11a
138
(K11a
138
)
A knot diagram
1
Linearized knot diagam
6 1 11 10 2 9 4 3 5 7 8
Solving Sequence
2,5 6,9
7 10 1 3 4 8 11
c
5
c
6
c
9
c
1
c
2
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.64020 × 10
132
u
93
− 4.93260 × 10
132
u
92
+ ··· + 3.94596 × 10
132
b + 2.57397 × 10
133
,
5.66772 × 10
133
u
93
+ 4.81293 × 10
132
u
92
+ ··· + 7.49732 × 10
133
a + 2.94172 × 10
134
,
u
94
+ 18u
92
+ ··· + 86u + 19i
I
u
2
= hu
13
+ u
12
+ 4u
11
+ 5u
10
+ 9u
9
+ 12u
8
+ 14u
7
+ 18u
6
+ 14u
5
+ 16u
4
+ 10u
3
+ 7u
2
+ b + 3u + 2,
2u
11
+ u
10
+ 6u
9
+ 3u
8
+ 10u
7
+ 6u
6
+ 11u
5
+ 6u
4
+ 5u
3
+ u
2
+ a + 2u,
u
14
+ u
13
+ 4u
12
+ 4u
11
+ 9u
10
+ 9u
9
+ 14u
8
+ 13u
7
+ 14u
6
+ 11u
5
+ 10u
4
+ 6u
3
+ 4u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 108 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
= h4.64 × 10
132
u
93
− 4.93 × 10
132
u
92
+ · · · + 3.95 × 10
132
b + 2.57 ×
10
133
, 5.67 × 10
133
u
93
+ 4.81 × 10
132
u
92
+ · · · + 7.50 × 10
133
a + 2.94 ×
10
134
, u
94
+ 18u
92
+ · · · + 86u + 19i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
9
=
−0.755966u
93
− 0.0641953u
92
+ ··· − 15.1145u − 3.92369
−1.17594u
93
+ 1.25004u
92
+ ··· − 56.7451u − 6.52306
a
7
=
−2.28733u
93
+ 2.35688u
92
+ ··· − 121.002u − 13.5839
1.36980u
93
− 1.75146u
92
+ ··· − 20.3031u − 19.9674
a
10
=
0.419971u
93
− 1.31423u
92
+ ··· + 41.6306u + 2.59936
−1.17594u
93
+ 1.25004u
92
+ ··· − 56.7451u − 6.52306
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
4
=
1.02372u
93
+ 2.01186u
92
+ ··· + 240.302u + 51.4766
2.60768u
93
− 0.842489u
92
+ ··· + 189.866u + 42.1854
a
8
=
−1.25959u
93
− 0.266213u
92
+ ··· − 77.3471u − 18.8004
−1.08401u
93
+ 1.21540u
92
+ ··· − 51.7820u − 4.28835
a
11
=
−2.05177u
93
+ 1.06053u
92
+ ··· − 195.102u − 45.8558
1.21606u
93
− 0.797164u
92
+ ··· + 40.0767u − 1.76508
a
11
=
−2.05177u
93
+ 1.06053u
92
+ ··· − 195.102u − 45.8558
1.21606u
93
− 0.797164u
92
+ ··· + 40.0767u − 1.76508
(ii) Obstruction class = −1
(iii) Cusp Shapes = −17.7102u
93
+ 16.3821u
92
+ ··· − 633.419u − 58.7338
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
94
+ 18u
92
+ ··· − 86u + 19
c
2
u
94
+ 36u
93
+ ··· + 8108u + 361
c
3
u
94
+ 5u
93
+ ··· + 88u + 11
c
4
, c
9
u
94
− u
93
+ ··· − 724u + 59
c
6
u
94
+ u
93
+ ··· + 33u + 781
c
7
u
94
+ 3u
93
+ ··· − 872u + 184
c
8
u
94
− u
93
+ ··· + 6u + 1
c
10
u
94
− 2u
93
+ ··· − 22u + 1
c
11
u
94
− 3u
93
+ ··· + 519u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
94
+ 36y
93
+ ··· + 8108y + 361
c
2
y
94
+ 48y
93
+ ··· + 13235584y + 130321
c
3
y
94
+ 9y
93
+ ··· + 7084y + 121
c
4
, c
9
y
94
+ 69y
93
+ ··· − 23148y + 3481
c
6
y
94
+ 27y
93
+ ··· + 20468921y + 609961
c
7
y
94
+ 23y
93
+ ··· + 1507232y + 33856
c
8
y
94
− 5y
93
+ ··· − 10y + 1
c
10
y
94
+ 8y
93
+ ··· − 18y + 1
c
11
y
94
− 15y
93
+ ··· − 72597y + 361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772806 + 0.634311I
a = 0.654406 − 0.353128I
b = 0.323430 + 1.127770I
2.72382 − 3.59329I 0
u = 0.772806 − 0.634311I
a = 0.654406 + 0.353128I
b = 0.323430 − 1.127770I
2.72382 + 3.59329I 0
u = 0.274173 + 0.962209I
a = −1.50690 − 0.97979I
b = −0.396852 + 0.187929I
−4.34588 + 0.86890I 0
u = 0.274173 − 0.962209I
a = −1.50690 + 0.97979I
b = −0.396852 − 0.187929I
−4.34588 − 0.86890I 0
u = −0.668968 + 0.720659I
a = 1.016990 − 0.259896I
b = 0.775819 + 0.307672I
0.151749 − 0.477282I 0
u = −0.668968 − 0.720659I
a = 1.016990 + 0.259896I
b = 0.775819 − 0.307672I
0.151749 + 0.477282I 0
u = −0.850683 + 0.581825I
a = 0.246185 − 0.369614I
b = −0.406184 + 0.185472I
1.11160 − 3.31196I 0
u = −0.850683 − 0.581825I
a = 0.246185 + 0.369614I
b = −0.406184 − 0.185472I
1.11160 + 3.31196I 0
u = −0.592379 + 0.857518I
a = −1.82681 + 0.35619I
b = −0.07407 − 1.92793I
2.76989 − 2.34388I 0
u = −0.592379 − 0.857518I
a = −1.82681 − 0.35619I
b = −0.07407 + 1.92793I
2.76989 + 2.34388I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.695476 + 0.779469I
a = −0.0831373 − 0.0411398I
b = 0.49756 + 1.48450I
6.51815 − 3.45234I 0
u = 0.695476 − 0.779469I
a = −0.0831373 + 0.0411398I
b = 0.49756 − 1.48450I
6.51815 + 3.45234I 0
u = 0.788570 + 0.519422I
a = −0.156445 − 0.492745I
b = −1.038060 − 0.306914I
0.81606 − 6.58212I 0
u = 0.788570 − 0.519422I
a = −0.156445 + 0.492745I
b = −1.038060 + 0.306914I
0.81606 + 6.58212I 0
u = −0.634876 + 0.844268I
a = −0.46562 − 1.35344I
b = 0.021145 + 1.273010I
5.15766 − 6.81146I 0
u = −0.634876 − 0.844268I
a = −0.46562 + 1.35344I
b = 0.021145 − 1.273010I
5.15766 + 6.81146I 0
u = −0.055511 + 1.062530I
a = −1.33304 − 1.27786I
b = −0.309524 − 0.906382I
−3.10746 − 3.06338I 0
u = −0.055511 − 1.062530I
a = −1.33304 + 1.27786I
b = −0.309524 + 0.906382I
−3.10746 + 3.06338I 0
u = 0.236372 + 0.894495I
a = 0.584905 − 0.267844I
b = 0.511218 + 0.245300I
−1.55461 − 1.18795I 0
u = 0.236372 − 0.894495I
a = 0.584905 + 0.267844I
b = 0.511218 − 0.245300I
−1.55461 + 1.18795I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.641346 + 0.865360I
a = 2.75194 − 0.57405I
b = 0.016454 + 1.166590I
5.09034 + 1.82821I 0
u = −0.641346 − 0.865360I
a = 2.75194 + 0.57405I
b = 0.016454 − 1.166590I
5.09034 − 1.82821I 0
u = −0.525700 + 0.752927I
a = −0.89280 + 2.31089I
b = −1.98203 + 0.34607I
1.74995 − 1.48935I 0
u = −0.525700 − 0.752927I
a = −0.89280 − 2.31089I
b = −1.98203 − 0.34607I
1.74995 + 1.48935I 0
u = 0.745984 + 0.804640I
a = 0.518167 + 0.550405I
b = −0.017640 − 1.382970I
6.26917 + 2.63292I 0
u = 0.745984 − 0.804640I
a = 0.518167 − 0.550405I
b = −0.017640 + 1.382970I
6.26917 − 2.63292I 0
u = 0.671783 + 0.586083I
a = 0.914349 + 0.610791I
b = 0.058421 + 0.261763I
2.58045 − 2.08956I 0
u = 0.671783 − 0.586083I
a = 0.914349 − 0.610791I
b = 0.058421 − 0.261763I
2.58045 + 2.08956I 0
u = 0.526379 + 0.975572I
a = −1.44051 − 0.75191I
b = −0.763585 + 0.052468I
−2.74009 + 4.79051I 0
u = 0.526379 − 0.975572I
a = −1.44051 + 0.75191I
b = −0.763585 − 0.052468I
−2.74009 − 4.79051I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.074483 + 0.887023I
a = −2.35571 + 0.01736I
b = −0.392699 − 0.616020I
−4.11297 − 0.07058I 0
u = −0.074483 − 0.887023I
a = −2.35571 − 0.01736I
b = −0.392699 + 0.616020I
−4.11297 + 0.07058I 0
u = −0.580548 + 0.957210I
a = 0.925621 − 1.041840I
b = 1.55006 − 0.19164I
1.01885 − 3.00871I 0
u = −0.580548 − 0.957210I
a = 0.925621 + 1.041840I
b = 1.55006 + 0.19164I
1.01885 + 3.00871I 0
u = −0.951027 + 0.599721I
a = −0.111890 − 0.437886I
b = −0.44750 + 1.44323I
6.25206 + 11.87070I 0
u = −0.951027 − 0.599721I
a = −0.111890 + 0.437886I
b = −0.44750 − 1.44323I
6.25206 − 11.87070I 0
u = 0.732135 + 0.860734I
a = 1.005030 + 0.992719I
b = 0.028028 − 1.366640I
6.12499 + 2.78185I 0
u = 0.732135 − 0.860734I
a = 1.005030 − 0.992719I
b = 0.028028 + 1.366640I
6.12499 − 2.78185I 0
u = 0.958234 + 0.600549I
a = 0.123572 + 0.356908I
b = −0.42032 − 1.41277I
7.78536 − 3.65950I 0
u = 0.958234 − 0.600549I
a = 0.123572 − 0.356908I
b = −0.42032 + 1.41277I
7.78536 + 3.65950I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.005510 + 0.537423I
a = 0.122451 + 0.343879I
b = 0.037827 − 1.272200I
7.14357 + 2.45971I 0
u = −1.005510 − 0.537423I
a = 0.122451 − 0.343879I
b = 0.037827 + 1.272200I
7.14357 − 2.45971I 0
u = 0.675420 + 0.918989I
a = −2.18182 − 0.37521I
b = −0.61045 + 1.43716I
6.09111 + 8.73034I 0
u = 0.675420 − 0.918989I
a = −2.18182 + 0.37521I
b = −0.61045 − 1.43716I
6.09111 − 8.73034I 0
u = 0.712836 + 0.893503I
a = 1.53261 + 0.58456I
b = 0.091292 − 1.304300I
6.00363 + 2.90156I 0
u = 0.712836 − 0.893503I
a = 1.53261 − 0.58456I
b = 0.091292 + 1.304300I
6.00363 − 2.90156I 0
u = −0.345824 + 1.101660I
a = 1.141930 + 0.185898I
b = 0.603382 + 0.869419I
−0.62322 − 2.44856I 0
u = −0.345824 − 1.101660I
a = 1.141930 − 0.185898I
b = 0.603382 − 0.869419I
−0.62322 + 2.44856I 0
u = −0.000285 + 1.159920I
a = 1.54808 + 0.18416I
b = 1.026390 − 0.109768I
−5.00871 − 4.94387I 0
u = −0.000285 − 1.159920I
a = 1.54808 − 0.18416I
b = 1.026390 + 0.109768I
−5.00871 + 4.94387I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655266 + 0.957538I
a = −0.769510 + 0.926165I
b = −0.787945 + 0.438625I
−0.56730 − 4.67706I 0
u = −0.655266 − 0.957538I
a = −0.769510 − 0.926165I
b = −0.787945 − 0.438625I
−0.56730 + 4.67706I 0
u = −0.666004 + 0.953204I
a = 0.087492 + 0.245071I
b = −0.114983 + 0.471358I
0.27532 − 2.65301I 0
u = −0.666004 − 0.953204I
a = 0.087492 − 0.245071I
b = −0.114983 − 0.471358I
0.27532 + 2.65301I 0
u = 1.154050 + 0.229156I
a = −0.085538 − 0.424689I
b = −0.257221 + 1.181700I
4.11766 + 6.08651I 0
u = 1.154050 − 0.229156I
a = −0.085538 + 0.424689I
b = −0.257221 − 1.181700I
4.11766 − 6.08651I 0
u = −0.187919 + 1.179450I
a = −0.23806 + 1.49296I
b = −0.192572 + 1.202220I
−1.19365 + 1.54765I 0
u = −0.187919 − 1.179450I
a = −0.23806 − 1.49296I
b = −0.192572 − 1.202220I
−1.19365 − 1.54765I 0
u = −0.326338 + 0.736385I
a = 0.78017 + 1.23125I
b = −0.18957 + 1.50632I
1.27718 − 1.12906I 0. + 8.56512I
u = −0.326338 − 0.736385I
a = 0.78017 − 1.23125I
b = −0.18957 − 1.50632I
1.27718 + 1.12906I 0. − 8.56512I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626927 + 1.026070I
a = −0.887439 + 0.291449I
b = −0.219156 + 0.031541I
1.27843 + 7.16623I 0
u = 0.626927 − 1.026070I
a = −0.887439 − 0.291449I
b = −0.219156 − 0.031541I
1.27843 − 7.16623I 0
u = −0.596735 + 1.047630I
a = −2.34499 − 0.11082I
b = −0.335532 − 1.314630I
1.55735 − 8.77630I 0
u = −0.596735 − 1.047630I
a = −2.34499 + 0.11082I
b = −0.335532 + 1.314630I
1.55735 + 8.77630I 0
u = 0.685534 + 1.022400I
a = −2.16852 − 0.27137I
b = −0.393570 + 1.109630I
1.56372 + 9.12407I 0
u = 0.685534 − 1.022400I
a = −2.16852 + 0.27137I
b = −0.393570 − 1.109630I
1.56372 − 9.12407I 0
u = −0.047677 + 0.756229I
a = −0.42309 − 3.09688I
b = −0.395353 − 1.035110I
2.25517 − 5.11870I −2.20140 + 6.13323I
u = −0.047677 − 0.756229I
a = −0.42309 + 3.09688I
b = −0.395353 + 1.035110I
2.25517 + 5.11870I −2.20140 − 6.13323I
u = 0.655731 + 1.063820I
a = 1.22402 + 0.83471I
b = 1.224470 − 0.281109I
−0.78035 + 12.02030I 0
u = 0.655731 − 1.063820I
a = 1.22402 − 0.83471I
b = 1.224470 + 0.281109I
−0.78035 − 12.02030I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.182172 + 1.261940I
a = 1.121570 − 0.834834I
b = 0.488375 − 1.242020I
−1.47238 + 10.24950I 0
u = 0.182172 − 1.261940I
a = 1.121570 + 0.834834I
b = 0.488375 + 1.242020I
−1.47238 − 10.24950I 0
u = −0.603887 + 1.145810I
a = 0.953355 − 0.243039I
b = 0.591619 + 0.772499I
−0.76570 − 2.63619I 0
u = −0.603887 − 1.145810I
a = 0.953355 + 0.243039I
b = 0.591619 − 0.772499I
−0.76570 + 2.63619I 0
u = 0.737805 + 1.096790I
a = 1.67408 + 0.29049I
b = 0.52519 − 1.47427I
6.23852 + 9.84950I 0
u = 0.737805 − 1.096790I
a = 1.67408 − 0.29049I
b = 0.52519 + 1.47427I
6.23852 − 9.84950I 0
u = −0.735857 + 1.101580I
a = 1.89050 − 0.32118I
b = 0.50557 + 1.47563I
4.6871 − 18.0471I 0
u = −0.735857 − 1.101580I
a = 1.89050 + 0.32118I
b = 0.50557 − 1.47563I
4.6871 + 18.0471I 0
u = −0.566930 + 0.359574I
a = 0.754801 − 0.127800I
b = −0.023311 + 1.049270I
1.32685 − 1.54158I 1.03113 + 4.33342I
u = −0.566930 − 0.359574I
a = 0.754801 + 0.127800I
b = −0.023311 − 1.049270I
1.32685 + 1.54158I 1.03113 − 4.33342I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.890802 + 0.990398I
a = −0.817185 − 0.696866I
b = −0.056817 + 1.121290I
2.07734 + 3.40281I 0
u = 0.890802 − 0.990398I
a = −0.817185 + 0.696866I
b = −0.056817 − 1.121290I
2.07734 − 3.40281I 0
u = −0.348886 + 0.562301I
a = 1.195460 + 0.536521I
b = 0.247153 − 1.340050I
3.26202 + 4.12377I −3.82614 − 3.00808I
u = −0.348886 − 0.562301I
a = 1.195460 − 0.536521I
b = 0.247153 + 1.340050I
3.26202 − 4.12377I −3.82614 + 3.00808I
u = −0.558579 + 0.339705I
a = 0.768407 + 0.240717I
b = 0.256866 − 1.331450I
3.25748 + 4.05422I −1.13185 − 3.03795I
u = −0.558579 − 0.339705I
a = 0.768407 − 0.240717I
b = 0.256866 + 1.331450I
3.25748 − 4.05422I −1.13185 + 3.03795I
u = −0.734623 + 1.141250I
a = −1.44177 − 0.07493I
b = −0.148209 − 1.261650I
5.26894 − 8.76068I 0
u = −0.734623 − 1.141250I
a = −1.44177 + 0.07493I
b = −0.148209 + 1.261650I
5.26894 + 8.76068I 0
u = 0.191973 + 1.387140I
a = −0.263972 + 0.619990I
b = 0.106090 + 1.007680I
−0.794911 − 0.333244I 0
u = 0.191973 − 1.387140I
a = −0.263972 − 0.619990I
b = 0.106090 − 1.007680I
−0.794911 + 0.333244I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.372193 + 0.319512I
a = 0.998264 + 0.064184I
b = 0.607494 + 0.135159I
−1.35478 − 0.87382I −4.52639 + 1.86312I
u = 0.372193 − 0.319512I
a = 0.998264 − 0.064184I
b = 0.607494 − 0.135159I
−1.35478 + 0.87382I −4.52639 − 1.86312I
u = −0.331512 + 0.359265I
a = 1.78673 + 1.36730I
b = −0.620713 + 0.798404I
1.80205 − 1.10971I 0.93812 − 3.27932I
u = −0.331512 − 0.359265I
a = 1.78673 − 1.36730I
b = −0.620713 − 0.798404I
1.80205 + 1.10971I 0.93812 + 3.27932I
14
II.
I
u
2
= hu
13
+ u
12
+ · · · + b + 2, 2u
11
+ u
10
+ · · · + a + 2u, u
14
+ u
13
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
9
=
−2u
11
− u
10
− 6u
9
− 3u
8
− 10u
7
− 6u
6
− 11u
5
− 6u
4
− 5u
3
− u
2
− 2u
−u
13
− u
12
+ ··· − 3u − 2
a
7
=
u
13
+ 3u
11
− u
10
+ 5u
9
− 2u
8
+ 5u
7
− 4u
6
+ u
5
− 5u
4
− u
3
− 2u
2
− 2u − 1
−u
13
− u
12
+ ··· − u − 2
a
10
=
u
13
+ u
12
+ ··· + u + 2
−u
13
− u
12
+ ··· − 3u − 2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
4
=
−u
11
− 2u
10
+ ··· − 5u − 3
2u
13
+ 3u
12
+ ··· + 5u + 3
a
8
=
−u
13
− u
12
+ ··· − u
2
− 2u
−u
13
− u
12
+ ··· − 3u − 2
a
11
=
−u
12
+ u
11
+ ··· + 3u + 1
−u
11
− u
10
+ ··· − 2u − 1
a
11
=
−u
12
+ u
11
+ ··· + 3u + 1
−u
11
− u
10
+ ··· − 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
12u
12
+18u
11
+51u
10
+68u
9
+109u
8
+136u
7
+159u
6
+172u
5
+138u
4
+106u
3
+58u
2
+22u+3
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− u
13
+ ··· − 2u + 1
c
2
u
14
+ 7u
13
+ ··· + 4u + 1
c
3
u
14
− 2u
13
+ ··· + 2u + 1
c
4
u
14
− 2u
13
+ ··· + 4u + 1
c
5
u
14
+ u
13
+ ··· + 2u + 1
c
6
u
14
− 6u
13
+ ··· − 5u + 1
c
7
u
14
+ u
12
+ ··· + 4u + 1
c
8
u
14
+ 2u
13
+ ··· − 4u + 1
c
9
u
14
+ 2u
13
+ ··· − 4u + 1
c
10
u
14
− u
13
+ ··· + 6u + 1
c
11
u
14
+ 2u
13
+ ··· − 3u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
14
+ 7y
13
+ ··· + 4y + 1
c
2
y
14
+ 3y
13
+ ··· + 8y + 1
c
3
y
14
+ 14y
12
+ ··· + 4y + 1
c
4
, c
9
y
14
+ 8y
13
+ ··· + 8y + 1
c
6
y
14
+ 10y
13
+ ··· + 21y + 1
c
7
y
14
+ 2y
13
+ ··· + 8y + 1
c
8
y
14
− 6y
13
+ ··· − 2y + 1
c
10
y
14
+ 3y
13
+ ··· + 6y + 1
c
11
y
14
+ 4y
13
+ ··· − 9y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.218324 + 0.879322I
a = −1.96027 − 0.46467I
b = −0.162661 + 0.485719I
−3.70335 + 0.96919I −0.59112 − 6.46740I
u = 0.218324 − 0.879322I
a = −1.96027 + 0.46467I
b = −0.162661 − 0.485719I
−3.70335 − 0.96919I −0.59112 + 6.46740I
u = 0.473825 + 0.725334I
a = 0.01391 + 2.38263I
b = 1.60251 + 0.99512I
1.64938 + 1.47694I −29.7777 − 30.0683I
u = 0.473825 − 0.725334I
a = 0.01391 − 2.38263I
b = 1.60251 − 0.99512I
1.64938 − 1.47694I −29.7777 + 30.0683I
u = −0.595922 + 0.607204I
a = 0.945335 − 0.267349I
b = 0.302919 − 1.239800I
4.21333 + 4.10072I 5.58747 − 4.56335I
u = −0.595922 − 0.607204I
a = 0.945335 + 0.267349I
b = 0.302919 + 1.239800I
4.21333 − 4.10072I 5.58747 + 4.56335I
u = −0.629454 + 1.045370I
a = −2.09610 − 0.26908I
b = −0.349529 − 1.173940I
2.82526 − 9.05252I 3.02000 + 9.52611I
u = −0.629454 − 1.045370I
a = −2.09610 + 0.26908I
b = −0.349529 + 1.173940I
2.82526 + 9.05252I 3.02000 − 9.52611I
u = −0.667304 + 0.401977I
a = −0.431520 − 0.984997I
b = 0.192104 + 1.232700I
4.15226 − 5.01003I 2.89129 + 5.27661I
u = −0.667304 − 0.401977I
a = −0.431520 + 0.984997I
b = 0.192104 − 1.232700I
4.15226 + 5.01003I 2.89129 − 5.27661I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.741847 + 1.006640I
a = −0.577773 − 0.533636I
b = −0.366793 + 0.275377I
−0.27543 + 3.16621I −5.01739 − 7.56548I
u = 0.741847 − 1.006640I
a = −0.577773 + 0.533636I
b = −0.366793 − 0.275377I
−0.27543 − 3.16621I −5.01739 + 7.56548I
u = −0.041315 + 1.259020I
a = −0.393580 + 1.006660I
b = −0.218548 + 1.136130I
−0.636777 + 1.162530I 0.38748 − 2.64720I
u = −0.041315 − 1.259020I
a = −0.393580 − 1.006660I
b = −0.218548 − 1.136130I
−0.636777 − 1.162530I 0.38748 + 2.64720I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
− u
13
+ ··· − 2u + 1)(u
94
+ 18u
92
+ ··· − 86u + 19)
c
2
(u
14
+ 7u
13
+ ··· + 4u + 1)(u
94
+ 36u
93
+ ··· + 8108u + 361)
c
3
(u
14
− 2u
13
+ ··· + 2u + 1)(u
94
+ 5u
93
+ ··· + 88u + 11)
c
4
(u
14
− 2u
13
+ ··· + 4u + 1)(u
94
− u
93
+ ··· − 724u + 59)
c
5
(u
14
+ u
13
+ ··· + 2u + 1)(u
94
+ 18u
92
+ ··· − 86u + 19)
c
6
(u
14
− 6u
13
+ ··· − 5u + 1)(u
94
+ u
93
+ ··· + 33u + 781)
c
7
(u
14
+ u
12
+ ··· + 4u + 1)(u
94
+ 3u
93
+ ··· − 872u + 184)
c
8
(u
14
+ 2u
13
+ ··· − 4u + 1)(u
94
− u
93
+ ··· + 6u + 1)
c
9
(u
14
+ 2u
13
+ ··· − 4u + 1)(u
94
− u
93
+ ··· − 724u + 59)
c
10
(u
14
− u
13
+ ··· + 6u + 1)(u
94
− 2u
93
+ ··· − 22u + 1)
c
11
(u
14
+ 2u
13
+ ··· − 3u + 1)(u
94
− 3u
93
+ ··· + 519u + 19)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
14
+ 7y
13
+ ··· + 4y + 1)(y
94
+ 36y
93
+ ··· + 8108y + 361)
c
2
(y
14
+ 3y
13
+ ··· + 8y + 1)(y
94
+ 48y
93
+ ··· + 1.32356 × 10
7
y + 130321)
c
3
(y
14
+ 14y
12
+ ··· + 4y + 1)(y
94
+ 9y
93
+ ··· + 7084y + 121)
c
4
, c
9
(y
14
+ 8y
13
+ ··· + 8y + 1)(y
94
+ 69y
93
+ ··· − 23148y + 3481)
c
6
(y
14
+ 10y
13
+ ··· + 21y + 1)
· (y
94
+ 27y
93
+ ··· + 20468921y + 609961)
c
7
(y
14
+ 2y
13
+ ··· + 8y + 1)(y
94
+ 23y
93
+ ··· + 1507232y + 33856)
c
8
(y
14
− 6y
13
+ ··· − 2y + 1)(y
94
− 5y
93
+ ··· − 10y + 1)
c
10
(y
14
+ 3y
13
+ ··· + 6y + 1)(y
94
+ 8y
93
+ ··· − 18y + 1)
c
11
(y
14
+ 4y
13
+ ··· − 9y + 1)(y
94
− 15y
93
+ ··· − 72597y + 361)
21
