12a
0065
(K12a
0065
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 4 10 11 1 8 6 9
Solving Sequence
7,10
8 11
4,9
3 6 12 1 5 2
c
7
c
10
c
8
c
3
c
6
c
11
c
12
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.92249 × 10
169
u
111
+ 3.73944 × 10
170
u
110
+ ··· + 1.17142 × 10
167
b − 2.38948 × 10
169
,
− 4.45166 × 10
168
u
111
+ 5.26012 × 10
169
u
110
+ ··· + 5.85711 × 10
166
a − 7.08065 × 10
168
,
u
112
− 14u
111
+ ··· − 171u − 1i
I
u
2
= h313a
8
+ 2651a
7
− 1632a
6
+ 9330a
5
− 4960a
4
+ 9676a
3
− 3659a
2
+ 145b + 3312a − 888,
a
9
+ 8a
8
− 9a
7
+ 34a
6
− 30a
5
+ 42a
4
− 26a
3
+ 17a
2
− 7a + 1, u + 1i
I
u
3
= hb, 3u
7
− 5u
6
− 7u
5
+ 11u
4
+ 5u
3
− 3u
2
+ a − 7, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
u
4
= h3a
2
u − a
2
+ 10au + 11b − 7a + 9u − 3, a
3
− a
2
u + 3a
2
− au + 4a − u + 5, u
2
− u − 1i
* 4 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−2.92 × 10
169
u
111
+ 3.74 × 10
170
u
110
+ · · · + 1.17 × 10
167
b − 2.39 ×
10
169
, −4.45 × 10
168
u
111
+ 5.26 × 10
169
u
110
+ · · · + 5.86 × 10
166
a − 7.08 ×
10
168
, u
112
− 14u
111
+ · · · − 171u − 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
11
=
u
−u
3
+ u
a
4
=
76.0044u
111
− 898.076u
110
+ ··· + 4341.78u + 120.890
249.483u
111
− 3192.23u
110
+ ··· + 34958.2u + 203.982
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
325.487u
111
− 4090.30u
110
+ ··· + 39300.0u + 324.872
249.483u
111
− 3192.23u
110
+ ··· + 34958.2u + 203.982
a
6
=
−323.912u
111
+ 4095.13u
110
+ ··· − 41394.8u − 288.132
684.638u
111
− 8698.30u
110
+ ··· + 90947.7u + 529.205
a
12
=
17.9543u
111
− 189.370u
110
+ ··· − 880.998u − 18.0322
72.8595u
111
− 925.927u
110
+ ··· + 8953.79u + 52.0848
a
1
=
196.977u
111
− 2493.83u
110
+ ··· + 24770.7u + 131.202
311.051u
111
− 3876.48u
110
+ ··· + 33723.8u + 196.443
a
5
=
−270.582u
111
+ 3459.45u
110
+ ··· − 38028.8u − 272.024
−248.530u
111
+ 3130.15u
110
+ ··· − 30299.4u − 176.735
a
2
=
49.6326u
111
− 561.615u
110
+ ··· − 239.766u + 52.4969
248.530u
111
− 3130.15u
110
+ ··· + 30299.4u + 176.735
(ii) Obstruction class = −1
(iii) Cusp Shapes = −360.979u
111
+ 4669.85u
110
+ ··· − 55646.3u − 332.781
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
112
+ 52u
111
+ ··· + 6550u + 1
c
2
, c
4
u
112
− 12u
111
+ ··· + 78u + 1
c
3
, c
6
u
112
− 4u
111
+ ··· − 1664u + 256
c
5
, c
11
u
112
+ 3u
111
+ ··· − 224u − 64
c
7
, c
8
, c
10
u
112
+ 14u
111
+ ··· + 171u − 1
c
9
, c
12
u
112
− 5u
111
+ ··· − 5632u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
112
+ 28y
111
+ ··· − 43105022y + 1
c
2
, c
4
y
112
− 52y
111
+ ··· − 6550y + 1
c
3
, c
6
y
112
+ 60y
111
+ ··· − 3784704y + 65536
c
5
, c
11
y
112
+ 47y
111
+ ··· − 185344y + 4096
c
7
, c
8
, c
10
y
112
− 110y
111
+ ··· − 28983y + 1
c
9
, c
12
y
112
− 69y
111
+ ··· − 75235328y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.432227 + 0.899551I
a = 0.863303 − 0.682893I
b = 0.503098 + 1.270930I
3.43374 − 7.46948I 0
u = −0.432227 − 0.899551I
a = 0.863303 + 0.682893I
b = 0.503098 − 1.270930I
3.43374 + 7.46948I 0
u = −0.994475
a = 10.9938
b = 0.530791
0.460815 0
u = −0.807871 + 0.613058I
a = −0.88505 + 1.10731I
b = −0.906023 − 0.341572I
−0.13349 + 1.76727I 0
u = −0.807871 − 0.613058I
a = −0.88505 − 1.10731I
b = −0.906023 + 0.341572I
−0.13349 − 1.76727I 0
u = −0.397239 + 0.960530I
a = −1.051620 + 0.624722I
b = −0.68926 − 1.24272I
1.11481 − 13.24070I 0
u = −0.397239 − 0.960530I
a = −1.051620 − 0.624722I
b = −0.68926 + 1.24272I
1.11481 + 13.24070I 0
u = −0.846216 + 0.417781I
a = 0.01284 − 2.09013I
b = −0.291691 + 0.590527I
−0.994600 − 0.244702I 0
u = −0.846216 − 0.417781I
a = 0.01284 + 2.09013I
b = −0.291691 − 0.590527I
−0.994600 + 0.244702I 0
u = −0.371874 + 0.847663I
a = −0.637100 + 0.223721I
b = −1.082290 + 0.424589I
−1.50046 − 6.83730I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.371874 − 0.847663I
a = −0.637100 − 0.223721I
b = −1.082290 − 0.424589I
−1.50046 + 6.83730I 0
u = −1.063340 + 0.200741I
a = −0.591192 − 0.953846I
b = 0.378594 + 0.254527I
1.19166 − 0.82959I 0
u = −1.063340 − 0.200741I
a = −0.591192 + 0.953846I
b = 0.378594 − 0.254527I
1.19166 + 0.82959I 0
u = −0.784572 + 0.755080I
a = −0.521418 + 0.547316I
b = 0.363354 − 1.200850I
4.50061 + 1.87825I 0
u = −0.784572 − 0.755080I
a = −0.521418 − 0.547316I
b = 0.363354 + 1.200850I
4.50061 − 1.87825I 0
u = −0.471032 + 0.748109I
a = −1.383900 + 0.286927I
b = −0.298324 − 1.206400I
4.78310 − 1.56650I 0
u = −0.471032 − 0.748109I
a = −1.383900 − 0.286927I
b = −0.298324 + 1.206400I
4.78310 + 1.56650I 0
u = −0.093207 + 0.873514I
a = −0.248094 + 0.265549I
b = −0.254334 + 0.724132I
−3.38522 − 1.66545I 0
u = −0.093207 − 0.873514I
a = −0.248094 − 0.265549I
b = −0.254334 − 0.724132I
−3.38522 + 1.66545I 0
u = −0.579121 + 0.638010I
a = 0.060953 − 0.323627I
b = −0.113562 + 1.348640I
5.22079 − 3.15983I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.579121 − 0.638010I
a = 0.060953 + 0.323627I
b = −0.113562 − 1.348640I
5.22079 + 3.15983I 0
u = −0.338089 + 0.790027I
a = −0.70076 + 1.26311I
b = −0.299060 − 0.968197I
−2.53810 − 4.23062I 0
u = −0.338089 − 0.790027I
a = −0.70076 − 1.26311I
b = −0.299060 + 0.968197I
−2.53810 + 4.23062I 0
u = −0.348530 + 0.771421I
a = 1.54506 + 0.01288I
b = 0.555550 + 1.207580I
3.05226 − 7.00346I 0
u = −0.348530 − 0.771421I
a = 1.54506 − 0.01288I
b = 0.555550 − 1.207580I
3.05226 + 7.00346I 0
u = −0.883638 + 0.781694I
a = 0.260199 − 0.410597I
b = −0.600067 + 1.206120I
2.55654 + 7.34989I 0
u = −0.883638 − 0.781694I
a = 0.260199 + 0.410597I
b = −0.600067 − 1.206120I
2.55654 − 7.34989I 0
u = −0.814759 + 0.093064I
a = −0.02851 − 1.73024I
b = 0.238206 − 1.260910I
4.16876 + 2.73247I 0
u = −0.814759 − 0.093064I
a = −0.02851 + 1.73024I
b = 0.238206 + 1.260910I
4.16876 − 2.73247I 0
u = 1.203460 + 0.136661I
a = −0.118558 − 0.685848I
b = −0.768668 + 0.874149I
−1.53487 + 7.70823I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.203460 − 0.136661I
a = −0.118558 + 0.685848I
b = −0.768668 − 0.874149I
−1.53487 − 7.70823I 0
u = −0.650565 + 0.441531I
a = 0.284990 − 0.250884I
b = 0.367652 − 1.313380I
4.29062 + 2.64667I 0
u = −0.650565 − 0.441531I
a = 0.284990 + 0.250884I
b = 0.367652 + 1.313380I
4.29062 − 2.64667I 0
u = 0.148882 + 0.769082I
a = 0.117990 − 0.378727I
b = −0.484574 − 0.863585I
−4.31644 − 4.47828I 0
u = 0.148882 − 0.769082I
a = 0.117990 + 0.378727I
b = −0.484574 + 0.863585I
−4.31644 + 4.47828I 0
u = −0.366452 + 0.688893I
a = 0.755204 + 0.032850I
b = 1.008880 − 0.064509I
−0.37121 − 2.19836I 0
u = −0.366452 − 0.688893I
a = 0.755204 − 0.032850I
b = 1.008880 + 0.064509I
−0.37121 + 2.19836I 0
u = −0.467466 + 0.563340I
a = 1.34388 − 1.22707I
b = 0.859945 − 0.262119I
0.14318 − 1.74876I 0
u = −0.467466 − 0.563340I
a = 1.34388 + 1.22707I
b = 0.859945 + 0.262119I
0.14318 + 1.74876I 0
u = 1.287240 + 0.022425I
a = −0.134483 + 1.059500I
b = −0.892729 − 0.916704I
−1.49378 + 1.54613I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.287240 − 0.022425I
a = −0.134483 − 1.059500I
b = −0.892729 + 0.916704I
−1.49378 − 1.54613I 0
u = −1.178420 + 0.543469I
a = −0.624869 + 0.730757I
b = −0.346082 − 0.915365I
−0.08758 − 3.32486I 0
u = −1.178420 − 0.543469I
a = −0.624869 − 0.730757I
b = −0.346082 + 0.915365I
−0.08758 + 3.32486I 0
u = 1.296080 + 0.090517I
a = −0.0707977 + 0.0027500I
b = 0.364916 + 0.715321I
4.85807 − 1.15903I 0
u = 1.296080 − 0.090517I
a = −0.0707977 − 0.0027500I
b = 0.364916 − 0.715321I
4.85807 + 1.15903I 0
u = −1.304980 + 0.052610I
a = −0.976280 + 0.233968I
b = 0.934649 + 0.088342I
1.95897 − 0.23517I 0
u = −1.304980 − 0.052610I
a = −0.976280 − 0.233968I
b = 0.934649 − 0.088342I
1.95897 + 0.23517I 0
u = 0.516798 + 0.445951I
a = −0.83569 − 1.42900I
b = −0.661411 + 1.072790I
−2.60168 + 8.03413I 0
u = 0.516798 − 0.445951I
a = −0.83569 + 1.42900I
b = −0.661411 − 1.072790I
−2.60168 − 8.03413I 0
u = 1.318190 + 0.079343I
a = −0.074820 + 0.852835I
b = 0.957554 − 0.819023I
2.30876 + 3.35064I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.318190 − 0.079343I
a = −0.074820 − 0.852835I
b = 0.957554 + 0.819023I
2.30876 − 3.35064I 0
u = −1.341310 + 0.124775I
a = 0.95425 − 2.35835I
b = 0.491216 + 1.266830I
5.66523 − 4.88950I 0
u = −1.341310 − 0.124775I
a = 0.95425 + 2.35835I
b = 0.491216 − 1.266830I
5.66523 + 4.88950I 0
u = −1.342130 + 0.149243I
a = −0.31891 + 3.02941I
b = −0.215869 − 0.853947I
0.16000 − 2.10599I 0
u = −1.342130 − 0.149243I
a = −0.31891 − 3.02941I
b = −0.215869 + 0.853947I
0.16000 + 2.10599I 0
u = 1.325740 + 0.358457I
a = 0.271013 + 0.129202I
b = −0.171276 − 0.567977I
1.05711 + 6.04270I 0
u = 1.325740 − 0.358457I
a = 0.271013 − 0.129202I
b = −0.171276 + 0.567977I
1.05711 − 6.04270I 0
u = −1.318820 + 0.401872I
a = 0.622621 − 0.489176I
b = −0.254340 + 0.852722I
0.256128 + 0.215496I 0
u = −1.318820 − 0.401872I
a = 0.622621 + 0.489176I
b = −0.254340 − 0.852722I
0.256128 − 0.215496I 0
u = −1.386810 + 0.046390I
a = −0.62492 + 2.46511I
b = −0.223078 − 1.291580I
7.06933 + 0.77487I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.386810 − 0.046390I
a = −0.62492 − 2.46511I
b = −0.223078 + 1.291580I
7.06933 − 0.77487I 0
u = −1.40902 + 0.15485I
a = 0.830660 − 0.311139I
b = −1.020340 + 0.360384I
1.24304 − 4.46857I 0
u = −1.40902 − 0.15485I
a = 0.830660 + 0.311139I
b = −1.020340 − 0.360384I
1.24304 + 4.46857I 0
u = −0.483043 + 0.215736I
a = 3.86051 − 3.37738I
b = 0.156984 + 0.351295I
−0.844006 − 0.123701I 16.1538 + 18.4285I
u = −0.483043 − 0.215736I
a = 3.86051 + 3.37738I
b = 0.156984 − 0.351295I
−0.844006 + 0.123701I 16.1538 − 18.4285I
u = 1.46970 + 0.15723I
a = 0.98247 + 1.92963I
b = 0.359600 − 0.910132I
5.51452 + 2.03742I 0
u = 1.46970 − 0.15723I
a = 0.98247 − 1.92963I
b = 0.359600 + 0.910132I
5.51452 − 2.03742I 0
u = −1.47825 + 0.13277I
a = 0.13052 − 2.27825I
b = 0.429061 + 1.257640I
6.13010 − 4.83002I 0
u = −1.47825 − 0.13277I
a = 0.13052 + 2.27825I
b = 0.429061 − 1.257640I
6.13010 + 4.83002I 0
u = 1.46140 + 0.26442I
a = −0.511606 + 0.344188I
b = 1.227310 + 0.081127I
5.53294 + 5.70610I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46140 − 0.26442I
a = −0.511606 − 0.344188I
b = 1.227310 − 0.081127I
5.53294 − 5.70610I 0
u = 1.47525 + 0.20602I
a = −0.098033 + 0.267874I
b = 1.041090 + 0.451281I
6.42012 + 4.59902I 0
u = 1.47525 − 0.20602I
a = −0.098033 − 0.267874I
b = 1.041090 − 0.451281I
6.42012 − 4.59902I 0
u = 1.46114 + 0.29673I
a = 0.97779 + 1.46570I
b = 0.687327 − 1.222770I
8.88079 + 10.89320I 0
u = 1.46114 − 0.29673I
a = 0.97779 − 1.46570I
b = 0.687327 + 1.222770I
8.88079 − 10.89320I 0
u = 1.46088 + 0.30172I
a = −0.64951 − 2.15697I
b = −0.281381 + 1.150490I
3.26019 + 8.19420I 0
u = 1.46088 − 0.30172I
a = −0.64951 + 2.15697I
b = −0.281381 − 1.150490I
3.26019 − 8.19420I 0
u = 1.48570 + 0.15943I
a = −0.30881 − 1.81829I
b = 0.42621 + 1.53738I
10.99310 − 0.43900I 0
u = 1.48570 − 0.15943I
a = −0.30881 + 1.81829I
b = 0.42621 − 1.53738I
10.99310 + 0.43900I 0
u = 0.171131 + 0.474447I
a = −1.69736 − 1.98067I
b = −0.576856 + 0.782368I
−4.57208 − 0.19764I −4.59945 − 1.06567I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.171131 − 0.474447I
a = −1.69736 + 1.98067I
b = −0.576856 − 0.782368I
−4.57208 + 0.19764I −4.59945 + 1.06567I
u = 0.273040 + 0.418122I
a = 0.425909 − 0.260771I
b = −0.879000 − 0.584327I
−4.17219 + 2.32119I −4.98033 − 2.46632I
u = 0.273040 − 0.418122I
a = 0.425909 + 0.260771I
b = −0.879000 + 0.584327I
−4.17219 − 2.32119I −4.98033 + 2.46632I
u = 0.393025 + 0.303535I
a = 0.67790 + 1.99368I
b = 0.531389 − 0.999667I
−0.07044 + 3.09882I −0.02283 − 3.67348I
u = 0.393025 − 0.303535I
a = 0.67790 − 1.99368I
b = 0.531389 + 0.999667I
−0.07044 − 3.09882I −0.02283 + 3.67348I
u = −0.490972
a = −1.14637
b = −0.111084
0.859712 11.9150
u = −0.016936 + 0.487875I
a = 0.004227 + 0.732028I
b = 0.711801 + 0.445043I
−1.65451 − 1.50529I −0.79984 + 4.45690I
u = −0.016936 − 0.487875I
a = 0.004227 − 0.732028I
b = 0.711801 − 0.445043I
−1.65451 + 1.50529I −0.79984 − 4.45690I
u = 1.48029 + 0.32341I
a = 0.568474 − 0.204571I
b = −1.217120 − 0.434440I
4.46415 + 11.08430I 0
u = 1.48029 − 0.32341I
a = 0.568474 + 0.204571I
b = −1.217120 + 0.434440I
4.46415 − 11.08430I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50724 + 0.18614I
a = −0.27955 + 2.10507I
b = −0.641575 − 1.239850I
4.02685 − 10.51750I 0
u = −1.50724 − 0.18614I
a = −0.27955 − 2.10507I
b = −0.641575 + 1.239850I
4.02685 + 10.51750I 0
u = 1.50523 + 0.20911I
a = 0.38047 + 1.91365I
b = −0.12611 − 1.56432I
11.96300 + 6.19123I 0
u = 1.50523 − 0.20911I
a = 0.38047 − 1.91365I
b = −0.12611 + 1.56432I
11.96300 − 6.19123I 0
u = 1.52333 + 0.09341I
a = −0.142206 − 0.261687I
b = −0.866573 − 0.108863I
7.77601 + 0.27066I 0
u = 1.52333 − 0.09341I
a = −0.142206 + 0.261687I
b = −0.866573 + 0.108863I
7.77601 − 0.27066I 0
u = 1.50428 + 0.25893I
a = −0.88930 − 1.55607I
b = −0.499688 + 1.234710I
11.21670 + 5.22488I 0
u = 1.50428 − 0.25893I
a = −0.88930 + 1.55607I
b = −0.499688 − 1.234710I
11.21670 − 5.22488I 0
u = 0.087033 + 0.443804I
a = 2.27863 − 0.28531I
b = 0.368295 − 1.046920I
1.18207 + 2.86004I 1.78475 − 2.80266I
u = 0.087033 − 0.443804I
a = 2.27863 + 0.28531I
b = 0.368295 + 1.046920I
1.18207 − 2.86004I 1.78475 + 2.80266I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51407 + 0.33881I
a = 0.70174 + 1.88299I
b = 0.57280 − 1.36973I
9.7116 + 11.9730I 0
u = 1.51407 − 0.33881I
a = 0.70174 − 1.88299I
b = 0.57280 + 1.36973I
9.7116 − 11.9730I 0
u = 1.51034 + 0.37348I
a = −0.78717 − 1.80264I
b = −0.74549 + 1.29575I
7.2346 + 18.0734I 0
u = 1.51034 − 0.37348I
a = −0.78717 + 1.80264I
b = −0.74549 − 1.29575I
7.2346 − 18.0734I 0
u = 1.60190
a = −1.05384
b = −0.608469
7.84469 0
u = 1.64421 + 0.15299I
a = −0.43138 − 1.55932I
b = 0.135262 + 1.266720I
12.87440 + 1.42369I 0
u = 1.64421 − 0.15299I
a = −0.43138 + 1.55932I
b = 0.135262 − 1.266720I
12.87440 − 1.42369I 0
u = 1.69416 + 0.10741I
a = 0.27300 + 1.43131I
b = −0.429463 − 1.232960I
11.74710 − 4.07589I 0
u = 1.69416 − 0.10741I
a = 0.27300 − 1.43131I
b = −0.429463 + 1.232960I
11.74710 + 4.07589I 0
u = 0.217235 + 0.209677I
a = −2.69618 − 1.26446I
b = 0.007921 + 1.027490I
1.99985 − 1.66123I 2.31051 + 3.78283I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.217235 − 0.209677I
a = −2.69618 + 1.26446I
b = 0.007921 − 1.027490I
1.99985 + 1.66123I 2.31051 − 3.78283I
u = −0.00587426
a = 95.4733
b = 0.503878
−1.20372 −8.99900
16
II. I
u
2
= h313a
8
+ 145b + · · · + 3312a − 888, a
9
+ 8a
8
+ · · · − 7a + 1, u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
−1
a
8
=
1
−1
a
11
=
−1
0
a
4
=
a
−2.15862a
8
− 18.2828a
7
+ ··· − 22.8414a + 6.12414
a
9
=
0
−1
a
3
=
−2.15862a
8
− 18.2828a
7
+ ··· − 21.8414a + 6.12414
−2.15862a
8
− 18.2828a
7
+ ··· − 22.8414a + 6.12414
a
6
=
1.01379a
8
+ 8.17241a
7
+ ··· + 8.98621a − 1.15862
−1.38621a
8
− 10.8276a
7
+ ··· − 12.6138a + 3.44138
a
12
=
0
−1.64828a
8
− 12.9034a
7
+ ··· − 21.3517a + 5.25517
a
1
=
0
−1.64828a
8
− 12.9034a
7
+ ··· − 21.3517a + 5.25517
a
5
=
1.01379a
8
+ 8.17241a
7
+ ··· + 8.98621a − 1.15862
−1.90345a
8
− 15.5931a
7
+ ··· − 30.0966a + 8.68966
a
2
=
−0.365517a
8
− 3.26897a
7
+ ··· − 3.63448a + 1.90345
−1.90345a
8
− 15.5931a
7
+ ··· − 30.0966a + 8.68966
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
1338
145
a
8
+
11273
145
a
7
−
1505
29
a
6
+
7978
29
a
5
−
4404
29
a
4
+
40626
145
a
3
−
2938
29
a
2
+
12727
145
a −
479
29
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
6
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
7
, c
8
(u + 1)
9
c
9
, c
12
u
9
c
10
(u − 1)
9
c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
6
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
5
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
, c
8
, c
10
(y −1)
9
c
9
, c
12
y
9
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.223063 + 0.988364I
b = −0.628449 − 0.875112I
1.02799 − 2.45442I 5.04100 + 1.69416I
u = −1.00000
a = 0.223063 − 0.988364I
b = −0.628449 + 0.875112I
1.02799 + 2.45442I 5.04100 − 1.69416I
u = −1.00000
a = −0.026651 + 0.835796I
b = 0.728966 − 0.986295I
−1.95319 + 7.08493I 0.45449 − 1.34000I
u = −1.00000
a = −0.026651 − 0.835796I
b = 0.728966 + 0.986295I
−1.95319 − 7.08493I 0.45449 + 1.34000I
u = −1.00000
a = 0.194585 + 1.248300I
b = 0.796005 − 0.733148I
−2.72642 − 1.33617I −1.56769 + 0.26615I
u = −1.00000
a = 0.194585 − 1.248300I
b = 0.796005 + 0.733148I
−2.72642 + 1.33617I −1.56769 − 0.26615I
u = −1.00000
a = 0.302374 + 0.039314I
b = −0.140343 − 0.966856I
3.42837 − 2.09337I 7.68972 + 3.82038I
u = −1.00000
a = 0.302374 − 0.039314I
b = −0.140343 + 0.966856I
3.42837 + 2.09337I 7.68972 − 3.82038I
u = −1.00000
a = −9.38674
b = −0.512358
0.446489 −211.240
20
III. I
u
3
=
hb, 3u
7
−5u
6
−7u
5
+11u
4
+5u
3
−3u
2
+a−7, u
8
−u
7
−3u
6
+2u
5
+3u
4
−2u−1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
11
=
u
−u
3
+ u
a
4
=
−3u
7
+ 5u
6
+ 7u
5
− 11u
4
− 5u
3
+ 3u
2
+ 7
0
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
−3u
7
+ 5u
6
+ 7u
5
− 11u
4
− 5u
3
+ 3u
2
+ 7
0
a
6
=
1
0
a
12
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−u
6
+ 3u
4
− 2u
2
− 1
−u
6
+ 2u
4
− u
2
a
5
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
2
=
−3u
7
+ 4u
6
+ 7u
5
− 8u
4
− 5u
3
+ u
2
+ 6
−u
6
+ 2u
4
− u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −21u
7
+ 38u
6
+ 48u
5
− 85u
4
− 39u
3
+ 27u
2
+ 5u + 58
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
6
u
8
c
4
(u + 1)
8
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
7
, c
8
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
9
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 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
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
6
y
8
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
7
, c
8
, c
10
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
9
, c
12
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = −1.194470 + 0.635084I
b = 0
−0.604279 − 1.131230I 0.744211 − 0.553382I
u = −1.180120 − 0.268597I
a = −1.194470 − 0.635084I
b = 0
−0.604279 + 1.131230I 0.744211 + 0.553382I
u = −0.108090 + 0.747508I
a = −0.637416 + 0.344390I
b = 0
−3.80435 − 2.57849I −2.39106 + 4.72239I
u = −0.108090 − 0.747508I
a = −0.637416 − 0.344390I
b = 0
−3.80435 + 2.57849I −2.39106 − 4.72239I
u = 1.37100
a = 0.687555
b = 0
4.85780 8.45210
u = 1.334530 + 0.318930I
a = −0.286111 − 0.344558I
b = 0
0.73474 + 6.44354I 0.47538 − 9.99765I
u = 1.334530 − 0.318930I
a = −0.286111 + 0.344558I
b = 0
0.73474 − 6.44354I 0.47538 + 9.99765I
u = −0.463640
a = 7.54843
b = 0
−0.799899 60.8910
24
IV. I
u
4
=
h3a
2
u−a
2
+10au+11b−7a+9u−3, a
3
−a
2
u+3a
2
−au+4a−u+5, u
2
−u−1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u − 1
a
11
=
u
−u − 1
a
4
=
a
−0.272727a
2
u − 0.909091au + ··· + 0.636364a + 0.272727
a
9
=
−u
u
a
3
=
−0.272727a
2
u − 0.909091au + ··· + 1.63636a + 0.272727
−0.272727a
2
u − 0.909091au + ··· + 0.636364a + 0.272727
a
6
=
0.272727a
2
u − 0.0909091au + ··· + 0.363636a + 1.72727
−0.181818a
2
u − 0.272727au + ··· + 0.0909091a + 1.18182
a
12
=
u
−u − 1
a
1
=
−1
0
a
5
=
0.272727a
2
u − 0.0909091au + ··· + 0.363636a + 1.72727
−0.181818a
2
u − 0.272727au + ··· + 0.0909091a + 1.18182
a
2
=
0.0909091a
2
u − 0.363636au + ··· + 0.454545a + 0.909091
−0.181818a
2
u − 0.272727au + ··· + 0.0909091a + 1.18182
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
63
11
a
2
u −
67
11
a
2
+
76
11
au −
106
11
a −
57
11
u −
234
11
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
11
u
6
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
8
, c
9
(u
2
− u − 1)
3
c
10
, c
12
(u
2
+ u − 1)
3
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
11
y
6
c
7
, c
8
, c
9
c
10
, c
12
(y
2
− 3y + 1)
3
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = −0.47057 + 1.37014I
b = −0.215080 + 1.307140I
4.01109 + 2.82812I −7.3018 − 15.7639I
u = −0.618034
a = −0.47057 − 1.37014I
b = −0.215080 − 1.307140I
4.01109 − 2.82812I −7.3018 + 15.7639I
u = −0.618034
a = −2.67690
b = −0.569840
−0.126494 0.874100
u = 1.61803
a = −1.40270
b = −0.569840
7.76919 −62.0390
u = 1.61803
a = 0.01037 + 1.55272I
b = −0.215080 − 1.307140I
11.90680 − 2.82812I 7.38403 + 1.90115I
u = 1.61803
a = 0.01037 − 1.55272I
b = −0.215080 + 1.307140I
11.90680 + 2.82812I 7.38403 − 1.90115I
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
(u
3
− u
2
+ 2u − 1)
2
· (u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
112
+ 52u
111
+ ··· + 6550u + 1)
c
2
(u − 1)
8
(u
3
+ u
2
− 1)
2
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
112
− 12u
111
+ ··· + 78u + 1)
c
3
u
8
(u
3
− u
2
+ 2u − 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
112
− 4u
111
+ ··· − 1664u + 256)
c
4
(u + 1)
8
(u
3
− u
2
+ 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
112
− 12u
111
+ ··· + 78u + 1)
c
5
u
6
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
112
+ 3u
111
+ ··· − 224u − 64)
c
6
u
8
(u
3
+ u
2
+ 2u + 1)
2
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
112
− 4u
111
+ ··· − 1664u + 256)
c
7
, c
8
(u + 1)
9
(u
2
− u − 1)
3
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
112
+ 14u
111
+ ··· + 171u − 1)
c
9
u
9
(u
2
− u − 1)
3
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
112
− 5u
111
+ ··· − 5632u + 512)
c
10
(u − 1)
9
(u
2
+ u − 1)
3
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
112
+ 14u
111
+ ··· + 171u − 1)
c
11
u
6
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
112
+ 3u
111
+ ··· − 224u − 64)
c
12
u
9
(u
2
+ u − 1)
3
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
112
− 5u
111
+ ··· − 5632u + 512)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
(y
3
+ 3y
2
+ 2y −1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
112
+ 28y
111
+ ··· − 43105022y + 1)
c
2
, c
4
(y −1)
8
(y
3
− y
2
+ 2y −1)
2
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
112
− 52y
111
+ ··· − 6550y + 1)
c
3
, c
6
y
8
(y
3
+ 3y
2
+ 2y −1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
112
+ 60y
111
+ ··· − 3784704y + 65536)
c
5
, c
11
y
6
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
112
+ 47y
111
+ ··· − 185344y + 4096)
c
7
, c
8
, c
10
(y −1)
9
(y
2
− 3y + 1)
3
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
112
− 110y
111
+ ··· − 28983y + 1)
c
9
, c
12
y
9
(y
2
− 3y + 1)
3
(y
8
− 3y
7
+ ··· − 4y + 1)
· (y
112
− 69y
111
+ ··· − 75235328y + 262144)
30
