12n
0714
(K12n
0714
)
A knot diagram
1
Linearized knot diagam
4 6 7 8 10 9 12 2 3 5 7 8
Solving Sequence
8,12 1,5
4 2 9 7 3 6 11 10
c
12
c
4
c
1
c
8
c
7
c
3
c
6
c
11
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.87692 × 10
258
u
86
+ 7.24779 × 10
258
u
85
+ ··· + 2.73086 × 10
260
b + 1.29464 × 10
261
,
− 3.32833 × 10
258
u
86
+ 1.03709 × 10
259
u
85
+ ··· + 2.73086 × 10
260
a + 2.37253 × 10
261
,
u
87
− u
86
+ ··· − 144u + 67i
I
u
2
= h−32933031018u
21
+ 1113442853u
20
+ ··· + 9952263913b − 142566726414,
− 32258549399u
21
+ 13152988225u
20
+ ··· + 9952263913a + 5817215377,
u
22
− 8u
20
+ ··· + 7u + 1i
* 2 irreducible components of dim
C
= 0, with total 109 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−4.88 × 10
258
u
86
+ 7.25 × 10
258
u
85
+ · · · + 2.73 × 10
260
b + 1.29 ×
10
261
, −3.33 × 10
258
u
86
+ 1.04 × 10
259
u
85
+ · · · + 2.73 × 10
260
a + 2.37 ×
10
261
, u
87
− u
86
+ · · · − 144u + 67i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
0.0121878u
86
− 0.0379766u
85
+ ··· + 3.72518u − 8.68785
0.0178585u
86
− 0.0265403u
85
+ ··· − 4.57034u − 4.74075
a
4
=
0.0121878u
86
− 0.0379766u
85
+ ··· + 3.72518u − 8.68785
−0.0308890u
86
− 0.0224193u
85
+ ··· − 9.10052u − 3.01290
a
2
=
0.0204608u
86
− 0.00597308u
85
+ ··· − 3.14988u − 2.22578
0.0389753u
86
+ 0.00472462u
85
+ ··· + 15.9789u + 3.97260
a
9
=
0.00754574u
86
+ 0.00780789u
85
+ ··· − 1.85076u − 0.0940809
0.0253749u
86
+ 0.0235466u
85
+ ··· + 15.0954u + 6.13843
a
7
=
u
u
a
3
=
0.0132086u
86
− 0.0308291u
85
+ ··· + 2.64852u − 6.84404
−0.0298682u
86
− 0.0152718u
85
+ ··· − 10.1772u − 1.16910
a
6
=
−0.0197591u
86
+ 0.0413246u
85
+ ··· + 7.85051u + 9.58494
0.0940033u
86
− 0.0539560u
85
+ ··· + 28.9246u − 17.1001
a
11
=
−u
2
+ 1
−u
2
a
10
=
0.222309u
86
− 0.106889u
85
+ ··· + 14.9456u − 23.4599
0.00662288u
86
+ 0.0179377u
85
+ ··· + 12.6317u + 6.50996
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0570476u
86
+ 0.180502u
85
+ ··· + 46.1820u + 3.78747
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
87
+ 3u
86
+ ··· + 3937u + 511
c
2
u
87
− 5u
86
+ ··· − 2768u − 437
c
3
u
87
− 3u
86
+ ··· − 4842u − 1687
c
4
u
87
− u
86
+ ··· + 5250u + 811
c
5
, c
10
u
87
− u
86
+ ··· + 833881u + 81631
c
6
u
87
− u
86
+ ··· + 46u − 7
c
7
, c
11
, c
12
u
87
− u
86
+ ··· − 144u + 67
c
8
u
87
− 2u
86
+ ··· − 5106u + 38332
c
9
u
87
− 2u
86
+ ··· + 58u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
87
+ 67y
86
+ ··· − 8202255y −261121
c
2
y
87
+ 31y
86
+ ··· − 9342720y −190969
c
3
y
87
− y
86
+ ··· + 410351666y −2845969
c
4
y
87
− 61y
86
+ ··· + 13379732y −657721
c
5
, c
10
y
87
+ 71y
86
+ ··· − 125580302491y −6663620161
c
6
y
87
+ 5y
86
+ ··· + 1556y −49
c
7
, c
11
, c
12
y
87
− 29y
86
+ ··· + 80634y −4489
c
8
y
87
− 54y
86
+ ··· + 32610801148y −1469342224
c
9
y
87
+ 6y
86
+ ··· − 724y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.826900 + 0.601872I
a = 0.54423 − 1.32762I
b = −0.56972 − 1.57384I
0.42909 − 5.48515I 0
u = 0.826900 − 0.601872I
a = 0.54423 + 1.32762I
b = −0.56972 + 1.57384I
0.42909 + 5.48515I 0
u = 0.697175 + 0.780149I
a = −0.132182 + 0.977962I
b = 0.66470 + 1.50104I
0.625492 + 0.055899I 0
u = 0.697175 − 0.780149I
a = −0.132182 − 0.977962I
b = 0.66470 − 1.50104I
0.625492 − 0.055899I 0
u = −0.463012 + 0.940926I
a = 0.10772 + 1.55292I
b = −0.372458 + 1.213450I
2.67314 + 3.04460I 0
u = −0.463012 − 0.940926I
a = 0.10772 − 1.55292I
b = −0.372458 − 1.213450I
2.67314 − 3.04460I 0
u = 0.910023 + 0.239643I
a = 0.142324 + 0.218288I
b = −1.405030 − 0.028502I
−4.78233 − 1.85900I −14.9541 + 0.I
u = 0.910023 − 0.239643I
a = 0.142324 − 0.218288I
b = −1.405030 + 0.028502I
−4.78233 + 1.85900I −14.9541 + 0.I
u = −0.831969 + 0.431052I
a = −0.220619 + 0.362466I
b = −1.40851 − 0.56135I
−4.96402 + 0.26729I −13.27396 + 0.I
u = −0.831969 − 0.431052I
a = −0.220619 − 0.362466I
b = −1.40851 + 0.56135I
−4.96402 − 0.26729I −13.27396 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.920887 + 0.165274I
a = 0.32672 − 1.53222I
b = 0.142597 − 1.318170I
−7.30377 − 5.23114I −9.44716 + 0.I
u = −0.920887 − 0.165274I
a = 0.32672 + 1.53222I
b = 0.142597 + 1.318170I
−7.30377 + 5.23114I −9.44716 + 0.I
u = −0.562017 + 0.910670I
a = −0.503431 − 1.320090I
b = 0.09211 − 1.55852I
3.88938 − 3.53566I 0
u = −0.562017 − 0.910670I
a = −0.503431 + 1.320090I
b = 0.09211 + 1.55852I
3.88938 + 3.53566I 0
u = 0.433575 + 0.986609I
a = −0.800548 + 1.077630I
b = −0.052438 + 1.117500I
2.61513 + 1.86499I 0
u = 0.433575 − 0.986609I
a = −0.800548 − 1.077630I
b = −0.052438 − 1.117500I
2.61513 − 1.86499I 0
u = −0.668811 + 0.854317I
a = −0.853243 − 0.834595I
b = −0.451199 − 1.287840I
−0.85027 − 2.54351I 0
u = −0.668811 − 0.854317I
a = −0.853243 + 0.834595I
b = −0.451199 + 1.287840I
−0.85027 + 2.54351I 0
u = −0.718679 + 0.564160I
a = 0.591608 + 1.158870I
b = −1.329980 + 0.300668I
−4.48658 + 3.70741I −9.89156 − 7.12776I
u = −0.718679 − 0.564160I
a = 0.591608 − 1.158870I
b = −1.329980 − 0.300668I
−4.48658 − 3.70741I −9.89156 + 7.12776I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789666 + 0.455175I
a = 0.206483 + 0.013716I
b = 1.70611 − 0.43647I
−5.91935 − 9.21762I −7.80706 + 9.75144I
u = 0.789666 − 0.455175I
a = 0.206483 − 0.013716I
b = 1.70611 + 0.43647I
−5.91935 + 9.21762I −7.80706 − 9.75144I
u = −1.13014
a = −0.478350
b = −0.743354
−3.08331 0
u = −0.779955 + 0.377150I
a = −1.61943 − 0.84559I
b = 1.042790 − 0.380620I
−4.78974 + 2.80082I −12.7389 − 6.7012I
u = −0.779955 − 0.377150I
a = −1.61943 + 0.84559I
b = 1.042790 + 0.380620I
−4.78974 − 2.80082I −12.7389 + 6.7012I
u = −0.666824 + 0.496437I
a = −0.949620 + 0.543858I
b = 0.248068 + 0.412413I
−1.63086 + 1.85240I 0. − 4.46928I
u = −0.666824 − 0.496437I
a = −0.949620 − 0.543858I
b = 0.248068 − 0.412413I
−1.63086 − 1.85240I 0. + 4.46928I
u = 1.171080 + 0.061511I
a = −0.322885 − 0.873024I
b = −0.573003 + 0.574424I
−7.26129 + 1.30453I 0
u = 1.171080 − 0.061511I
a = −0.322885 + 0.873024I
b = −0.573003 − 0.574424I
−7.26129 − 1.30453I 0
u = 1.105580 + 0.500970I
a = −1.010930 + 0.378023I
b = 0.179303 + 1.341920I
−0.435109 + 1.276900I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.105580 − 0.500970I
a = −1.010930 − 0.378023I
b = 0.179303 − 1.341920I
−0.435109 − 1.276900I 0
u = 0.784472 + 0.035579I
a = −0.25017 − 2.35287I
b = −0.287280 + 0.096315I
−6.69981 + 1.00306I −13.25635 + 3.01209I
u = 0.784472 − 0.035579I
a = −0.25017 + 2.35287I
b = −0.287280 − 0.096315I
−6.69981 − 1.00306I −13.25635 − 3.01209I
u = 0.660908 + 0.370414I
a = −1.65412 + 1.13657I
b = 1.115980 − 0.084655I
−5.55071 + 5.89913I −8.87687 − 1.92618I
u = 0.660908 − 0.370414I
a = −1.65412 − 1.13657I
b = 1.115980 + 0.084655I
−5.55071 − 5.89913I −8.87687 + 1.92618I
u = −0.879473 + 0.892598I
a = 0.111795 + 1.198310I
b = −0.40197 + 1.35768I
1.39386 + 4.17528I 0
u = −0.879473 − 0.892598I
a = 0.111795 − 1.198310I
b = −0.40197 − 1.35768I
1.39386 − 4.17528I 0
u = −0.682765 + 1.069690I
a = 0.525669 + 0.650107I
b = 0.261339 + 1.297890I
−0.98150 − 1.91692I 0
u = −0.682765 − 1.069690I
a = 0.525669 − 0.650107I
b = 0.261339 − 1.297890I
−0.98150 + 1.91692I 0
u = 0.887280 + 0.919265I
a = −0.653503 + 1.063640I
b = 0.449194 + 1.328490I
5.84192 − 2.12639I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.887280 − 0.919265I
a = −0.653503 − 1.063640I
b = 0.449194 − 1.328490I
5.84192 + 2.12639I 0
u = 0.510264 + 0.489653I
a = 1.017580 + 0.966046I
b = −0.094246 − 0.287204I
−0.25603 − 4.10697I −3.49910 + 8.93719I
u = 0.510264 − 0.489653I
a = 1.017580 − 0.966046I
b = −0.094246 + 0.287204I
−0.25603 + 4.10697I −3.49910 − 8.93719I
u = −1.061880 + 0.759062I
a = 0.67218 + 1.27261I
b = −0.88368 + 1.45387I
−2.02209 + 8.59314I 0
u = −1.061880 − 0.759062I
a = 0.67218 − 1.27261I
b = −0.88368 − 1.45387I
−2.02209 − 8.59314I 0
u = 0.627124 + 0.296393I
a = −0.66346 − 2.28848I
b = −0.450291 − 0.995511I
−5.77440 − 2.55022I −5.68948 + 10.03956I
u = 0.627124 − 0.296393I
a = −0.66346 + 2.28848I
b = −0.450291 + 0.995511I
−5.77440 + 2.55022I −5.68948 − 10.03956I
u = 0.979254 + 0.889150I
a = 0.584027 − 0.906985I
b = −0.09677 − 1.45250I
5.55872 − 4.53544I 0
u = 0.979254 − 0.889150I
a = 0.584027 + 0.906985I
b = −0.09677 + 1.45250I
5.55872 + 4.53544I 0
u = −0.948317 + 0.923652I
a = −0.279312 − 1.117590I
b = 0.69137 − 1.61320I
2.59211 + 10.50510I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.948317 − 0.923652I
a = −0.279312 + 1.117590I
b = 0.69137 + 1.61320I
2.59211 − 10.50510I 0
u = −0.952539 + 0.929240I
a = −0.918601 − 0.679231I
b = 0.160027 − 0.907619I
1.16569 + 2.51429I 0
u = −0.952539 − 0.929240I
a = −0.918601 + 0.679231I
b = 0.160027 + 0.907619I
1.16569 − 2.51429I 0
u = 1.141100 + 0.685664I
a = 0.581015 − 0.421440I
b = −0.476699 − 1.180220I
−0.80622 − 5.62140I 0
u = 1.141100 − 0.685664I
a = 0.581015 + 0.421440I
b = −0.476699 + 1.180220I
−0.80622 + 5.62140I 0
u = −0.626341 + 0.189979I
a = −0.601874 + 0.451367I
b = −0.248372 + 0.235217I
−1.183180 + 0.695175I −6.70578 − 1.57840I
u = −0.626341 − 0.189979I
a = −0.601874 − 0.451367I
b = −0.248372 − 0.235217I
−1.183180 − 0.695175I −6.70578 + 1.57840I
u = 0.654724 + 1.181500I
a = 0.664538 − 0.850361I
b = 0.354261 − 1.323580I
−0.68635 + 10.51560I 0
u = 0.654724 − 1.181500I
a = 0.664538 + 0.850361I
b = 0.354261 + 1.323580I
−0.68635 − 10.51560I 0
u = −0.518604 + 0.387817I
a = 3.33694 − 1.80195I
b = 0.123907 + 0.119398I
−5.62804 + 7.62430I −3.5084 − 15.3680I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.518604 − 0.387817I
a = 3.33694 + 1.80195I
b = 0.123907 − 0.119398I
−5.62804 − 7.62430I −3.5084 + 15.3680I
u = −0.953528 + 0.962716I
a = 0.809443 + 0.506327I
b = −0.024424 + 1.231810I
2.61565 − 3.61386I 0
u = −0.953528 − 0.962716I
a = 0.809443 − 0.506327I
b = −0.024424 − 1.231810I
2.61565 + 3.61386I 0
u = −1.170390 + 0.725800I
a = 0.918705 + 0.823382I
b = −0.39022 + 1.53172I
1.99944 + 9.66121I 0
u = −1.170390 − 0.725800I
a = 0.918705 − 0.823382I
b = −0.39022 − 1.53172I
1.99944 − 9.66121I 0
u = 0.091542 + 0.605155I
a = −0.643725 + 0.349309I
b = 0.316647 + 0.447923I
1.12577 + 1.22347I 2.24149 − 1.97713I
u = 0.091542 − 0.605155I
a = −0.643725 − 0.349309I
b = 0.316647 − 0.447923I
1.12577 − 1.22347I 2.24149 + 1.97713I
u = 0.922433 + 1.070450I
a = 0.427757 − 1.329770I
b = −0.578333 − 1.015810I
1.28212 − 5.69320I 0
u = 0.922433 − 1.070450I
a = 0.427757 + 1.329770I
b = −0.578333 + 1.015810I
1.28212 + 5.69320I 0
u = −1.13000 + 0.86180I
a = −0.499373 − 0.993413I
b = 0.90010 − 1.31563I
−2.34996 + 8.89069I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.13000 − 0.86180I
a = −0.499373 + 0.993413I
b = 0.90010 + 1.31563I
−2.34996 − 8.89069I 0
u = 1.18516 + 0.86733I
a = −0.515811 + 1.142830I
b = 0.82351 + 1.48067I
−2.3733 − 17.7998I 0
u = 1.18516 − 0.86733I
a = −0.515811 − 1.142830I
b = 0.82351 − 1.48067I
−2.3733 + 17.7998I 0
u = −1.24810 + 0.78025I
a = −0.723961 − 0.634032I
b = 0.138071 − 1.099330I
0.29433 + 3.47130I 0
u = −1.24810 − 0.78025I
a = −0.723961 + 0.634032I
b = 0.138071 + 1.099330I
0.29433 − 3.47130I 0
u = 0.99277 + 1.10862I
a = −0.378506 + 0.797429I
b = −0.305418 + 0.978314I
1.09930 − 2.01981I 0
u = 0.99277 − 1.10862I
a = −0.378506 − 0.797429I
b = −0.305418 − 0.978314I
1.09930 + 2.01981I 0
u = 1.27655 + 0.81192I
a = 0.419881 − 1.024650I
b = −0.57213 − 1.44013I
0.02085 − 8.57265I 0
u = 1.27655 − 0.81192I
a = 0.419881 + 1.024650I
b = −0.57213 + 1.44013I
0.02085 + 8.57265I 0
u = 0.458264 + 0.146029I
a = 1.69886 + 0.35112I
b = −1.196350 + 0.713768I
−3.10181 + 0.47570I −5.29751 − 2.60698I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.458264 − 0.146029I
a = 1.69886 − 0.35112I
b = −1.196350 − 0.713768I
−3.10181 − 0.47570I −5.29751 + 2.60698I
u = 1.59928 + 0.17427I
a = 0.252466 + 0.129113I
b = −0.178640 − 0.313172I
−9.08258 − 1.96810I 0
u = 1.59928 − 0.17427I
a = 0.252466 − 0.129113I
b = −0.178640 + 0.313172I
−9.08258 + 1.96810I 0
u = −0.145781 + 0.354589I
a = 0.619188 + 0.413783I
b = 1.75644 + 2.82127I
−3.31878 − 0.04041I −23.4527 − 15.7274I
u = −0.145781 − 0.354589I
a = 0.619188 − 0.413783I
b = 1.75644 − 2.82127I
−3.31878 + 0.04041I −23.4527 + 15.7274I
u = −1.71018 + 0.04465I
a = 0.188770 + 0.083516I
b = 0.052313 + 0.658440I
−9.70700 − 5.87952I 0
u = −1.71018 − 0.04465I
a = 0.188770 − 0.083516I
b = 0.052313 − 0.658440I
−9.70700 + 5.87952I 0
13
II.
I
u
2
= h−3.29×10
10
u
21
+1.11×10
9
u
20
+· · ·+9.95×10
9
b−1.43×10
11
, −3.23×
10
10
u
21
+1.32×10
10
u
20
+· · ·+9.95×10
9
a+5.82×10
9
, u
22
−8u
20
+· · ·+7u+1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
3.24133u
21
− 1.32161u
20
+ ··· − 3.62531u − 0.584512
3.30910u
21
− 0.111878u
20
+ ··· + 37.7176u + 14.3251
a
4
=
3.24133u
21
− 1.32161u
20
+ ··· − 3.62531u − 0.584512
5.18964u
21
− 0.408859u
20
+ ··· + 43.7275u + 15.6467
a
2
=
2.94299u
21
+ 0.485488u
20
+ ··· + 31.3762u + 12.8396
14.8897u
21
− 2.30887u
20
+ ··· + 165.030u + 65.7091
a
9
=
4.23720u
21
− 0.950521u
20
+ ··· + 27.8535u + 10.5976
16.9528u
21
− 2.89931u
20
+ ··· + 187.557u + 69.3435
a
7
=
u
u
a
3
=
1.76919u
21
− 0.445000u
20
+ ··· − 11.9629u − 1.49726
3.71750u
21
+ 0.467748u
20
+ ··· + 35.3900u + 14.7339
a
6
=
8.37457u
21
− 1.23232u
20
+ ··· + 122.450u + 50.2111
75.6531u
21
− 18.5917u
20
+ ··· + 890.451u + 325.412
a
11
=
−u
2
+ 1
−u
2
a
10
=
7.32505u
21
− 2.30910u
20
+ ··· + 90.2938u + 22.5578
14.2011u
21
− 2.31490u
20
+ ··· + 159.942u + 62.8029
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
1424127743710
9952263913
u
21
+
340116765766
9952263913
u
20
+ ··· −
16949185078163
9952263913
u −
6352077428057
9952263913
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 10u
21
+ ··· + 4u + 1
c
2
u
22
+ 8u
20
+ ··· − 11u + 1
c
3
u
22
+ 6u
21
+ ··· + 65u + 11
c
4
u
22
− 2u
20
+ ··· + 5u + 1
c
5
u
22
+ 6u
21
+ ··· + 16u + 7
c
6
u
22
+ 4u
21
+ ··· + 3u + 1
c
7
u
22
− 8u
20
+ ··· − 7u + 1
c
8
u
22
+ 3u
21
+ ··· + 18u + 4
c
9
u
22
+ u
21
+ ··· − 5u + 1
c
10
u
22
− 6u
21
+ ··· − 16u + 7
c
11
, c
12
u
22
− 8u
20
+ ··· + 7u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 20y
21
+ ··· − 16y + 1
c
2
y
22
+ 16y
21
+ ··· − 47y + 1
c
3
y
22
+ 8y
21
+ ··· − 3125y + 121
c
4
y
22
− 4y
21
+ ··· − 47y + 1
c
5
, c
10
y
22
− 4y
21
+ ··· + 444y + 49
c
6
y
22
− 26y
21
+ ··· − 19y + 1
c
7
, c
11
, c
12
y
22
− 16y
21
+ ··· − 33y + 1
c
8
y
22
− 21y
21
+ ··· − 156y + 16
c
9
y
22
− y
21
+ ··· − 23y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.689646 + 0.731117I
a = 0.892611 + 0.673718I
b = −0.036753 + 1.292750I
1.43694 − 2.16906I −2.67250 + 3.66995I
u = −0.689646 − 0.731117I
a = 0.892611 − 0.673718I
b = −0.036753 − 1.292750I
1.43694 + 2.16906I −2.67250 − 3.66995I
u = 1.089690 + 0.084115I
a = 0.411457 + 1.135850I
b = 0.794749 − 0.468906I
−7.64222 + 1.24596I −23.8515 − 3.0661I
u = 1.089690 − 0.084115I
a = 0.411457 − 1.135850I
b = 0.794749 + 0.468906I
−7.64222 − 1.24596I −23.8515 + 3.0661I
u = −0.899268
a = 0.347566
b = 1.27618
−3.56961 −12.4310
u = −0.792158 + 0.366921I
a = −0.916716 − 0.499164I
b = 1.114910 − 0.251162I
−3.56033 + 2.09844I −6.52547 − 4.25542I
u = −0.792158 − 0.366921I
a = −0.916716 + 0.499164I
b = 1.114910 + 0.251162I
−3.56033 − 2.09844I −6.52547 + 4.25542I
u = 0.719041 + 0.983858I
a = −0.166355 + 1.358040I
b = 0.272914 + 1.195270I
2.68903 − 3.88617I 2.04251 + 7.16256I
u = 0.719041 − 0.983858I
a = −0.166355 − 1.358040I
b = 0.272914 − 1.195270I
2.68903 + 3.88617I 2.04251 − 7.16256I
u = 0.707893 + 0.062157I
a = −0.41559 + 2.21549I
b = 0.691014 + 0.697209I
−6.18665 − 1.95182I −13.20160 + 2.52334I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707893 − 0.062157I
a = −0.41559 − 2.21549I
b = 0.691014 − 0.697209I
−6.18665 + 1.95182I −13.20160 − 2.52334I
u = −1.167100 + 0.769333I
a = −0.524110 − 1.013700I
b = 0.66774 − 1.44550I
−0.27838 + 8.00011I −7.03623 − 4.71619I
u = −1.167100 − 0.769333I
a = −0.524110 + 1.013700I
b = 0.66774 + 1.44550I
−0.27838 − 8.00011I −7.03623 + 4.71619I
u = −0.456432 + 0.227700I
a = 3.48387 − 1.57572I
b = −0.736499 − 0.288334I
−5.92592 + 7.21272I −12.48421 − 3.10300I
u = −0.456432 − 0.227700I
a = 3.48387 + 1.57572I
b = −0.736499 + 0.288334I
−5.92592 − 7.21272I −12.48421 + 3.10300I
u = 1.13411 + 1.02905I
a = 0.657006 − 0.757043I
b = −0.097956 − 0.941245I
1.52864 − 3.47332I 1.80817 + 6.65351I
u = 1.13411 − 1.02905I
a = 0.657006 + 0.757043I
b = −0.097956 + 0.941245I
1.52864 + 3.47332I 1.80817 − 6.65351I
u = −1.53567 + 0.06089I
a = −0.047861 − 0.531327I
b = −0.356622 − 0.079517I
−10.48400 − 5.80432I −12.69968 + 4.16414I
u = −1.53567 − 0.06089I
a = −0.047861 + 0.531327I
b = −0.356622 + 0.079517I
−10.48400 + 5.80432I −12.69968 − 4.16414I
u = 1.55684 + 0.15697I
a = 0.129002 + 0.163150I
b = −0.448678 − 0.325269I
−9.27686 − 2.12244I −21.9473 + 10.7965I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55684 − 0.15697I
a = 0.129002 − 0.163150I
b = −0.448678 + 0.325269I
−9.27686 + 2.12244I −21.9473 − 10.7965I
u = −0.233875
a = 0.645810
b = 4.99418
−3.27765 −239.430
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 10u
21
+ ··· + 4u + 1)(u
87
+ 3u
86
+ ··· + 3937u + 511)
c
2
(u
22
+ 8u
20
+ ··· − 11u + 1)(u
87
− 5u
86
+ ··· − 2768u − 437)
c
3
(u
22
+ 6u
21
+ ··· + 65u + 11)(u
87
− 3u
86
+ ··· − 4842u − 1687)
c
4
(u
22
− 2u
20
+ ··· + 5u + 1)(u
87
− u
86
+ ··· + 5250u + 811)
c
5
(u
22
+ 6u
21
+ ··· + 16u + 7)(u
87
− u
86
+ ··· + 833881u + 81631)
c
6
(u
22
+ 4u
21
+ ··· + 3u + 1)(u
87
− u
86
+ ··· + 46u − 7)
c
7
(u
22
− 8u
20
+ ··· − 7u + 1)(u
87
− u
86
+ ··· − 144u + 67)
c
8
(u
22
+ 3u
21
+ ··· + 18u + 4)(u
87
− 2u
86
+ ··· − 5106u + 38332)
c
9
(u
22
+ u
21
+ ··· − 5u + 1)(u
87
− 2u
86
+ ··· + 58u + 7)
c
10
(u
22
− 6u
21
+ ··· − 16u + 7)(u
87
− u
86
+ ··· + 833881u + 81631)
c
11
, c
12
(u
22
− 8u
20
+ ··· + 7u + 1)(u
87
− u
86
+ ··· − 144u + 67)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 20y
21
+ ··· − 16y + 1)
· (y
87
+ 67y
86
+ ··· − 8202255y −261121)
c
2
(y
22
+ 16y
21
+ ··· − 47y + 1)
· (y
87
+ 31y
86
+ ··· − 9342720y −190969)
c
3
(y
22
+ 8y
21
+ ··· − 3125y + 121)
· (y
87
− y
86
+ ··· + 410351666y −2845969)
c
4
(y
22
− 4y
21
+ ··· − 47y + 1)
· (y
87
− 61y
86
+ ··· + 13379732y −657721)
c
5
, c
10
(y
22
− 4y
21
+ ··· + 444y + 49)
· (y
87
+ 71y
86
+ ··· − 125580302491y −6663620161)
c
6
(y
22
− 26y
21
+ ··· − 19y + 1)(y
87
+ 5y
86
+ ··· + 1556y −49)
c
7
, c
11
, c
12
(y
22
− 16y
21
+ ··· − 33y + 1)(y
87
− 29y
86
+ ··· + 80634y −4489)
c
8
(y
22
− 21y
21
+ ··· − 156y + 16)
· (y
87
− 54y
86
+ ··· + 32610801148y −1469342224)
c
9
(y
22
− y
21
+ ··· − 23y + 1)(y
87
+ 6y
86
+ ··· − 724y −49)
21
