12n
0646
(K12n
0646
)
A knot diagram
1
Linearized knot diagam
3 8 11 12 8 10 2 4 3 6 9 5
Solving Sequence
4,12
5
1,9
8 6 11 3 2 7 10
c
4
c
12
c
8
c
5
c
11
c
3
c
2
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.58803 × 10
237
u
73
+ 9.98357 × 10
236
u
72
+ ··· + 1.04871 × 10
239
b − 4.84351 × 10
239
,
2.36054 × 10
238
u
73
+ 1.15336 × 10
239
u
72
+ ··· + 6.18737 × 10
240
a + 6.07876 × 10
241
,
u
74
− 23u
72
+ ··· − 1348u + 59i
I
u
2
= h10945u
22
+ 124117u
21
+ ··· + 323513b − 770040,
− 1292813u
22
− 1139926u
21
+ ··· + 2264591a − 1752915, u
23
+ u
22
+ ··· + 6u + 7i
* 2 irreducible components of dim
C
= 0, with total 97 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
= h1.59 × 10
237
u
73
+ 9.98 × 10
236
u
72
+ · · · + 1.05 × 10
239
b − 4.84 ×
10
239
, 2.36 × 10
238
u
73
+ 1.15 × 10
239
u
72
+ · · · + 6.19 × 10
240
a + 6.08 ×
10
241
, u
74
− 23u
72
+ · · · − 1348u + 59i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
9
=
−0.00381509u
73
− 0.0186406u
72
+ ··· + 143.928u − 9.82446
−0.0151427u
73
− 0.00951988u
72
+ ··· − 57.5931u + 4.61855
a
8
=
0.0113276u
73
− 0.00912068u
72
+ ··· + 201.521u − 14.4430
−0.0151427u
73
− 0.00951988u
72
+ ··· − 57.5931u + 4.61855
a
6
=
0.0317970u
73
+ 0.0254113u
72
+ ··· + 41.9592u − 9.10400
−0.0151377u
73
− 0.0157835u
72
+ ··· + 8.09941u − 0.430016
a
11
=
−0.0232878u
73
− 0.0230889u
72
+ ··· + 5.49692u − 4.11660
0.0139050u
73
+ 0.00829155u
72
+ ··· + 29.1837u − 0.868546
a
3
=
−0.0319762u
73
− 0.0216255u
72
+ ··· − 71.9715u + 6.77566
0.0246533u
73
+ 0.0189372u
72
+ ··· + 32.4888u − 1.70516
a
2
=
0.0124870u
73
+ 0.0121558u
72
+ ··· + 18.8902u − 1.56877
−0.0138331u
73
− 0.0119768u
72
+ ··· − 19.0668u + 0.944486
a
7
=
−0.0344961u
73
− 0.0473584u
72
+ ··· + 140.483u − 11.9122
0.0110322u
73
+ 0.0116464u
72
+ ··· − 18.3283u + 2.94677
a
10
=
−0.0361091u
73
− 0.0518980u
72
+ ··· + 169.740u − 14.6086
0.0250197u
73
+ 0.0231141u
72
+ ··· − 2.04277u + 2.76319
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00383692u
73
+ 0.0116603u
72
+ ··· − 82.4847u + 0.241670
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 83u
73
+ ··· − 742961u + 32761
c
2
, c
7
u
74
+ u
73
+ ··· − 1071u + 181
c
3
u
74
+ 5u
73
+ ··· + 35u + 67
c
4
, c
12
u
74
− 23u
72
+ ··· − 1348u + 59
c
5
u
74
+ 12u
73
+ ··· + 241794036u + 20549479
c
6
, c
10
u
74
+ 9u
72
+ ··· + 14u + 1
c
8
u
74
− 3u
73
+ ··· + 9u − 1
c
9
u
74
− u
73
+ ··· + 5432040u − 294541
c
11
u
74
− u
73
+ ··· + 26u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
− 171y
73
+ ··· − 248386801315y + 1073283121
c
2
, c
7
y
74
− 83y
73
+ ··· + 742961y + 32761
c
3
y
74
− 23y
73
+ ··· − 170601y + 4489
c
4
, c
12
y
74
− 46y
73
+ ··· − 867912y + 3481
c
5
y
74
+ 72y
73
+ ··· + 4872087324166162y + 422281087171441
c
6
, c
10
y
74
+ 18y
73
+ ··· − 460y + 1
c
8
y
74
− 9y
73
+ ··· − 129y + 1
c
9
y
74
− 41y
73
+ ··· − 4467923151064y + 86754400681
c
11
y
74
+ 7y
73
+ ··· − 144y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655798 + 0.766408I
a = 0.869120 + 0.744224I
b = −1.35513 + 0.70847I
−8.29346 + 2.75368I 0
u = −0.655798 − 0.766408I
a = 0.869120 − 0.744224I
b = −1.35513 − 0.70847I
−8.29346 − 2.75368I 0
u = −0.965313 + 0.158931I
a = 0.972971 − 0.580114I
b = −0.574458 + 0.287498I
1.82145 − 4.11786I 0. + 8.23328I
u = −0.965313 − 0.158931I
a = 0.972971 + 0.580114I
b = −0.574458 − 0.287498I
1.82145 + 4.11786I 0. − 8.23328I
u = −0.915463 + 0.481248I
a = −1.301600 − 0.360841I
b = 1.42148 − 0.29716I
−7.16001 − 3.26958I 0
u = −0.915463 − 0.481248I
a = −1.301600 + 0.360841I
b = 1.42148 + 0.29716I
−7.16001 + 3.26958I 0
u = −0.846052 + 0.596785I
a = −0.148846 − 0.608636I
b = −1.10293 − 1.17110I
−7.32108 − 1.01128I 0
u = −0.846052 − 0.596785I
a = −0.148846 + 0.608636I
b = −1.10293 + 1.17110I
−7.32108 + 1.01128I 0
u = −0.964557 + 0.396965I
a = −0.392535 − 1.170080I
b = 1.22014 − 1.00039I
1.18006 − 5.95366I 0
u = −0.964557 − 0.396965I
a = −0.392535 + 1.170080I
b = 1.22014 + 1.00039I
1.18006 + 5.95366I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.985961 + 0.412954I
a = −2.13540 − 0.84349I
b = 0.367620 + 0.144013I
−5.83823 + 6.62476I 0
u = 0.985961 − 0.412954I
a = −2.13540 + 0.84349I
b = 0.367620 − 0.144013I
−5.83823 − 6.62476I 0
u = 0.774737 + 0.472773I
a = 0.78398 + 1.88499I
b = −0.437396 + 0.860845I
−6.51675 − 3.02533I −7.09255 + 5.00598I
u = 0.774737 − 0.472773I
a = 0.78398 − 1.88499I
b = −0.437396 − 0.860845I
−6.51675 + 3.02533I −7.09255 − 5.00598I
u = −0.894325
a = −1.14517
b = 0.120420
−0.954299 −9.82620
u = 0.021010 + 0.882929I
a = −0.855935 − 0.904683I
b = −0.535620 − 0.743252I
−2.26108 + 2.43230I −9.75705 − 2.77573I
u = 0.021010 − 0.882929I
a = −0.855935 + 0.904683I
b = −0.535620 + 0.743252I
−2.26108 − 2.43230I −9.75705 + 2.77573I
u = 0.753306 + 0.428451I
a = −0.01914 + 1.95753I
b = 0.815160 + 0.718326I
2.81045 + 5.61623I −4.20124 − 6.00638I
u = 0.753306 − 0.428451I
a = −0.01914 − 1.95753I
b = 0.815160 − 0.718326I
2.81045 − 5.61623I −4.20124 + 6.00638I
u = 0.845381 + 0.156772I
a = −0.179363 + 0.806483I
b = 0.937521 + 0.034650I
2.50679 + 0.22280I 1.160362 − 0.536343I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845381 − 0.156772I
a = −0.179363 − 0.806483I
b = 0.937521 − 0.034650I
2.50679 − 0.22280I 1.160362 + 0.536343I
u = −0.747820 + 0.348453I
a = 0.02740 − 1.73267I
b = 0.281766 − 0.913256I
−1.09279 − 2.96806I −12.4081 + 9.2557I
u = −0.747820 − 0.348453I
a = 0.02740 + 1.73267I
b = 0.281766 + 0.913256I
−1.09279 + 2.96806I −12.4081 − 9.2557I
u = 1.097690 + 0.464463I
a = −0.09607 − 1.62484I
b = 0.098368 − 0.983912I
−6.21900 + 4.81585I 0
u = 1.097690 − 0.464463I
a = −0.09607 + 1.62484I
b = 0.098368 + 0.983912I
−6.21900 − 4.81585I 0
u = −1.049620 + 0.578940I
a = 0.147679 + 0.427039I
b = 0.92680 + 1.54482I
−7.02322 − 7.85025I 0
u = −1.049620 − 0.578940I
a = 0.147679 − 0.427039I
b = 0.92680 − 1.54482I
−7.02322 + 7.85025I 0
u = −1.202410 + 0.158541I
a = 0.089960 + 0.140257I
b = −0.784654 − 0.680195I
1.55515 + 3.70197I 0
u = −1.202410 − 0.158541I
a = 0.089960 − 0.140257I
b = −0.784654 + 0.680195I
1.55515 − 3.70197I 0
u = 0.771268 + 0.039152I
a = 0.981686 − 0.957054I
b = −1.49247 − 0.58340I
1.74698 + 0.32926I −1.62591 + 0.32056I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.771268 − 0.039152I
a = 0.981686 + 0.957054I
b = −1.49247 + 0.58340I
1.74698 − 0.32926I −1.62591 − 0.32056I
u = 0.919006 + 0.821173I
a = −0.192595 + 0.795743I
b = 1.17685 + 0.91692I
1.35546 + 3.43403I 0
u = 0.919006 − 0.821173I
a = −0.192595 − 0.795743I
b = 1.17685 − 0.91692I
1.35546 − 3.43403I 0
u = −1.243770 + 0.270809I
a = 0.596369 + 1.181910I
b = −0.997710 + 0.666984I
6.67491 − 4.74644I 0
u = −1.243770 − 0.270809I
a = 0.596369 − 1.181910I
b = −0.997710 − 0.666984I
6.67491 + 4.74644I 0
u = 0.470959 + 0.537045I
a = 2.62151 − 1.11038I
b = −0.046697 − 0.372483I
−8.14386 − 0.75783I −15.9338 − 3.9359I
u = 0.470959 − 0.537045I
a = 2.62151 + 1.11038I
b = −0.046697 + 0.372483I
−8.14386 + 0.75783I −15.9338 + 3.9359I
u = 1.282620 + 0.200693I
a = 0.554347 − 0.664419I
b = −1.40018 − 1.15063I
2.91081 + 4.20783I 0
u = 1.282620 − 0.200693I
a = 0.554347 + 0.664419I
b = −1.40018 + 1.15063I
2.91081 − 4.20783I 0
u = −1.298030 + 0.205140I
a = −0.432301 − 1.003540I
b = 1.09376 − 1.17630I
1.90861 − 6.12809I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.298030 − 0.205140I
a = −0.432301 + 1.003540I
b = 1.09376 + 1.17630I
1.90861 + 6.12809I 0
u = 1.312430 + 0.246619I
a = −0.159546 + 0.445122I
b = 0.847012 + 0.717184I
2.74861 + 1.42952I 0
u = 1.312430 − 0.246619I
a = −0.159546 − 0.445122I
b = 0.847012 − 0.717184I
2.74861 − 1.42952I 0
u = −0.328781 + 1.323690I
a = 0.348126 + 0.339963I
b = 0.525286 + 0.880984I
−1.14232 + 4.08189I 0
u = −0.328781 − 1.323690I
a = 0.348126 − 0.339963I
b = 0.525286 − 0.880984I
−1.14232 − 4.08189I 0
u = 0.396021 + 0.484207I
a = −0.478537 + 0.330222I
b = −0.14607 + 1.42484I
−1.06612 + 2.28791I −9.94456 − 3.29711I
u = 0.396021 − 0.484207I
a = −0.478537 − 0.330222I
b = −0.14607 − 1.42484I
−1.06612 − 2.28791I −9.94456 + 3.29711I
u = −0.378716 + 0.457118I
a = 1.64287 − 0.19150I
b = 0.780151 − 0.056187I
3.34314 + 2.04546I −1.45171 − 1.17441I
u = −0.378716 − 0.457118I
a = 1.64287 + 0.19150I
b = 0.780151 + 0.056187I
3.34314 − 2.04546I −1.45171 + 1.17441I
u = −1.23386 + 0.70848I
a = 0.298842 + 0.935259I
b = −1.27459 + 1.00051I
1.59205 − 10.86400I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.23386 − 0.70848I
a = 0.298842 − 0.935259I
b = −1.27459 − 1.00051I
1.59205 + 10.86400I 0
u = 1.39427 + 0.45022I
a = −0.240132 − 0.502315I
b = −0.452753 − 0.074158I
4.81856 − 1.48237I 0
u = 1.39427 − 0.45022I
a = −0.240132 + 0.502315I
b = −0.452753 + 0.074158I
4.81856 + 1.48237I 0
u = −1.47129
a = −0.811222
b = 0.288330
−1.54712 0
u = 1.43434 + 0.38897I
a = −0.540506 + 0.537467I
b = 1.36368 + 0.82268I
2.16075 + 2.17644I 0
u = 1.43434 − 0.38897I
a = −0.540506 − 0.537467I
b = 1.36368 − 0.82268I
2.16075 − 2.17644I 0
u = 0.11140 + 1.48650I
a = −0.446418 + 0.632857I
b = −0.726218 + 0.933179I
−10.06450 − 9.11027I 0
u = 0.11140 − 1.48650I
a = −0.446418 − 0.632857I
b = −0.726218 − 0.933179I
−10.06450 + 9.11027I 0
u = 1.27797 + 0.77796I
a = 0.054128 − 0.537788I
b = −0.661480 − 0.188312I
2.27044 + 3.86617I 0
u = 1.27797 − 0.77796I
a = 0.054128 + 0.537788I
b = −0.661480 + 0.188312I
2.27044 − 3.86617I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50265 + 1.41427I
a = 0.552978 − 0.455848I
b = 0.585875 − 0.772913I
−9.71632 − 1.35291I 0
u = 0.50265 − 1.41427I
a = 0.552978 + 0.455848I
b = 0.585875 + 0.772913I
−9.71632 + 1.35291I 0
u = 1.26097 + 0.83176I
a = 0.199374 − 1.092040I
b = −1.05828 − 1.03852I
−7.22130 + 8.96738I 0
u = 1.26097 − 0.83176I
a = 0.199374 + 1.092040I
b = −1.05828 + 1.03852I
−7.22130 − 8.96738I 0
u = −0.478233
a = −1.48533
b = −0.193213
−1.01756 −9.85560
u = 1.44910 + 0.71346I
a = −0.339147 + 0.994028I
b = 1.20794 + 1.04725I
−5.8720 + 16.6158I 0
u = 1.44910 − 0.71346I
a = −0.339147 − 0.994028I
b = 1.20794 − 1.04725I
−5.8720 − 16.6158I 0
u = −1.43999 + 0.91289I
a = 0.078936 − 0.637578I
b = 0.840470 − 0.448062I
−3.71000 − 8.50390I 0
u = −1.43999 − 0.91289I
a = 0.078936 + 0.637578I
b = 0.840470 + 0.448062I
−3.71000 + 8.50390I 0
u = −1.20485 + 1.21909I
a = −0.197169 + 0.455659I
b = −0.678604 + 0.449090I
−5.22524 − 0.83630I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20485 − 1.21909I
a = −0.197169 − 0.455659I
b = −0.678604 − 0.449090I
−5.22524 + 0.83630I 0
u = 0.0777028 + 0.0283731I
a = 2.71739 + 4.75753I
b = 0.447185 − 1.220730I
−0.88271 − 2.35880I −7.30268 − 2.94254I
u = 0.0777028 − 0.0283731I
a = 2.71739 − 4.75753I
b = 0.447185 + 1.220730I
−0.88271 + 2.35880I −7.30268 + 2.94254I
u = −2.48363
a = 0.0328074
b = 0.360820
−2.98919 0
12
II.
I
u
2
= h1.09 × 10
4
u
22
+ 1.24 × 10
5
u
21
+ · · · + 3.24 × 10
5
b − 7.70 × 10
5
, −1.29 ×
10
6
u
22
− 1.14 × 10
6
u
21
+ · · · + 2.26 × 10
6
a − 1.75 × 10
6
, u
23
+ u
22
+ · · · + 6u + 7i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
9
=
0.570881u
22
+ 0.503369u
21
+ ··· + 0.996580u + 0.774054
−0.0338317u
22
− 0.383654u
21
+ ··· + 4.19368u + 2.38024
a
8
=
0.604713u
22
+ 0.887023u
21
+ ··· − 3.19710u − 1.60619
−0.0338317u
22
− 0.383654u
21
+ ··· + 4.19368u + 2.38024
a
6
=
0.715072u
22
+ 1.60066u
21
+ ··· − 8.26166u − 0.692739
0.140643u
22
+ 0.0151895u
21
+ ··· + 3.15600u + 2.81671
a
11
=
−0.174507u
22
− 1.00570u
21
+ ··· + 6.80089u + 5.50371
0.444573u
22
+ 0.348014u
21
+ ··· − 3.73106u + 0.847542
a
3
=
−0.741805u
22
− 0.369258u
21
+ ··· − 2.84354u − 2.11154
0.00713109u
22
+ 0.988770u
21
+ ··· − 3.38884u − 3.70637
a
2
=
−1.32743u
22
− 0.253648u
21
+ ··· − 5.63410u − 1.62524
−0.143311u
22
+ 0.692522u
21
+ ··· − 1.19043u − 3.87800
a
7
=
−0.448108u
22
− 0.0775385u
21
+ ··· − 5.26590u − 2.41661
−0.00353927u
22
− 0.180382u
21
+ ··· + 5.47344u + 2.04846
a
10
=
−0.274671u
22
+ 0.497193u
21
+ ··· + 4.96111u − 2.93448
−0.0900397u
22
− 0.245724u
21
+ ··· + 1.23296u + 2.27996
(ii) Obstruction class = 1
(iii) Cusp Shapes =
116070
323513
u
22
−
673312
323513
u
21
+ ··· +
8778130
323513
u +
3192863
323513
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
23
− 22u
22
+ ··· + 13u − 1
c
2
u
23
− 11u
21
+ ··· + 3u − 1
c
3
u
23
− 5u
21
+ ··· − u + 1
c
4
u
23
+ u
22
+ ··· + 6u + 7
c
5
u
23
+ u
22
+ ··· − 214u − 19
c
6
u
23
+ u
22
+ ··· − 2u + 1
c
7
u
23
− 11u
21
+ ··· + 3u + 1
c
8
u
23
− 2u
21
+ ··· + 3u − 1
c
9
u
23
− 4u
21
+ ··· − 130u + 77
c
10
u
23
− u
22
+ ··· − 2u − 1
c
11
u
23
+ 4u
21
+ ··· + 2u − 1
c
12
u
23
− u
22
+ ··· + 6u − 7
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 30y
22
+ ··· − 39y −1
c
2
, c
7
y
23
− 22y
22
+ ··· + 13y −1
c
3
y
23
− 10y
22
+ ··· + 11y −1
c
4
, c
12
y
23
− 25y
22
+ ··· + 414y −49
c
5
y
23
+ 9y
22
+ ··· − 7860y −361
c
6
, c
10
y
23
+ 15y
22
+ ··· − 22y −1
c
8
y
23
− 4y
22
+ ··· + 31y −1
c
9
y
23
− 8y
22
+ ··· + 27526y −5929
c
11
y
23
+ 8y
22
+ ··· − 6y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.940151 + 0.436724I
a = 1.38542 − 1.03904I
b = −0.375096 − 0.652275I
−6.14502 − 6.06691I −7.76620 + 2.70001I
u = −0.940151 − 0.436724I
a = 1.38542 + 1.03904I
b = −0.375096 + 0.652275I
−6.14502 + 6.06691I −7.76620 − 2.70001I
u = −0.899734 + 0.566100I
a = 0.666138 − 0.686902I
b = 0.587866 + 0.237361I
3.26577 + 3.29082I 1.12702 − 5.35953I
u = −0.899734 − 0.566100I
a = 0.666138 + 0.686902I
b = 0.587866 − 0.237361I
3.26577 − 3.29082I 1.12702 + 5.35953I
u = 1.167050 + 0.232734I
a = −0.746928 + 1.034470I
b = 1.145920 + 0.467030I
5.42529 + 3.86107I 0.38428 − 3.23578I
u = 1.167050 − 0.232734I
a = −0.746928 − 1.034470I
b = 1.145920 − 0.467030I
5.42529 − 3.86107I 0.38428 + 3.23578I
u = −0.193140 + 0.771651I
a = −0.749439 − 0.320841I
b = −0.598832 − 0.904838I
−0.70593 + 3.60670I −4.29911 − 3.93608I
u = −0.193140 − 0.771651I
a = −0.749439 + 0.320841I
b = −0.598832 + 0.904838I
−0.70593 − 3.60670I −4.29911 + 3.93608I
u = −1.203350 + 0.187731I
a = 0.50630 + 1.32809I
b = −0.956631 + 0.862062I
4.95788 − 5.88075I −0.13221 + 5.80716I
u = −1.203350 − 0.187731I
a = 0.50630 − 1.32809I
b = −0.956631 − 0.862062I
4.95788 + 5.88075I −0.13221 − 5.80716I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.154040 + 0.447461I
a = −0.362840 − 0.500105I
b = −0.706629 − 0.294864I
4.63415 − 0.90682I 1.28962 − 4.52518I
u = 1.154040 − 0.447461I
a = −0.362840 + 0.500105I
b = −0.706629 + 0.294864I
4.63415 + 0.90682I 1.28962 + 4.52518I
u = −1.280170 + 0.173459I
a = −0.442367 − 0.893767I
b = 1.23555 − 1.29461I
2.71445 − 6.27245I 2.92402 + 8.05584I
u = −1.280170 − 0.173459I
a = −0.442367 + 0.893767I
b = 1.23555 + 1.29461I
2.71445 + 6.27245I 2.92402 − 8.05584I
u = 0.637930 + 0.249825I
a = −0.023201 − 1.259190I
b = −0.400551 − 1.237650I
−0.49072 + 2.75096I 2.90356 − 6.14599I
u = 0.637930 − 0.249825I
a = −0.023201 + 1.259190I
b = −0.400551 + 1.237650I
−0.49072 − 2.75096I 2.90356 + 6.14599I
u = −0.430937 + 0.491432I
a = −1.97377 − 0.90570I
b = 0.716053 + 0.206167I
−7.54393 + 1.02790I −3.87032 − 0.83091I
u = −0.430937 − 0.491432I
a = −1.97377 + 0.90570I
b = 0.716053 − 0.206167I
−7.54393 − 1.02790I −3.87032 + 0.83091I
u = 1.361540 + 0.157735I
a = −0.127050 + 0.265071I
b = 0.941423 + 0.657717I
3.28773 + 2.35398I 1.50757 − 4.79947I
u = 1.361540 − 0.157735I
a = −0.127050 − 0.265071I
b = 0.941423 − 0.657717I
3.28773 − 2.35398I 1.50757 + 4.79947I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307310 + 0.445348I
a = 0.501766 − 0.593735I
b = −1.48600 − 0.92539I
2.02704 + 2.55701I −2.41189 − 10.60905I
u = 1.307310 − 0.445348I
a = 0.501766 + 0.593735I
b = −1.48600 + 0.92539I
2.02704 − 2.55701I −2.41189 + 10.60905I
u = −2.36076
a = 0.160525
b = −0.206162
−3.11418 −34.3130
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 22u
22
+ ··· + 13u − 1)(u
74
+ 83u
73
+ ··· − 742961u + 32761)
c
2
(u
23
− 11u
21
+ ··· + 3u − 1)(u
74
+ u
73
+ ··· − 1071u + 181)
c
3
(u
23
− 5u
21
+ ··· − u + 1)(u
74
+ 5u
73
+ ··· + 35u + 67)
c
4
(u
23
+ u
22
+ ··· + 6u + 7)(u
74
− 23u
72
+ ··· − 1348u + 59)
c
5
(u
23
+ u
22
+ ··· − 214u − 19)
· (u
74
+ 12u
73
+ ··· + 241794036u + 20549479)
c
6
(u
23
+ u
22
+ ··· − 2u + 1)(u
74
+ 9u
72
+ ··· + 14u + 1)
c
7
(u
23
− 11u
21
+ ··· + 3u + 1)(u
74
+ u
73
+ ··· − 1071u + 181)
c
8
(u
23
− 2u
21
+ ··· + 3u − 1)(u
74
− 3u
73
+ ··· + 9u − 1)
c
9
(u
23
− 4u
21
+ ··· − 130u + 77)(u
74
− u
73
+ ··· + 5432040u − 294541)
c
10
(u
23
− u
22
+ ··· − 2u − 1)(u
74
+ 9u
72
+ ··· + 14u + 1)
c
11
(u
23
+ 4u
21
+ ··· + 2u − 1)(u
74
− u
73
+ ··· + 26u − 1)
c
12
(u
23
− u
22
+ ··· + 6u − 7)(u
74
− 23u
72
+ ··· − 1348u + 59)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
− 30y
22
+ ··· − 39y −1)
· (y
74
− 171y
73
+ ··· − 248386801315y + 1073283121)
c
2
, c
7
(y
23
− 22y
22
+ ··· + 13y −1)(y
74
− 83y
73
+ ··· + 742961y + 32761)
c
3
(y
23
− 10y
22
+ ··· + 11y −1)(y
74
− 23y
73
+ ··· − 170601y + 4489)
c
4
, c
12
(y
23
− 25y
22
+ ··· + 414y −49)(y
74
− 46y
73
+ ··· − 867912y + 3481)
c
5
(y
23
+ 9y
22
+ ··· − 7860y −361)
· (y
74
+ 72y
73
+ ··· + 4872087324166162y + 422281087171441)
c
6
, c
10
(y
23
+ 15y
22
+ ··· − 22y −1)(y
74
+ 18y
73
+ ··· − 460y + 1)
c
8
(y
23
− 4y
22
+ ··· + 31y −1)(y
74
− 9y
73
+ ··· − 129y + 1)
c
9
(y
23
− 8y
22
+ ··· + 27526y −5929)
· (y
74
− 41y
73
+ ··· − 4467923151064y + 86754400681)
c
11
(y
23
+ 8y
22
+ ··· − 6y −1)(y
74
+ 7y
73
+ ··· − 144y + 1)
22
