12a
0092
(K12a
0092
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 4 12 7 6 1 9
Solving Sequence
5,10
6 11
3,7
2 1 4 8 9 12
c
5
c
10
c
6
c
2
c
1
c
4
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.29904 × 10
129
u
111
+ 2.66514 × 10
129
u
110
+ ··· + 3.21272 × 10
129
b + 1.30058 × 10
129
,
5.52996 × 10
129
u
111
− 1.09032 × 10
130
u
110
+ ··· + 6.42545 × 10
129
a − 1.03393 × 10
130
,
u
112
− 2u
111
+ ··· + 24u + 8i
I
u
2
= hb + 1, 2u
7
− u
6
− 5u
5
+ 2u
4
+ 3u
3
+ a + 2u − 1, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
u
3
= h32a
2
u + 14a
2
+ 6au + 463b + 292a + 118u − 122, 4a
3
+ 6a
2
u − 4a
2
+ 8au + 3u − 20, u
2
− 2i
I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v −1i
* 4 irreducible components of dim
C
= 0, with total 129 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
= h−1.30 × 10
129
u
111
+ 2.67 × 10
129
u
110
+ · · · + 3.21 × 10
129
b + 1.30 ×
10
129
, 5.53 × 10
129
u
111
− 1.09 × 10
130
u
110
+ · · · + 6.43 × 10
129
a − 1.03 ×
10
130
, u
112
− 2u
111
+ · · · + 24u + 8i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
11
=
u
−u
3
+ u
a
3
=
−0.860634u
111
+ 1.69688u
110
+ ··· + 1.28833u + 1.60912
0.404343u
111
− 0.829559u
110
+ ··· − 2.02982u − 0.404820
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−0.456291u
111
+ 0.867320u
110
+ ··· − 0.741493u + 1.20430
0.404343u
111
− 0.829559u
110
+ ··· − 2.02982u − 0.404820
a
1
=
0.0400195u
111
− 0.574902u
110
+ ··· + 6.54098u + 2.08781
−0.0638486u
111
+ 0.551541u
110
+ ··· − 3.22913u − 1.01041
a
4
=
0.278988u
111
− 0.807051u
110
+ ··· + 0.947750u + 3.03165
−0.597516u
111
+ 1.47686u
110
+ ··· + 0.793252u − 1.62436
a
8
=
0.0413526u
111
− 0.529064u
110
+ ··· + 4.64588u + 1.51965
0.183846u
111
+ 0.260857u
110
+ ··· − 9.04776u − 3.12862
a
9
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
12
=
−0.0392866u
111
− 0.413970u
110
+ ··· + 9.42044u + 2.69703
−0.101407u
111
+ 0.424993u
110
+ ··· − 2.32534u − 0.770762
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.31338u
111
− 3.41480u
110
+ ··· + 22.4635u + 1.55814
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
112
+ 52u
111
+ ··· + 2998u + 1
c
2
, c
4
u
112
− 12u
111
+ ··· + 54u + 1
c
3
, c
7
u
112
+ 2u
111
+ ··· + 2688u − 256
c
5
, c
6
, c
10
u
112
− 2u
111
+ ··· + 24u + 8
c
8
, c
12
u
112
− 5u
111
+ ··· − 113u + 7
c
9
u
112
+ 6u
111
+ ··· + 84024u + 12200
c
11
u
112
− 57u
111
+ ··· − 4733u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
112
+ 28y
111
+ ··· − 8620798y + 1
c
2
, c
4
y
112
− 52y
111
+ ··· − 2998y + 1
c
3
, c
7
y
112
+ 60y
111
+ ··· − 3850240y + 65536
c
5
, c
6
, c
10
y
112
− 104y
111
+ ··· − 960y + 64
c
8
, c
12
y
112
− 57y
111
+ ··· − 4733y + 49
c
9
y
112
− 8y
111
+ ··· − 4167168576y + 148840000
c
11
y
112
+ 7y
111
+ ··· − 16407805y + 2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.018720 + 0.149036I
a = 0.076859 − 0.861231I
b = −1.158720 + 0.319869I
−1.29796 − 1.03206I 0
u = −1.018720 − 0.149036I
a = 0.076859 + 0.861231I
b = −1.158720 − 0.319869I
−1.29796 + 1.03206I 0
u = 0.814215 + 0.446584I
a = −0.037466 − 0.261223I
b = 1.067950 + 0.549015I
0.00125 − 3.68506I 0
u = 0.814215 − 0.446584I
a = −0.037466 + 0.261223I
b = 1.067950 − 0.549015I
0.00125 + 3.68506I 0
u = −0.711966 + 0.574552I
a = −0.174449 + 0.367324I
b = 1.131830 − 0.614451I
1.90412 + 8.94633I 0
u = −0.711966 − 0.574552I
a = −0.174449 − 0.367324I
b = 1.131830 + 0.614451I
1.90412 − 8.94633I 0
u = 1.036270 + 0.398425I
a = 0.447897 + 0.876758I
b = 0.979382 − 0.404050I
−0.78854 + 2.81223I 0
u = 1.036270 − 0.398425I
a = 0.447897 − 0.876758I
b = 0.979382 + 0.404050I
−0.78854 − 2.81223I 0
u = 1.116570 + 0.051427I
a = 0.657850 − 0.997380I
b = −0.177665 + 0.553771I
1.74796 + 0.16171I 0
u = 1.116570 − 0.051427I
a = 0.657850 + 0.997380I
b = −0.177665 − 0.553771I
1.74796 − 0.16171I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.110930 + 0.219371I
a = −0.14481 − 1.71768I
b = −1.153040 + 0.367430I
−1.22070 + 3.54389I 0
u = 1.110930 − 0.219371I
a = −0.14481 + 1.71768I
b = −1.153040 − 0.367430I
−1.22070 − 3.54389I 0
u = −0.355833 + 0.788222I
a = 1.05625 − 1.50575I
b = 1.170610 + 0.637818I
0.72546 − 13.62000I 0. + 9.98825I
u = −0.355833 − 0.788222I
a = 1.05625 + 1.50575I
b = 1.170610 − 0.637818I
0.72546 + 13.62000I 0. − 9.98825I
u = 0.146754 + 0.822078I
a = 0.893745 + 0.277347I
b = 0.911228 + 0.313596I
−3.54227 + 1.59081I 1.56582 + 2.52489I
u = 0.146754 − 0.822078I
a = 0.893745 − 0.277347I
b = 0.911228 − 0.313596I
−3.54227 − 1.59081I 1.56582 − 2.52489I
u = −1.167790 + 0.097848I
a = 0.725202 − 0.286646I
b = 0.881268 − 0.521081I
6.34503 + 2.09810I 0
u = −1.167790 − 0.097848I
a = 0.725202 + 0.286646I
b = 0.881268 + 0.521081I
6.34503 − 2.09810I 0
u = −0.624872 + 0.541441I
a = 0.485440 − 1.097800I
b = 0.392106 + 0.829105I
4.11190 + 3.56494I 7.21254 − 1.29951I
u = −0.624872 − 0.541441I
a = 0.485440 + 1.097800I
b = 0.392106 − 0.829105I
4.11190 − 3.56494I 7.21254 + 1.29951I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.274658 + 0.777797I
a = 1.28184 + 1.22191I
b = 1.134650 − 0.590961I
−1.75122 + 8.04540I −0.69722 − 6.48181I
u = 0.274658 − 0.777797I
a = 1.28184 − 1.22191I
b = 1.134650 + 0.590961I
−1.75122 − 8.04540I −0.69722 + 6.48181I
u = −0.011399 + 0.820861I
a = 1.141370 + 0.028393I
b = 1.003200 − 0.397478I
−4.15841 + 4.21135I −1.12819 − 7.26950I
u = −0.011399 − 0.820861I
a = 1.141370 − 0.028393I
b = 1.003200 + 0.397478I
−4.15841 − 4.21135I −1.12819 + 7.26950I
u = −0.358023 + 0.736800I
a = −0.605113 + 0.240449I
b = 0.369589 − 0.924331I
3.15487 − 7.91029I 5.30872 + 6.56414I
u = −0.358023 − 0.736800I
a = −0.605113 − 0.240449I
b = 0.369589 + 0.924331I
3.15487 + 7.91029I 5.30872 − 6.56414I
u = 0.303360 + 0.725677I
a = −0.65527 − 1.79904I
b = −1.015110 + 0.566452I
−1.69797 + 7.17522I 0.68379 − 7.57915I
u = 0.303360 − 0.725677I
a = −0.65527 + 1.79904I
b = −1.015110 − 0.566452I
−1.69797 − 7.17522I 0.68379 + 7.57915I
u = 0.652565 + 0.422024I
a = 0.774209 + 0.886160I
b = −0.995831 − 0.466362I
−0.38831 − 3.14093I 2.48859 + 2.59563I
u = 0.652565 − 0.422024I
a = 0.774209 − 0.886160I
b = −0.995831 + 0.466362I
−0.38831 + 3.14093I 2.48859 − 2.59563I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.217770 + 0.231362I
a = 0.066728 + 0.949450I
b = 0.002019 − 0.679432I
2.29898 − 4.70132I 0
u = −1.217770 − 0.231362I
a = 0.066728 − 0.949450I
b = 0.002019 + 0.679432I
2.29898 + 4.70132I 0
u = −0.263923 + 0.703760I
a = −0.978990 + 0.422628I
b = −1.309070 + 0.166176I
−2.65149 − 4.51648I 1.07409 + 6.59561I
u = −0.263923 − 0.703760I
a = −0.978990 − 0.422628I
b = −1.309070 − 0.166176I
−2.65149 + 4.51648I 1.07409 − 6.59561I
u = 0.294109 + 0.686488I
a = −0.364849 + 0.009699I
b = 0.339982 + 0.789548I
0.57903 + 2.86162I 2.21640 − 3.05288I
u = 0.294109 − 0.686488I
a = −0.364849 − 0.009699I
b = 0.339982 − 0.789548I
0.57903 − 2.86162I 2.21640 + 3.05288I
u = −1.196320 + 0.379749I
a = 0.446586 − 1.195840I
b = 1.071020 + 0.461092I
−0.50009 − 8.52415I 0
u = −1.196320 − 0.379749I
a = 0.446586 + 1.195840I
b = 1.071020 − 0.461092I
−0.50009 + 8.52415I 0
u = 0.584146 + 0.424260I
a = 0.495792 + 0.880233I
b = 0.508203 − 0.602695I
1.72036 + 0.90594I 4.78781 − 4.00969I
u = 0.584146 − 0.424260I
a = 0.495792 − 0.880233I
b = 0.508203 + 0.602695I
1.72036 − 0.90594I 4.78781 + 4.00969I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.229960 + 0.360736I
a = 0.037108 + 0.251367I
b = 0.915433 + 0.334717I
−0.329456 + 0.040199I 0
u = 1.229960 − 0.360736I
a = 0.037108 − 0.251367I
b = 0.915433 − 0.334717I
−0.329456 − 0.040199I 0
u = −0.654491 + 0.272544I
a = 0.04579 + 1.78125I
b = −1.182700 − 0.184351I
−1.085270 + 0.846553I 3.79032 − 3.13132I
u = −0.654491 − 0.272544I
a = 0.04579 − 1.78125I
b = −1.182700 + 0.184351I
−1.085270 − 0.846553I 3.79032 + 3.13132I
u = −0.188194 + 0.675147I
a = −1.11851 + 1.65238I
b = −1.051720 − 0.452819I
−3.69167 − 2.26136I −3.60384 + 2.58351I
u = −0.188194 − 0.675147I
a = −1.11851 − 1.65238I
b = −1.051720 + 0.452819I
−3.69167 + 2.26136I −3.60384 − 2.58351I
u = 0.240940 + 0.637061I
a = 0.719669 + 0.632063I
b = −0.562579 − 0.604506I
−0.34785 + 2.50804I 1.82220 − 3.40193I
u = 0.240940 − 0.637061I
a = 0.719669 − 0.632063I
b = −0.562579 + 0.604506I
−0.34785 − 2.50804I 1.82220 + 3.40193I
u = 0.112061 + 0.664682I
a = −1.48275 + 0.14053I
b = −1.214020 − 0.246890I
−4.20929 − 0.20936I −3.46102 − 1.21494I
u = 0.112061 − 0.664682I
a = −1.48275 − 0.14053I
b = −1.214020 + 0.246890I
−4.20929 + 0.20936I −3.46102 + 1.21494I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.327970 + 0.003111I
a = −0.87431 + 1.66645I
b = 0.894917 − 0.825816I
8.09882 + 3.06301I 0
u = −1.327970 − 0.003111I
a = −0.87431 − 1.66645I
b = 0.894917 + 0.825816I
8.09882 − 3.06301I 0
u = 1.324830 + 0.184519I
a = 1.29142 + 1.08887I
b = −0.530536 − 0.575105I
2.68371 + 1.14617I 0
u = 1.324830 − 0.184519I
a = 1.29142 − 1.08887I
b = −0.530536 + 0.575105I
2.68371 − 1.14617I 0
u = −0.332085 + 0.570168I
a = −0.823871 − 0.740483I
b = 0.570546 − 0.745691I
5.19659 + 0.52268I 7.07371 + 1.25938I
u = −0.332085 − 0.570168I
a = −0.823871 + 0.740483I
b = 0.570546 + 0.745691I
5.19659 − 0.52268I 7.07371 − 1.25938I
u = −0.213775 + 0.619265I
a = 2.33602 − 1.25730I
b = 1.026980 + 0.623990I
3.82789 − 4.68728I 3.46609 + 6.29400I
u = −0.213775 − 0.619265I
a = 2.33602 + 1.25730I
b = 1.026980 − 0.623990I
3.82789 + 4.68728I 3.46609 − 6.29400I
u = −1.339170 + 0.244598I
a = 0.128580 + 0.409997I
b = −1.292610 + 0.172501I
0.35822 − 3.05224I 0
u = −1.339170 − 0.244598I
a = 0.128580 − 0.409997I
b = −1.292610 − 0.172501I
0.35822 + 3.05224I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.003632 + 0.612874I
a = 0.533006 − 0.318247I
b = −0.213424 + 0.523869I
−1.41839 + 1.56464I −0.45093 − 4.40997I
u = −0.003632 − 0.612874I
a = 0.533006 + 0.318247I
b = −0.213424 − 0.523869I
−1.41839 − 1.56464I −0.45093 + 4.40997I
u = −1.38959
a = 0.908732
b = −0.0184563
6.53354 0
u = −1.346640 + 0.354641I
a = −0.027424 − 0.336567I
b = 0.849993 − 0.240388I
1.14529 − 5.82695I 0
u = −1.346640 − 0.354641I
a = −0.027424 + 0.336567I
b = 0.849993 + 0.240388I
1.14529 + 5.82695I 0
u = 1.372090 + 0.263367I
a = 0.10678 − 2.41007I
b = −1.015250 + 0.548202I
1.26200 + 5.66357I 0
u = 1.372090 − 0.263367I
a = 0.10678 + 2.41007I
b = −1.015250 − 0.548202I
1.26200 − 5.66357I 0
u = 1.389480 + 0.176832I
a = −1.12892 − 1.39935I
b = 1.035730 + 0.807448I
9.96290 + 0.00502I 0
u = 1.389480 − 0.176832I
a = −1.12892 + 1.39935I
b = 1.035730 − 0.807448I
9.96290 − 0.00502I 0
u = −0.333286 + 0.497276I
a = 0.205344 − 0.950156I
b = 0.722048 + 0.843897I
5.42986 − 3.71507I 6.56090 + 8.40821I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.333286 − 0.497276I
a = 0.205344 + 0.950156I
b = 0.722048 − 0.843897I
5.42986 + 3.71507I 6.56090 − 8.40821I
u = 1.398300 + 0.107009I
a = −0.59433 − 1.65394I
b = −1.165440 − 0.052793I
5.03887 + 0.33340I 0
u = 1.398300 − 0.107009I
a = −0.59433 + 1.65394I
b = −1.165440 + 0.052793I
5.03887 − 0.33340I 0
u = −1.394040 + 0.168090I
a = −0.05486 + 2.88093I
b = −0.899734 − 0.466308I
6.09712 − 2.33253I 0
u = −1.394040 − 0.168090I
a = −0.05486 − 2.88093I
b = −0.899734 + 0.466308I
6.09712 + 2.33253I 0
u = 1.386180 + 0.248074I
a = 0.67456 + 2.27430I
b = 1.098480 − 0.642310I
8.93573 + 7.87318I 0
u = 1.386180 − 0.248074I
a = 0.67456 − 2.27430I
b = 1.098480 + 0.642310I
8.93573 − 7.87318I 0
u = −1.39563 + 0.25220I
a = 1.35096 − 1.26835I
b = −0.652912 + 0.690244I
4.87673 − 5.76508I 0
u = −1.39563 − 0.25220I
a = 1.35096 + 1.26835I
b = −0.652912 − 0.690244I
4.87673 + 5.76508I 0
u = 1.41403 + 0.20520I
a = −0.39049 + 1.93565I
b = 0.695558 − 0.941026I
10.99240 + 6.37614I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41403 − 0.20520I
a = −0.39049 − 1.93565I
b = 0.695558 + 0.941026I
10.99240 − 6.37614I 0
u = 1.43186
a = 7.47358
b = −0.970695
4.97680 0
u = 1.40615 + 0.27781I
a = 0.451286 − 0.581959I
b = −1.358830 − 0.131787I
2.67390 + 8.08693I 0
u = 1.40615 − 0.27781I
a = 0.451286 + 0.581959I
b = −1.358830 + 0.131787I
2.67390 − 8.08693I 0
u = 1.42100 + 0.21744I
a = −1.228290 − 0.553828I
b = 0.474203 + 0.831698I
10.80900 + 2.37680I 0
u = 1.42100 − 0.21744I
a = −1.228290 + 0.553828I
b = 0.474203 − 0.831698I
10.80900 − 2.37680I 0
u = −1.41572 + 0.27049I
a = −0.978454 + 0.922450I
b = 0.368700 − 0.903629I
6.03543 − 6.35471I 0
u = −1.41572 − 0.27049I
a = −0.978454 − 0.922450I
b = 0.368700 + 0.903629I
6.03543 + 6.35471I 0
u = −1.44321 + 0.10269I
a = −0.43536 − 1.61858I
b = 0.716567 + 0.769054I
8.22583 − 2.63796I 0
u = −1.44321 − 0.10269I
a = −0.43536 + 1.61858I
b = 0.716567 − 0.769054I
8.22583 + 2.63796I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41705 + 0.31061I
a = 0.23451 − 2.12729I
b = 1.162710 + 0.631820I
3.63940 − 11.98600I 0
u = −1.41705 − 0.31061I
a = 0.23451 + 2.12729I
b = 1.162710 − 0.631820I
3.63940 + 11.98600I 0
u = −1.42523 + 0.28547I
a = 0.28388 + 2.43754I
b = −0.995964 − 0.623300I
3.82611 − 10.85450I 0
u = −1.42523 − 0.28547I
a = 0.28388 − 2.43754I
b = −0.995964 + 0.623300I
3.82611 + 10.85450I 0
u = −1.46859 + 0.11194I
a = 1.69922 − 1.26036I
b = −0.841564 + 0.435407I
6.34093 + 1.39160I 0
u = −1.46859 − 0.11194I
a = 1.69922 + 1.26036I
b = −0.841564 − 0.435407I
6.34093 − 1.39160I 0
u = 1.45063 + 0.28488I
a = −1.11139 − 1.11493I
b = 0.397230 + 0.978223I
8.9567 + 11.6332I 0
u = 1.45063 − 0.28488I
a = −1.11139 + 1.11493I
b = 0.397230 − 0.978223I
8.9567 − 11.6332I 0
u = 1.45761 + 0.30717I
a = 0.05506 + 2.27142I
b = 1.184370 − 0.665894I
6.5408 + 17.6016I 0
u = 1.45761 − 0.30717I
a = 0.05506 − 2.27142I
b = 1.184370 + 0.665894I
6.5408 − 17.6016I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50703 + 0.02402I
a = −0.74209 + 1.21258I
b = 0.927314 − 0.617513I
7.63433 + 2.61707I 0
u = −1.50703 − 0.02402I
a = −0.74209 − 1.21258I
b = 0.927314 + 0.617513I
7.63433 − 2.61707I 0
u = 1.50704 + 0.14911I
a = −0.10240 + 1.73413I
b = 0.513892 − 0.813284I
11.06290 − 1.16602I 0
u = 1.50704 − 0.14911I
a = −0.10240 − 1.73413I
b = 0.513892 + 0.813284I
11.06290 + 1.16602I 0
u = −0.237025 + 0.395062I
a = 0.003829 + 0.713299I
b = 0.958789 − 0.771571I
4.74030 + 2.24272I 3.61623 + 6.16785I
u = −0.237025 − 0.395062I
a = 0.003829 − 0.713299I
b = 0.958789 + 0.771571I
4.74030 − 2.24272I 3.61623 − 6.16785I
u = 1.53699 + 0.12427I
a = −0.99596 − 1.13045I
b = 1.073900 + 0.645562I
9.38113 − 6.62724I 0
u = 1.53699 − 0.12427I
a = −0.99596 + 1.13045I
b = 1.073900 − 0.645562I
9.38113 + 6.62724I 0
u = 0.276680 + 0.321195I
a = −0.57913 − 4.82110I
b = −0.757806 + 0.273988I
0.771024 + 0.267712I 2.70998 − 9.56080I
u = 0.276680 − 0.321195I
a = −0.57913 + 4.82110I
b = −0.757806 − 0.273988I
0.771024 − 0.267712I 2.70998 + 9.56080I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.417834
a = 1.69611
b = −0.141393
0.992954 11.5370
u = −0.236458
a = 2.76698
b = −0.881202
−1.26916 −9.80040
16
II. I
u
2
=
hb+1, 2u
7
−u
6
−5u
5
+2u
4
+3u
3
+a+2u−1, u
8
−u
7
−3u
6
+2u
5
+3u
4
−2u−1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
11
=
u
−u
3
+ u
a
3
=
−2u
7
+ u
6
+ 5u
5
− 2u
4
− 3u
3
− 2u + 1
−1
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−2u
7
+ u
6
+ 5u
5
− 2u
4
− 3u
3
− 2u
−1
a
1
=
−1
0
a
4
=
−2u
7
+ u
6
+ 5u
5
− 2u
4
− 3u
3
− 2u + 1
−1
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
12
=
−u
3
+ 2u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
7
+ 9u
6
− 10u
5
− 27u
4
− 2u
3
+ 18u
2
+ 20u + 17
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
, c
6
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
8
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
9
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
10
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
11
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
12
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
6
, c
10
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
8
, c
12
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
9
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = −0.085690 + 0.514779I
b = −1.00000
−0.604279 − 1.131230I 1.38132 + 1.25921I
u = −1.180120 − 0.268597I
a = −0.085690 − 0.514779I
b = −1.00000
−0.604279 + 1.131230I 1.38132 − 1.25921I
u = −0.108090 + 0.747508I
a = −1.036110 + 0.260696I
b = −1.00000
−3.80435 − 2.57849I −1.74277 + 4.63100I
u = −0.108090 − 0.747508I
a = −1.036110 − 0.260696I
b = −1.00000
−3.80435 + 2.57849I −1.74277 − 4.63100I
u = 1.37100
a = −3.88842
b = −1.00000
4.85780 25.4550
u = 1.334530 + 0.318930I
a = 0.043072 − 0.634428I
b = −1.00000
0.73474 + 6.44354I 1.71699 − 7.87618I
u = 1.334530 − 0.318930I
a = 0.043072 + 0.634428I
b = −1.00000
0.73474 − 6.44354I 1.71699 + 7.87618I
u = −0.463640
a = 2.04588
b = −1.00000
−0.799899 10.8330
20
III.
I
u
3
= h32a
2
u+6au+· · ·+292a −122, 4a
3
+6a
2
u−4a
2
+8au+3u−20, u
2
−2i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−2
a
11
=
u
−u
a
3
=
a
−0.0691145a
2
u − 0.0129590au + ··· − 0.630670a + 0.263499
a
7
=
−1
0
a
2
=
−0.0691145a
2
u − 0.0129590au + ··· + 0.369330a + 0.263499
−0.0691145a
2
u − 0.0129590au + ··· − 0.630670a + 0.263499
a
1
=
0.0604752a
2
u + 0.261339au + ··· + 0.0518359a − 0.980562
−0.0604752a
2
u − 0.261339au + ··· − 0.0518359a + 0.980562
a
4
=
0.0453564a
2
u − 0.0539957au + ··· + 0.0388769a + 0.764579
0.00863931a
2
u − 0.248380au + ··· + 0.578834a − 0.282937
a
8
=
0.0604752a
2
u + 0.261339au + ··· + 0.0518359a − 0.980562
−0.0604752a
2
u − 0.261339au + ··· − 0.0518359a + 0.980562
a
9
=
−u
u
a
12
=
0.0604752a
2
u + 0.261339au + ··· + 0.0518359a − 0.980562
−0.0604752a
2
u − 0.261339au + ··· − 0.0518359a + 0.980562
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
128
463
a
2
u −
56
463
a
2
−
24
463
au −
1168
463
a −
472
463
u +
4192
463
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
(u
3
+ u
2
+ 2u + 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
9
c
10
(u
2
− 2)
3
c
8
(u − 1)
6
c
11
, c
12
(u + 1)
6
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
9
c
10
(y −2)
6
c
8
, c
11
, c
12
(y −1)
6
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 0.865932
b = −0.754878
5.46628 4.98050
u = 1.41421
a = −0.99363 + 1.88732I
b = 0.877439 − 0.744862I
9.60386 + 2.82812I 11.50976 − 2.97945I
u = 1.41421
a = −0.99363 − 1.88732I
b = 0.877439 + 0.744862I
9.60386 − 2.82812I 11.50976 + 2.97945I
u = −1.41421
a = −0.516129 + 1.092130I
b = 0.877439 − 0.744862I
9.60386 + 2.82812I 11.50976 − 2.97945I
u = −1.41421
a = −0.516129 − 1.092130I
b = 0.877439 + 0.744862I
9.60386 − 2.82812I 11.50976 + 2.97945I
u = −1.41421
a = 4.15358
b = −0.754878
5.46628 4.98050
24
IV. I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
6
=
1
0
a
11
=
v
0
a
3
=
0
v
2
− 3v − 1
a
7
=
1
0
a
2
=
v
2
− 3v − 1
v
2
− 3v − 1
a
1
=
v
2
− 3v − 1
−v
2
+ 2v + 3
a
4
=
−2v
2
+ 5v + 4
−2v
2
+ 5v + 3
a
8
=
−v
2
+ 3v + 1
v
2
− 2v − 3
a
9
=
v
0
a
12
=
v
2
− 2v − 1
−v
2
+ 2v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8v
2
− 26v − 14
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
, c
9
c
10
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
11
(u + 1)
3
c
12
(u − 1)
3
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
y
3
− y
2
+ 2y − 1
c
5
, c
6
, c
9
c
10
y
3
c
8
, c
11
, c
12
(y − 1)
3
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.539798 + 0.182582I
a = 0
b = 0.877439 − 0.744862I
4.66906 + 2.82812I 2.09911 − 6.32406I
v = −0.539798 − 0.182582I
a = 0
b = 0.877439 + 0.744862I
4.66906 − 2.82812I 2.09911 + 6.32406I
v = 3.07960
a = 0
b = −0.754878
0.531480 −18.1980
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
3
− u
2
+ 2u − 1)
3
(u
112
+ 52u
111
+ ··· + 2998u + 1)
c
2
((u − 1)
8
)(u
3
+ u
2
− 1)
3
(u
112
− 12u
111
+ ··· + 54u + 1)
c
3
u
8
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
· (u
112
+ 2u
111
+ ··· + 2688u − 256)
c
4
((u + 1)
8
)(u
3
− u
2
+ 1)
3
(u
112
− 12u
111
+ ··· + 54u + 1)
c
5
, c
6
u
3
(u
2
− 2)
3
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
112
− 2u
111
+ ··· + 24u + 8)
c
7
u
8
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)
· (u
112
+ 2u
111
+ ··· + 2688u − 256)
c
8
(u − 1)
6
(u + 1)
3
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
112
− 5u
111
+ ··· − 113u + 7)
c
9
u
3
(u
2
− 2)
3
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
112
+ 6u
111
+ ··· + 84024u + 12200)
c
10
u
3
(u
2
− 2)
3
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
112
− 2u
111
+ ··· + 24u + 8)
c
11
(u + 1)
9
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
112
− 57u
111
+ ··· − 4733u + 49)
c
12
(u − 1)
3
(u + 1)
6
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
112
− 5u
111
+ ··· − 113u + 7)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
8
)(y
3
+ 3y
2
+ 2y − 1)
3
(y
112
+ 28y
111
+ ··· − 8620798y + 1)
c
2
, c
4
((y − 1)
8
)(y
3
− y
2
+ 2y − 1)
3
(y
112
− 52y
111
+ ··· − 2998y + 1)
c
3
, c
7
y
8
(y
3
+ 3y
2
+ 2y − 1)
3
(y
112
+ 60y
111
+ ··· − 3850240y + 65536)
c
5
, c
6
, c
10
y
3
(y − 2)
6
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
112
− 104y
111
+ ··· − 960y + 64)
c
8
, c
12
(y − 1)
9
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
112
− 57y
111
+ ··· − 4733y + 49)
c
9
y
3
(y − 2)
6
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
112
− 8y
111
+ ··· − 4167168576y + 148840000)
c
11
(y − 1)
9
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
112
+ 7y
111
+ ··· − 16407805y + 2401)
30
