12a
0751
(K12a
0751
)
A knot diagram
1
Linearized knot diagam
3 8 10 9 12 11 2 5 1 7 6 4
Solving Sequence
2,7
8 3
1,11
6 12 5 10 4 9
c
7
c
2
c
1
c
6
c
11
c
5
c
10
c
3
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5.59626 × 10
121
u
99
+ 7.57270 × 10
121
u
98
+ ··· + 1.04618 × 10
122
b + 1.03099 × 10
124
,
3.41104 × 10
123
u
99
+ 1.78701 × 10
123
u
98
+ ··· + 1.15079 × 10
123
a + 4.33722 × 10
125
,
u
100
+ u
99
+ ··· + 192u + 88i
I
u
2
= h−u
17
− u
16
+ ··· + b − 4, u
19
− u
18
+ ··· + a − 5, u
20
− 5u
18
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 120 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
= h5.60 × 10
121
u
99
+ 7.57 × 10
121
u
98
+ · · · + 1.05 × 10
122
b + 1.03 ×
10
124
, 3.41 × 10
123
u
99
+ 1.79 × 10
123
u
98
+ · · · + 1.15 × 10
123
a + 4.34 ×
10
125
, u
100
+ u
99
+ · · · + 192u + 88i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−2.96408u
99
− 1.55285u
98
+ ··· − 374.031u − 376.889
−0.534925u
99
− 0.723846u
98
+ ··· − 84.1661u − 98.5485
a
6
=
0.617617u
99
− 1.17346u
98
+ ··· + 37.6546u − 38.2669
2.51995u
99
− 0.410169u
98
+ ··· + 285.419u + 168.064
a
12
=
2.09671u
99
+ 1.08332u
98
+ ··· + 250.069u + 258.434
1.72681u
99
+ 0.999934u
98
+ ··· + 237.814u + 210.154
a
5
=
−2.27990u
99
+ 1.58306u
98
+ ··· − 240.947u − 25.0792
−3.87185u
99
− 0.0865608u
98
+ ··· − 443.404u − 309.362
a
10
=
−2.42915u
99
− 0.829001u
98
+ ··· − 289.865u − 278.341
−0.534925u
99
− 0.723846u
98
+ ··· − 84.1661u − 98.5485
a
4
=
−0.845112u
99
+ 0.558376u
98
+ ··· − 83.0591u − 2.45370
−1.36008u
99
+ 0.253366u
98
+ ··· − 116.779u − 81.9261
a
9
=
−2.85480u
99
− 1.37610u
98
+ ··· − 351.640u − 359.046
−0.790636u
99
− 0.977449u
98
+ ··· − 118.031u − 144.290
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.86987u
99
− 0.145177u
98
+ ··· − 447.994u − 326.668
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
100
+ 45u
99
+ ··· + 119584u + 7744
c
2
, c
7
u
100
+ u
99
+ ··· + 192u + 88
c
3
u
100
+ 3u
98
+ ··· + 1720u + 379
c
4
, c
8
u
100
+ 2u
99
+ ··· + 2370u + 1621
c
5
, c
6
, c
10
c
11
u
100
− u
99
+ ··· + 6u + 1
c
9
u
100
− 3u
99
+ ··· + 566u + 1753
c
12
u
100
+ 9u
99
+ ··· + 45u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
100
+ 31y
99
+ ··· + 454960640y + 59969536
c
2
, c
7
y
100
− 45y
99
+ ··· − 119584y + 7744
c
3
y
100
+ 6y
99
+ ··· + 2142182y + 143641
c
4
, c
8
y
100
+ 62y
99
+ ··· + 49983400y + 2627641
c
5
, c
6
, c
10
c
11
y
100
+ 121y
99
+ ··· + 32y + 1
c
9
y
100
− 31y
99
+ ··· − 158167488y + 3073009
c
12
y
100
+ y
99
+ ··· − 499y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.457128 + 0.895092I
a = 0.277346 − 0.131143I
b = −0.591223 − 0.738873I
3.20370 + 8.08248I 0
u = 0.457128 − 0.895092I
a = 0.277346 + 0.131143I
b = −0.591223 + 0.738873I
3.20370 − 8.08248I 0
u = −0.949475 + 0.353004I
a = −0.0965409 − 0.0295078I
b = −0.501613 + 0.333772I
−1.61218 + 1.26315I 0
u = −0.949475 − 0.353004I
a = −0.0965409 + 0.0295078I
b = −0.501613 − 0.333772I
−1.61218 − 1.26315I 0
u = 0.487153 + 0.858326I
a = −0.411419 + 0.471713I
b = 0.08719 + 1.60914I
−8.68625 + 4.27677I 0
u = 0.487153 − 0.858326I
a = −0.411419 − 0.471713I
b = 0.08719 − 1.60914I
−8.68625 − 4.27677I 0
u = −0.811221 + 0.558161I
a = −0.610382 − 0.676529I
b = 0.456846 − 0.636360I
2.56446 − 0.54418I 0
u = −0.811221 − 0.558161I
a = −0.610382 + 0.676529I
b = 0.456846 + 0.636360I
2.56446 + 0.54418I 0
u = −0.909159 + 0.370130I
a = 1.00785 − 2.56119I
b = 0.04380 − 1.79990I
−12.07290 + 1.51771I 0
u = −0.909159 − 0.370130I
a = 1.00785 + 2.56119I
b = 0.04380 + 1.79990I
−12.07290 − 1.51771I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.943267 + 0.393422I
a = −1.16845 + 1.06220I
b = 0.549467 + 0.827812I
−1.80876 + 1.49561I 0
u = −0.943267 − 0.393422I
a = −1.16845 − 1.06220I
b = 0.549467 − 0.827812I
−1.80876 − 1.49561I 0
u = 0.049849 + 1.035490I
a = −0.119703 − 1.284840I
b = −0.07255 − 1.55357I
−3.35710 + 0.84569I 0
u = 0.049849 − 1.035490I
a = −0.119703 + 1.284840I
b = −0.07255 + 1.55357I
−3.35710 − 0.84569I 0
u = −0.345894 + 0.892402I
a = 0.043148 + 0.616596I
b = −0.378598 + 0.534759I
3.66695 + 0.64439I 0
u = −0.345894 − 0.892402I
a = 0.043148 − 0.616596I
b = −0.378598 − 0.534759I
3.66695 − 0.64439I 0
u = −0.875061 + 0.578879I
a = 1.12333 − 1.91481I
b = −0.313739 − 0.731171I
2.36569 + 5.08929I 0
u = −0.875061 − 0.578879I
a = 1.12333 + 1.91481I
b = −0.313739 + 0.731171I
2.36569 − 5.08929I 0
u = −0.971552 + 0.444847I
a = −2.90650 + 2.58483I
b = 0.01149 + 1.56483I
−6.12144 − 1.12485I 0
u = −0.971552 − 0.444847I
a = −2.90650 − 2.58483I
b = 0.01149 − 1.56483I
−6.12144 + 1.12485I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.068870 + 0.136323I
a = −0.01112 − 1.51128I
b = −0.228583 − 0.936404I
−5.43132 + 1.06691I 0
u = 1.068870 − 0.136323I
a = −0.01112 + 1.51128I
b = −0.228583 + 0.936404I
−5.43132 − 1.06691I 0
u = −0.532098 + 0.746302I
a = 0.624469 − 0.643270I
b = −0.754980 − 0.223997I
4.77059 − 3.60253I 0
u = −0.532098 − 0.746302I
a = 0.624469 + 0.643270I
b = −0.754980 + 0.223997I
4.77059 + 3.60253I 0
u = 0.901590 + 0.137482I
a = −0.225698 − 0.574004I
b = 0.656804 + 0.210978I
0.01670 + 2.78694I 0
u = 0.901590 − 0.137482I
a = −0.225698 + 0.574004I
b = 0.656804 − 0.210978I
0.01670 − 2.78694I 0
u = −0.407065 + 1.010870I
a = 0.255522 + 0.839954I
b = −0.17440 + 1.62012I
−4.76816 − 10.95720I 0
u = −0.407065 − 1.010870I
a = 0.255522 − 0.839954I
b = −0.17440 − 1.62012I
−4.76816 + 10.95720I 0
u = 0.973821 + 0.494263I
a = 2.07761 + 3.20985I
b = −0.09275 + 1.62754I
−5.79792 − 6.63756I 0
u = 0.973821 − 0.494263I
a = 2.07761 − 3.20985I
b = −0.09275 − 1.62754I
−5.79792 + 6.63756I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.982131 + 0.534639I
a = 0.573213 + 0.834066I
b = 0.550859 + 1.189730I
−0.83659 − 3.90380I 0
u = 0.982131 − 0.534639I
a = 0.573213 − 0.834066I
b = 0.550859 − 1.189730I
−0.83659 + 3.90380I 0
u = 0.480220 + 0.730326I
a = −0.391373 − 0.230176I
b = −0.05183 − 1.60666I
−8.61603 − 0.90830I 0
u = 0.480220 − 0.730326I
a = −0.391373 + 0.230176I
b = −0.05183 + 1.60666I
−8.61603 + 0.90830I 0
u = 0.790912 + 0.351475I
a = −2.42436 − 1.13611I
b = 0.040636 − 0.416164I
0.88125 + 1.31215I 0
u = 0.790912 − 0.351475I
a = −2.42436 + 1.13611I
b = 0.040636 + 0.416164I
0.88125 − 1.31215I 0
u = −1.055800 + 0.416304I
a = −0.477868 + 0.407449I
b = −0.501700 + 0.764707I
−2.26962 + 1.47318I 0
u = −1.055800 − 0.416304I
a = −0.477868 − 0.407449I
b = −0.501700 − 0.764707I
−2.26962 − 1.47318I 0
u = 1.023140 + 0.506583I
a = 0.579107 + 0.555358I
b = −0.471189 − 0.035664I
−0.45591 − 4.68155I 0
u = 1.023140 − 0.506583I
a = 0.579107 − 0.555358I
b = −0.471189 + 0.035664I
−0.45591 + 4.68155I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662351 + 0.538131I
a = 1.43717 + 1.53013I
b = −0.400932 + 1.267270I
0.179494 − 0.448818I 0
u = 0.662351 − 0.538131I
a = 1.43717 − 1.53013I
b = −0.400932 − 1.267270I
0.179494 + 0.448818I 0
u = −0.480432 + 0.704035I
a = −0.720306 + 0.070361I
b = 0.311817 − 0.699242I
−0.75596 − 2.78991I 0. + 5.33071I
u = −0.480432 − 0.704035I
a = −0.720306 − 0.070361I
b = 0.311817 + 0.699242I
−0.75596 + 2.78991I 0. − 5.33071I
u = 0.919034 + 0.695465I
a = −0.388402 + 0.015091I
b = 0.450194 − 0.156366I
3.85181 − 2.66231I 0
u = 0.919034 − 0.695465I
a = −0.388402 − 0.015091I
b = 0.450194 + 0.156366I
3.85181 + 2.66231I 0
u = 1.061530 + 0.451220I
a = 0.64755 + 1.28489I
b = −0.686878 + 0.598970I
−2.00804 − 5.39813I 0
u = 1.061530 − 0.451220I
a = 0.64755 − 1.28489I
b = −0.686878 − 0.598970I
−2.00804 + 5.39813I 0
u = 0.855748 + 0.776003I
a = −0.059404 + 0.560020I
b = −0.147280 − 0.150368I
4.15579 − 3.00585I 0
u = 0.855748 − 0.776003I
a = −0.059404 − 0.560020I
b = −0.147280 + 0.150368I
4.15579 + 3.00585I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.699689 + 0.447370I
a = −0.85775 + 1.47416I
b = 0.12893 + 1.57137I
−4.86721 + 2.69174I 2.00000 + 3.09443I
u = 0.699689 − 0.447370I
a = −0.85775 − 1.47416I
b = 0.12893 − 1.57137I
−4.86721 − 2.69174I 2.00000 − 3.09443I
u = 1.044530 + 0.567090I
a = −1.74491 − 1.52556I
b = 0.13770 − 1.64610I
−10.30000 − 4.00533I 0
u = 1.044530 − 0.567090I
a = −1.74491 + 1.52556I
b = 0.13770 + 1.64610I
−10.30000 + 4.00533I 0
u = 0.721663 + 0.945843I
a = 0.175629 + 0.357102I
b = −0.277462 + 0.330746I
4.29505 − 3.25009I 0
u = 0.721663 − 0.945843I
a = 0.175629 − 0.357102I
b = −0.277462 − 0.330746I
4.29505 + 3.25009I 0
u = −1.198440 + 0.068526I
a = 0.18829 + 2.88134I
b = −0.04624 + 1.67782I
−14.5866 − 2.0802I 0
u = −1.198440 − 0.068526I
a = 0.18829 − 2.88134I
b = −0.04624 − 1.67782I
−14.5866 + 2.0802I 0
u = −0.883097 + 0.813802I
a = −0.955482 + 0.128175I
b = 0.01310 + 1.53039I
−1.99200 + 3.03411I 0
u = −0.883097 − 0.813802I
a = −0.955482 − 0.128175I
b = 0.01310 − 1.53039I
−1.99200 − 3.03411I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.167680 + 0.328905I
a = −0.70668 − 2.37685I
b = −0.12071 − 1.64095I
−10.63490 + 0.79325I 0
u = 1.167680 − 0.328905I
a = −0.70668 + 2.37685I
b = −0.12071 + 1.64095I
−10.63490 − 0.79325I 0
u = −1.052900 + 0.617585I
a = 0.009037 + 0.412192I
b = 0.867881 − 0.150365I
3.20806 + 8.79860I 0
u = −1.052900 − 0.617585I
a = 0.009037 − 0.412192I
b = 0.867881 + 0.150365I
3.20806 − 8.79860I 0
u = 1.139320 + 0.445638I
a = 0.825300 + 0.952464I
b = −0.090239 + 0.314591I
−0.57512 − 4.30546I 0
u = 1.139320 − 0.445638I
a = 0.825300 − 0.952464I
b = −0.090239 − 0.314591I
−0.57512 + 4.30546I 0
u = −1.064410 + 0.604122I
a = 1.24875 − 0.98974I
b = −0.426728 − 0.748134I
−2.46212 + 7.84489I 0
u = −1.064410 − 0.604122I
a = 1.24875 + 0.98974I
b = −0.426728 + 0.748134I
−2.46212 − 7.84489I 0
u = −0.714472 + 0.297648I
a = −1.85378 + 0.42902I
b = 0.059035 + 0.980030I
−0.92305 + 1.41574I 1.53824 − 4.41774I
u = −0.714472 − 0.297648I
a = −1.85378 − 0.42902I
b = 0.059035 − 0.980030I
−0.92305 − 1.41574I 1.53824 + 4.41774I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688380 + 0.344991I
a = 0.577273 − 0.199424I
b = 0.05291 + 1.47826I
−5.14023 + 4.60516I −2.03923 − 7.77612I
u = −0.688380 − 0.344991I
a = 0.577273 + 0.199424I
b = 0.05291 − 1.47826I
−5.14023 − 4.60516I −2.03923 + 7.77612I
u = −1.134260 + 0.510215I
a = 1.77296 − 2.03650I
b = −0.22540 − 1.60286I
−9.42325 + 8.84178I 0
u = −1.134260 − 0.510215I
a = 1.77296 + 2.03650I
b = −0.22540 + 1.60286I
−9.42325 − 8.84178I 0
u = −1.260620 + 0.008171I
a = 0.292978 + 1.077860I
b = 0.334506 + 0.803931I
−3.13898 + 5.62440I 0
u = −1.260620 − 0.008171I
a = 0.292978 − 1.077860I
b = 0.334506 − 0.803931I
−3.13898 − 5.62440I 0
u = −0.165190 + 0.708418I
a = −0.529068 − 0.355693I
b = 0.16439 − 1.57090I
−6.70390 − 4.29246I −0.60052 + 3.33872I
u = −0.165190 − 0.708418I
a = −0.529068 + 0.355693I
b = 0.16439 + 1.57090I
−6.70390 + 4.29246I −0.60052 − 3.33872I
u = 1.113440 + 0.659702I
a = 2.01350 + 1.56051I
b = −0.12374 + 1.62349I
−10.5794 − 9.9278I 0
u = 1.113440 − 0.659702I
a = 2.01350 − 1.56051I
b = −0.12374 − 1.62349I
−10.5794 + 9.9278I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.125530 + 0.654798I
a = −0.77851 − 1.24846I
b = 0.647617 − 0.821693I
1.17041 − 13.78430I 0
u = 1.125530 − 0.654798I
a = −0.77851 + 1.24846I
b = 0.647617 + 0.821693I
1.17041 + 13.78430I 0
u = 0.412523 + 0.527683I
a = −0.979778 + 0.055130I
b = 0.401276 + 0.042780I
1.274940 + 0.490112I 7.83258 − 0.20587I
u = 0.412523 − 0.527683I
a = −0.979778 − 0.055130I
b = 0.401276 − 0.042780I
1.274940 − 0.490112I 7.83258 + 0.20587I
u = −1.153210 + 0.689575I
a = −0.565447 + 1.134440I
b = 0.335549 + 0.781521I
1.29974 + 5.19343I 0
u = −1.153210 − 0.689575I
a = −0.565447 − 1.134440I
b = 0.335549 − 0.781521I
1.29974 − 5.19343I 0
u = −1.188740 + 0.673765I
a = −1.64301 + 1.89720I
b = 0.19731 + 1.65104I
−7.1910 + 17.0346I 0
u = −1.188740 − 0.673765I
a = −1.64301 − 1.89720I
b = 0.19731 − 1.65104I
−7.1910 − 17.0346I 0
u = −1.278800 + 0.554028I
a = 1.36310 − 2.26576I
b = −0.01874 − 1.55514I
−7.31672 + 4.64807I 0
u = −1.278800 − 0.554028I
a = 1.36310 + 2.26576I
b = −0.01874 + 1.55514I
−7.31672 − 4.64807I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.475485 + 0.356600I
a = −1.054600 − 0.397241I
b = 0.016367 + 0.691404I
−0.75049 + 1.42692I −1.23605 − 5.05204I
u = −0.475485 − 0.356600I
a = −1.054600 + 0.397241I
b = 0.016367 − 0.691404I
−0.75049 − 1.42692I −1.23605 + 5.05204I
u = 1.41675 + 0.05485I
a = 0.03074 + 2.54396I
b = 0.10040 + 1.63547I
−11.52460 + 7.31973I 0
u = 1.41675 − 0.05485I
a = 0.03074 − 2.54396I
b = 0.10040 − 1.63547I
−11.52460 − 7.31973I 0
u = 1.29924 + 0.64879I
a = −1.06766 − 2.20720I
b = 0.09769 − 1.63714I
−7.05187 − 6.85612I 0
u = 1.29924 − 0.64879I
a = −1.06766 + 2.20720I
b = 0.09769 + 1.63714I
−7.05187 + 6.85612I 0
u = −0.87310 + 1.16661I
a = 0.489018 − 1.141310I
b = −0.03392 − 1.54941I
−2.33918 + 3.99799I 0
u = −0.87310 − 1.16661I
a = 0.489018 + 1.141310I
b = −0.03392 + 1.54941I
−2.33918 − 3.99799I 0
u = 0.058286 + 0.489208I
a = −0.907430 − 0.127080I
b = 0.517643 + 0.539466I
0.43996 + 1.77224I 1.45803 − 4.64107I
u = 0.058286 − 0.489208I
a = −0.907430 + 0.127080I
b = 0.517643 − 0.539466I
0.43996 − 1.77224I 1.45803 + 4.64107I
14
II.
I
u
2
= h−u
17
− u
16
+ · · · + b − 4, u
19
− u
18
+ · · · + a − 5, u
20
− 5u
18
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−u
19
+ u
18
+ ··· + 3u + 5
u
17
+ u
16
+ ··· + u + 4
a
6
=
−2u
19
+ 3u
18
+ ··· + 4u + 5
−3u
19
+ 12u
17
+ ··· − u − 2
a
12
=
−6u
19
− u
18
+ ··· − 6u
2
− 1
u
19
− 5u
17
+ ··· − u − 4
a
5
=
5u
19
+ u
18
+ ··· − 4u − 1
3u
19
− 12u
17
+ ··· + 4u
2
+ u
a
10
=
−u
19
+ u
18
+ ··· + 2u + 1
u
17
+ u
16
+ ··· + u + 4
a
4
=
3u
19
− 11u
17
+ ··· + 6u + 2
−u
19
− u
18
+ ··· + 3u + 5
a
9
=
u
18
+ u
17
+ ··· + 2u + 1
u
17
+ u
16
+ ··· + u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −9u
19
+ 35u
17
+ 12u
16
− 92u
15
− 49u
14
+ 160u
13
+ 112u
12
− 221u
11
− 183u
10
+
211u
9
+ 227u
8
− 138u
7
− 201u
6
+ 38u
5
+ 123u
4
+ 13u
3
− 56u
2
− 13u + 14
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 10u
19
+ ··· − 13u + 1
c
2
u
20
− 5u
18
+ ··· + u + 1
c
3
u
20
+ u
19
+ ··· + 2u + 1
c
4
u
20
+ u
19
+ ··· + 10u
2
+ 1
c
5
, c
6
u
20
+ 14u
18
+ ··· + 2u + 1
c
7
u
20
− 5u
18
+ ··· − u + 1
c
8
u
20
− u
19
+ ··· + 10u
2
+ 1
c
9
u
20
− 4u
19
+ ··· − 4u + 1
c
10
, c
11
u
20
+ 14u
18
+ ··· − 2u + 1
c
12
u
20
− 3u
17
+ ··· + 3u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 10y
19
+ ··· + 7y + 1
c
2
, c
7
y
20
− 10y
19
+ ··· − 13y + 1
c
3
y
20
− 3y
19
+ ··· + 2y + 1
c
4
, c
8
y
20
+ 17y
19
+ ··· + 20y + 1
c
5
, c
6
, c
10
c
11
y
20
+ 28y
19
+ ··· + 24y + 1
c
9
y
20
− 12y
19
+ ··· − 12y + 1
c
12
y
20
− 6y
18
+ ··· + y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.945567 + 0.247254I
a = 1.12868 − 2.58212I
b = 0.02340 − 1.76437I
−12.48050 + 1.02035I −6.90663 + 2.24541I
u = −0.945567 − 0.247254I
a = 1.12868 + 2.58212I
b = 0.02340 + 1.76437I
−12.48050 − 1.02035I −6.90663 − 2.24541I
u = 1.005350 + 0.363840I
a = 0.533622 + 0.298950I
b = 0.367128 + 0.974221I
−2.05613 − 2.40154I −1.92475 + 5.24351I
u = 1.005350 − 0.363840I
a = 0.533622 − 0.298950I
b = 0.367128 − 0.974221I
−2.05613 + 2.40154I −1.92475 − 5.24351I
u = −0.867805 + 0.703439I
a = −0.785443 + 1.054200I
b = −0.052377 + 1.156930I
1.24861 + 2.70464I 3.70481 − 2.83294I
u = −0.867805 − 0.703439I
a = −0.785443 − 1.054200I
b = −0.052377 − 1.156930I
1.24861 − 2.70464I 3.70481 + 2.83294I
u = 0.792758 + 0.306881I
a = 2.12301 + 1.56831I
b = −0.305080 + 1.107830I
−1.217270 − 0.434477I −1.98252 − 2.13576I
u = 0.792758 − 0.306881I
a = 2.12301 − 1.56831I
b = −0.305080 − 1.107830I
−1.217270 + 0.434477I −1.98252 + 2.13576I
u = 0.830890 + 0.851184I
a = 0.0017229 − 0.1293230I
b = −0.068980 + 0.354498I
3.84716 − 3.17204I −9.02326 + 6.39041I
u = 0.830890 − 0.851184I
a = 0.0017229 + 0.1293230I
b = −0.068980 − 0.354498I
3.84716 + 3.17204I −9.02326 − 6.39041I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.109460 + 0.447037I
a = −0.65444 + 1.44954I
b = 0.364945 + 0.517562I
−0.60400 + 5.07290I 1.00087 − 10.67343I
u = −1.109460 − 0.447037I
a = −0.65444 − 1.44954I
b = 0.364945 − 0.517562I
−0.60400 − 5.07290I 1.00087 + 10.67343I
u = −0.811158 + 0.969033I
a = 0.416898 − 0.696335I
b = −0.02269 − 1.54816I
−2.87450 + 3.50843I −2.42701 − 2.27980I
u = −0.811158 − 0.969033I
a = 0.416898 + 0.696335I
b = −0.02269 + 1.54816I
−2.87450 − 3.50843I −2.42701 + 2.27980I
u = −0.647271 + 0.292294I
a = 2.00402 − 0.22283I
b = −0.313317 + 0.344019I
1.26691 − 1.85750I 6.25683 + 6.64675I
u = −0.647271 − 0.292294I
a = 2.00402 + 0.22283I
b = −0.313317 − 0.344019I
1.26691 + 1.85750I 6.25683 − 6.64675I
u = 1.219100 + 0.499119I
a = −1.34740 − 2.58399I
b = 0.10159 − 1.60734I
−8.12931 − 6.77394I −3.97445 + 5.78529I
u = 1.219100 − 0.499119I
a = −1.34740 + 2.58399I
b = 0.10159 + 1.60734I
−8.12931 + 6.77394I −3.97445 − 5.78529I
u = 0.533169 + 0.273157I
a = 2.07932 − 1.13267I
b = −0.09462 − 1.53848I
−5.31995 + 3.31110I −2.72389 − 4.69129I
u = 0.533169 − 0.273157I
a = 2.07932 + 1.13267I
b = −0.09462 + 1.53848I
−5.31995 − 3.31110I −2.72389 + 4.69129I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 10u
19
+ ··· − 13u + 1)(u
100
+ 45u
99
+ ··· + 119584u + 7744)
c
2
(u
20
− 5u
18
+ ··· + u + 1)(u
100
+ u
99
+ ··· + 192u + 88)
c
3
(u
20
+ u
19
+ ··· + 2u + 1)(u
100
+ 3u
98
+ ··· + 1720u + 379)
c
4
(u
20
+ u
19
+ ··· + 10u
2
+ 1)(u
100
+ 2u
99
+ ··· + 2370u + 1621)
c
5
, c
6
(u
20
+ 14u
18
+ ··· + 2u + 1)(u
100
− u
99
+ ··· + 6u + 1)
c
7
(u
20
− 5u
18
+ ··· − u + 1)(u
100
+ u
99
+ ··· + 192u + 88)
c
8
(u
20
− u
19
+ ··· + 10u
2
+ 1)(u
100
+ 2u
99
+ ··· + 2370u + 1621)
c
9
(u
20
− 4u
19
+ ··· − 4u + 1)(u
100
− 3u
99
+ ··· + 566u + 1753)
c
10
, c
11
(u
20
+ 14u
18
+ ··· − 2u + 1)(u
100
− u
99
+ ··· + 6u + 1)
c
12
(u
20
− 3u
17
+ ··· + 3u + 1)(u
100
+ 9u
99
+ ··· + 45u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 10y
19
+ ··· + 7y + 1)
· (y
100
+ 31y
99
+ ··· + 454960640y + 59969536)
c
2
, c
7
(y
20
− 10y
19
+ ··· − 13y + 1)(y
100
− 45y
99
+ ··· − 119584y + 7744)
c
3
(y
20
− 3y
19
+ ··· + 2y + 1)(y
100
+ 6y
99
+ ··· + 2142182y + 143641)
c
4
, c
8
(y
20
+ 17y
19
+ ··· + 20y + 1)
· (y
100
+ 62y
99
+ ··· + 49983400y + 2627641)
c
5
, c
6
, c
10
c
11
(y
20
+ 28y
19
+ ··· + 24y + 1)(y
100
+ 121y
99
+ ··· + 32y + 1)
c
9
(y
20
− 12y
19
+ ··· − 12y + 1)
· (y
100
− 31y
99
+ ··· − 158167488y + 3073009)
c
12
(y
20
− 6y
18
+ ··· + y + 1)(y
100
+ y
99
+ ··· − 499y + 1)
21
