12a
0005
(K12a
0005
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 10 4 12 7 1 9 11
Solving Sequence
2,5
3 6
4,10
7 8 1 11 9 12
c
2
c
5
c
3
c
6
c
7
c
1
c
10
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.83259 × 10
67
u
116
− 1.82204 × 10
70
u
115
+ ··· + 8.69873 × 10
68
b + 1.33324 × 10
70
,
1.23817 × 10
66
u
116
− 2.75088 × 10
67
u
115
+ ··· + 1.86668 × 10
66
a + 2.43651 × 10
67
, u
117
− 7u
116
+ ··· + 2u − 1i
I
u
2
= hb − a, −u
4
a + u
3
a − 2u
4
− u
2
a + 2u
3
+ a
2
− 2u
2
+ a − u + 2, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
u
3
= ha
3
u + a
3
− 2a
2
− 3au + b − a + u + 1, a
4
+ 2a
3
u − 3a
2
u − 3a
2
+ a + u, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 135 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−3.83 × 10
67
u
116
− 1.82 × 10
70
u
115
+ · · · + 8.70 × 10
68
b + 1.33 ×
10
70
, 1.24 × 10
66
u
116
− 2.75 × 10
67
u
115
+ · · · + 1.87 × 10
66
a + 2.44 ×
10
67
, u
117
− 7u
116
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
−0.663298u
116
+ 14.7367u
115
+ ··· + 13.8589u − 13.0526
0.0440592u
116
+ 20.9461u
115
+ ··· + 23.6452u − 15.3268
a
7
=
2.35575u
116
− 24.2437u
115
+ ··· − 23.3034u + 10.4991
5.54126u
116
− 59.4144u
115
+ ··· − 31.4570u + 17.5214
a
8
=
−0.226928u
116
− 3.84631u
115
+ ··· − 16.0087u + 7.28280
9.37936u
116
− 80.9730u
115
+ ··· − 36.3781u + 19.4890
a
1
=
u
2
+ 1
−u
4
a
11
=
−0.645907u
116
+ 15.9064u
115
+ ··· + 11.8738u − 13.0533
−0.477605u
116
+ 28.9600u
115
+ ··· + 28.1091u − 17.8115
a
9
=
−1.40166u
116
+ 21.6224u
115
+ ··· + 23.6425u − 15.1337
−3.20159u
116
+ 49.5014u
115
+ ··· + 34.8907u − 20.7044
a
12
=
−1.10727u
116
+ 8.57956u
115
+ ··· + 12.9847u − 2.44428
2.05987u
116
− 13.3894u
115
+ ··· − 1.35478u + 2.83905
(ii) Obstruction class = −1
(iii) Cusp Shapes = −17.0712u
116
+ 107.696u
115
+ ··· − 8.94784u − 8.30782
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
117
+ 57u
116
+ ··· − 52u − 1
c
2
, c
5
u
117
+ 7u
116
+ ··· + 2u + 1
c
3
u
117
− 7u
116
+ ··· − 2123180u + 148289
c
4
, c
7
u
117
+ 3u
116
+ ··· + 384u + 256
c
6
, c
9
u
117
− 3u
116
+ ··· − 6144u + 1024
c
8
, c
11
u
117
+ 8u
116
+ ··· + 5u + 1
c
10
, c
12
u
117
+ 38u
116
+ ··· − 199u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
117
+ 13y
116
+ ··· − 1116y −1
c
2
, c
5
y
117
+ 57y
116
+ ··· − 52y −1
c
3
y
117
− 31y
116
+ ··· − 741103690564y −21989627521
c
4
, c
7
y
117
− 55y
116
+ ··· + 245760y −65536
c
6
, c
9
y
117
+ 65y
116
+ ··· − 33554432y −1048576
c
8
, c
11
y
117
+ 38y
116
+ ··· − 199y −1
c
10
, c
12
y
117
+ 90y
116
+ ··· + 15017y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.788050 + 0.643963I
a = 0.441133 − 0.436719I
b = −0.030091 + 0.782506I
6.38871 − 3.43951I 0
u = −0.788050 − 0.643963I
a = 0.441133 + 0.436719I
b = −0.030091 − 0.782506I
6.38871 + 3.43951I 0
u = −0.436106 + 0.936175I
a = 0.78008 + 3.14764I
b = 0.51824 + 3.56972I
−0.482514 + 0.107557I 0
u = −0.436106 − 0.936175I
a = 0.78008 − 3.14764I
b = 0.51824 − 3.56972I
−0.482514 − 0.107557I 0
u = −0.650362 + 0.706698I
a = −0.958278 − 0.474899I
b = −0.59593 − 1.35751I
−0.40559 − 4.29098I 0
u = −0.650362 − 0.706698I
a = −0.958278 + 0.474899I
b = −0.59593 + 1.35751I
−0.40559 + 4.29098I 0
u = −0.459329 + 0.839596I
a = −2.18263 − 3.06586I
b = −1.97132 − 3.38773I
−0.15385 − 3.78902I 0
u = −0.459329 − 0.839596I
a = −2.18263 + 3.06586I
b = −1.97132 + 3.38773I
−0.15385 + 3.78902I 0
u = −0.795690 + 0.676627I
a = −0.258135 + 0.303256I
b = 0.139411 − 0.928846I
5.60113 − 9.33628I 0
u = −0.795690 − 0.676627I
a = −0.258135 − 0.303256I
b = 0.139411 + 0.928846I
5.60113 + 9.33628I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.622734 + 0.853712I
a = 1.130780 + 0.426011I
b = 0.368893 + 0.451916I
−0.816274 − 0.627025I 0
u = −0.622734 − 0.853712I
a = 1.130780 − 0.426011I
b = 0.368893 − 0.451916I
−0.816274 + 0.627025I 0
u = −0.387152 + 0.859674I
a = 0.438751 − 0.612774I
b = 0.142021 − 0.759816I
−0.34124 − 1.65771I 0
u = −0.387152 − 0.859674I
a = 0.438751 + 0.612774I
b = 0.142021 + 0.759816I
−0.34124 + 1.65771I 0
u = 0.863128 + 0.357713I
a = −1.87347 − 0.80598I
b = −0.646595 + 0.167847I
3.70909 − 12.80720I 0
u = 0.863128 − 0.357713I
a = −1.87347 + 0.80598I
b = −0.646595 − 0.167847I
3.70909 + 12.80720I 0
u = 0.842943 + 0.374277I
a = 1.75421 + 0.78574I
b = 0.544568 − 0.230616I
4.83595 − 6.78698I 0
u = 0.842943 − 0.374277I
a = 1.75421 − 0.78574I
b = 0.544568 + 0.230616I
4.83595 + 6.78698I 0
u = 0.259158 + 1.065270I
a = 0.375121 + 0.409369I
b = −0.662192 + 0.708860I
−2.20289 − 1.03572I 0
u = 0.259158 − 1.065270I
a = 0.375121 − 0.409369I
b = −0.662192 − 0.708860I
−2.20289 + 1.03572I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.495668 + 0.977957I
a = 0.395468 − 0.391923I
b = −1.047470 − 0.895669I
6.56810 − 0.57006I 0
u = 0.495668 − 0.977957I
a = 0.395468 + 0.391923I
b = −1.047470 + 0.895669I
6.56810 + 0.57006I 0
u = 0.291276 + 1.064330I
a = −0.066879 + 1.287670I
b = 0.18397 + 2.32609I
−2.46003 + 2.02278I 0
u = 0.291276 − 1.064330I
a = −0.066879 − 1.287670I
b = 0.18397 − 2.32609I
−2.46003 − 2.02278I 0
u = 0.887934 + 0.028589I
a = −0.175661 + 1.187160I
b = −0.064609 + 0.239852I
−1.47278 + 2.54621I 0
u = 0.887934 − 0.028589I
a = −0.175661 − 1.187160I
b = −0.064609 − 0.239852I
−1.47278 − 2.54621I 0
u = 0.520884 + 0.991503I
a = −0.319131 + 0.493403I
b = 1.02158 + 1.13380I
6.78221 + 5.92923I 0
u = 0.520884 − 0.991503I
a = −0.319131 − 0.493403I
b = 1.02158 − 1.13380I
6.78221 − 5.92923I 0
u = −0.558143 + 0.981636I
a = 0.06180 − 1.84492I
b = −0.36559 − 2.44954I
0.918923 − 0.592170I 0
u = −0.558143 − 0.981636I
a = 0.06180 + 1.84492I
b = −0.36559 + 2.44954I
0.918923 + 0.592170I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.241670 + 1.106980I
a = −0.03421 − 1.53422I
b = −0.36187 − 2.52798I
−3.52324 − 3.49244I 0
u = 0.241670 − 1.106980I
a = −0.03421 + 1.53422I
b = −0.36187 + 2.52798I
−3.52324 + 3.49244I 0
u = −0.636348 + 0.587639I
a = 1.65981 + 0.37698I
b = 0.754385 − 0.268951I
2.08032 − 4.09466I 0
u = −0.636348 − 0.587639I
a = 1.65981 − 0.37698I
b = 0.754385 + 0.268951I
2.08032 + 4.09466I 0
u = −0.402200 + 1.067810I
a = 0.43074 + 1.47123I
b = 1.16303 + 1.75138I
−2.93679 − 1.28935I 0
u = −0.402200 − 1.067810I
a = 0.43074 − 1.47123I
b = 1.16303 − 1.75138I
−2.93679 + 1.28935I 0
u = 0.331096 + 1.100150I
a = −0.854097 − 0.483958I
b = 0.097301 − 0.669536I
−4.41468 + 3.80335I 0
u = 0.331096 − 1.100150I
a = −0.854097 + 0.483958I
b = 0.097301 + 0.669536I
−4.41468 − 3.80335I 0
u = 0.788143 + 0.307476I
a = −1.78183 − 0.40923I
b = −0.723918 + 0.564808I
−2.40584 − 6.41831I 0
u = 0.788143 − 0.307476I
a = −1.78183 + 0.40923I
b = −0.723918 − 0.564808I
−2.40584 + 6.41831I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.597169 + 0.597551I
a = 0.836553 + 0.317154I
b = −0.300337 − 1.081280I
7.95045 − 1.49171I 0
u = 0.597169 − 0.597551I
a = 0.836553 − 0.317154I
b = −0.300337 + 1.081280I
7.95045 + 1.49171I 0
u = −0.562393 + 1.012380I
a = −0.04278 − 1.50341I
b = 0.59004 − 2.01129I
1.40553 − 3.26753I 0
u = −0.562393 − 1.012380I
a = −0.04278 + 1.50341I
b = 0.59004 + 2.01129I
1.40553 + 3.26753I 0
u = 0.552045 + 0.635041I
a = −0.777686 − 0.173295I
b = 0.343721 + 1.274540I
7.59257 + 4.78397I 0
u = 0.552045 − 0.635041I
a = −0.777686 + 0.173295I
b = 0.343721 − 1.274540I
7.59257 − 4.78397I 0
u = −0.642479 + 0.537916I
a = 1.50891 − 0.45918I
b = 0.760280 + 0.486993I
2.80307 − 1.45282I 0
u = −0.642479 − 0.537916I
a = 1.50891 + 0.45918I
b = 0.760280 − 0.486993I
2.80307 + 1.45282I 0
u = −0.241010 + 1.137390I
a = −0.994770 − 0.885964I
b = −1.94230 − 0.88243I
2.14923 − 2.38133I 0
u = −0.241010 − 1.137390I
a = −0.994770 + 0.885964I
b = −1.94230 + 0.88243I
2.14923 + 2.38133I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.536282 + 1.031720I
a = 0.03646 + 1.86790I
b = 0.60835 + 2.44313I
0.57777 − 5.74969I 0
u = −0.536282 − 1.031720I
a = 0.03646 − 1.86790I
b = 0.60835 − 2.44313I
0.57777 + 5.74969I 0
u = −0.749091 + 0.335717I
a = 1.67621 − 1.39851I
b = 0.630951 − 0.165919I
6.64713 + 0.36834I 0
u = −0.749091 − 0.335717I
a = 1.67621 + 1.39851I
b = 0.630951 + 0.165919I
6.64713 − 0.36834I 0
u = 0.743090 + 0.344565I
a = −1.37666 + 0.62863I
b = −0.296731 − 0.415869I
0.90323 − 6.10586I 0
u = 0.743090 − 0.344565I
a = −1.37666 − 0.62863I
b = −0.296731 + 0.415869I
0.90323 + 6.10586I 0
u = −0.498147 + 1.077050I
a = −0.51304 + 2.12295I
b = −1.01752 + 2.82627I
−2.25240 − 5.67314I 0
u = −0.498147 − 1.077050I
a = −0.51304 − 2.12295I
b = −1.01752 − 2.82627I
−2.25240 + 5.67314I 0
u = −0.286372 + 1.155600I
a = 1.03487 + 1.11825I
b = 1.99849 + 1.20360I
1.61709 + 3.18256I 0
u = −0.286372 − 1.155600I
a = 1.03487 − 1.11825I
b = 1.99849 − 1.20360I
1.61709 − 3.18256I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.242947 + 1.167530I
a = −0.213044 − 1.030830I
b = 0.73246 − 1.40141I
−7.04923 − 3.39820I 0
u = 0.242947 − 1.167530I
a = −0.213044 + 1.030830I
b = 0.73246 + 1.40141I
−7.04923 + 3.39820I 0
u = −0.751272 + 0.284916I
a = −1.80885 + 1.49561I
b = −0.698513 + 0.241621I
5.93364 + 6.27192I 0
u = −0.751272 − 0.284916I
a = −1.80885 − 1.49561I
b = −0.698513 − 0.241621I
5.93364 − 6.27192I 0
u = −0.714184 + 0.960943I
a = 0.217324 + 0.091526I
b = −0.810052 + 0.410513I
4.75806 + 3.70162I 0
u = −0.714184 − 0.960943I
a = 0.217324 − 0.091526I
b = −0.810052 − 0.410513I
4.75806 − 3.70162I 0
u = 0.714416 + 0.366021I
a = 1.43841 + 0.41582I
b = 0.399059 − 0.722002I
2.01022 − 3.40590I 0
u = 0.714416 − 0.366021I
a = 1.43841 − 0.41582I
b = 0.399059 + 0.722002I
2.01022 + 3.40590I 0
u = 0.784133 + 0.167033I
a = −0.946265 + 0.770926I
b = −0.220586 − 0.048660I
−4.22647 − 1.60861I 0
u = 0.784133 − 0.167033I
a = −0.946265 − 0.770926I
b = −0.220586 + 0.048660I
−4.22647 + 1.60861I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.694981 + 0.982159I
a = −0.073453 − 0.271762I
b = 0.906822 − 0.651608I
5.38630 − 2.11378I 0
u = −0.694981 − 0.982159I
a = −0.073453 + 0.271762I
b = 0.906822 + 0.651608I
5.38630 + 2.11378I 0
u = 0.152478 + 1.194550I
a = −0.423715 + 0.926756I
b = −1.43935 + 1.33380I
−0.47338 − 3.99674I 0
u = 0.152478 − 1.194550I
a = −0.423715 − 0.926756I
b = −1.43935 − 1.33380I
−0.47338 + 3.99674I 0
u = 0.436147 + 1.131570I
a = 0.042081 + 0.819809I
b = −0.08366 + 1.52333I
−4.67639 + 3.90668I 0
u = 0.436147 − 1.131570I
a = 0.042081 − 0.819809I
b = −0.08366 − 1.52333I
−4.67639 − 3.90668I 0
u = −0.601257 + 0.504673I
a = −1.71238 − 0.62803I
b = −0.829199 + 0.215477I
2.13316 + 1.22336I 0
u = −0.601257 − 0.504673I
a = −1.71238 + 0.62803I
b = −0.829199 − 0.215477I
2.13316 − 1.22336I 0
u = 0.523972 + 1.106740I
a = 0.64089 − 1.39244I
b = −0.13170 − 1.98598I
−3.09840 + 3.62785I 0
u = 0.523972 − 1.106740I
a = 0.64089 + 1.39244I
b = −0.13170 + 1.98598I
−3.09840 − 3.62785I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.549843 + 1.100120I
a = −0.132774 + 1.076900I
b = −0.84858 + 1.88003I
−0.67169 + 5.16920I 0
u = 0.549843 − 1.100120I
a = −0.132774 − 1.076900I
b = −0.84858 − 1.88003I
−0.67169 − 5.16920I 0
u = 0.681708 + 0.356666I
a = 1.32997 − 0.53776I
b = 0.160489 + 0.459931I
1.48482 − 0.40443I 0
u = 0.681708 − 0.356666I
a = 1.32997 + 0.53776I
b = 0.160489 − 0.459931I
1.48482 + 0.40443I 0
u = 0.345072 + 1.184100I
a = −0.471587 − 1.087290I
b = −0.76488 − 1.84916I
−8.31174 + 2.09718I 0
u = 0.345072 − 1.184100I
a = −0.471587 + 1.087290I
b = −0.76488 + 1.84916I
−8.31174 − 2.09718I 0
u = 0.170264 + 1.223690I
a = 0.439760 − 1.157850I
b = 1.44857 − 1.59171I
−1.64372 − 9.78312I 0
u = 0.170264 − 1.223690I
a = 0.439760 + 1.157850I
b = 1.44857 + 1.59171I
−1.64372 + 9.78312I 0
u = 0.561453 + 1.104500I
a = −0.18042 + 1.42465I
b = 0.60353 + 2.19281I
−0.14818 + 8.29193I 0
u = 0.561453 − 1.104500I
a = −0.18042 − 1.42465I
b = 0.60353 − 2.19281I
−0.14818 − 8.29193I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.565539 + 1.117910I
a = 0.205821 − 1.138550I
b = 0.99445 − 1.86392I
−1.36213 + 11.07080I 0
u = 0.565539 − 1.117910I
a = 0.205821 + 1.138550I
b = 0.99445 + 1.86392I
−1.36213 − 11.07080I 0
u = −0.567660 + 1.120280I
a = 0.92774 − 1.58823I
b = 1.61984 − 2.36858I
4.35518 − 5.35177I 0
u = −0.567660 − 1.120280I
a = 0.92774 + 1.58823I
b = 1.61984 + 2.36858I
4.35518 + 5.35177I 0
u = −0.112035 + 0.733492I
a = −0.252312 − 0.649208I
b = −0.801580 + 0.061448I
−0.98803 − 1.33457I 0
u = −0.112035 − 0.733492I
a = −0.252312 + 0.649208I
b = −0.801580 − 0.061448I
−0.98803 + 1.33457I 0
u = −0.553058 + 1.137830I
a = −1.04926 + 1.73476I
b = −1.71134 + 2.56327I
3.44904 − 11.19340I 0
u = −0.553058 − 1.137830I
a = −1.04926 − 1.73476I
b = −1.71134 − 2.56327I
3.44904 + 11.19340I 0
u = 0.567903 + 1.141310I
a = 0.05003 − 1.87100I
b = −0.57280 − 2.68050I
−4.86384 + 11.49110I 0
u = 0.567903 − 1.141310I
a = 0.05003 + 1.87100I
b = −0.57280 + 2.68050I
−4.86384 − 11.49110I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.510014 + 1.175500I
a = 0.392295 − 0.764542I
b = 0.93895 − 1.16346I
−7.19643 + 6.38755I 0
u = 0.510014 − 1.175500I
a = 0.392295 + 0.764542I
b = 0.93895 + 1.16346I
−7.19643 − 6.38755I 0
u = 0.606775 + 1.139680I
a = 0.39981 + 1.72045I
b = 1.05381 + 2.69039I
2.54035 + 12.16610I 0
u = 0.606775 − 1.139680I
a = 0.39981 − 1.72045I
b = 1.05381 − 2.69039I
2.54035 − 12.16610I 0
u = 0.608130 + 1.152820I
a = −0.46729 − 1.85484I
b = −1.07127 − 2.83937I
1.3174 + 18.2419I 0
u = 0.608130 − 1.152820I
a = −0.46729 + 1.85484I
b = −1.07127 + 2.83937I
1.3174 − 18.2419I 0
u = 0.627397 + 0.276713I
a = −1.306950 − 0.118664I
b = −0.472407 + 1.076420I
−0.769601 + 0.898386I −2.60850 + 0.I
u = 0.627397 − 0.276713I
a = −1.306950 + 0.118664I
b = −0.472407 − 1.076420I
−0.769601 − 0.898386I −2.60850 + 0.I
u = 0.427334 + 1.247820I
a = −0.888943 − 0.363772I
b = −1.37018 − 0.74441I
−5.43715 + 7.16206I 0
u = 0.427334 − 1.247820I
a = −0.888943 + 0.363772I
b = −1.37018 + 0.74441I
−5.43715 − 7.16206I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.461672 + 1.241970I
a = 0.833419 − 0.024090I
b = 1.352030 + 0.152225I
−5.20525 + 2.24961I 0
u = 0.461672 − 1.241970I
a = 0.833419 + 0.024090I
b = 1.352030 − 0.152225I
−5.20525 − 2.24961I 0
u = 0.621668
a = 1.04985
b = −0.0115780
−1.62182 −5.59140
u = −0.438939 + 0.373264I
a = −2.41763 + 0.85684I
b = −1.131840 + 0.153994I
−0.20699 + 1.55538I −2.49928 − 3.27405I
u = −0.438939 − 0.373264I
a = −2.41763 − 0.85684I
b = −1.131840 − 0.153994I
−0.20699 − 1.55538I −2.49928 + 3.27405I
u = −0.076965 + 0.143848I
a = −4.44920 + 0.48531I
b = −0.585057 + 0.558252I
−0.32935 + 1.53120I −2.54159 − 4.51341I
u = −0.076965 − 0.143848I
a = −4.44920 − 0.48531I
b = −0.585057 − 0.558252I
−0.32935 − 1.53120I −2.54159 + 4.51341I
16
II. I
u
2
= hb − a, −u
4
a − 2u
4
+ · · · + a + 2, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
a
a
a
7
=
u
u
a
8
=
−u
2
− 1
u
4
a
1
=
u
2
+ 1
−u
4
a
11
=
−u
4
a + u
3
a − 2u
2
a − a
2u
3
a + au
a
9
=
a
a
a
12
=
−u
4
a + u
3
a − u
4
− 2u
2
a + u
3
− u
2
− a + 1
2u
3
a − u
4
+ u
3
+ au − u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
a + u
3
a − u
4
− u
2
a + 3u
3
− 2au − 2u
2
− 2a − u − 7
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
3
, c
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
6
, c
9
u
10
c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
8
, c
12
(u
2
+ u + 1)
5
c
10
, c
11
(u
2
− u + 1)
5
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
2
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
3
, c
4
, c
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
6
, c
9
y
10
c
8
, c
10
, c
11
c
12
(y
2
+ y + 1)
5
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −1.39836 − 1.74033I
b = −1.39836 − 1.74033I
−0.329100 + 0.499304I 1.93681 + 0.71136I
u = −0.339110 + 0.822375I
a = −0.80799 + 2.08118I
b = −0.80799 + 2.08118I
−0.32910 − 3.56046I −7.97351 + 2.70956I
u = −0.339110 − 0.822375I
a = −1.39836 + 1.74033I
b = −1.39836 + 1.74033I
−0.329100 − 0.499304I 1.93681 − 0.71136I
u = −0.339110 − 0.822375I
a = −0.80799 − 2.08118I
b = −0.80799 − 2.08118I
−0.32910 + 3.56046I −7.97351 − 2.70956I
u = 0.766826
a = −0.258559 + 0.447838I
b = −0.258559 + 0.447838I
−2.40108 + 2.02988I −6.80799 − 1.95361I
u = 0.766826
a = −0.258559 − 0.447838I
b = −0.258559 − 0.447838I
−2.40108 − 2.02988I −6.80799 + 1.95361I
u = 0.455697 + 1.200150I
a = −0.556121 − 0.280562I
b = −0.556121 − 0.280562I
−5.87256 + 2.37095I −12.81148 − 1.72217I
u = 0.455697 + 1.200150I
a = 0.521035 − 0.341334I
b = 0.521035 − 0.341334I
−5.87256 + 6.43072I −8.34383 − 2.96651I
u = 0.455697 − 1.200150I
a = −0.556121 + 0.280562I
b = −0.556121 + 0.280562I
−5.87256 − 2.37095I −12.81148 + 1.72217I
u = 0.455697 − 1.200150I
a = 0.521035 + 0.341334I
b = 0.521035 + 0.341334I
−5.87256 − 6.43072I −8.34383 + 2.96651I
20
III.
I
u
3
= ha
3
u+a
3
−2a
2
−3au+b−a+u+1, a
4
+2a
3
u−3a
2
u−3a
2
+a+u, u
2
+u+1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
4
=
0
u
a
10
=
a
−a
3
u − a
3
+ 2a
2
+ 3au + a − u − 1
a
7
=
0
−a
3
u − a
3
+ a
2
+ au + 2u + 2
a
8
=
0
−a
3
u − a
3
+ a
2
+ au + 2u + 2
a
1
=
−u
−u
a
11
=
−a
3
u + 2a
2
u + 2a
2
− 2a − u
−2a
3
u − a
3
+ 2a
2
u + 4a
2
+ 3au − 2a − 2u − 1
a
9
=
a
a
3
u + a
3
− 3a
2
− 4au + a + 2u + 2
a
12
=
−a
3
u + a
2
u + a
2
− a
−2a
3
u − a
3
+ a
2
u + 2a
2
+ au − a + 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
3
u + 3a
3
+ 3a
2
u − a
2
− 8au − 5a − u − 2
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
4
, c
7
u
8
c
6
, c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
8
(u
4
− u
3
+ u
2
+ 1)
2
c
9
, c
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
11
(u
4
+ u
3
+ u
2
+ 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
4
c
4
, c
7
y
8
c
6
, c
9
, c
10
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
8
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.576953 + 0.283088I
b = −0.819983 + 0.968508I
6.79074 − 5.19385I −4.47320 + 2.03656I
u = −0.500000 + 0.866025I
a = −0.533637 − 0.358112I
b = 0.75842 − 1.22518I
6.79074 + 1.13408I −1.68800 − 4.61015I
u = −0.500000 + 0.866025I
a = −0.58443 − 1.44211I
b = −0.34305 − 2.03771I
−0.21101 − 3.44499I −3.64182 + 2.68374I
u = −0.500000 + 0.866025I
a = 1.54112 − 0.21492I
b = 0.904615 − 0.303685I
−0.211005 − 0.614778I 1.30302 − 4.44028I
u = −0.500000 − 0.866025I
a = 0.576953 − 0.283088I
b = −0.819983 − 0.968508I
6.79074 + 5.19385I −4.47320 − 2.03656I
u = −0.500000 − 0.866025I
a = −0.533637 + 0.358112I
b = 0.75842 + 1.22518I
6.79074 − 1.13408I −1.68800 + 4.61015I
u = −0.500000 − 0.866025I
a = −0.58443 + 1.44211I
b = −0.34305 + 2.03771I
−0.21101 + 3.44499I −3.64182 − 2.68374I
u = −0.500000 − 0.866025I
a = 1.54112 + 0.21492I
b = 0.904615 + 0.303685I
−0.211005 + 0.614778I 1.30302 + 4.44028I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· (u
117
+ 57u
116
+ ··· − 52u − 1)
c
2
((u
2
+ u + 1)
4
)(u
5
− u
4
+ ··· + u − 1)
2
(u
117
+ 7u
116
+ ··· + 2u + 1)
c
3
(u
2
− u + 1)
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
117
− 7u
116
+ ··· − 2123180u + 148289)
c
4
u
8
(u
5
+ u
4
+ ··· + u − 1)
2
(u
117
+ 3u
116
+ ··· + 384u + 256)
c
5
((u
2
− u + 1)
4
)(u
5
+ u
4
+ ··· + u + 1)
2
(u
117
+ 7u
116
+ ··· + 2u + 1)
c
6
u
10
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
(u
117
− 3u
116
+ ··· − 6144u + 1024)
c
7
u
8
(u
5
− u
4
+ ··· + u + 1)
2
(u
117
+ 3u
116
+ ··· + 384u + 256)
c
8
((u
2
+ u + 1)
5
)(u
4
− u
3
+ u
2
+ 1)
2
(u
117
+ 8u
116
+ ··· + 5u + 1)
c
9
u
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
(u
117
− 3u
116
+ ··· − 6144u + 1024)
c
10
((u
2
− u + 1)
5
)(u
4
− u
3
+ 3u
2
− 2u + 1)
2
(u
117
+ 38u
116
+ ··· − 199u − 1)
c
11
((u
2
− u + 1)
5
)(u
4
+ u
3
+ u
2
+ 1)
2
(u
117
+ 8u
116
+ ··· + 5u + 1)
c
12
((u
2
+ u + 1)
5
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
(u
117
+ 38u
116
+ ··· − 199u − 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
4
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
· (y
117
+ 13y
116
+ ··· − 1116y −1)
c
2
, c
5
(y
2
+ y + 1)
4
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
117
+ 57y
116
+ ··· − 52y −1)
c
3
(y
2
+ y + 1)
4
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
117
− 31y
116
+ ··· − 741103690564y −21989627521)
c
4
, c
7
y
8
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
117
− 55y
116
+ ··· + 245760y −65536)
c
6
, c
9
y
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
· (y
117
+ 65y
116
+ ··· − 33554432y −1048576)
c
8
, c
11
((y
2
+ y + 1)
5
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
(y
117
+ 38y
116
+ ··· − 199y −1)
c
10
, c
12
(y
2
+ y + 1)
5
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
· (y
117
+ 90y
116
+ ··· + 15017y −1)
26
