12a
0227
(K12a
0227
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 1 5 12 4 8 10
Solving Sequence
9,12
10
1,5
4 8 7 3 11 6 2
c
9
c
12
c
4
c
8
c
7
c
3
c
11
c
5
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.95039 × 10
487
u
126
+ 2.56995 × 10
488
u
125
+ ··· + 6.32406 × 10
487
b − 1.63483 × 10
490
,
− 5.75750 × 10
488
u
126
− 1.83682 × 10
490
u
125
+ ··· + 3.65530 × 10
490
a + 4.29408 × 10
492
,
u
127
+ 6u
126
+ ··· − 4456u − 289i
I
u
2
= h408a
4
+ 322a
3
+ 13a
2
+ 29b − 150a − 27, 17a
5
+ 12a
4
− 4a
3
− 7a
2
+ 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 132 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
= h4.95 × 10
487
u
126
+ 2.57 × 10
488
u
125
+ · · · + 6.32 × 10
487
b − 1.63 ×
10
490
, −5.76 × 10
488
u
126
− 1.84 × 10
490
u
125
+ · · · + 3.66 × 10
490
a + 4.29 ×
10
492
, u
127
+ 6u
126
+ · · · − 4456u − 289i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
−u
3
+ u
a
5
=
0.0157511u
126
+ 0.502508u
125
+ ··· − 1625.76u − 117.475
−0.782788u
126
− 4.06377u
125
+ ··· + 3675.88u + 258.509
a
4
=
−0.767037u
126
− 3.56126u
125
+ ··· + 2050.12u + 141.034
−0.782788u
126
− 4.06377u
125
+ ··· + 3675.88u + 258.509
a
8
=
0.325046u
126
+ 1.66964u
125
+ ··· − 1469.09u − 101.084
1.48773u
126
+ 7.64401u
125
+ ··· − 6389.62u − 439.447
a
7
=
1.43965u
126
+ 7.65363u
125
+ ··· − 7403.82u − 515.811
0.627650u
126
+ 3.35407u
125
+ ··· − 3268.21u − 228.073
a
3
=
0.0752549u
126
+ 0.493597u
125
+ ··· − 467.578u − 21.8549
−0.323000u
126
− 1.55448u
125
+ ··· + 1076.67u + 75.5079
a
11
=
0.0868161u
126
+ 0.553087u
125
+ ··· − 871.738u − 62.8207
−0.326280u
126
− 1.32698u
125
+ ··· − 51.1311u − 12.2547
a
6
=
0.597942u
126
+ 3.24568u
125
+ ··· − 3738.93u − 252.966
−0.343979u
126
− 1.59473u
125
+ ··· + 745.172u + 49.8287
a
2
=
−0.447356u
126
− 1.94031u
125
+ ··· − 444.375u − 31.5491
−0.913367u
126
− 5.14785u
125
+ ··· + 6295.33u + 447.308
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.841205u
126
− 6.08545u
125
+ ··· + 12477.0u + 905.235
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
127
+ 60u
126
+ ··· + 2u − 1
c
2
, c
6
u
127
− 2u
126
+ ··· − u
2
+ 1
c
3
u
127
+ 2u
126
+ ··· + 87846u + 10961
c
4
, c
8
u
127
+ 2u
126
+ ··· + 4u + 1
c
5
u
127
+ u
126
+ ··· + 134368u + 9248
c
7
u
127
− 10u
126
+ ··· − 28635552u + 3955392
c
9
, c
12
u
127
− 6u
126
+ ··· − 4456u + 289
c
10
17(17u
127
+ 219u
126
+ ··· + 1318123u + 177763)
c
11
17(17u
127
− 213u
126
+ ··· − 65771u + 7177)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
127
+ 16y
126
+ ··· + 14y −1
c
2
, c
6
y
127
+ 60y
126
+ ··· + 2y −1
c
3
y
127
− 28y
126
+ ··· + 6473657330y −120143521
c
4
, c
8
y
127
+ 68y
126
+ ··· + 2y −1
c
5
y
127
+ 33y
126
+ ··· + 1848564224y −85525504
c
7
y
127
+ 36y
126
+ ··· − 534622349001600y −15645125873664
c
9
, c
12
y
127
− 72y
126
+ ··· + 7252068y −83521
c
10
289(289y
127
− 11547y
126
+ ··· − 3.38566 × 10
11
y −3.15997 × 10
10
)
c
11
289(289y
127
+ 25283y
126
+ ··· − 3.86260 × 10
9
y −5.15093 × 10
7
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.852701 + 0.540301I
a = −1.34277 − 0.93308I
b = −0.609646 + 1.164040I
5.72289 + 3.58734I 0
u = −0.852701 − 0.540301I
a = −1.34277 + 0.93308I
b = −0.609646 − 1.164040I
5.72289 − 3.58734I 0
u = −1.014830 + 0.102099I
a = −0.405389 − 0.081079I
b = −1.41236 − 0.38918I
−7.60578 − 4.18983I 0
u = −1.014830 − 0.102099I
a = −0.405389 + 0.081079I
b = −1.41236 + 0.38918I
−7.60578 + 4.18983I 0
u = −0.879964 + 0.429525I
a = −0.122431 − 0.894058I
b = 0.32988 + 1.45127I
2.31409 + 8.20324I 0
u = −0.879964 − 0.429525I
a = −0.122431 + 0.894058I
b = 0.32988 − 1.45127I
2.31409 − 8.20324I 0
u = 0.145194 + 0.964926I
a = 0.20478 + 1.71176I
b = −0.333801 − 1.133100I
−0.42685 − 6.05740I 0
u = 0.145194 − 0.964926I
a = 0.20478 − 1.71176I
b = −0.333801 + 1.133100I
−0.42685 + 6.05740I 0
u = 0.966417 + 0.023996I
a = −6.60150 + 0.91190I
b = −0.071131 − 0.985873I
−1.82223 − 0.98089I 0
u = 0.966417 − 0.023996I
a = −6.60150 − 0.91190I
b = −0.071131 + 0.985873I
−1.82223 + 0.98089I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.026420 + 0.175064I
a = 0.374744 + 0.152595I
b = 1.268490 + 0.333071I
−4.30492 + 0.43151I 0
u = −1.026420 − 0.175064I
a = 0.374744 − 0.152595I
b = 1.268490 − 0.333071I
−4.30492 − 0.43151I 0
u = 0.896921 + 0.533977I
a = 0.294430 − 0.441663I
b = −0.424264 + 0.189155I
−2.29093 + 3.74594I 0
u = 0.896921 − 0.533977I
a = 0.294430 + 0.441663I
b = −0.424264 − 0.189155I
−2.29093 − 3.74594I 0
u = −0.609834 + 0.717118I
a = −0.339685 − 1.133880I
b = 0.323059 + 1.314320I
5.29418 − 3.85660I 0
u = −0.609834 − 0.717118I
a = −0.339685 + 1.133880I
b = 0.323059 − 1.314320I
5.29418 + 3.85660I 0
u = −0.817941 + 0.452259I
a = 0.179258 + 0.897431I
b = −0.31067 − 1.42866I
4.69061 + 3.13207I 0
u = −0.817941 − 0.452259I
a = 0.179258 − 0.897431I
b = −0.31067 + 1.42866I
4.69061 − 3.13207I 0
u = −0.911216 + 0.575095I
a = 1.27057 + 1.00453I
b = 0.604539 − 1.190270I
4.39753 + 8.75064I 0
u = −0.911216 − 0.575095I
a = 1.27057 − 1.00453I
b = 0.604539 + 1.190270I
4.39753 − 8.75064I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.668794 + 0.850025I
a = −0.29873 + 1.74665I
b = −0.326607 − 1.027610I
−0.091432 + 0.584746I 0
u = 0.668794 − 0.850025I
a = −0.29873 − 1.74665I
b = −0.326607 + 1.027610I
−0.091432 − 0.584746I 0
u = −0.679771 + 0.609705I
a = 0.309119 + 1.029780I
b = −0.310849 − 1.350500I
6.23156 + 0.94338I 0
u = −0.679771 − 0.609705I
a = 0.309119 − 1.029780I
b = −0.310849 + 1.350500I
6.23156 − 0.94338I 0
u = −0.838598 + 0.355662I
a = 1.253440 + 0.620849I
b = 0.697957 − 1.121430I
−0.19206 + 2.87859I 0
u = −0.838598 − 0.355662I
a = 1.253440 − 0.620849I
b = 0.697957 + 1.121430I
−0.19206 − 2.87859I 0
u = 0.905744 + 0.042812I
a = −4.35368 − 4.03692I
b = −0.098574 + 1.035330I
0.22852 − 5.78675I 0
u = 0.905744 − 0.042812I
a = −4.35368 + 4.03692I
b = −0.098574 − 1.035330I
0.22852 + 5.78675I 0
u = 1.020750 + 0.410520I
a = −0.229262 + 0.389474I
b = 0.362254 − 0.230244I
−0.531400 − 0.664928I 0
u = 1.020750 − 0.410520I
a = −0.229262 − 0.389474I
b = 0.362254 + 0.230244I
−0.531400 + 0.664928I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.874294 + 0.018592I
a = 3.98628 + 3.44373I
b = 0.112976 − 1.026810I
2.20337 − 0.95953I 0
u = 0.874294 − 0.018592I
a = 3.98628 − 3.44373I
b = 0.112976 + 1.026810I
2.20337 + 0.95953I 0
u = −1.029780 + 0.468480I
a = 0.225034 + 0.332957I
b = 1.045950 + 0.219050I
0.012322 + 0.568494I 0
u = −1.029780 − 0.468480I
a = 0.225034 − 0.332957I
b = 1.045950 − 0.219050I
0.012322 − 0.568494I 0
u = −1.124280 + 0.180795I
a = −0.294506 − 0.129350I
b = −1.261790 − 0.205517I
−8.09446 + 4.49424I 0
u = −1.124280 − 0.180795I
a = −0.294506 + 0.129350I
b = −1.261790 + 0.205517I
−8.09446 − 4.49424I 0
u = −0.717437 + 0.463098I
a = −1.55187 − 0.74544I
b = −0.607863 + 1.091750I
4.97586 + 0.74438I 0
u = −0.717437 − 0.463098I
a = −1.55187 + 0.74544I
b = −0.607863 − 1.091750I
4.97586 − 0.74438I 0
u = −0.029470 + 0.837233I
a = −0.217734 + 0.748893I
b = 0.652250 + 0.043201I
0.53107 − 8.60738I 0
u = −0.029470 − 0.837233I
a = −0.217734 − 0.748893I
b = 0.652250 − 0.043201I
0.53107 + 8.60738I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.408417 + 1.106130I
a = −0.253561 − 1.380940I
b = 0.377568 + 1.233580I
5.96486 − 0.16558I 0
u = −0.408417 − 1.106130I
a = −0.253561 + 1.380940I
b = 0.377568 − 1.233580I
5.96486 + 0.16558I 0
u = −0.755531 + 0.316294I
a = −0.194572 − 0.752235I
b = 0.24174 + 1.46206I
0.096131 + 0.260592I 0
u = −0.755531 − 0.316294I
a = −0.194572 + 0.752235I
b = 0.24174 − 1.46206I
0.096131 − 0.260592I 0
u = −1.101670 + 0.487832I
a = −0.188407 − 0.304665I
b = −1.059130 − 0.185882I
0.86608 + 5.64943I 0
u = −1.101670 − 0.487832I
a = −0.188407 + 0.304665I
b = −1.059130 + 0.185882I
0.86608 − 5.64943I 0
u = −0.648207 + 0.444177I
a = 1.69452 + 0.67956I
b = 0.589917 − 1.058670I
2.97420 − 4.45774I 0
u = −0.648207 − 0.444177I
a = 1.69452 − 0.67956I
b = 0.589917 + 1.058670I
2.97420 + 4.45774I 0
u = −0.353742 + 1.162250I
a = 0.23638 + 1.40821I
b = −0.383655 − 1.220840I
7.21684 − 5.07057I 0
u = −0.353742 − 1.162250I
a = 0.23638 − 1.40821I
b = −0.383655 + 1.220840I
7.21684 + 5.07057I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.070426 + 0.781275I
a = 0.200965 − 0.782956I
b = −0.648612 − 0.067576I
2.60757 − 3.58583I 0
u = −0.070426 − 0.781275I
a = 0.200965 + 0.782956I
b = −0.648612 + 0.067576I
2.60757 + 3.58583I 0
u = −0.183040 + 1.202740I
a = −0.21628 − 1.47407I
b = 0.382764 + 1.190200I
1.56779 − 5.07438I 0
u = −0.183040 − 1.202740I
a = −0.21628 + 1.47407I
b = 0.382764 − 1.190200I
1.56779 + 5.07438I 0
u = 1.209210 + 0.230205I
a = −0.872059 + 0.432961I
b = −0.197040 − 0.810735I
−1.06593 − 1.10261I 0
u = 1.209210 − 0.230205I
a = −0.872059 − 0.432961I
b = −0.197040 + 0.810735I
−1.06593 + 1.10261I 0
u = 0.896049 + 0.853495I
a = 0.41426 − 1.53788I
b = 0.341377 + 0.982621I
1.31495 − 3.76899I 0
u = 0.896049 − 0.853495I
a = 0.41426 + 1.53788I
b = 0.341377 − 0.982621I
1.31495 + 3.76899I 0
u = 0.560206 + 0.515752I
a = 0.451441 − 0.515159I
b = −0.458401 + 0.075256I
−3.32415 − 2.87892I 0
u = 0.560206 − 0.515752I
a = 0.451441 + 0.515159I
b = −0.458401 − 0.075256I
−3.32415 + 2.87892I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.751197 + 0.024211I
a = 2.79279 − 3.22065I
b = 0.152354 + 1.028160I
2.52127 − 0.93793I 0
u = 0.751197 − 0.024211I
a = 2.79279 + 3.22065I
b = 0.152354 − 1.028160I
2.52127 + 0.93793I 0
u = −1.201760 + 0.399307I
a = −0.847325 − 0.984650I
b = −0.65214 + 1.30518I
−4.26341 + 2.69423I 0
u = −1.201760 − 0.399307I
a = −0.847325 + 0.984650I
b = −0.65214 − 1.30518I
−4.26341 − 2.69423I 0
u = −0.028343 + 0.729196I
a = −0.54338 − 1.72726I
b = 0.283010 + 1.170220I
2.32539 − 2.52729I 0
u = −0.028343 − 0.729196I
a = −0.54338 + 1.72726I
b = 0.283010 − 1.170220I
2.32539 + 2.52729I 0
u = −1.211370 + 0.427564I
a = 0.169366 + 0.237297I
b = 1.101290 + 0.152960I
−5.61618 + 5.48676I 0
u = −1.211370 − 0.427564I
a = 0.169366 − 0.237297I
b = 1.101290 − 0.152960I
−5.61618 − 5.48676I 0
u = −0.353933 + 0.620488I
a = 0.041314 + 0.841105I
b = 0.706967 + 0.191328I
1.87141 + 3.67539I 0
u = −0.353933 − 0.620488I
a = 0.041314 − 0.841105I
b = 0.706967 − 0.191328I
1.87141 − 3.67539I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.271409 + 1.257460I
a = 0.20297 + 1.43887I
b = −0.395164 − 1.202670I
6.24468 − 7.44634I 0
u = −0.271409 − 1.257460I
a = 0.20297 − 1.43887I
b = −0.395164 + 1.202670I
6.24468 + 7.44634I 0
u = −1.198690 + 0.467402I
a = 0.897126 + 1.037910I
b = 0.63347 − 1.29188I
−1.03817 + 6.95015I 0
u = −1.198690 − 0.467402I
a = 0.897126 − 1.037910I
b = 0.63347 + 1.29188I
−1.03817 − 6.95015I 0
u = −0.237781 + 0.665114I
a = 0.071797 − 0.855025I
b = −0.670987 − 0.146539I
3.30781 − 1.25100I 0
u = −0.237781 − 0.665114I
a = 0.071797 + 0.855025I
b = −0.670987 + 0.146539I
3.30781 + 1.25100I 0
u = −1.208050 + 0.491552I
a = −0.148140 − 0.263017I
b = −1.077310 − 0.146919I
−0.71550 + 8.27093I 0
u = −1.208050 − 0.491552I
a = −0.148140 + 0.263017I
b = −1.077310 + 0.146919I
−0.71550 − 8.27093I 0
u = −0.252316 + 1.296670I
a = −0.18984 − 1.44321I
b = 0.400598 + 1.198070I
4.09272 − 12.51100I 0
u = −0.252316 − 1.296670I
a = −0.18984 + 1.44321I
b = 0.400598 − 1.198070I
4.09272 + 12.51100I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083628 + 0.673445I
a = −0.322639 + 0.808199I
b = 0.580249 + 0.049725I
−1.95208 − 1.41580I 0
u = 0.083628 − 0.673445I
a = −0.322639 − 0.808199I
b = 0.580249 − 0.049725I
−1.95208 + 1.41580I 0
u = 1.260780 + 0.407052I
a = −0.128975 + 0.444802I
b = 0.366914 − 0.346876I
−1.11053 − 2.13759I 0
u = 1.260780 − 0.407052I
a = −0.128975 − 0.444802I
b = 0.366914 + 0.346876I
−1.11053 + 2.13759I 0
u = −1.238570 + 0.498015I
a = 0.135097 + 0.254706I
b = 1.078830 + 0.136046I
−3.03620 + 13.45980I 0
u = −1.238570 − 0.498015I
a = 0.135097 − 0.254706I
b = 1.078830 − 0.136046I
−3.03620 − 13.45980I 0
u = 0.651572 + 0.009687I
a = −2.39930 + 3.54321I
b = −0.167469 − 1.039610I
0.80850 − 5.62228I −8.00000 + 6.14117I
u = 0.651572 − 0.009687I
a = −2.39930 − 3.54321I
b = −0.167469 + 1.039610I
0.80850 + 5.62228I −8.00000 − 6.14117I
u = −1.265070 + 0.472844I
a = −0.848771 − 1.083270I
b = −0.62201 + 1.30751I
−4.55047 + 10.90910I 0
u = −1.265070 − 0.472844I
a = −0.848771 + 1.083270I
b = −0.62201 − 1.30751I
−4.55047 − 10.90910I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.210730 + 0.659204I
a = 0.98061 + 1.20435I
b = 0.585204 − 1.278490I
3.36662 + 6.40956I 0
u = −1.210730 − 0.659204I
a = 0.98061 − 1.20435I
b = 0.585204 + 1.278490I
3.36662 − 6.40956I 0
u = 1.342020 + 0.379840I
a = −0.583833 + 0.781666I
b = −0.290946 − 0.805939I
−1.11970 − 1.03596I 0
u = 1.342020 − 0.379840I
a = −0.583833 − 0.781666I
b = −0.290946 + 0.805939I
−1.11970 + 1.03596I 0
u = 1.326160 + 0.441251I
a = 0.120414 − 0.474901I
b = −0.391107 + 0.370722I
−3.25281 − 6.89189I 0
u = 1.326160 − 0.441251I
a = 0.120414 + 0.474901I
b = −0.391107 − 0.370722I
−3.25281 + 6.89189I 0
u = 1.368300 + 0.296535I
a = 0.055203 − 0.452326I
b = −0.336674 + 0.419621I
−5.07869 + 0.30171I 0
u = 1.368300 − 0.296535I
a = 0.055203 + 0.452326I
b = −0.336674 − 0.419621I
−5.07869 − 0.30171I 0
u = −1.25122 + 0.66759I
a = −0.95105 − 1.22530I
b = −0.581822 + 1.286560I
4.32872 + 11.49530I 0
u = −1.25122 − 0.66759I
a = −0.95105 + 1.22530I
b = −0.581822 − 1.286560I
4.32872 − 11.49530I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.08470 + 0.93222I
a = 0.36108 − 1.37118I
b = 0.373143 + 0.953420I
0.41231 − 5.47477I 0
u = 1.08470 − 0.93222I
a = 0.36108 + 1.37118I
b = 0.373143 − 0.953420I
0.41231 + 5.47477I 0
u = 1.18333 + 0.84536I
a = −0.409604 + 1.282880I
b = −0.367940 − 0.925587I
−3.80312 − 2.99685I 0
u = 1.18333 − 0.84536I
a = −0.409604 − 1.282880I
b = −0.367940 + 0.925587I
−3.80312 + 2.99685I 0
u = −1.31677 + 0.62741I
a = 0.88756 + 1.21991I
b = 0.58569 − 1.30127I
−2.01313 + 11.43770I 0
u = −1.31677 − 0.62741I
a = 0.88756 − 1.21991I
b = 0.58569 + 1.30127I
−2.01313 − 11.43770I 0
u = −1.31563 + 0.66936I
a = −0.90391 − 1.24906I
b = −0.57835 + 1.29849I
2.8882 + 14.1361I 0
u = −1.31563 − 0.66936I
a = −0.90391 + 1.24906I
b = −0.57835 − 1.29849I
2.8882 − 14.1361I 0
u = 1.34735 + 0.60684I
a = 0.486164 − 1.038140I
b = 0.345625 + 0.856806I
−4.52009 − 3.74465I 0
u = 1.34735 − 0.60684I
a = 0.486164 + 1.038140I
b = 0.345625 − 0.856806I
−4.52009 + 3.74465I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13202 + 0.97300I
a = −0.329075 + 1.341660I
b = −0.385231 − 0.949157I
−1.77596 − 10.33220I 0
u = 1.13202 − 0.97300I
a = −0.329075 − 1.341660I
b = −0.385231 + 0.949157I
−1.77596 + 10.33220I 0
u = −1.33535 + 0.67326I
a = 0.89154 + 1.25860I
b = 0.57662 − 1.30165I
0.6061 + 19.3205I 0
u = −1.33535 − 0.67326I
a = 0.89154 − 1.25860I
b = 0.57662 + 1.30165I
0.6061 − 19.3205I 0
u = 1.49643 + 0.06250I
a = 0.110195 + 0.495314I
b = 0.307955 − 0.568239I
−5.26758 − 0.53968I 0
u = 1.49643 − 0.06250I
a = 0.110195 − 0.495314I
b = 0.307955 + 0.568239I
−5.26758 + 0.53968I 0
u = 1.49949 + 0.08387I
a = −0.234880 + 0.536039I
b = −0.298438 − 0.648883I
−1.50701 − 2.01147I 0
u = 1.49949 − 0.08387I
a = −0.234880 − 0.536039I
b = −0.298438 + 0.648883I
−1.50701 + 2.01147I 0
u = 1.46135 + 0.46595I
a = 0.430521 − 0.869662I
b = 0.342924 + 0.802331I
−3.23960 + 3.37368I 0
u = 1.46135 − 0.46595I
a = 0.430521 + 0.869662I
b = 0.342924 − 0.802331I
−3.23960 − 3.37368I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57282 + 0.05672I
a = 0.181839 − 0.580581I
b = 0.334663 + 0.635570I
−3.66947 − 6.64198I 0
u = 1.57282 − 0.05672I
a = 0.181839 + 0.580581I
b = 0.334663 − 0.635570I
−3.66947 + 6.64198I 0
u = 0.419987
a = −0.913065
b = 0.365399
−0.823929 −11.9850
u = 0.183609 + 0.274430I
a = 1.08021 + 3.79951I
b = −0.184938 − 1.093960I
−0.476819 + 0.646119I −8.74335 − 1.28978I
u = 0.183609 − 0.274430I
a = 1.08021 − 3.79951I
b = −0.184938 + 1.093960I
−0.476819 − 0.646119I −8.74335 + 1.28978I
u = −0.148078 + 0.052331I
a = 0.65547 + 3.28320I
b = 0.245977 + 0.464218I
−0.52571 − 1.47397I −4.82957 + 4.26305I
u = −0.148078 − 0.052331I
a = 0.65547 − 3.28320I
b = 0.245977 − 0.464218I
−0.52571 + 1.47397I −4.82957 − 4.26305I
17
II.
I
u
2
= h408a
4
+322 a
3
+13 a
2
+29 b−150a−27, 17a
5
+12 a
4
−4a
3
−7a
2
+1 , u−1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
1
a
10
=
1
1
a
1
=
−1
0
a
5
=
a
−14.0690a
4
− 11.1034a
3
+ ··· + 5.17241a + 0.931034
a
4
=
−14.0690a
4
− 11.1034a
3
+ ··· + 6.17241a + 0.931034
−14.0690a
4
− 11.1034a
3
+ ··· + 5.17241a + 0.931034
a
8
=
1.17241a
4
+ 3.75862a
3
+ ··· − 0.931034a + 0.172414
15.8276a
4
+ 25.2414a
3
+ ··· − 6.06897a − 4.17241
a
7
=
17a
4
+ 29a
3
+ 8a
2
− 7a − 4
15.8276a
4
+ 25.2414a
3
+ ··· − 6.06897a − 4.17241
a
3
=
42.7931a
4
+ 43.6897a
3
+ ··· − 9.48276a − 4.20690
42.7931a
4
+ 43.6897a
3
+ ··· − 11.4828a − 4.20690
a
11
=
1.17241a
4
+ 3.75862a
3
+ ··· − 0.931034a + 0.172414
1.17241a
4
+ 3.75862a
3
+ ··· − 0.931034a + 0.172414
a
6
=
a
−14.0690a
4
− 11.1034a
3
+ ··· + 5.17241a + 0.931034
a
2
=
57.4483a
4
+ 65.1724a
3
+ ··· − 13.6207a − 6.55172
84.4138a
4
+ 100.621a
3
+ ··· − 22.0345a − 10.5862
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
13685
29
a
4
−
17497
29
a
3
−
4867
29
a
2
+
3893
29
a +
1743
29
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
4
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
u
5
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
u
5
+ 5u
4
+ 8u
3
+ 3u
2
− u + 1
c
8
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
9
(u − 1)
5
c
10
17(17u
5
− 12u
4
− 4u
3
+ 7u
2
− 1)
c
11
17(17u
5
+ 54u
4
+ 67u
3
+ 38u
2
+ 10u + 1)
c
12
(u + 1)
5
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
6
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
, c
4
, c
8
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
5
y
5
c
7
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1
c
9
, c
12
(y −1)
5
c
10
289(289y
5
− 280y
4
+ 184y
3
− 73y
2
+ 14y −1)
c
11
289(289y
5
− 638y
4
+ 725y
3
− 212y
2
+ 24y −1)
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.580925 + 0.443398I
b = −0.309916 + 0.549911I
−1.97403 + 1.53058I −14.0920 − 3.7761I
u = 1.00000
a = −0.580925 − 0.443398I
b = −0.309916 − 0.549911I
−1.97403 − 1.53058I −14.0920 + 3.7761I
u = 1.00000
a = −0.490453
b = −1.21774
−4.04602 −2.23020
u = 1.00000
a = 0.473210 + 0.025337I
b = 1.41878 − 0.21917I
−7.51750 + 4.40083I −0.4849 − 15.9362I
u = 1.00000
a = 0.473210 − 0.025337I
b = 1.41878 + 0.21917I
−7.51750 − 4.40083I −0.4849 + 15.9362I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
127
+ 60u
126
+ ··· + 2u − 1)
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
127
− 2u
126
+ ··· − u
2
+ 1)
c
3
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
127
+ 2u
126
+ ··· + 87846u + 10961)
c
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
127
+ 2u
126
+ ··· + 4u + 1)
c
5
u
5
(u
127
+ u
126
+ ··· + 134368u + 9248)
c
6
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
127
− 2u
126
+ ··· − u
2
+ 1)
c
7
(u
5
+ 5u
4
+ 8u
3
+ 3u
2
− u + 1)
· (u
127
− 10u
126
+ ··· − 28635552u + 3955392)
c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
127
+ 2u
126
+ ··· + 4u + 1)
c
9
((u − 1)
5
)(u
127
− 6u
126
+ ··· − 4456u + 289)
c
10
289(17u
5
− 12u
4
− 4u
3
+ 7u
2
− 1)
· (17u
127
+ 219u
126
+ ··· + 1318123u + 177763)
c
11
289(17u
5
+ 54u
4
+ 67u
3
+ 38u
2
+ 10u + 1)
· (17u
127
− 213u
126
+ ··· − 65771u + 7177)
c
12
((u + 1)
5
)(u
127
− 6u
126
+ ··· − 4456u + 289)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
127
+ 16y
126
+ ··· + 14y −1)
c
2
, c
6
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
127
+ 60y
126
+ ··· + 2y −1)
c
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
127
− 28y
126
+ ··· + 6473657330y −120143521)
c
4
, c
8
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
127
+ 68y
126
+ ··· + 2y −1)
c
5
y
5
(y
127
+ 33y
126
+ ··· + 1.84856 × 10
9
y −8.55255 × 10
7
)
c
7
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1)
· (y
127
+ 36y
126
+ ··· − 534622349001600y −15645125873664)
c
9
, c
12
((y −1)
5
)(y
127
− 72y
126
+ ··· + 7252068y −83521)
c
10
83521(289y
5
− 280y
4
+ 184y
3
− 73y
2
+ 14y −1)
· (289y
127
− 11547y
126
+ ··· − 338566196047y −31599684169)
c
11
83521(289y
5
− 638y
4
+ 725y
3
− 212y
2
+ 24y −1)
· (289y
127
+ 25283y
126
+ ··· − 3862601461y −51509329)
23
