12a
0747
(K12a
0747
)
A knot diagram
1
Linearized knot diagam
3 8 10 9 11 12 2 5 1 7 6 4
Solving Sequence
5,11
6 12
7,9
4 1 8 10 3 2
c
5
c
11
c
6
c
4
c
12
c
8
c
10
c
3
c
2
c
1
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.65000 × 10
193
u
128
+ 2.34665 × 10
193
u
127
+ ··· + 7.02232 × 10
193
b + 2.48355 × 10
193
,
9.06725 × 10
193
u
128
− 2.07720 × 10
193
u
127
+ ··· + 7.02232 × 10
193
a − 8.70594 × 10
193
, u
129
+ u
128
+ ··· − 7u − 1i
I
u
2
= h−u
23
+ 11u
21
+ ··· + b − 1, −3u
23
+ 32u
21
+ ··· + a − 1, u
24
− 12u
22
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 153 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
= h2.65 × 10
193
u
128
+ 2.35 × 10
193
u
127
+ · · · + 7.02 × 10
193
b + 2.48 ×
10
193
, 9.07 × 10
193
u
128
− 2.08 × 10
193
u
127
+ · · · + 7.02 × 10
193
a − 8.71 ×
10
193
, u
129
+ u
128
+ · · · − 7u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−1.29120u
128
+ 0.295799u
127
+ ··· − 1.43860u + 1.23975
−0.377368u
128
− 0.334169u
127
+ ··· + 6.73997u − 0.353666
a
4
=
0.871040u
128
+ 0.866622u
127
+ ··· − 3.40452u + 4.53826
−0.636934u
128
− 0.772674u
127
+ ··· + 13.3430u + 3.37451
a
1
=
−1.41319u
128
− 1.35974u
127
+ ··· + 33.0349u + 4.89525
−0.339303u
128
− 0.689419u
127
+ ··· + 12.1122u + 0.840007
a
8
=
−1.66857u
128
− 0.0383699u
127
+ ··· + 5.30137u + 0.886086
−0.377368u
128
− 0.334169u
127
+ ··· + 6.73997u − 0.353666
a
10
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
1.45033u
128
+ 0.399931u
127
+ ··· − 5.09571u + 4.28260
−1.10470u
128
− 0.557067u
127
+ ··· + 15.0987u + 3.65637
a
2
=
0.478498u
128
+ 0.430788u
127
+ ··· + 3.50990u + 2.48438
0.0216946u
128
− 0.0576587u
127
+ ··· + 1.10851u + 1.82083
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.51289u
128
− 1.95504u
127
+ ··· + 86.3712u + 22.6515
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
129
+ 53u
128
+ ··· + 241100u + 10201
c
2
, c
7
u
129
+ u
128
+ ··· − 268u − 101
c
3
u
129
− 6u
127
+ ··· − 141u − 9
c
4
, c
8
u
129
+ 2u
128
+ ··· − 21685u − 15853
c
5
, c
6
, c
11
u
129
+ u
128
+ ··· − 7u − 1
c
9
u
129
− 7u
128
+ ··· + 31027u + 4567
c
10
u
129
− 3u
128
+ ··· + 22569u + 1491
c
12
u
129
+ 11u
128
+ ··· − 170u + 29
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
129
+ 59y
128
+ ··· + 6188411064y −104060401
c
2
, c
7
y
129
− 53y
128
+ ··· + 241100y −10201
c
3
y
129
− 12y
128
+ ··· + 369y −81
c
4
, c
8
y
129
+ 92y
128
+ ··· − 5214202691y −251317609
c
5
, c
6
, c
11
y
129
− 117y
128
+ ··· − 19y −1
c
9
y
129
− 37y
128
+ ··· + 3096724221y −20857489
c
10
y
129
+ 15y
128
+ ··· + 34052817y −2223081
c
12
y
129
− 17y
128
+ ··· + 61496y −841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.051970 + 0.993015I
a = 0.0380113 − 0.0039953I
b = 0.098904 + 0.986419I
−1.64979 − 2.02859I 0
u = 0.051970 − 0.993015I
a = 0.0380113 + 0.0039953I
b = 0.098904 − 0.986419I
−1.64979 + 2.02859I 0
u = 0.837971 + 0.567834I
a = 0.477899 + 0.591226I
b = −0.496140 − 1.298570I
3.24310 − 9.68057I 0
u = 0.837971 − 0.567834I
a = 0.477899 − 0.591226I
b = −0.496140 + 1.298570I
3.24310 + 9.68057I 0
u = 1.025480 + 0.237033I
a = −0.162210 + 1.010220I
b = −0.520771 − 1.046700I
−0.73696 − 2.43278I 0
u = 1.025480 − 0.237033I
a = −0.162210 − 1.010220I
b = −0.520771 + 1.046700I
−0.73696 + 2.43278I 0
u = −0.509412 + 0.784048I
a = 0.783191 − 0.998753I
b = 0.321116 + 0.820314I
−1.33885 − 5.56038I 0
u = −0.509412 − 0.784048I
a = 0.783191 + 0.998753I
b = 0.321116 − 0.820314I
−1.33885 + 5.56038I 0
u = 1.053430 + 0.175522I
a = −0.353167 − 0.153552I
b = 0.059796 − 1.051140I
3.69303 − 2.14193I 0
u = 1.053430 − 0.175522I
a = −0.353167 + 0.153552I
b = 0.059796 + 1.051140I
3.69303 + 2.14193I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.732149 + 0.526761I
a = −0.772088 − 1.096370I
b = −0.420090 + 0.967338I
0.11355 + 2.39050I 0
u = 0.732149 − 0.526761I
a = −0.772088 + 1.096370I
b = −0.420090 − 0.967338I
0.11355 − 2.39050I 0
u = −0.732811 + 0.525422I
a = −0.659964 + 0.737980I
b = 0.398953 − 1.261590I
4.91057 + 4.11692I 0
u = −0.732811 − 0.525422I
a = −0.659964 − 0.737980I
b = 0.398953 + 1.261590I
4.91057 − 4.11692I 0
u = 0.309866 + 0.831253I
a = 1.243500 + 0.568619I
b = 0.58944 − 1.35556I
1.5905 + 14.5341I 0
u = 0.309866 − 0.831253I
a = 1.243500 − 0.568619I
b = 0.58944 + 1.35556I
1.5905 − 14.5341I 0
u = 1.113440 + 0.093009I
a = −0.227047 + 0.880009I
b = 0.804580 − 0.313020I
1.64515 − 0.14115I 0
u = 1.113440 − 0.093009I
a = −0.227047 − 0.880009I
b = 0.804580 + 0.313020I
1.64515 + 0.14115I 0
u = −1.124460 + 0.151681I
a = 0.682863 + 0.052497I
b = −0.586833 + 1.072260I
4.88050 + 2.27576I 0
u = −1.124460 − 0.151681I
a = 0.682863 − 0.052497I
b = −0.586833 − 1.072260I
4.88050 − 2.27576I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.321690 + 0.772157I
a = −1.206270 + 0.699130I
b = −0.50767 − 1.34684I
3.55448 − 8.60382I 0
u = −0.321690 − 0.772157I
a = −1.206270 − 0.699130I
b = −0.50767 + 1.34684I
3.55448 + 8.60382I 0
u = −0.242794 + 0.796642I
a = 0.428709 − 0.858731I
b = 0.107481 + 0.811941I
−2.10827 + 0.88291I 0
u = −0.242794 − 0.796642I
a = 0.428709 + 0.858731I
b = 0.107481 − 0.811941I
−2.10827 − 0.88291I 0
u = 0.228527 + 0.798986I
a = 0.188913 − 0.123671I
b = 0.409325 + 0.670158I
−1.67570 + 2.20914I 0
u = 0.228527 − 0.798986I
a = 0.188913 + 0.123671I
b = 0.409325 − 0.670158I
−1.67570 − 2.20914I 0
u = −0.826691 + 0.041202I
a = −0.06131 + 1.44905I
b = −0.712028 − 0.154552I
−0.54483 + 4.69995I 0
u = −0.826691 − 0.041202I
a = −0.06131 − 1.44905I
b = −0.712028 + 0.154552I
−0.54483 − 4.69995I 0
u = −1.143590 + 0.286522I
a = −0.365462 + 0.654972I
b = −0.781152 − 0.421442I
−2.66439 − 2.38185I 0
u = −1.143590 − 0.286522I
a = −0.365462 − 0.654972I
b = −0.781152 + 0.421442I
−2.66439 + 2.38185I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.209850 + 0.231073I
a = −0.006204 − 1.069620I
b = 0.580455 + 0.696591I
2.68604 − 4.47896I 0
u = −1.209850 − 0.231073I
a = −0.006204 + 1.069620I
b = 0.580455 − 0.696591I
2.68604 + 4.47896I 0
u = −0.093034 + 0.753912I
a = 0.692986 − 0.562528I
b = 0.787377 − 0.323100I
−5.84209 − 1.43644I −6.45657 + 1.49198I
u = −0.093034 − 0.753912I
a = 0.692986 + 0.562528I
b = 0.787377 + 0.323100I
−5.84209 + 1.43644I −6.45657 − 1.49198I
u = −0.241534 + 0.709885I
a = 0.876196 − 0.390382I
b = 1.218590 − 0.100809I
−2.40215 − 8.26114I −0.87236 + 9.14716I
u = −0.241534 − 0.709885I
a = 0.876196 + 0.390382I
b = 1.218590 + 0.100809I
−2.40215 + 8.26114I −0.87236 − 9.14716I
u = 0.399018 + 0.623768I
a = −0.874191 − 0.740196I
b = −0.243009 + 0.990794I
0.71421 + 1.90496I 2.00000 − 4.65501I
u = 0.399018 − 0.623768I
a = −0.874191 + 0.740196I
b = −0.243009 − 0.990794I
0.71421 − 1.90496I 2.00000 + 4.65501I
u = 0.181659 + 0.706610I
a = 1.65849 + 0.89371I
b = 0.450536 − 1.148240I
−3.24329 + 6.01733I −2.16925 − 7.40566I
u = 0.181659 − 0.706610I
a = 1.65849 − 0.89371I
b = 0.450536 + 1.148240I
−3.24329 − 6.01733I −2.16925 + 7.40566I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.185623 + 0.701396I
a = 1.86550 − 0.58997I
b = 0.165893 − 1.071950I
1.21465 + 5.56964I 5.61858 − 8.19173I
u = 0.185623 − 0.701396I
a = 1.86550 + 0.58997I
b = 0.165893 + 1.071950I
1.21465 − 5.56964I 5.61858 + 8.19173I
u = 1.144770 + 0.562586I
a = −0.505538 − 0.793395I
b = −0.235197 + 1.068220I
1.70104 + 7.45697I 0
u = 1.144770 − 0.562586I
a = −0.505538 + 0.793395I
b = −0.235197 − 1.068220I
1.70104 − 7.45697I 0
u = 0.295679 + 0.651657I
a = −1.48088 − 0.06488I
b = −0.57041 + 1.38485I
2.72621 + 0.81441I 6.95955 − 1.10717I
u = 0.295679 − 0.651657I
a = −1.48088 + 0.06488I
b = −0.57041 − 1.38485I
2.72621 − 0.81441I 6.95955 + 1.10717I
u = −0.706698 + 0.009775I
a = −0.04253 + 1.54520I
b = −0.661366 − 0.064571I
−0.54610 + 4.70193I 0.76536 − 4.65762I
u = −0.706698 − 0.009775I
a = −0.04253 − 1.54520I
b = −0.661366 + 0.064571I
−0.54610 − 4.70193I 0.76536 + 4.65762I
u = −0.188008 + 0.672153I
a = 1.66160 + 0.13653I
b = 0.76344 + 1.31899I
2.30526 − 5.39595I 4.61743 + 7.91302I
u = −0.188008 − 0.672153I
a = 1.66160 − 0.13653I
b = 0.76344 − 1.31899I
2.30526 + 5.39595I 4.61743 − 7.91302I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31835
a = −0.682453
b = 0.815064
3.05905 0
u = 0.191951 + 0.647839I
a = −0.794070 − 0.291142I
b = −1.083280 + 0.054850I
−0.79396 + 3.05732I 0.59352 − 5.00231I
u = 0.191951 − 0.647839I
a = −0.794070 + 0.291142I
b = −1.083280 − 0.054850I
−0.79396 − 3.05732I 0.59352 + 5.00231I
u = 1.331690 + 0.153637I
a = −0.90494 − 2.57744I
b = −0.657321 + 1.119200I
5.10259 + 3.32211I 0
u = 1.331690 − 0.153637I
a = −0.90494 + 2.57744I
b = −0.657321 − 1.119200I
5.10259 − 3.32211I 0
u = −1.249700 + 0.492475I
a = 0.398034 − 0.700256I
b = 0.049981 + 0.968730I
2.35727 − 3.21528I 0
u = −1.249700 − 0.492475I
a = 0.398034 + 0.700256I
b = 0.049981 − 0.968730I
2.35727 + 3.21528I 0
u = −1.343850 + 0.142360I
a = −1.45232 + 3.03674I
b = 0.028054 − 1.023450I
3.74547 + 2.60657I 0
u = −1.343850 − 0.142360I
a = −1.45232 − 3.03674I
b = 0.028054 + 1.023450I
3.74547 − 2.60657I 0
u = 1.314300 + 0.320206I
a = 0.404246 − 0.664630I
b = −0.758072 − 0.266299I
−1.43950 + 5.31733I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.314300 − 0.320206I
a = 0.404246 + 0.664630I
b = −0.758072 + 0.266299I
−1.43950 − 5.31733I 0
u = −1.347630 + 0.125395I
a = 0.42870 + 2.55795I
b = 0.229918 − 1.343880I
8.43775 + 2.00284I 0
u = −1.347630 − 0.125395I
a = 0.42870 − 2.55795I
b = 0.229918 + 1.343880I
8.43775 − 2.00284I 0
u = −1.360310 + 0.084915I
a = 0.819748 − 0.021975I
b = 0.145792 − 0.333836I
6.59527 − 1.16256I 0
u = −1.360310 − 0.084915I
a = 0.819748 + 0.021975I
b = 0.145792 + 0.333836I
6.59527 + 1.16256I 0
u = −1.354540 + 0.171932I
a = 0.673046 + 0.107343I
b = −1.081530 + 0.769859I
5.44556 − 0.86088I 0
u = −1.354540 − 0.171932I
a = 0.673046 − 0.107343I
b = −1.081530 − 0.769859I
5.44556 + 0.86088I 0
u = 1.368210 + 0.143378I
a = −1.18519 − 2.16747I
b = 0.50495 + 1.76954I
9.08592 − 1.40627I 0
u = 1.368210 − 0.143378I
a = −1.18519 + 2.16747I
b = 0.50495 − 1.76954I
9.08592 + 1.40627I 0
u = −0.274204 + 0.559986I
a = −2.20159 + 0.37589I
b = 0.023992 − 1.078520I
3.75901 + 0.50385I 8.87364 + 0.38982I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274204 − 0.559986I
a = −2.20159 − 0.37589I
b = 0.023992 + 1.078520I
3.75901 − 0.50385I 8.87364 − 0.38982I
u = 1.372760 + 0.178307I
a = −0.835735 + 0.072782I
b = −0.376647 − 0.507264I
4.34556 + 6.41095I 0
u = 1.372760 − 0.178307I
a = −0.835735 − 0.072782I
b = −0.376647 + 0.507264I
4.34556 − 6.41095I 0
u = −0.396188 + 0.471004I
a = −0.203653 − 0.409084I
b = −0.485022 + 0.338354I
−1.47214 + 1.29483I −2.21582 − 0.22695I
u = −0.396188 − 0.471004I
a = −0.203653 + 0.409084I
b = −0.485022 − 0.338354I
−1.47214 − 1.29483I −2.21582 + 0.22695I
u = 1.370430 + 0.219938I
a = −0.244267 − 0.140422I
b = 0.697716 + 0.149710I
3.72148 + 1.22839I 0
u = 1.370430 − 0.219938I
a = −0.244267 + 0.140422I
b = 0.697716 − 0.149710I
3.72148 − 1.22839I 0
u = −1.373840 + 0.254943I
a = −0.586959 − 0.911580I
b = 1.272080 + 0.161262I
4.18347 − 6.34498I 0
u = −1.373840 − 0.254943I
a = −0.586959 + 0.911580I
b = 1.272080 − 0.161262I
4.18347 + 6.34498I 0
u = 1.384740 + 0.189290I
a = 0.36841 + 3.00144I
b = 0.064495 − 1.369760I
9.53240 + 5.59842I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.384740 − 0.189290I
a = 0.36841 − 3.00144I
b = 0.064495 + 1.369760I
9.53240 − 5.59842I 0
u = −1.370920 + 0.280112I
a = −1.31613 + 2.52051I
b = −0.398798 − 1.227510I
1.68222 − 9.58894I 0
u = −1.370920 − 0.280112I
a = −1.31613 − 2.52051I
b = −0.398798 + 1.227510I
1.68222 + 9.58894I 0
u = −1.372400 + 0.281414I
a = −1.85494 + 1.11740I
b = −0.264635 − 1.089620I
6.15824 − 9.13709I 0
u = −1.372400 − 0.281414I
a = −1.85494 − 1.11740I
b = −0.264635 + 1.089620I
6.15824 + 9.13709I 0
u = 1.375060 + 0.269737I
a = −0.95851 − 2.06127I
b = −0.88247 + 1.43103I
7.27555 + 8.82792I 0
u = 1.375060 − 0.269737I
a = −0.95851 + 2.06127I
b = −0.88247 − 1.43103I
7.27555 − 8.82792I 0
u = 1.369120 + 0.306078I
a = −0.87240 − 1.81546I
b = −0.034331 + 1.052870I
2.89929 + 3.08195I 0
u = 1.369120 − 0.306078I
a = −0.87240 + 1.81546I
b = −0.034331 − 1.052870I
2.89929 − 3.08195I 0
u = 1.399630 + 0.109020I
a = −0.645838 + 0.105964I
b = 1.127990 + 0.538753I
5.29099 − 3.66734I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.399630 − 0.109020I
a = −0.645838 − 0.105964I
b = 1.127990 − 0.538753I
5.29099 + 3.66734I 0
u = −1.397650 + 0.160671I
a = 0.97905 − 2.19902I
b = −0.19402 + 1.81909I
9.45925 − 4.38662I 0
u = −1.397650 − 0.160671I
a = 0.97905 + 2.19902I
b = −0.19402 − 1.81909I
9.45925 + 4.38662I 0
u = 1.394040 + 0.220696I
a = 1.77494 + 1.98003I
b = 0.118955 − 1.147790I
9.06095 + 2.37625I 0
u = 1.394040 − 0.220696I
a = 1.77494 − 1.98003I
b = 0.118955 + 1.147790I
9.06095 − 2.37625I 0
u = −0.024671 + 0.584980I
a = −0.276759 − 0.145754I
b = −0.529039 + 0.431451I
−0.91305 + 1.41710I −0.90431 − 4.43635I
u = −0.024671 − 0.584980I
a = −0.276759 + 0.145754I
b = −0.529039 − 0.431451I
−0.91305 − 1.41710I −0.90431 + 4.43635I
u = −1.38738 + 0.31055I
a = 0.249142 − 0.351466I
b = −0.510340 + 0.450923I
3.42434 − 6.17735I 0
u = −1.38738 − 0.31055I
a = 0.249142 + 0.351466I
b = −0.510340 − 0.450923I
3.42434 + 6.17735I 0
u = 1.39776 + 0.28297I
a = 0.654260 − 0.804738I
b = −1.384640 − 0.052450I
2.81876 + 11.87040I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39776 − 0.28297I
a = 0.654260 + 0.804738I
b = −1.384640 + 0.052450I
2.81876 − 11.87040I 0
u = 0.502006 + 0.272910I
a = −0.988686 − 0.156094I
b = 0.176092 + 1.388870I
3.85596 + 2.58784I 8.74880 − 3.93172I
u = 0.502006 − 0.272910I
a = −0.988686 + 0.156094I
b = 0.176092 − 1.388870I
3.85596 − 2.58784I 8.74880 + 3.93172I
u = −1.41460 + 0.24844I
a = 0.83312 − 2.06498I
b = 0.73018 + 1.54072I
8.19657 − 4.09308I 0
u = −1.41460 − 0.24844I
a = 0.83312 + 2.06498I
b = 0.73018 − 1.54072I
8.19657 + 4.09308I 0
u = 1.43711 + 0.30413I
a = 0.97716 + 2.18387I
b = 0.53286 − 1.43243I
9.1753 + 12.5096I 0
u = 1.43711 − 0.30413I
a = 0.97716 − 2.18387I
b = 0.53286 + 1.43243I
9.1753 − 12.5096I 0
u = −1.46242 + 0.19439I
a = 0.57417 − 2.04808I
b = 0.441988 + 1.294660I
6.91451 − 4.98429I 0
u = −1.46242 − 0.19439I
a = 0.57417 + 2.04808I
b = 0.441988 − 1.294660I
6.91451 + 4.98429I 0
u = −1.44158 + 0.33198I
a = −1.01719 + 2.05262I
b = −0.62682 − 1.42123I
7.1819 − 18.7415I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44158 − 0.33198I
a = −1.01719 − 2.05262I
b = −0.62682 + 1.42123I
7.1819 + 18.7415I 0
u = −1.48260 + 0.25763I
a = 0.64483 − 1.84971I
b = 0.355801 + 1.189960I
6.82951 − 5.17040I 0
u = −1.48260 − 0.25763I
a = 0.64483 + 1.84971I
b = 0.355801 − 1.189960I
6.82951 + 5.17040I 0
u = 1.52291 + 0.07834I
a = 0.51728 + 2.06654I
b = −0.212942 − 1.357070I
12.45090 − 2.25628I 0
u = 1.52291 − 0.07834I
a = 0.51728 − 2.06654I
b = −0.212942 + 1.357070I
12.45090 + 2.25628I 0
u = 0.460833 + 0.061428I
a = −1.099430 − 0.859371I
b = 0.379491 − 0.017585I
1.243970 + 0.474324I 7.78614 − 0.28988I
u = 0.460833 − 0.061428I
a = −1.099430 + 0.859371I
b = 0.379491 + 0.017585I
1.243970 − 0.474324I 7.78614 + 0.28988I
u = 1.50496 + 0.32943I
a = −0.70081 − 1.70277I
b = −0.365558 + 1.032550I
5.10642 + 9.75274I 0
u = 1.50496 − 0.32943I
a = −0.70081 + 1.70277I
b = −0.365558 − 1.032550I
5.10642 − 9.75274I 0
u = −0.259325 + 0.376841I
a = −0.21027 + 2.06481I
b = −0.165139 − 1.301050I
4.32902 − 3.26983I 12.5880 + 9.3339I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.259325 − 0.376841I
a = −0.21027 − 2.06481I
b = −0.165139 + 1.301050I
4.32902 + 3.26983I 12.5880 − 9.3339I
u = −1.55854 + 0.03206I
a = −0.31241 + 1.97733I
b = 0.31007 − 1.39056I
11.56080 + 8.01928I 0
u = −1.55854 − 0.03206I
a = −0.31241 − 1.97733I
b = 0.31007 + 1.39056I
11.56080 − 8.01928I 0
u = 0.037155 + 0.408356I
a = 2.89093 + 0.93424I
b = 0.767376 + 0.840542I
0.85376 − 1.30121I −0.66690 − 1.86791I
u = 0.037155 − 0.408356I
a = 2.89093 − 0.93424I
b = 0.767376 − 0.840542I
0.85376 + 1.30121I −0.66690 + 1.86791I
u = −0.090369 + 0.319235I
a = 4.67887 − 0.60447I
b = −0.081944 − 0.627555I
−0.58032 − 4.31606I 1.05693 + 2.05653I
u = −0.090369 − 0.319235I
a = 4.67887 + 0.60447I
b = −0.081944 + 0.627555I
−0.58032 + 4.31606I 1.05693 − 2.05653I
u = −0.150162 + 0.156312I
a = 1.75639 + 1.01392I
b = −0.29398 + 1.47752I
4.15787 + 3.00573I 12.46090 + 3.53493I
u = −0.150162 − 0.156312I
a = 1.75639 − 1.01392I
b = −0.29398 − 1.47752I
4.15787 − 3.00573I 12.46090 − 3.53493I
17
II. I
u
2
=
h−u
23
+11u
21
+· · ·+b−1, −3u
23
+32u
21
+· · ·+a−1, u
24
−12u
22
+· · ·+2u+1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
3u
23
− 32u
21
+ ··· − 4u + 1
u
23
− 11u
21
+ ··· + 4u + 1
a
4
=
−u
23
+ 3u
22
+ ··· − 5u − 2
−3u
22
+ u
21
+ ··· + 12u
2
+ 3
a
1
=
3u
23
− 32u
21
+ ··· − u − 1
−u
23
+ 11u
21
+ ··· − 5u − 1
a
8
=
4u
23
− 43u
21
+ ··· − u
2
+ 2
u
23
− 11u
21
+ ··· + 4u + 1
a
10
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
−u
23
+ 2u
22
+ ··· − 4u − 1
−3u
22
+ u
21
+ ··· + u + 3
a
2
=
u
23
+ 2u
22
+ ··· − 4u − 1
3u
23
− 3u
22
+ ··· + 3u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
23
+ 8u
22
− 51u
21
− 84u
20
+ 276u
19
+ 360u
18
− 821u
17
−
759u
16
+ 1423u
15
+ 629u
14
− 1314u
13
+ 463u
12
+ 231u
11
− 1393u
10
+ 809u
9
+ 881u
8
−
820u
7
+ 85u
6
+ 274u
5
− 159u
4
− 22u
3
− 39u
2
+ 12u − 7
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 12u
23
+ ··· − 15u + 1
c
2
u
24
− 6u
22
+ ··· + u + 1
c
3
u
24
+ u
23
+ ··· − 2u
3
+ 1
c
4
u
24
+ u
23
+ ··· + 10u
2
+ 1
c
5
, c
6
u
24
− 12u
22
+ ··· + 2u + 1
c
7
u
24
− 6u
22
+ ··· − u + 1
c
8
u
24
− u
23
+ ··· + 10u
2
+ 1
c
9
u
24
− 6u
22
+ ··· − 4u + 1
c
10
u
24
+ 4u
22
+ ··· − 2u + 1
c
11
u
24
− 12u
22
+ ··· − 2u + 1
c
12
u
24
− 2u
22
+ ··· + 3u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 12y
23
+ ··· + 5y + 1
c
2
, c
7
y
24
− 12y
23
+ ··· − 15y + 1
c
3
y
24
− 7y
23
+ ··· − 4y
2
+ 1
c
4
, c
8
y
24
+ 21y
23
+ ··· + 20y + 1
c
5
, c
6
, c
11
y
24
− 24y
23
+ ··· + 12y + 1
c
9
y
24
− 12y
23
+ ··· − 12y + 1
c
10
y
24
+ 8y
23
+ ··· + 8y + 1
c
12
y
24
− 4y
23
+ ··· − 3y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.068651 + 0.929424I
a = −0.295075 − 0.486660I
b = −0.034779 + 0.697797I
−2.61709 − 1.40699I −9.58923 + 2.02213I
u = 0.068651 − 0.929424I
a = −0.295075 + 0.486660I
b = −0.034779 − 0.697797I
−2.61709 + 1.40699I −9.58923 − 2.02213I
u = 1.169690 + 0.336481I
a = 0.488164 − 0.921824I
b = −0.136599 + 0.612169I
0.56997 + 5.96107I 2.69042 − 6.99804I
u = 1.169690 − 0.336481I
a = 0.488164 + 0.921824I
b = −0.136599 − 0.612169I
0.56997 − 5.96107I 2.69042 + 6.99804I
u = 1.216630 + 0.130232I
a = 0.387646 + 1.077390I
b = 0.380957 + 0.629569I
2.19974 − 3.04838I 1.76668 + 4.68501I
u = 1.216630 − 0.130232I
a = 0.387646 − 1.077390I
b = 0.380957 − 0.629569I
2.19974 + 3.04838I 1.76668 − 4.68501I
u = −1.249520 + 0.073520I
a = 1.114900 + 0.294345I
b = −0.773198 + 0.591099I
4.35814 + 0.56071I 6.19041 − 1.68050I
u = −1.249520 − 0.073520I
a = 1.114900 − 0.294345I
b = −0.773198 − 0.591099I
4.35814 − 0.56071I 6.19041 + 1.68050I
u = −1.231740 + 0.410206I
a = 0.312702 − 1.101620I
b = 0.231352 + 0.644772I
1.31532 − 3.43328I −1.16883 + 5.13510I
u = −1.231740 − 0.410206I
a = 0.312702 + 1.101620I
b = 0.231352 − 0.644772I
1.31532 + 3.43328I −1.16883 − 5.13510I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.324470 + 0.572839I
a = −2.10332 − 1.03381I
b = −0.324272 + 0.798048I
−0.48935 + 5.20044I 2.82779 − 9.17180I
u = 0.324470 − 0.572839I
a = −2.10332 + 1.03381I
b = −0.324272 − 0.798048I
−0.48935 − 5.20044I 2.82779 + 9.17180I
u = −1.335640 + 0.131798I
a = 0.21492 − 2.09510I
b = −0.37287 + 1.44038I
8.05506 + 1.46228I 5.22915 + 2.07758I
u = −1.335640 − 0.131798I
a = 0.21492 + 2.09510I
b = −0.37287 − 1.44038I
8.05506 − 1.46228I 5.22915 − 2.07758I
u = 1.382630 + 0.158548I
a = −0.51531 − 2.59501I
b = −0.14394 + 1.56262I
8.68692 + 5.11184I 6.98030 − 6.38269I
u = 1.382630 − 0.158548I
a = −0.51531 + 2.59501I
b = −0.14394 − 1.56262I
8.68692 − 5.11184I 6.98030 + 6.38269I
u = −1.41196 + 0.28189I
a = 1.16270 − 1.50449I
b = 0.421050 + 0.963530I
5.07360 − 8.57178I 5.14320 + 5.72643I
u = −1.41196 − 0.28189I
a = 1.16270 + 1.50449I
b = 0.421050 − 0.963530I
5.07360 + 8.57178I 5.14320 − 5.72643I
u = 1.44505 + 0.20614I
a = −0.66536 − 1.94894I
b = −0.603560 + 1.240880I
7.17636 + 4.27371I 6.99693 + 0.13663I
u = 1.44505 − 0.20614I
a = −0.66536 + 1.94894I
b = −0.603560 − 1.240880I
7.17636 − 4.27371I 6.99693 − 0.13663I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.312652 + 0.364008I
a = 2.47000 − 0.97405I
b = 0.612935 + 0.887283I
1.31476 − 1.86915I 7.03000 + 5.67897I
u = −0.312652 − 0.364008I
a = 2.47000 + 0.97405I
b = 0.612935 − 0.887283I
1.31476 + 1.86915I 7.03000 − 5.67897I
u = −0.065601 + 0.351466I
a = 0.928024 − 1.028750I
b = 0.24292 + 1.45794I
3.83500 − 3.18351I −7.59682 + 6.37689I
u = −0.065601 − 0.351466I
a = 0.928024 + 1.028750I
b = 0.24292 − 1.45794I
3.83500 + 3.18351I −7.59682 − 6.37689I
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
24
− 12u
23
+ ··· − 15u + 1)(u
129
+ 53u
128
+ ··· + 241100u + 10201)
c
2
(u
24
− 6u
22
+ ··· + u + 1)(u
129
+ u
128
+ ··· − 268u − 101)
c
3
(u
24
+ u
23
+ ··· − 2u
3
+ 1)(u
129
− 6u
127
+ ··· − 141u − 9)
c
4
(u
24
+ u
23
+ ··· + 10u
2
+ 1)(u
129
+ 2u
128
+ ··· − 21685u − 15853)
c
5
, c
6
(u
24
− 12u
22
+ ··· + 2u + 1)(u
129
+ u
128
+ ··· − 7u − 1)
c
7
(u
24
− 6u
22
+ ··· − u + 1)(u
129
+ u
128
+ ··· − 268u − 101)
c
8
(u
24
− u
23
+ ··· + 10u
2
+ 1)(u
129
+ 2u
128
+ ··· − 21685u − 15853)
c
9
(u
24
− 6u
22
+ ··· − 4u + 1)(u
129
− 7u
128
+ ··· + 31027u + 4567)
c
10
(u
24
+ 4u
22
+ ··· − 2u + 1)(u
129
− 3u
128
+ ··· + 22569u + 1491)
c
11
(u
24
− 12u
22
+ ··· − 2u + 1)(u
129
+ u
128
+ ··· − 7u − 1)
c
12
(u
24
− 2u
22
+ ··· + 3u + 1)(u
129
+ 11u
128
+ ··· − 170u + 29)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
24
+ 12y
23
+ ··· + 5y + 1)
· (y
129
+ 59y
128
+ ··· + 6188411064y −104060401)
c
2
, c
7
(y
24
− 12y
23
+ ··· − 15y + 1)(y
129
− 53y
128
+ ··· + 241100y −10201)
c
3
(y
24
− 7y
23
+ ··· − 4y
2
+ 1)(y
129
− 12y
128
+ ··· + 369y −81)
c
4
, c
8
(y
24
+ 21y
23
+ ··· + 20y + 1)
· (y
129
+ 92y
128
+ ··· − 5214202691y −251317609)
c
5
, c
6
, c
11
(y
24
− 24y
23
+ ··· + 12y + 1)(y
129
− 117y
128
+ ··· − 19y −1)
c
9
(y
24
− 12y
23
+ ··· − 12y + 1)
· (y
129
− 37y
128
+ ··· + 3096724221y −20857489)
c
10
(y
24
+ 8y
23
+ ··· + 8y + 1)
· (y
129
+ 15y
128
+ ··· + 34052817y −2223081)
c
12
(y
24
− 4y
23
+ ··· − 3y + 1)(y
129
− 17y
128
+ ··· + 61496y −841)
25
