12a
0225
(K12a
0225
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 12 10 5 4 1 8
Solving Sequence
4,9
5 10 11 6
8,12
1 7 3 2
c
4
c
9
c
10
c
5
c
8
c
12
c
7
c
3
c
2
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.07777 × 10
66
u
126
+ 2.16707 × 10
66
u
125
+ ··· + 1.72852 × 10
66
b − 4.32805 × 10
66
,
7.32061 × 10
65
u
126
− 1.66742 × 10
66
u
125
+ ··· + 1.72852 × 10
66
a − 1.52406 × 10
67
, u
127
+ u
126
+ ··· − 4u − 4i
I
u
2
= hu
2
a − u
3
+ 2b + u, −6u
3
a + 2u
2
a + 2a
2
+ 5u
2
− 4a + 6u − 14, u
4
− 2u
2
+ 2i
I
v
1
= ha, b − v + 1, v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 137 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
= h4.08 × 10
66
u
126
+ 2.17 × 10
66
u
125
+ · · · + 1.73 × 10
66
b − 4.33 ×
10
66
, 7.32 × 10
65
u
126
− 1.67 × 10
66
u
125
+ · · · + 1.73 × 10
66
a − 1.52 ×
10
67
, u
127
+ u
126
+ · · · − 4u − 4i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
10
=
u
−u
3
+ u
a
11
=
u
3
−u
3
+ u
a
6
=
u
8
− u
6
+ u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
8
=
−u
3
u
5
− u
3
+ u
a
12
=
−0.423519u
126
+ 0.964650u
125
+ ··· + 9.44857u + 8.81712
−2.35911u
126
− 1.25371u
125
+ ··· + 6.16306u + 2.50390
a
1
=
−0.00503774u
126
+ 0.683855u
125
+ ··· + 7.43488u + 5.05619
−1.38708u
126
− 0.530217u
125
+ ··· + 5.40266u + 1.20161
a
7
=
−0.189021u
126
− 0.0433393u
125
+ ··· − 5.68886u − 0.558061
−0.137798u
126
+ 0.166256u
125
+ ··· + 3.26326u − 0.549191
a
3
=
−0.406855u
126
+ 0.266501u
125
+ ··· + 5.53868u + 7.25484
−3.21774u
126
− 1.72302u
125
+ ··· + 6.64167u + 4.67939
a
2
=
−0.202280u
126
− 0.184206u
125
+ ··· + 3.16129u + 3.06932
−2.22568u
126
− 1.02528u
125
+ ··· + 5.29101u + 3.62099
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.57051u
126
+ 2.63831u
125
+ ··· + 11.3436u + 1.19661
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
127
+ 62u
126
+ ··· − 34u − 25
c
2
, c
6
u
127
− 2u
126
+ ··· + 24u − 5
c
3
u
127
+ 2u
126
+ ··· − 4532584u − 667745
c
4
, c
9
u
127
+ u
126
+ ··· − 4u − 4
c
5
u
127
− u
126
+ ··· − 7705060u − 2511892
c
7
, c
12
u
127
− 3u
126
+ ··· + 11u − 1
c
8
u
127
− 61u
126
+ ··· + 80u − 16
c
10
u
127
+ 3u
126
+ ··· + 54716u − 9292
c
11
u
127
− 63u
126
+ ··· − 9u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
127
+ 14y
126
+ ··· + 23706y −625
c
2
, c
6
y
127
+ 62y
126
+ ··· − 34y −25
c
3
y
127
− 34y
126
+ ··· + 8331046653166y −445883385025
c
4
, c
9
y
127
− 61y
126
+ ··· + 80y −16
c
5
y
127
− 29y
126
+ ··· + 382290475250896y −6309601419664
c
7
, c
12
y
127
− 63y
126
+ ··· − 9y −1
c
8
y
127
+ 15y
126
+ ··· − 5888y −256
c
10
y
127
+ 31y
126
+ ··· − 5880391024y −86341264
c
11
y
127
+ 17y
126
+ ··· − 473y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655892 + 0.693362I
a = 1.314510 + 0.510372I
b = 1.08376 + 1.72394I
−4.37389 − 10.57070I 0
u = −0.655892 − 0.693362I
a = 1.314510 − 0.510372I
b = 1.08376 − 1.72394I
−4.37389 + 10.57070I 0
u = −1.047020 + 0.069569I
a = −0.051726 + 0.443444I
b = −0.550463 + 0.034451I
−1.72547 − 2.55576I 0
u = −1.047020 − 0.069569I
a = −0.051726 − 0.443444I
b = −0.550463 − 0.034451I
−1.72547 + 2.55576I 0
u = 0.634680 + 0.668715I
a = −1.136010 + 0.469975I
b = −0.91228 + 1.61811I
−1.74528 + 5.54287I 0
u = 0.634680 − 0.668715I
a = −1.136010 − 0.469975I
b = −0.91228 − 1.61811I
−1.74528 − 5.54287I 0
u = −0.592109 + 0.702459I
a = 1.158410 + 0.186330I
b = 1.01589 + 1.27934I
−6.26975 − 2.25990I 0
u = −0.592109 − 0.702459I
a = 1.158410 − 0.186330I
b = 1.01589 − 1.27934I
−6.26975 + 2.25990I 0
u = 0.594900 + 0.697956I
a = −0.419012 + 0.778242I
b = 0.308147 + 0.247704I
−6.21986 + 4.89035I 0
u = 0.594900 − 0.697956I
a = −0.419012 − 0.778242I
b = 0.308147 − 0.247704I
−6.21986 − 4.89035I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.001370 + 0.414476I
a = 0.66137 + 1.98187I
b = −0.297044 − 0.197706I
2.70969 + 4.19118I 0
u = 1.001370 − 0.414476I
a = 0.66137 − 1.98187I
b = −0.297044 + 0.197706I
2.70969 − 4.19118I 0
u = 1.072370 + 0.217558I
a = 0.464726 + 0.287632I
b = 0.1216410 + 0.0127233I
2.07695 − 0.23674I 0
u = 1.072370 − 0.217558I
a = 0.464726 − 0.287632I
b = 0.1216410 − 0.0127233I
2.07695 + 0.23674I 0
u = 1.065100 + 0.279580I
a = 1.41979 + 1.74741I
b = −1.55858 − 1.11538I
4.67472 − 1.72073I 0
u = 1.065100 − 0.279580I
a = 1.41979 − 1.74741I
b = −1.55858 + 1.11538I
4.67472 + 1.72073I 0
u = 0.938234 + 0.584174I
a = 1.43618 − 1.11948I
b = −0.79409 − 1.30755I
−0.848878 − 0.677204I 0
u = 0.938234 − 0.584174I
a = 1.43618 + 1.11948I
b = −0.79409 + 1.30755I
−0.848878 + 0.677204I 0
u = 0.522467 + 0.724113I
a = −0.668044 + 0.645481I
b = −0.1164460 − 0.0318385I
−7.09599 − 3.42822I 0
u = 0.522467 − 0.724113I
a = −0.668044 − 0.645481I
b = −0.1164460 + 0.0318385I
−7.09599 + 3.42822I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.067000 + 0.297601I
a = 0.81276 − 3.46883I
b = −1.01802 + 1.65962I
4.82423 + 2.64205I 0
u = 1.067000 − 0.297601I
a = 0.81276 + 3.46883I
b = −1.01802 − 1.65962I
4.82423 − 2.64205I 0
u = −0.924048 + 0.616765I
a = −1.38793 − 1.36500I
b = 0.86619 − 1.49707I
−3.57918 + 5.53649I 0
u = −0.924048 − 0.616765I
a = −1.38793 + 1.36500I
b = 0.86619 + 1.49707I
−3.57918 − 5.53649I 0
u = −0.779035 + 0.415744I
a = −0.077329 + 0.485124I
b = −0.580693 − 0.119824I
−1.31566 − 1.85053I 0
u = −0.779035 − 0.415744I
a = −0.077329 − 0.485124I
b = −0.580693 + 0.119824I
−1.31566 + 1.85053I 0
u = −1.092840 + 0.268150I
a = −0.06360 − 3.32675I
b = 0.41687 + 1.99039I
5.88768 + 2.49783I 0
u = −1.092840 − 0.268150I
a = −0.06360 + 3.32675I
b = 0.41687 − 1.99039I
5.88768 − 2.49783I 0
u = −0.339339 + 0.800350I
a = 1.095760 − 0.061560I
b = 1.34841 − 2.14040I
−2.69050 + 13.09910I 0
u = −0.339339 − 0.800350I
a = 1.095760 + 0.061560I
b = 1.34841 + 2.14040I
−2.69050 − 13.09910I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073940 + 0.356945I
a = 0.693583 + 0.828577I
b = 0.123195 − 0.578978I
3.23724 + 1.23193I 0
u = 1.073940 − 0.356945I
a = 0.693583 − 0.828577I
b = 0.123195 + 0.578978I
3.23724 − 1.23193I 0
u = 1.118950 + 0.174031I
a = −0.74468 − 2.11605I
b = 0.84591 + 1.47100I
−0.31356 − 2.38535I 0
u = 1.118950 − 0.174031I
a = −0.74468 + 2.11605I
b = 0.84591 − 1.47100I
−0.31356 + 2.38535I 0
u = −0.551054 + 0.669205I
a = 0.458769 + 0.611592I
b = −0.283645 − 0.016918I
−3.25053 − 0.33817I 0
u = −0.551054 − 0.669205I
a = 0.458769 − 0.611592I
b = −0.283645 + 0.016918I
−3.25053 + 0.33817I 0
u = 0.436742 + 0.748516I
a = −0.690511 − 0.365304I
b = −0.375553 + 0.221479I
−6.66752 + 0.81220I 0
u = 0.436742 − 0.748516I
a = −0.690511 + 0.365304I
b = −0.375553 − 0.221479I
−6.66752 − 0.81220I 0
u = −1.118640 + 0.183032I
a = −0.394837 + 0.057370I
b = −0.099667 + 0.275327I
−0.26843 + 4.93831I 0
u = −1.118640 − 0.183032I
a = −0.394837 − 0.057370I
b = −0.099667 − 0.275327I
−0.26843 − 4.93831I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.380278 + 0.777084I
a = 1.017260 + 0.138781I
b = 1.00049 − 1.50794I
−5.16483 + 4.82923I 0
u = −0.380278 − 0.777084I
a = 1.017260 − 0.138781I
b = 1.00049 + 1.50794I
−5.16483 − 4.82923I 0
u = 0.374985 + 0.775788I
a = −0.469058 − 0.484153I
b = 0.0369528 − 0.0699892I
−5.07821 − 7.41786I 0
u = 0.374985 − 0.775788I
a = −0.469058 + 0.484153I
b = 0.0369528 + 0.0699892I
−5.07821 + 7.41786I 0
u = −1.095530 + 0.317267I
a = −1.35010 + 2.04037I
b = 1.10692 − 1.44630I
6.35011 − 2.92708I 0
u = −1.095530 − 0.317267I
a = −1.35010 − 2.04037I
b = 1.10692 + 1.44630I
6.35011 + 2.92708I 0
u = 1.028870 + 0.503372I
a = 1.89786 + 0.40949I
b = −0.50476 − 1.44118I
2.19843 + 0.73185I 0
u = 1.028870 − 0.503372I
a = 1.89786 − 0.40949I
b = −0.50476 + 1.44118I
2.19843 − 0.73185I 0
u = 0.341008 + 0.780195I
a = −1.007820 − 0.033895I
b = −1.03417 − 2.09665I
−0.23646 − 7.86331I 4.00000 + 4.73656I
u = 0.341008 − 0.780195I
a = −1.007820 + 0.033895I
b = −1.03417 + 2.09665I
−0.23646 + 7.86331I 4.00000 − 4.73656I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978936 + 0.603644I
a = −0.102279 − 0.120716I
b = 0.457141 − 0.368803I
−5.08445 + 0.11410I 0
u = 0.978936 − 0.603644I
a = −0.102279 + 0.120716I
b = 0.457141 + 0.368803I
−5.08445 − 0.11410I 0
u = −0.981498 + 0.605801I
a = −1.01938 − 1.02209I
b = 0.98919 − 1.13852I
−5.11812 − 2.76345I 0
u = −0.981498 − 0.605801I
a = −1.01938 + 1.02209I
b = 0.98919 + 1.13852I
−5.11812 + 2.76345I 0
u = −1.007530 + 0.577065I
a = 0.552583 − 0.119569I
b = −0.441940 − 0.101137I
−1.90343 − 4.50154I 0
u = −1.007530 − 0.577065I
a = 0.552583 + 0.119569I
b = −0.441940 + 0.101137I
−1.90343 + 4.50154I 0
u = −1.073660 + 0.444900I
a = −0.50889 + 1.45609I
b = −0.520955 − 0.961785I
2.41666 − 5.68494I 0
u = −1.073660 − 0.444900I
a = −0.50889 − 1.45609I
b = −0.520955 + 0.961785I
2.41666 + 5.68494I 0
u = −1.144340 + 0.219800I
a = 1.02599 − 2.80930I
b = −0.73122 + 2.21113I
4.46493 + 5.09634I 0
u = −1.144340 − 0.219800I
a = 1.02599 + 2.80930I
b = −0.73122 − 2.21113I
4.46493 − 5.09634I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.379009 + 0.738997I
a = 0.485722 − 0.361571I
b = −0.024435 + 0.180978I
−2.40706 + 2.55125I 1.111011 − 0.764217I
u = −0.379009 − 0.738997I
a = 0.485722 + 0.361571I
b = −0.024435 − 0.180978I
−2.40706 − 2.55125I 1.111011 + 0.764217I
u = −1.045400 + 0.531152I
a = −0.48217 + 2.74765I
b = −1.210830 − 0.115292I
1.73485 − 1.96309I 0
u = −1.045400 − 0.531152I
a = −0.48217 − 2.74765I
b = −1.210830 + 0.115292I
1.73485 + 1.96309I 0
u = 1.164820 + 0.211735I
a = −1.36701 − 2.70402I
b = 1.09385 + 2.31525I
2.14759 − 10.24030I 0
u = 1.164820 − 0.211735I
a = −1.36701 + 2.70402I
b = 1.09385 − 2.31525I
2.14759 + 10.24030I 0
u = −1.069030 + 0.511554I
a = −0.989284 + 0.998987I
b = −0.034858 − 1.174900I
2.25602 − 5.77634I 0
u = −1.069030 − 0.511554I
a = −0.989284 − 0.998987I
b = −0.034858 + 1.174900I
2.25602 + 5.77634I 0
u = 1.032330 + 0.604329I
a = −0.526615 − 0.693515I
b = 0.0453003 − 0.0801337I
−5.58962 + 8.50219I 0
u = 1.032330 − 0.604329I
a = −0.526615 + 0.693515I
b = 0.0453003 + 0.0801337I
−5.58962 − 8.50219I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.148850 + 0.361119I
a = −1.20539 + 2.45569I
b = 0.39797 − 2.03492I
6.10363 − 4.57828I 0
u = −1.148850 − 0.361119I
a = −1.20539 − 2.45569I
b = 0.39797 + 2.03492I
6.10363 + 4.57828I 0
u = 0.548473 + 0.560041I
a = −0.581186 + 0.351504I
b = −0.22696 + 1.62569I
0.75526 + 3.53954I 2.18149 − 7.44702I
u = 0.548473 − 0.560041I
a = −0.581186 − 0.351504I
b = −0.22696 − 1.62569I
0.75526 − 3.53954I 2.18149 + 7.44702I
u = 0.336858 + 0.705301I
a = −0.727968 + 0.008197I
b = 0.05618 − 2.03611I
1.72929 − 5.09594I 4.50177 + 6.41579I
u = 0.336858 − 0.705301I
a = −0.727968 − 0.008197I
b = 0.05618 + 2.03611I
1.72929 + 5.09594I 4.50177 − 6.41579I
u = −1.096330 + 0.544084I
a = 3.14009 − 0.94983I
b = −0.70129 + 1.90152I
3.13491 − 4.52494I 0
u = −1.096330 − 0.544084I
a = 3.14009 + 0.94983I
b = −0.70129 − 1.90152I
3.13491 + 4.52494I 0
u = 1.105780 + 0.526642I
a = 1.01949 + 2.90721I
b = 1.46293 − 1.04888I
4.93192 + 4.48056I 0
u = 1.105780 − 0.526642I
a = 1.01949 − 2.90721I
b = 1.46293 + 1.04888I
4.93192 − 4.48056I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.151020 + 0.425079I
a = 0.78313 + 2.34689I
b = 0.40099 − 1.68007I
2.62164 + 2.63644I 0
u = 1.151020 − 0.425079I
a = 0.78313 − 2.34689I
b = 0.40099 + 1.68007I
2.62164 − 2.63644I 0
u = −1.144610 + 0.442128I
a = −1.27381 + 1.82051I
b = −0.25604 − 1.47655I
2.51187 − 5.44029I 0
u = −1.144610 − 0.442128I
a = −1.27381 − 1.82051I
b = −0.25604 + 1.47655I
2.51187 + 5.44029I 0
u = −0.361548 + 0.682305I
a = −1.83457 − 0.39466I
b = −1.69471 + 0.68902I
0.67795 + 4.12128I 1.69824 − 4.80167I
u = −0.361548 − 0.682305I
a = −1.83457 + 0.39466I
b = −1.69471 − 0.68902I
0.67795 − 4.12128I 1.69824 + 4.80167I
u = −1.098060 + 0.552571I
a = −0.85856 + 3.15191I
b = −1.88171 − 0.79380I
2.81252 − 8.89904I 0
u = −1.098060 − 0.552571I
a = −0.85856 − 3.15191I
b = −1.88171 + 0.79380I
2.81252 + 8.89904I 0
u = 1.174090 + 0.371824I
a = 1.13122 + 2.65591I
b = −0.11533 − 2.34747I
4.12793 + 9.21027I 0
u = 1.174090 − 0.371824I
a = 1.13122 − 2.65591I
b = −0.11533 + 2.34747I
4.12793 − 9.21027I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.488163 + 0.591831I
a = −2.04232 − 0.83927I
b = −1.326360 − 0.239711I
0.08170 − 2.52372I −0.58545 + 4.26188I
u = −0.488163 − 0.591831I
a = −2.04232 + 0.83927I
b = −1.326360 + 0.239711I
0.08170 + 2.52372I −0.58545 − 4.26188I
u = 1.084050 + 0.590895I
a = −0.0089860 − 0.0249450I
b = −0.458796 − 0.290974I
−4.75361 + 4.27265I 0
u = 1.084050 − 0.590895I
a = −0.0089860 + 0.0249450I
b = −0.458796 + 0.290974I
−4.75361 − 4.27265I 0
u = 1.109410 + 0.553706I
a = −3.03682 − 1.73830I
b = 0.09113 + 2.21326I
3.96786 + 9.92336I 0
u = 1.109410 − 0.553706I
a = −3.03682 + 1.73830I
b = 0.09113 − 2.21326I
3.96786 − 9.92336I 0
u = −0.117052 + 0.750778I
a = −0.737414 + 0.053249I
b = −0.31228 + 1.89008I
0.31311 − 5.40989I 2.36073 + 6.41671I
u = −0.117052 − 0.750778I
a = −0.737414 − 0.053249I
b = −0.31228 − 1.89008I
0.31311 + 5.40989I 2.36073 − 6.41671I
u = 1.141040 + 0.496267I
a = 1.42646 + 2.59104I
b = 0.98282 − 1.66344I
5.19001 + 3.42902I 0
u = 1.141040 − 0.496267I
a = 1.42646 − 2.59104I
b = 0.98282 + 1.66344I
5.19001 − 3.42902I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.105750 + 0.573417I
a = 0.137679 + 0.419713I
b = 0.063170 − 0.253101I
−0.27192 − 7.54326I 0
u = −1.105750 − 0.573417I
a = 0.137679 − 0.419713I
b = 0.063170 + 0.253101I
−0.27192 + 7.54326I 0
u = 0.754116
a = 0.825854
b = 0.314311
1.13040 9.07550
u = −0.349393 + 0.659519I
a = 0.600807 + 0.066067I
b = −0.63424 − 1.72068I
0.985822 − 0.166582I 2.39777 − 1.42911I
u = −0.349393 − 0.659519I
a = 0.600807 − 0.066067I
b = −0.63424 + 1.72068I
0.985822 + 0.166582I 2.39777 + 1.42911I
u = −1.115030 + 0.587093I
a = 1.88328 − 2.36949I
b = 0.99585 + 1.59024I
−2.99180 − 9.96544I 0
u = −1.115030 − 0.587093I
a = 1.88328 + 2.36949I
b = 0.99585 − 1.59024I
−2.99180 + 9.96544I 0
u = 1.116770 + 0.584980I
a = −0.402630 + 0.369336I
b = −0.0457545 − 0.0068386I
−2.88540 + 12.54230I 0
u = 1.116770 − 0.584980I
a = −0.402630 − 0.369336I
b = −0.0457545 + 0.0068386I
−2.88540 − 12.54230I 0
u = −1.164320 + 0.486707I
a = −1.71758 + 2.42899I
b = −0.73763 − 2.01383I
3.34857 + 0.86730I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.164320 − 0.486707I
a = −1.71758 − 2.42899I
b = −0.73763 + 2.01383I
3.34857 − 0.86730I 0
u = 0.614855 + 0.401071I
a = 1.91212 − 1.04537I
b = 0.440779 − 0.377899I
1.53140 − 0.74058I 3.74515 − 2.34440I
u = 0.614855 − 0.401071I
a = 1.91212 + 1.04537I
b = 0.440779 + 0.377899I
1.53140 + 0.74058I 3.74515 + 2.34440I
u = 1.129590 + 0.576340I
a = −2.36365 − 2.78458I
b = −1.11075 + 2.23670I
2.09039 + 12.95930I 0
u = 1.129590 − 0.576340I
a = −2.36365 + 2.78458I
b = −1.11075 − 2.23670I
2.09039 − 12.95930I 0
u = −1.136580 + 0.582078I
a = 2.19581 − 3.06172I
b = 1.45759 + 2.24892I
−0.3278 − 18.2674I 0
u = −1.136580 − 0.582078I
a = 2.19581 + 3.06172I
b = 1.45759 − 2.24892I
−0.3278 + 18.2674I 0
u = −0.465434 + 0.541208I
a = 0.432078 + 0.182590I
b = −0.33838 + 1.37788I
0.43543 + 1.49452I −0.137410 + 0.422109I
u = −0.465434 − 0.541208I
a = 0.432078 − 0.182590I
b = −0.33838 − 1.37788I
0.43543 − 1.49452I −0.137410 − 0.422109I
u = 0.148712 + 0.696621I
a = 0.889152 − 0.195413I
b = 0.54825 + 1.52268I
2.39138 + 1.04019I 6.89517 − 1.91377I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.148712 − 0.696621I
a = 0.889152 + 0.195413I
b = 0.54825 − 1.52268I
2.39138 − 1.04019I 6.89517 + 1.91377I
u = 0.278659 + 0.645657I
a = 1.46759 − 0.46420I
b = 1.15484 + 0.94905I
2.60462 + 0.08121I 6.61280 + 0.64113I
u = 0.278659 − 0.645657I
a = 1.46759 + 0.46420I
b = 1.15484 − 0.94905I
2.60462 − 0.08121I 6.61280 − 0.64113I
u = −0.010679 + 0.697595I
a = −0.330791 − 0.161147I
b = 0.207698 + 1.339730I
−0.68317 + 1.36679I −0.201662 − 0.614999I
u = −0.010679 − 0.697595I
a = −0.330791 + 0.161147I
b = 0.207698 − 1.339730I
−0.68317 − 1.36679I −0.201662 + 0.614999I
u = −0.185011 + 0.556332I
a = 0.150859 − 0.107616I
b = −0.347326 + 0.610817I
0.01599 + 1.73819I 0.64899 − 4.14521I
u = −0.185011 − 0.556332I
a = 0.150859 + 0.107616I
b = −0.347326 − 0.610817I
0.01599 − 1.73819I 0.64899 + 4.14521I
17
II.
I
u
2
= hu
2
a−u
3
+2b+u, −6u
3
a+2u
2
a+2a
2
+5u
2
−4a+6u−14, u
4
−2u
2
+2i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
10
=
u
−u
3
+ u
a
11
=
u
3
−u
3
+ u
a
6
=
−1
0
a
8
=
−u
3
u
3
− u
a
12
=
a
−
1
2
u
2
a +
1
2
u
3
−
1
2
u
a
1
=
−u
3
+ a
−
1
2
u
2
a +
3
2
u
3
−
3
2
u
a
7
=
−u
3
+ a
−
1
2
u
2
a +
3
2
u
3
−
3
2
u
a
3
=
1
2
u
3
a −
3
2
u
3
+ ··· + a +
1
2
−
1
2
u
2
a +
3
2
u
3
−
3
2
u + 1
a
2
=
1
2
u
3
a − 3u
3
+ ··· + a −
1
2
−
1
2
u
2
a +
3
2
u
3
−
3
2
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
a − 6u
3
− 4u
2
+ 6u + 12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
4
c
3
, c
6
(u
2
+ u + 1)
4
c
4
, c
9
(u
4
− 2u
2
+ 2)
2
c
5
, c
10
(u
4
+ 2u
2
+ 2)
2
c
7
(u − 1)
8
c
8
(u
2
+ 2u + 2)
4
c
11
, c
12
(u + 1)
8
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
4
c
4
, c
9
(y
2
− 2y + 2)
4
c
5
, c
10
(y
2
+ 2y + 2)
4
c
7
, c
11
, c
12
(y −1)
8
c
8
(y
2
+ 4)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098680 + 0.455090I
a = 0.599366 + 0.964636I
b = −0.044910 − 0.232659I
4.11234 + 5.69375I 10.0000 − 7.46410I
u = 1.098680 + 0.455090I
a = 2.33142 + 2.69669I
b = −0.04491 − 1.96471I
4.11234 + 1.63398I 10.0000 − 0.53590I
u = 1.098680 − 0.455090I
a = 0.599366 − 0.964636I
b = −0.044910 + 0.232659I
4.11234 − 5.69375I 10.0000 + 7.46410I
u = 1.098680 − 0.455090I
a = 2.33142 − 2.69669I
b = −0.04491 + 1.96471I
4.11234 − 1.63398I 10.0000 + 0.53590I
u = −1.098680 + 0.455090I
a = 0.40063 + 1.96464I
b = −0.955090 − 0.232659I
4.11234 − 1.63398I 10.00000 + 0.53590I
u = −1.098680 + 0.455090I
a = −1.33142 + 3.69669I
b = −0.95509 − 1.96471I
4.11234 − 5.69375I 10.00000 + 7.46410I
u = −1.098680 − 0.455090I
a = 0.40063 − 1.96464I
b = −0.955090 + 0.232659I
4.11234 + 1.63398I 10.00000 − 0.53590I
u = −1.098680 − 0.455090I
a = −1.33142 − 3.69669I
b = −0.95509 + 1.96471I
4.11234 + 5.69375I 10.00000 − 7.46410I
21
III. I
v
1
= ha, b − v + 1, v
2
− v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
10
=
v
0
a
11
=
v
0
a
6
=
1
0
a
8
=
v
0
a
12
=
0
v − 1
a
1
=
−v
v − 1
a
7
=
v
−v + 1
a
3
=
0
v
a
2
=
−v
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 8
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
, c
10
u
2
c
7
, c
11
(u + 1)
2
c
12
(u − 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
y
2
+ y + 1
c
4
, c
5
, c
8
c
9
, c
10
y
2
c
7
, c
11
, c
12
(y − 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 + 0.866025I
1.64493 + 2.02988I 6.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 − 0.866025I
1.64493 − 2.02988I 6.00000 + 3.46410I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
127
+ 62u
126
+ ··· − 34u − 25)
c
2
((u
2
− u + 1)
4
)(u
2
+ u + 1)(u
127
− 2u
126
+ ··· + 24u − 5)
c
3
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
127
+ 2u
126
+ ··· − 4532584u − 667745)
c
4
, c
9
u
2
(u
4
− 2u
2
+ 2)
2
(u
127
+ u
126
+ ··· − 4u − 4)
c
5
u
2
(u
4
+ 2u
2
+ 2)
2
(u
127
− u
126
+ ··· − 7705060u − 2511892)
c
6
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
127
− 2u
126
+ ··· + 24u − 5)
c
7
((u − 1)
8
)(u + 1)
2
(u
127
− 3u
126
+ ··· + 11u − 1)
c
8
u
2
(u
2
+ 2u + 2)
4
(u
127
− 61u
126
+ ··· + 80u − 16)
c
10
u
2
(u
4
+ 2u
2
+ 2)
2
(u
127
+ 3u
126
+ ··· + 54716u − 9292)
c
11
((u + 1)
10
)(u
127
− 63u
126
+ ··· − 9u − 1)
c
12
((u − 1)
2
)(u + 1)
8
(u
127
− 3u
126
+ ··· + 11u − 1)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
127
+ 14y
126
+ ··· + 23706y − 625)
c
2
, c
6
((y
2
+ y + 1)
5
)(y
127
+ 62y
126
+ ··· − 34y − 25)
c
3
(y
2
+ y + 1)
5
· (y
127
− 34y
126
+ ··· + 8331046653166y − 445883385025)
c
4
, c
9
y
2
(y
2
− 2y + 2)
4
(y
127
− 61y
126
+ ··· + 80y − 16)
c
5
y
2
(y
2
+ 2y + 2)
4
· (y
127
− 29y
126
+ ··· + 382290475250896y − 6309601419664)
c
7
, c
12
((y − 1)
10
)(y
127
− 63y
126
+ ··· − 9y − 1)
c
8
y
2
(y
2
+ 4)
4
(y
127
+ 15y
126
+ ··· − 5888y − 256)
c
10
y
2
(y
2
+ 2y + 2)
4
(y
127
+ 31y
126
+ ··· − 5.88039 × 10
9
y − 8.63413 × 10
7
)
c
11
((y − 1)
10
)(y
127
+ 17y
126
+ ··· − 473y − 1)
27
