146790 + 0.591982I 6.49485 − 1.54474I
u = 0.321236 + 0.613505I
a = 1.49841 + 0.44718I
b = 0.363298 − 0.635825I
4.61231 − 3.82498I 1.69669 + 0.30945I
u = 0.321236 − 0.613505I
a = 1.49841 − 0.44718I
b = 0.363298 + 0.635825I
4.61231 + 3.82498I 1.69669 − 0.30945I
u = 1.338900 + 0.124894I
a = 0.78918 − 1.77567I
b = −1.18956 + 0.83118I
−0.06296 + 3.70917I 0
u = 1.338900 − 0.124894I
a = 0.78918 + 1.77567I
b = −1.18956 − 0.83118I
−0.06296 − 3.70917I 0
u = 1.353990 + 0.016673I
a = −0.834167 − 0.766801I
b = −1.168080 + 0.080602I
1.89369 + 0.02531I 0
u = 1.353990 − 0.016673I
a = −0.834167 + 0.766801I
b = −1.168080 − 0.080602I
1.89369 − 0.02531I 0
u = 1.360990 + 0.155619I
a = 0.63332 − 2.01476I
b = −0.98925 + 1.12317I
4.77740 + 8.35511I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.360990 − 0.155619I
a = 0.63332 + 2.01476I
b = −0.98925 − 1.12317I
4.77740 − 8.35511I 0
u = 0.417961 + 0.467588I
a = 0.077572 − 0.589308I
b = −0.094014 + 0.749714I
−1.06119 + 3.30659I −3.60035 − 9.06831I
u = 0.417961 − 0.467588I
a = 0.077572 + 0.589308I
b = −0.094014 − 0.749714I
−1.06119 − 3.30659I −3.60035 + 9.06831I
u = −1.370750 + 0.094332I
a = 0.58842 + 1.75045I
b = −0.938648 − 0.549645I
3.04859 − 2.23764I 0
u = −1.370750 − 0.094332I
a = 0.58842 − 1.75045I
b = −0.938648 + 0.549645I
3.04859 + 2.23764I 0
u = −1.373450 + 0.150990I
a = 0.54418 + 1.95382I
b = −0.863399 − 1.075360I
5.36707 − 2.82780I 0
u = −1.373450 − 0.150990I
a = 0.54418 − 1.95382I
b = −0.863399 + 1.075360I
5.36707 + 2.82780I 0
u = 1.41758 + 0.04983I
a = 2.13899 − 2.92262I
b = −0.820464 + 0.008321I
6.72398 − 2.80070I 0
u = 1.41758 − 0.04983I
a = 2.13899 + 2.92262I
b = −0.820464 − 0.008321I
6.72398 + 2.80070I 0
u = −1.41743 + 0.05890I
a = 1.89221 + 2.25946I
b = −0.735464 − 0.033098I
6.92096 − 2.88647I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41743 − 0.05890I
a = 1.89221 − 2.25946I
b = −0.735464 + 0.033098I
6.92096 + 2.88647I 0
u = −0.196684 + 0.513849I
a = −0.354453 + 0.932054I
b = −1.132040 − 0.750035I
−0.11950 − 5.94878I −5.44478 + 9.17655I
u = −0.196684 − 0.513849I
a = −0.354453 − 0.932054I
b = −1.132040 + 0.750035I
−0.11950 + 5.94878I −5.44478 − 9.17655I
u = 0.221448 + 0.498623I
a = −0.290394 − 0.994151I
b = −0.989290 + 0.743082I
0.333283 + 0.495333I −3.97583 − 3.89260I
u = 0.221448 − 0.498623I
a = −0.290394 + 0.994151I
b = −0.989290 − 0.743082I
0.333283 − 0.495333I −3.97583 + 3.89260I
u = −1.42650 + 0.28467I
a = 0.487682 − 1.290430I
b = 0.798971 + 0.614933I
10.09940 + 0.42622I 0
u = −1.42650 − 0.28467I
a = 0.487682 + 1.290430I
b = 0.798971 − 0.614933I
10.09940 − 0.42622I 0
u = 1.44291 + 0.28759I
a = 0.39822 + 1.39202I
b = 0.868280 − 0.653053I
10.67610 + 5.79876I 0
u = 1.44291 − 0.28759I
a = 0.39822 − 1.39202I
b = 0.868280 + 0.653053I
10.67610 − 5.79876I 0
u = −1.46807 + 0.17113I
a = −0.31675 + 1.45982I
b = 0.153260 − 1.105640I
5.08717 − 5.68044I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46807 − 0.17113I
a = −0.31675 − 1.45982I
b = 0.153260 + 1.105640I
5.08717 + 5.68044I 0
u = −1.47757 + 0.19945I
a = −0.69290 + 1.56154I
b = 0.382716 − 1.339380I
11.3102 − 10.3824I 0
u = −1.47757 − 0.19945I
a = −0.69290 − 1.56154I
b = 0.382716 + 1.339380I
11.3102 + 10.3824I 0
u = 1.48389 + 0.19736I
a = −0.71198 − 1.46988I
b = 0.433648 + 1.280640I
11.98830 + 4.43121I 0
u = 1.48389 − 0.19736I
a = −0.71198 + 1.46988I
b = 0.433648 − 1.280640I
11.98830 − 4.43121I 0
u = −0.019785 + 0.498386I
a = −0.867519 + 0.145622I
b = −1.51285 − 0.08023I
−1.45387 + 2.58739I −7.88342 − 2.89181I
u = −0.019785 − 0.498386I
a = −0.867519 − 0.145622I
b = −1.51285 + 0.08023I
−1.45387 − 2.58739I −7.88342 + 2.89181I
u = −0.122494 + 0.481151I
a = −0.714382 + 0.841174I
b = −1.290580 − 0.423315I
−4.60245 − 1.56147I −13.5432 + 4.6448I
u = −0.122494 − 0.481151I
a = −0.714382 − 0.841174I
b = −1.290580 + 0.423315I
−4.60245 + 1.56147I −13.5432 − 4.6448I
u = 1.49943 + 0.16275I
a = −0.427368 − 1.103110I
b = 0.385106 + 0.904863I
7.94574 + 2.75539I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49943 − 0.16275I
a = −0.427368 + 1.103110I
b = 0.385106 − 0.904863I
7.94574 − 2.75539I 0
u = −1.48030 + 0.33222I
a = −0.065804 − 1.268560I
b = 1.099420 + 0.493860I
2.38632 − 4.46773I 0
u = −1.48030 − 0.33222I
a = −0.065804 + 1.268560I
b = 1.099420 − 0.493860I
2.38632 + 4.46773I 0
u = 1.48751 + 0.30794I
a = −0.06205 + 1.50463I
b = 1.144410 − 0.624455I
5.64050 + 8.33802I 0
u = 1.48751 − 0.30794I
a = −0.06205 − 1.50463I
b = 1.144410 + 0.624455I
5.64050 − 8.33802I 0
u = −1.51878 + 0.10601I
a = −0.095323 + 0.663397I
b = 0.339093 − 0.482819I
4.59539 − 0.33868I 0
u = −1.51878 − 0.10601I
a = −0.095323 − 0.663397I
b = 0.339093 + 0.482819I
4.59539 + 0.33868I 0
u = 1.50456 + 0.29310I
a = −0.20692 + 1.76757I
b = 1.27782 − 0.74165I
9.2181 + 11.4691I 0
u = 1.50456 − 0.29310I
a = −0.20692 − 1.76757I
b = 1.27782 + 0.74165I
9.2181 − 11.4691I 0
u = −1.50426 + 0.30859I
a = −0.25757 − 1.54880I
b = 1.261580 + 0.609340I
1.71020 − 11.63330I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50426 − 0.30859I
a = −0.25757 + 1.54880I
b = 1.261580 − 0.609340I
1.71020 + 11.63330I 0
u = −1.50851 + 0.29342I
a = −0.27033 − 1.78274I
b = 1.31646 + 0.73734I
8.2521 − 17.5605I 0
u = −1.50851 − 0.29342I
a = −0.27033 + 1.78274I
b = 1.31646 − 0.73734I
8.2521 + 17.5605I 0
u = 0.388560 + 0.226499I
a = 3.47210 − 1.47453I
b = −0.939752 − 0.290967I
1.28524 + 1.87668I 1.39389 − 10.00654I
u = 0.388560 − 0.226499I
a = 3.47210 + 1.47453I
b = −0.939752 + 0.290967I
1.28524 − 1.87668I 1.39389 + 10.00654I
u = −0.405275 + 0.182370I
a = 4.00898 + 1.36668I
b = −1.040670 + 0.259813I
1.05835 + 3.63480I 3.32848 + 4.63258I
u = −0.405275 − 0.182370I
a = 4.00898 − 1.36668I
b = −1.040670 − 0.259813I
1.05835 − 3.63480I 3.32848 − 4.63258I
u = 0.259608 + 0.355711I
a = 1.36832 − 0.40634I
b = −0.162394 − 0.150466I
−1.35358 − 0.59802I −5.31839 − 0.10830I
u = 0.259608 − 0.355711I
a = 1.36832 + 0.40634I
b = −0.162394 + 0.150466I
−1.35358 + 0.59802I −5.31839 + 0.10830I
u = 1.55443 + 0.17460I
a = −0.699112 − 0.633690I
b = 0.760656 + 0.693747I
11.00460 + 0.65235I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55443 − 0.17460I
a = −0.699112 + 0.633690I
b = 0.760656 − 0.693747I
11.00460 − 0.65235I 0
u = −1.57253 + 0.17459I
a = −0.702518 + 0.492334I
b = 0.820732 − 0.598566I
10.03080 + 5.18475I 0
u = −1.57253 − 0.17459I
a = −0.702518 − 0.492334I
b = 0.820732 + 0.598566I
10.03080 − 5.18475I 0
u = 0.149227 + 0.346264I
a = −1.08762 − 2.24547I
b = −0.988148 + 0.176860I
−1.76677 + 0.65508I −4.67837 + 0.58281I
u = 0.149227 − 0.346264I
a = −1.08762 + 2.24547I
b = −0.988148 − 0.176860I
−1.76677 − 0.65508I −4.67837 − 0.58281I
u = −0.325727
a = 6.87271
b = −1.07784
−3.07701 21.8700
14
II.
I
u
2
= hb+1, 12u
5
+2u
4
−25u
3
+14u
2
+23a+24u−7, u
6
−u
5
−u
4
+2u
3
−u+1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
5
=
u
−u
3
+ u
a
9
=
−0.521739u
5
− 0.0869565u
4
+ ··· − 1.04348u + 0.304348
−1
a
6
=
0.330813u
5
− 0.0680529u
4
+ ··· + 1.27032u + 0.238185
−0.391304u
5
+ 0.434783u
4
+ ··· + 1.21739u + 0.478261
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
−0.521739u
5
− 0.0869565u
4
+ ··· − 1.04348u − 0.695652
−1
a
7
=
−0.262760u
5
− 1.09452u
4
+ ··· − 0.568998u − 0.669187
0.956522u
5
− 1.17391u
4
+ ··· + 0.913043u − 1.39130
a
10
=
−0.521739u
5
− 0.0869565u
4
+ ··· − 1.04348u + 0.304348
−1
a
3
=
−0.0264650u
5
+ 0.285444u
4
+ ··· + 0.338374u + 0.500945
−0.608696u
5
+ 0.565217u
4
+ ··· + 0.782609u + 0.521739
a
2
=
0.219282u
5
− 0.0793951u
4
+ ··· + 0.482042u + 1.27788
0.0434783u
5
+ 0.173913u
4
+ ··· + 0.0869565u + 0.391304
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1575
529
u
5
−
1911
529
u
4
−
2712
529
u
3
+
1803
529
u
2
−
300
529
u −
4156
529
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
4
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
23(23u
6
+ 18u
5
+ 25u
4
+ 8u
3
+ 7u
2
+ u + 1)
c
5
23(23u
6
+ 5u
5
− 17u
4
− 10u
3
+ 3u
2
+ 4u + 1)
c
6
, c
11
, c
12
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
7
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
8
(u − 1)
6
c
9
u
6
c
10
(u + 1)
6
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
4
, c
6
c
11
, c
12
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
3
529(529y
6
+ 826y
5
+ 659y
4
+ 296y
3
+ 83y
2
+ 13y + 1)
c
5
529(529y
6
− 807y
5
+ 527y
4
− 196y
3
+ 55y
2
− 10y + 1)
c
8
, c
10
(y −1)
6
c
9
y
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.029335 + 0.442893I
b = −1.00000
0.245672 − 0.924305I −2.62482 + 0.97831I
u = −1.002190 − 0.295542I
a = 0.029335 − 0.442893I
b = −1.00000
0.245672 + 0.924305I −2.62482 − 0.97831I
u = 0.428243 + 0.664531I
a = −0.538704 − 0.781014I
b = −1.00000
−3.53554 − 0.92430I −5.29043 + 1.37115I
u = 0.428243 − 0.664531I
a = −0.538704 + 0.781014I
b = −1.00000
−3.53554 + 0.92430I −5.29043 − 1.37115I
u = 1.073950 + 0.558752I
a = −0.012370 − 0.494977I
b = −1.00000
−1.64493 + 5.69302I −9.84656 − 7.30057I
u = 1.073950 − 0.558752I
a = −0.012370 + 0.494977I
b = −1.00000
−1.64493 − 5.69302I −9.84656 + 7.30057I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
96
+ 30u
95
+ ··· − 4u + 1)
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
96
− 2u
95
+ ··· − 2u + 1)
c
3
529(23u
6
+ 18u
5
+ 25u
4
+ 8u
3
+ 7u
2
+ u + 1)
· (23u
96
− 123u
95
+ ··· − 9356946u + 601141)
c
4
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
96
− 2u
95
+ ··· + 2u
2
+ 1)
c
5
529(23u
6
+ 5u
5
− 17u
4
− 10u
3
+ 3u
2
+ 4u + 1)
· (23u
96
+ 8u
95
+ ··· − 2521819u + 368999)
c
6
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
96
− 2u
95
+ ··· − 2u + 1)
c
7
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
96
+ 30u
95
+ ··· − 4u + 1)
c
8
((u − 1)
6
)(u
96
− 7u
95
+ ··· − 4077u + 529)
c
9
u
6
(u
96
− 7u
95
+ ··· − 375360u + 33856)
c
10
((u + 1)
6
)(u
96
− 7u
95
+ ··· − 4077u + 529)
c
11
, c
12
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
96
− 2u
95
+ ··· + 2u
2
+ 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
96
+ 74y
95
+ ··· + 192y + 1)
c
2
, c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
96
− 30y
95
+ ··· + 4y + 1)
c
3
279841(529y
6
+ 826y
5
+ 659y
4
+ 296y
3
+ 83y
2
+ 13y + 1)
· (529y
96
− 25893y
95
+ ··· − 85531184791874y + 361370501881)
c
4
, c
11
, c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
96
− 90y
95
+ ··· + 4y + 1)
c
5
279841(529y
6
− 807y
5
+ 527y
4
− 196y
3
+ 55y
2
− 10y + 1)
· (529y
96
+ 8354y
95
+ ··· + 6225987047943y + 136160262001)
c
8
, c
10
((y −1)
6
)(y
96
− 49y
95
+ ··· − 6810037y + 279841)
c
9
y
6
(y
96
− 39y
95
+ ··· − 2.38520 × 10
10
y + 1.14623 × 10
9
)
20
