12a
0377
(K12a
0377
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 1 5 11 12 8 4 7
Solving Sequence
8,10
11
5,9
4 12 3 7 1 6 2
c
10
c
8
c
4
c
11
c
3
c
7
c
12
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3.60458 × 10
351
u
112
− 1.49802 × 10
352
u
111
+ ··· + 1.58423 × 10
352
b + 8.96032 × 10
351
,
3.98283 × 10
351
u
112
− 1.51474 × 10
352
u
111
+ ··· + 1.58423 × 10
352
a − 6.48283 × 10
352
, u
113
+ 2u
112
+ ··· + 5u + 1i
I
u
2
= hb + 1, a − 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 114 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
= h3.60 × 10
351
u
112
− 1.50 × 10
352
u
111
+ · · · + 1.58 × 10
352
b + 8.96 ×
10
351
, 3.98 × 10
351
u
112
− 1.51 × 10
352
u
111
+ · · · + 1.58 × 10
352
a − 6.48 ×
10
352
, u
113
+ 2u
112
+ · · · + 5u + 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
5
=
−0.251405u
112
+ 0.956139u
111
+ ··· − 51.3075u + 4.09211
−0.227529u
112
+ 0.945582u
111
+ ··· − 6.03599u − 0.565596
a
9
=
u
−u
3
+ u
a
4
=
−0.0238759u
112
+ 0.0105577u
111
+ ··· − 45.2715u + 4.65770
−0.227529u
112
+ 0.945582u
111
+ ··· − 6.03599u − 0.565596
a
12
=
3.74173u
112
+ 1.87309u
111
+ ··· + 31.7286u + 1.20630
−1.57162u
112
− 1.04502u
111
+ ··· − 6.80780u − 1.86865
a
3
=
−0.601635u
112
+ 0.284080u
111
+ ··· − 50.9813u + 3.32938
0.267924u
112
+ 1.62204u
111
+ ··· − 5.17838u − 0.464880
a
7
=
0.925335u
112
+ 0.0971187u
111
+ ··· + 20.9526u − 4.66114
−1.77138u
112
− 1.42443u
111
+ ··· − 3.14980u − 1.70177
a
1
=
−0.155973u
112
− 1.13087u
111
+ ··· + 31.7267u − 2.05511
0.479124u
112
+ 0.772006u
111
+ ··· − 0.580322u − 0.354009
a
6
=
−1.60565u
112
− 1.74713u
111
+ ··· + 15.2116u − 7.47774
−1.73965u
112
− 1.54559u
111
+ ··· − 1.04522u − 1.46991
a
2
=
0.273879u
112
− 0.0294619u
111
+ ··· + 5.15495u + 3.64220
1.52493u
112
+ 1.56504u
111
+ ··· + 1.07514u + 0.790347
(ii) Obstruction class = −1
(iii) Cusp Shapes = −9.37846u
112
− 6.07388u
111
+ ··· + 8.52876u − 10.5678
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
113
+ 60u
112
+ ··· + 5u + 1
c
2
, c
5
u
113
+ 2u
112
+ ··· − u + 1
c
3
u
113
+ 66u
111
+ ··· − 5294u + 11036
c
4
u
113
+ 2u
112
+ ··· + 779133u + 135659
c
6
, c
12
u
113
+ 3u
112
+ ··· + 1248u + 288
c
7
u
113
− 10u
112
+ ··· + 170569u + 7433
c
8
, c
10
u
113
+ 2u
112
+ ··· + 5u + 1
c
9
u
113
− 19u
112
+ ··· + 6u − 2
c
11
u
113
− 2u
112
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
113
− 12y
112
+ ··· + 73y −1
c
2
, c
5
y
113
− 60y
112
+ ··· + 5y −1
c
3
y
113
+ 132y
112
+ ··· − 7542338484y −121793296
c
4
y
113
+ 76y
112
+ ··· + 814063865689y −18403364281
c
6
, c
12
y
113
+ 81y
112
+ ··· + 2154816y −82944
c
7
y
113
+ 48y
112
+ ··· − 12384794263y −55249489
c
8
, c
10
y
113
− 80y
112
+ ··· + 201y −1
c
9
y
113
+ 9y
112
+ ··· − 64y −4
c
11
y
113
− 20y
112
+ ··· + 5y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628994 + 0.805074I
a = 0.469841 − 0.263890I
b = 0.283186 + 0.181705I
−2.56577 + 5.23147I 0
u = 0.628994 − 0.805074I
a = 0.469841 + 0.263890I
b = 0.283186 − 0.181705I
−2.56577 − 5.23147I 0
u = 0.325320 + 0.898186I
a = −0.556699 − 0.146988I
b = −0.544491 − 0.403405I
0.61481 + 1.65437I 0
u = 0.325320 − 0.898186I
a = −0.556699 + 0.146988I
b = −0.544491 + 0.403405I
0.61481 − 1.65437I 0
u = 0.943592 + 0.030818I
a = −0.522216 + 0.154103I
b = 0.68200 + 2.38604I
0.340243 + 0.243306I 0
u = 0.943592 − 0.030818I
a = −0.522216 − 0.154103I
b = 0.68200 − 2.38604I
0.340243 − 0.243306I 0
u = 1.057710 + 0.097573I
a = 0.579526 − 0.832827I
b = 0.11853 − 3.24830I
−2.42343 − 1.00273I 0
u = 1.057710 − 0.097573I
a = 0.579526 + 0.832827I
b = 0.11853 + 3.24830I
−2.42343 + 1.00273I 0
u = 0.465316 + 0.964816I
a = 0.665764 − 0.055613I
b = 0.544662 + 0.234872I
−2.10528 − 2.72389I 0
u = 0.465316 − 0.964816I
a = 0.665764 + 0.055613I
b = 0.544662 − 0.234872I
−2.10528 + 2.72389I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373895 + 0.843598I
a = −0.46944 − 1.35921I
b = −0.469024 − 1.043280I
−7.94586 + 5.17796I 0
u = −0.373895 − 0.843598I
a = −0.46944 + 1.35921I
b = −0.469024 + 1.043280I
−7.94586 − 5.17796I 0
u = −0.043363 + 0.920452I
a = 0.565594 + 0.784941I
b = 0.624966 + 0.748908I
−2.70032 + 3.74058I 0
u = −0.043363 − 0.920452I
a = 0.565594 − 0.784941I
b = 0.624966 − 0.748908I
−2.70032 − 3.74058I 0
u = 1.079330 + 0.075300I
a = −0.440245 + 0.926018I
b = −0.09491 + 3.38127I
1.38276 + 2.70786I 0
u = 1.079330 − 0.075300I
a = −0.440245 − 0.926018I
b = −0.09491 − 3.38127I
1.38276 − 2.70786I 0
u = −1.084540 + 0.070158I
a = 1.48569 − 0.82488I
b = −0.540270 − 0.042016I
0.203429 − 0.594606I 0
u = −1.084540 − 0.070158I
a = 1.48569 + 0.82488I
b = −0.540270 + 0.042016I
0.203429 + 0.594606I 0
u = 1.091440 + 0.016134I
a = −0.095452 + 0.960345I
b = −0.01184 + 3.51911I
3.80508 + 2.14831I 0
u = 1.091440 − 0.016134I
a = −0.095452 − 0.960345I
b = −0.01184 − 3.51911I
3.80508 − 2.14831I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.018950 + 0.404204I
a = −1.47062 − 0.80723I
b = 0.466320 − 0.706084I
−5.96540 − 0.84182I 0
u = −1.018950 − 0.404204I
a = −1.47062 + 0.80723I
b = 0.466320 + 0.706084I
−5.96540 + 0.84182I 0
u = 1.093210 + 0.088942I
a = 0.502305 − 1.010920I
b = 0.16728 − 3.39536I
−1.54854 + 7.37352I 0
u = 1.093210 − 0.088942I
a = 0.502305 + 1.010920I
b = 0.16728 + 3.39536I
−1.54854 − 7.37352I 0
u = 0.197625 + 1.091860I
a = −0.866578 − 0.364637I
b = −0.785843 − 0.477687I
2.22897 + 2.53204I 0
u = 0.197625 − 1.091860I
a = −0.866578 + 0.364637I
b = −0.785843 + 0.477687I
2.22897 − 2.53204I 0
u = −1.097280 + 0.189897I
a = −0.39958 − 1.74478I
b = 0.544175 − 0.702514I
−2.04635 − 1.56955I 0
u = −1.097280 − 0.189897I
a = −0.39958 + 1.74478I
b = 0.544175 + 0.702514I
−2.04635 + 1.56955I 0
u = −0.435334 + 0.770110I
a = −0.37253 − 1.46521I
b = −0.374521 − 1.062230I
−7.77300 − 3.54516I 0
u = −0.435334 − 0.770110I
a = −0.37253 + 1.46521I
b = −0.374521 + 1.062230I
−7.77300 + 3.54516I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.368978 + 0.774867I
a = 0.362705 + 1.366110I
b = 0.410428 + 1.008490I
−4.39067 + 0.89920I 0
u = −0.368978 − 0.774867I
a = 0.362705 − 1.366110I
b = 0.410428 − 1.008490I
−4.39067 − 0.89920I 0
u = −1.068650 + 0.407745I
a = 1.29200 + 0.78651I
b = −0.577199 + 0.719807I
−2.22585 − 5.28549I 0
u = −1.068650 − 0.407745I
a = 1.29200 − 0.78651I
b = −0.577199 − 0.719807I
−2.22585 + 5.28549I 0
u = 0.142388 + 1.145910I
a = 0.960435 + 0.457518I
b = 0.860997 + 0.532401I
1.88293 + 6.96291I 0
u = 0.142388 − 1.145910I
a = 0.960435 − 0.457518I
b = 0.860997 − 0.532401I
1.88293 − 6.96291I 0
u = −1.073490 + 0.450936I
a = −1.25020 − 0.93708I
b = 0.582668 − 0.819628I
−5.75547 − 9.90220I 0
u = −1.073490 − 0.450936I
a = −1.25020 + 0.93708I
b = 0.582668 + 0.819628I
−5.75547 + 9.90220I 0
u = 1.069790 + 0.462990I
a = −0.161941 + 0.433741I
b = 0.518943 − 0.112408I
1.40063 + 2.37957I 0
u = 1.069790 − 0.462990I
a = −0.161941 − 0.433741I
b = 0.518943 + 0.112408I
1.40063 − 2.37957I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.150660 + 0.187578I
a = 0.35704 + 1.62839I
b = −0.656035 + 0.699053I
2.32331 − 5.37707I 0
u = −1.150660 − 0.187578I
a = 0.35704 − 1.62839I
b = −0.656035 − 0.699053I
2.32331 + 5.37707I 0
u = −1.160570 + 0.216923I
a = −0.29068 − 1.64577I
b = 0.673011 − 0.761982I
−0.63504 − 10.38720I 0
u = −1.160570 − 0.216923I
a = −0.29068 + 1.64577I
b = 0.673011 + 0.761982I
−0.63504 + 10.38720I 0
u = −0.007650 + 1.182640I
a = −1.028660 − 0.719034I
b = −0.919799 − 0.715399I
−5.18160 + 3.86014I 0
u = −0.007650 − 1.182640I
a = −1.028660 + 0.719034I
b = −0.919799 + 0.715399I
−5.18160 − 3.86014I 0
u = 0.036372 + 1.198960I
a = 1.056530 + 0.640937I
b = 0.939210 + 0.658803I
−1.12840 + 7.66560I 0
u = 0.036372 − 1.198960I
a = 1.056530 − 0.640937I
b = 0.939210 − 0.658803I
−1.12840 − 7.66560I 0
u = −1.200230 + 0.083318I
a = 0.499588 + 1.306680I
b = −0.783855 + 0.468733I
5.81921 − 4.07245I 0
u = −1.200230 − 0.083318I
a = 0.499588 − 1.306680I
b = −0.783855 − 0.468733I
5.81921 + 4.07245I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.208560 + 0.027333I
a = −0.599859 − 1.105330I
b = 0.817363 − 0.334604I
6.34378 + 0.77670I 0
u = −1.208560 − 0.027333I
a = −0.599859 + 1.105330I
b = 0.817363 + 0.334604I
6.34378 − 0.77670I 0
u = −1.213050 + 0.095341I
a = −0.767196 + 0.574275I
b = 0.866219 + 0.032953I
4.98123 − 2.74814I 0
u = −1.213050 − 0.095341I
a = −0.767196 − 0.574275I
b = 0.866219 − 0.032953I
4.98123 + 2.74814I 0
u = 0.028775 + 1.228150I
a = −1.108380 − 0.653518I
b = −0.977482 − 0.667107I
−4.11564 + 12.48680I 0
u = 0.028775 − 1.228150I
a = −1.108380 + 0.653518I
b = −0.977482 + 0.667107I
−4.11564 − 12.48680I 0
u = 1.242600 + 0.045176I
a = −0.0276375 − 0.0507761I
b = −1.180830 + 0.038251I
2.42702 + 0.01183I 0
u = 1.242600 − 0.045176I
a = −0.0276375 + 0.0507761I
b = −1.180830 − 0.038251I
2.42702 − 0.01183I 0
u = −1.250790 + 0.154376I
a = 0.634697 − 0.293779I
b = −0.976609 + 0.100492I
2.91293 − 7.47396I 0
u = −1.250790 − 0.154376I
a = 0.634697 + 0.293779I
b = −0.976609 − 0.100492I
2.91293 + 7.47396I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.701259 + 0.144851I
a = 1.144400 + 0.459612I
b = 0.49489 − 1.53937I
−3.24230 + 2.05640I 0
u = 0.701259 − 0.144851I
a = 1.144400 − 0.459612I
b = 0.49489 + 1.53937I
−3.24230 − 2.05640I 0
u = 0.440662 + 0.462304I
a = −0.046408 + 0.267922I
b = −0.213264 − 0.552181I
0.42820 + 1.49790I 2.53334 − 4.59564I
u = 0.440662 − 0.462304I
a = −0.046408 − 0.267922I
b = −0.213264 + 0.552181I
0.42820 − 1.49790I 2.53334 + 4.59564I
u = 0.588990 + 0.202664I
a = 1.36583 + 0.83573I
b = 0.74578 − 1.28388I
−2.64087 − 6.22131I −0.76202 + 8.45882I
u = 0.588990 − 0.202664I
a = 1.36583 − 0.83573I
b = 0.74578 + 1.28388I
−2.64087 + 6.22131I −0.76202 − 8.45882I
u = −1.308970 + 0.458145I
a = 0.397768 + 0.885864I
b = −1.16408 + 0.85769I
1.29630 − 8.68434I 0
u = −1.308970 − 0.458145I
a = 0.397768 − 0.885864I
b = −1.16408 − 0.85769I
1.29630 + 8.68434I 0
u = 0.575385 + 0.107972I
a = −1.026690 − 0.880371I
b = −0.532572 + 1.184350I
0.30421 − 1.73030I 3.07892 + 4.83803I
u = 0.575385 − 0.107972I
a = −1.026690 + 0.880371I
b = −0.532572 − 1.184350I
0.30421 + 1.73030I 3.07892 − 4.83803I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36635 + 0.37132I
a = 0.197704 + 0.560028I
b = −1.31064 + 0.62747I
3.35454 − 1.59435I 0
u = −1.36635 − 0.37132I
a = 0.197704 − 0.560028I
b = −1.31064 − 0.62747I
3.35454 + 1.59435I 0
u = −1.36494 + 0.41142I
a = −0.199331 − 0.707642I
b = 1.31031 − 0.73341I
5.63063 − 6.27986I 0
u = −1.36494 − 0.41142I
a = −0.199331 + 0.707642I
b = 1.31031 + 0.73341I
5.63063 + 6.27986I 0
u = −1.39656 + 0.46863I
a = −0.078320 − 0.912668I
b = 1.39758 − 0.88545I
7.18518 − 7.94484I 0
u = −1.39656 − 0.46863I
a = −0.078320 + 0.912668I
b = 1.39758 + 0.88545I
7.18518 + 7.94484I 0
u = −1.37243 + 0.55193I
a = −0.156077 − 1.215360I
b = 1.32944 − 1.11206I
−0.87461 − 9.89086I 0
u = −1.37243 − 0.55193I
a = −0.156077 + 1.215360I
b = 1.32944 + 1.11206I
−0.87461 + 9.89086I 0
u = −1.40258 + 0.49611I
a = 0.053738 + 1.011370I
b = −1.41429 + 0.96029I
6.7272 − 12.6581I 0
u = −1.40258 − 0.49611I
a = 0.053738 − 1.011370I
b = −1.41429 − 0.96029I
6.7272 + 12.6581I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39217 + 0.54597I
a = 0.085947 + 1.191860I
b = −1.38418 + 1.09703I
3.37354 − 13.72260I 0
u = −1.39217 − 0.54597I
a = 0.085947 − 1.191860I
b = −1.38418 − 1.09703I
3.37354 + 13.72260I 0
u = −1.39844 + 0.55749I
a = −0.062272 − 1.232500I
b = 1.40081 − 1.12928I
0.3881 − 18.6695I 0
u = −1.39844 − 0.55749I
a = −0.062272 + 1.232500I
b = 1.40081 + 1.12928I
0.3881 + 18.6695I 0
u = 1.36071 + 0.70792I
a = 0.026718 − 0.771692I
b = −0.564595 − 0.480204I
−0.47080 + 1.40907I 0
u = 1.36071 − 0.70792I
a = 0.026718 + 0.771692I
b = −0.564595 + 0.480204I
−0.47080 − 1.40907I 0
u = −0.251377 + 0.353254I
a = −0.43444 + 1.56479I
b = 0.188310 + 0.768978I
−1.95709 − 0.92883I −7.24124 + 2.89402I
u = −0.251377 − 0.353254I
a = −0.43444 − 1.56479I
b = 0.188310 − 0.768978I
−1.95709 + 0.92883I −7.24124 − 2.89402I
u = 1.54035 + 0.32085I
a = 0.344109 + 0.409500I
b = 1.097320 + 0.240828I
0.21148 + 2.38742I 0
u = 1.54035 − 0.32085I
a = 0.344109 − 0.409500I
b = 1.097320 − 0.240828I
0.21148 − 2.38742I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42146 + 0.69310I
a = 0.046277 + 0.794068I
b = 0.649309 + 0.526292I
3.47790 + 5.04492I 0
u = 1.42146 − 0.69310I
a = 0.046277 − 0.794068I
b = 0.649309 − 0.526292I
3.47790 − 5.04492I 0
u = 1.43181 + 0.72769I
a = −0.035518 − 0.838342I
b = −0.625849 − 0.577051I
0.58758 + 9.79544I 0
u = 1.43181 − 0.72769I
a = −0.035518 + 0.838342I
b = −0.625849 + 0.577051I
0.58758 − 9.79544I 0
u = 1.49012 + 0.60003I
a = 0.176424 + 0.728302I
b = 0.818810 + 0.487302I
6.08390 + 4.22100I 0
u = 1.49012 − 0.60003I
a = 0.176424 − 0.728302I
b = 0.818810 − 0.487302I
6.08390 − 4.22100I 0
u = 1.55381 + 0.41726I
a = −0.332191 − 0.534509I
b = −1.042680 − 0.343807I
3.96178 − 1.10057I 0
u = 1.55381 − 0.41726I
a = −0.332191 + 0.534509I
b = −1.042680 + 0.343807I
3.96178 + 1.10057I 0
u = 1.51641 + 0.54311I
a = −0.235544 − 0.673866I
b = −0.899912 − 0.447513I
6.18256 − 0.22975I 0
u = 1.51641 − 0.54311I
a = −0.235544 + 0.673866I
b = −0.899912 + 0.447513I
6.18256 + 0.22975I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.008885 + 0.372670I
a = −3.14424 − 2.38230I
b = −0.970450 + 0.095132I
−3.90860 + 8.00126I −3.67874 − 4.22294I
u = 0.008885 − 0.372670I
a = −3.14424 + 2.38230I
b = −0.970450 − 0.095132I
−3.90860 − 8.00126I −3.67874 + 4.22294I
u = 1.60137 + 0.40534I
a = 0.397015 + 0.535555I
b = 1.100940 + 0.365544I
1.15325 − 5.74846I 0
u = 1.60137 − 0.40534I
a = 0.397015 − 0.535555I
b = 1.100940 − 0.365544I
1.15325 + 5.74846I 0
u = 0.274845 + 0.191918I
a = −1.44889 − 2.31072I
b = −0.777246 + 0.630363I
2.19844 − 1.34984I 4.07300 + 4.60487I
u = 0.274845 − 0.191918I
a = −1.44889 + 2.31072I
b = −0.777246 − 0.630363I
2.19844 + 1.34984I 4.07300 − 4.60487I
u = 0.014064 + 0.326696I
a = 3.16731 + 2.57181I
b = 0.902246 − 0.132703I
−0.87468 + 3.26263I −0.502379 − 1.300822I
u = 0.014064 − 0.326696I
a = 3.16731 − 2.57181I
b = 0.902246 + 0.132703I
−0.87468 − 3.26263I −0.502379 + 1.300822I
u = −0.055397 + 0.315273I
a = −3.48784 − 2.46576I
b = −0.843379 + 0.037852I
−4.79112 − 0.61003I −5.51607 + 2.01393I
u = −0.055397 − 0.315273I
a = −3.48784 + 2.46576I
b = −0.843379 − 0.037852I
−4.79112 + 0.61003I −5.51607 − 2.01393I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.175939 + 0.254021I
a = 2.14702 + 2.68542I
b = 0.859196 − 0.437395I
1.94875 + 2.87687I 2.57908 − 3.31245I
u = 0.175939 − 0.254021I
a = 2.14702 − 2.68542I
b = 0.859196 + 0.437395I
1.94875 − 2.87687I 2.57908 + 3.31245I
u = −0.0666513
a = 10.2674
b = 0.481876
−1.46742 −6.65250
16
II. I
u
2
= hb + 1, a − 1, u − 1i
(i) Arc colorings
a
8
=
0
1
a
10
=
1
0
a
11
=
1
−1
a
5
=
1
−1
a
9
=
1
0
a
4
=
2
−1
a
12
=
−1
0
a
3
=
1
−1
a
7
=
1
0
a
1
=
−1
0
a
6
=
1
0
a
2
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
10
, c
11
u − 1
c
5
, c
7
, c
8
u + 1
c
6
, c
9
, c
12
u
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
10
, c
11
y −1
c
6
, c
9
, c
12
y
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −1.00000
0 0
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
113
+ 60u
112
+ ··· + 5u + 1)
c
2
(u − 1)(u
113
+ 2u
112
+ ··· − u + 1)
c
3
(u − 1)(u
113
+ 66u
111
+ ··· − 5294u + 11036)
c
4
(u − 1)(u
113
+ 2u
112
+ ··· + 779133u + 135659)
c
5
(u + 1)(u
113
+ 2u
112
+ ··· − u + 1)
c
6
, c
12
u(u
113
+ 3u
112
+ ··· + 1248u + 288)
c
7
(u + 1)(u
113
− 10u
112
+ ··· + 170569u + 7433)
c
8
(u + 1)(u
113
+ 2u
112
+ ··· + 5u + 1)
c
9
u(u
113
− 19u
112
+ ··· + 6u − 2)
c
10
(u − 1)(u
113
+ 2u
112
+ ··· + 5u + 1)
c
11
(u − 1)(u
113
− 2u
112
+ ··· − u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
113
− 12y
112
+ ··· + 73y −1)
c
2
, c
5
(y −1)(y
113
− 60y
112
+ ··· + 5y −1)
c
3
(y −1)(y
113
+ 132y
112
+ ··· − 7.54234 × 10
9
y −1.21793 × 10
8
)
c
4
(y −1)(y
113
+ 76y
112
+ ··· + 8.14064 × 10
11
y −1.84034 × 10
10
)
c
6
, c
12
y(y
113
+ 81y
112
+ ··· + 2154816y −82944)
c
7
(y −1)(y
113
+ 48y
112
+ ··· − 1.23848 × 10
10
y −5.52495 × 10
7
)
c
8
, c
10
(y −1)(y
113
− 80y
112
+ ··· + 201y −1)
c
9
y(y
113
+ 9y
112
+ ··· − 64y −4)
c
11
(y −1)(y
113
− 20y
112
+ ··· + 5y −1)
22
