12a
0780
(K12a
0780
)
A knot diagram
1
Linearized knot diagam
3 8 10 1 11 9 12 2 6 4 7 5
Solving Sequence
3,10
4
8,11
2 9 1 5 6 12 7
c
3
c
10
c
2
c
8
c
1
c
4
c
5
c
12
c
7
c
6
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.19508 × 10
19
u
30
+ 3.73360 × 10
19
u
29
+ ··· + 4.83245 × 10
19
b + 3.36053 × 10
19
,
2.65488 × 10
19
u
30
− 4.25989 × 10
19
u
29
+ ··· + 4.83245 × 10
19
a − 9.79800 × 10
19
, u
31
− u
30
+ ··· + 4u
2
− 1i
I
u
2
= h6.81132 × 10
282
u
103
+ 3.29331 × 10
282
u
102
+ ··· + 2.47281 × 10
283
b + 2.22084 × 10
285
,
4.11438 × 10
284
u
103
+ 2.15076 × 10
284
u
102
+ ··· + 1.47544 × 10
285
a + 1.58373 × 10
287
,
u
104
+ u
103
+ ··· + 1113u + 179i
I
u
3
= h2.88283 × 10
16
u
39
+ 2.47312 × 10
16
u
38
+ ··· + 5.40032 × 10
14
b − 1.88417 × 10
16
,
5041365482875379u
39
− 1853997132134618u
38
+ ··· + 49093794862181a + 5201527324398439,
u
40
− 13u
38
+ ··· + u + 1i
I
u
4
= h−u
5
− u
3
+ u
2
+ b + u, u
7
− u
6
+ 2u
5
− 3u
4
− u
2
+ a − u + 2, u
8
+ u
6
− u
5
− 2u
4
+ u + 1i
I
u
5
= h402075u
23
+ 134432u
22
+ ··· + 844628b − 3815144,
1297281615u
23
+ 828936233u
22
+ ··· + 956118896a − 5354919116, u
24
− 4u
22
+ ··· − 14u + 4i
I
u
6
= hb, a + 1, u + 1i
* 6 irreducible components of dim
C
= 0, with total 208 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−2.20×10
19
u
30
+3.73×10
19
u
29
+· · ·+4.83×10
19
b+3.36×10
19
, 2.65×
10
19
u
30
−4.26×10
19
u
29
+· · ·+4.83 ×10
19
a−9.80×10
19
, u
31
−u
30
+· · ·+4u
2
−1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
8
=
−0.549385u
30
+ 0.881518u
29
+ ··· − 1.41104u + 2.02754
0.454238u
30
− 0.772609u
29
+ ··· + 0.861654u − 0.695408
a
11
=
−u
−u
3
+ u
a
2
=
−0.222511u
30
+ 0.978508u
29
+ ··· − 2.10042u + 2.65064
0.713966u
30
− 1.10192u
29
+ ··· + 2.28533u − 1.27168
a
9
=
0.400492u
30
− 0.295551u
29
+ ··· − 3.68422u + 2.01348
0.987830u
30
− 1.78027u
29
+ ··· + 6.06348u − 2.16930
a
1
=
0.491456u
30
− 0.123412u
29
+ ··· + 0.184905u + 1.37896
0.713966u
30
− 1.10192u
29
+ ··· + 2.28533u − 1.27168
a
5
=
2.35112u
30
− 2.14216u
29
+ ··· + 6.17496u − 0.993465
0.995518u
30
− 0.205887u
29
+ ··· + 4.36460u + 0.609450
a
6
=
1.63972u
30
− 1.94514u
29
+ ··· + 3.71889u − 1.79387
1.69270u
30
− 0.224587u
29
+ ··· + 6.10926u + 0.895478
a
12
=
0.0447065u
30
+ 0.378481u
29
+ ··· + 3.07225u − 0.126197
−0.332133u
30
+ 0.427280u
29
+ ··· − 2.02754u + 0.549385
a
7
=
−0.126197u
30
+ 0.170904u
29
+ ··· − 1.53724u + 2.07225
0.549385u
30
− 0.881518u
29
+ ··· + 1.41104u − 1.02754
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
10502766013328767806
4832454620042859899
u
30
+
9053641948115436650
4832454620042859899
u
29
+ ··· −
13369065530498617863
4832454620042859899
u −
55516682932002117692
4832454620042859899
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 13u
30
+ ··· − 5076u − 1296
c
2
, c
8
u
31
− u
30
+ ··· − 54u + 36
c
3
, c
7
, c
10
c
11
u
31
+ u
30
+ ··· − 4u
2
+ 1
c
4
, c
6
, c
9
c
12
u
31
− 2u
30
+ ··· + 3u + 1
c
5
u
31
+ 6u
30
+ ··· + 6656u + 1024
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 13y
30
+ ··· + 17064432y −1679616
c
2
, c
8
y
31
+ 13y
30
+ ··· − 5076y −1296
c
3
, c
7
, c
10
c
11
y
31
− 11y
30
+ ··· + 8y −1
c
4
, c
6
, c
9
c
12
y
31
+ 18y
30
+ ··· + 13y −1
c
5
y
31
+ 2y
30
+ ··· − 1310720y −1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904739 + 0.291878I
a = 0.65346 − 1.50562I
b = −0.702786 + 0.584481I
−3.78119 + 0.29851I −10.04466 − 5.69317I
u = −0.904739 − 0.291878I
a = 0.65346 + 1.50562I
b = −0.702786 − 0.584481I
−3.78119 − 0.29851I −10.04466 + 5.69317I
u = −1.023540 + 0.276276I
a = −1.127830 + 0.645457I
b = 0.426119 + 1.184880I
−4.48013 + 3.96005I −9.16910 − 4.26747I
u = −1.023540 − 0.276276I
a = −1.127830 − 0.645457I
b = 0.426119 − 1.184880I
−4.48013 − 3.96005I −9.16910 + 4.26747I
u = 1.005490 + 0.429232I
a = 2.30114 + 0.46275I
b = −0.624836 + 1.042950I
−5.18236 − 5.45253I −10.41007 + 8.28014I
u = 1.005490 − 0.429232I
a = 2.30114 − 0.46275I
b = −0.624836 − 1.042950I
−5.18236 + 5.45253I −10.41007 − 8.28014I
u = 1.059200 + 0.322674I
a = −0.92727 − 1.08013I
b = 0.70406 − 1.33659I
1.36245 − 7.78965I −7.00543 + 8.80272I
u = 1.059200 − 0.322674I
a = −0.92727 + 1.08013I
b = 0.70406 + 1.33659I
1.36245 + 7.78965I −7.00543 − 8.80272I
u = 0.796557 + 0.316743I
a = −1.160500 − 0.402760I
b = 1.20965 − 0.90259I
5.08416 − 5.15512I −3.79747 + 9.54392I
u = 0.796557 − 0.316743I
a = −1.160500 + 0.402760I
b = 1.20965 + 0.90259I
5.08416 + 5.15512I −3.79747 − 9.54392I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667071 + 0.461492I
a = 0.280234 + 0.536083I
b = 0.882837 + 0.031450I
5.33055 + 1.69004I −1.97215 − 4.21413I
u = −0.667071 − 0.461492I
a = 0.280234 − 0.536083I
b = 0.882837 − 0.031450I
5.33055 − 1.69004I −1.97215 + 4.21413I
u = 1.195060 + 0.171054I
a = −0.520257 − 1.094170I
b = −0.159112 − 1.058030I
−8.22893 + 0.97469I −16.7057 − 1.4101I
u = 1.195060 − 0.171054I
a = −0.520257 + 1.094170I
b = −0.159112 + 1.058030I
−8.22893 − 0.97469I −16.7057 + 1.4101I
u = 0.740357
a = −0.402635
b = 0.633812
−1.21453 −8.10490
u = −1.188210 + 0.435471I
a = −0.401213 + 0.319230I
b = 0.01900 + 1.52100I
−4.40480 + 9.52849I −10.46510 − 9.09050I
u = −1.188210 − 0.435471I
a = −0.401213 − 0.319230I
b = 0.01900 − 1.52100I
−4.40480 − 9.52849I −10.46510 + 9.09050I
u = −0.666570 + 1.157020I
a = 1.379760 − 0.003498I
b = −0.724812 − 0.579148I
7.48792 − 0.22792I −1.69345 + 0.87575I
u = −0.666570 − 1.157020I
a = 1.379760 + 0.003498I
b = −0.724812 + 0.579148I
7.48792 + 0.22792I −1.69345 − 0.87575I
u = 0.268926 + 1.349580I
a = 1.164290 − 0.318035I
b = −0.220775 + 0.993543I
3.13273 − 0.69529I −3.01718 − 5.31456I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.268926 − 1.349580I
a = 1.164290 + 0.318035I
b = −0.220775 − 0.993543I
3.13273 + 0.69529I −3.01718 + 5.31456I
u = 1.202140 + 0.675507I
a = 0.715667 + 0.660411I
b = −1.069400 − 0.469167I
3.20086 − 13.35560I −6.05212 + 7.56492I
u = 1.202140 − 0.675507I
a = 0.715667 − 0.660411I
b = −1.069400 + 0.469167I
3.20086 + 13.35560I −6.05212 − 7.56492I
u = 0.63713 + 1.30118I
a = 0.964989 + 0.428697I
b = −0.630715 − 1.038540I
6.10362 + 5.43386I −5.40395 − 7.12702I
u = 0.63713 − 1.30118I
a = 0.964989 − 0.428697I
b = −0.630715 + 1.038540I
6.10362 − 5.43386I −5.40395 + 7.12702I
u = −1.28784 + 0.72177I
a = 1.60965 − 0.43290I
b = −0.720905 − 1.192920I
0.9302 + 19.7770I −8.22431 − 10.67419I
u = −1.28784 − 0.72177I
a = 1.60965 + 0.43290I
b = −0.720905 + 1.192920I
0.9302 − 19.7770I −8.22431 + 10.67419I
u = −0.445478 + 0.168753I
a = 0.072282 + 1.197850I
b = 0.950130 − 0.854767I
5.19711 − 2.48842I −5.94667 − 0.27240I
u = −0.445478 − 0.168753I
a = 0.072282 − 1.197850I
b = 0.950130 + 0.854767I
5.19711 + 2.48842I −5.94667 + 0.27240I
u = 0.148770 + 0.313871I
a = 1.196920 − 0.605935I
b = −0.155369 + 0.670608I
−0.452805 − 0.851501I −9.04017 + 7.90614I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.148770 − 0.313871I
a = 1.196920 + 0.605935I
b = −0.155369 − 0.670608I
−0.452805 + 0.851501I −9.04017 − 7.90614I
8
II. I
u
2
= h6.81 × 10
282
u
103
+ 3.29 × 10
282
u
102
+ · · · + 2.47 × 10
283
b + 2.22 ×
10
285
, 4.11 × 10
284
u
103
+ 2.15 × 10
284
u
102
+ · · · + 1.48 × 10
285
a + 1.58 ×
10
287
, u
104
+ u
103
+ · · · + 1113u + 179i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
8
=
−0.278857u
103
− 0.145771u
102
+ ··· − 444.690u − 107.339
−0.275449u
103
− 0.133181u
102
+ ··· − 387.865u − 89.8105
a
11
=
−u
−u
3
+ u
a
2
=
0.138599u
103
+ 0.0628452u
102
+ ··· + 203.354u + 43.1149
0.379465u
103
+ 0.164274u
102
+ ··· + 515.620u + 114.775
a
9
=
0.527518u
103
+ 0.240212u
102
+ ··· + 759.866u + 172.400
−0.118601u
103
− 0.0345118u
102
+ ··· − 119.986u − 23.6052
a
1
=
0.518063u
103
+ 0.227119u
102
+ ··· + 718.974u + 157.890
0.379465u
103
+ 0.164274u
102
+ ··· + 515.620u + 114.775
a
5
=
−0.742309u
103
− 0.317728u
102
+ ··· − 1025.35u − 229.236
−0.250029u
103
− 0.127595u
102
+ ··· − 348.210u − 80.6180
a
6
=
−0.507770u
103
− 0.207804u
102
+ ··· − 709.952u − 157.194
−0.407976u
103
− 0.200416u
102
+ ··· − 566.896u − 130.354
a
12
=
0.759797u
103
+ 0.363025u
102
+ ··· + 1108.90u + 249.762
0.253134u
103
+ 0.111697u
102
+ ··· + 369.260u + 82.3263
a
7
=
0.425454u
103
+ 0.132471u
102
+ ··· + 517.181u + 106.621
0.273070u
103
+ 0.109295u
102
+ ··· + 376.488u + 83.1111
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.410905u
103
− 0.0915954u
102
+ ··· − 435.964u − 92.7804
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
52
+ 22u
51
+ ··· + 7092u + 1296)
2
c
2
, c
8
(u
52
− 6u
51
+ ··· − 222u + 36)
2
c
3
, c
7
, c
10
c
11
u
104
− u
103
+ ··· − 1113u + 179
c
4
, c
6
, c
9
c
12
u
104
− 2u
103
+ ··· − 854u + 101
c
5
(u
52
− 2u
51
+ ··· − 2u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
52
+ 22y
51
+ ··· − 195696y + 1679616)
2
c
2
, c
8
(y
52
+ 22y
51
+ ··· + 7092y + 1296)
2
c
3
, c
7
, c
10
c
11
y
104
− 59y
103
+ ··· − 398901y + 32041
c
4
, c
6
, c
9
c
12
y
104
+ 68y
103
+ ··· + 541870y + 10201
c
5
(y
52
+ 2y
51
+ ··· + 88y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.102845 + 0.986526I
a = 1.152070 − 0.336899I
b = −0.679085 + 0.979076I
0.92368 − 7.36867I 0
u = −0.102845 − 0.986526I
a = 1.152070 + 0.336899I
b = −0.679085 − 0.979076I
0.92368 + 7.36867I 0
u = −0.895609 + 0.412250I
a = 0.900813 − 0.074076I
b = −1.156730 − 0.485977I
4.71477 + 1.98139I 0
u = −0.895609 − 0.412250I
a = 0.900813 + 0.074076I
b = −1.156730 + 0.485977I
4.71477 − 1.98139I 0
u = −0.289820 + 0.982689I
a = −0.811227 − 0.072611I
b = 0.567925 + 0.761675I
4.01439 + 2.26335I 0
u = −0.289820 − 0.982689I
a = −0.811227 + 0.072611I
b = 0.567925 − 0.761675I
4.01439 − 2.26335I 0
u = 0.874210 + 0.400885I
a = −0.095639 + 0.534519I
b = −1.156730 − 0.485977I
4.71477 + 1.98139I 0
u = 0.874210 − 0.400885I
a = −0.095639 − 0.534519I
b = −1.156730 + 0.485977I
4.71477 − 1.98139I 0
u = 1.032780 + 0.202468I
a = 0.580411 − 1.029680I
b = −0.244589 − 1.108580I
−2.04183 − 0.59281I 0
u = 1.032780 − 0.202468I
a = 0.580411 + 1.029680I
b = −0.244589 + 1.108580I
−2.04183 + 0.59281I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.722154 + 0.603978I
a = 1.50477 + 0.76745I
b = −0.713966 − 0.905612I
4.55373 + 6.92827I 0
u = −0.722154 − 0.603978I
a = 1.50477 − 0.76745I
b = −0.713966 + 0.905612I
4.55373 − 6.92827I 0
u = 0.998184 + 0.358526I
a = −0.697910 − 0.237940I
b = 0.819922
−1.26420 0
u = 0.998184 − 0.358526I
a = −0.697910 + 0.237940I
b = 0.819922
−1.26420 0
u = 0.289618 + 0.878855I
a = 1.273880 − 0.233717I
b = −0.762222 + 0.692209I
1.80098 + 1.90056I 0
u = 0.289618 − 0.878855I
a = 1.273880 + 0.233717I
b = −0.762222 − 0.692209I
1.80098 − 1.90056I 0
u = 0.196990 + 0.894165I
a = −0.76496 − 1.35196I
b = 0.037214 + 1.116100I
−0.48936 − 5.43427I 0
u = 0.196990 − 0.894165I
a = −0.76496 + 1.35196I
b = 0.037214 − 1.116100I
−0.48936 + 5.43427I 0
u = −1.061790 + 0.300527I
a = 0.023114 − 1.136220I
b = 0.073870 − 1.235250I
−6.67841 + 5.00577I 0
u = −1.061790 − 0.300527I
a = 0.023114 + 1.136220I
b = 0.073870 + 1.235250I
−6.67841 − 5.00577I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.014560 + 0.437960I
a = 1.86019 − 1.47654I
b = −0.713966 − 0.905612I
4.55373 + 6.92827I 0
u = −1.014560 − 0.437960I
a = 1.86019 + 1.47654I
b = −0.713966 + 0.905612I
4.55373 − 6.92827I 0
u = −0.134840 + 0.878343I
a = 0.309334 − 0.753555I
b = −0.244589 + 1.108580I
−2.04183 + 0.59281I −8.00000 + 0.I
u = −0.134840 − 0.878343I
a = 0.309334 + 0.753555I
b = −0.244589 − 1.108580I
−2.04183 − 0.59281I −8.00000 + 0.I
u = 0.902711 + 0.651850I
a = 0.720986 + 0.445018I
b = −0.649638 + 0.235121I
−1.38772 − 4.38785I 0
u = 0.902711 − 0.651850I
a = 0.720986 − 0.445018I
b = −0.649638 − 0.235121I
−1.38772 + 4.38785I 0
u = 0.975998 + 0.583484I
a = 0.004335 + 1.068440I
b = −0.770308 − 0.842569I
4.77173 − 1.29519I 0
u = 0.975998 − 0.583484I
a = 0.004335 − 1.068440I
b = −0.770308 + 0.842569I
4.77173 + 1.29519I 0
u = 0.748068 + 0.859406I
a = 0.800339 + 1.074350I
b = −0.327524 − 0.686330I
−2.49314 − 4.00946I 0
u = 0.748068 − 0.859406I
a = 0.800339 − 1.074350I
b = −0.327524 + 0.686330I
−2.49314 + 4.00946I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.434237 + 1.057630I
a = −1.52364 − 0.11098I
b = 0.883774 − 0.518629I
5.65528 + 7.13741I 0
u = 0.434237 − 1.057630I
a = −1.52364 + 0.11098I
b = 0.883774 + 0.518629I
5.65528 − 7.13741I 0
u = −0.980062 + 0.615305I
a = 0.047671 + 0.182111I
b = −0.423320 + 1.145930I
−4.25004 + 0.23491I 0
u = −0.980062 − 0.615305I
a = 0.047671 − 0.182111I
b = −0.423320 − 1.145930I
−4.25004 − 0.23491I 0
u = 0.334120 + 0.773008I
a = 1.40358 + 1.52546I
b = −0.539106 − 1.066420I
−0.13905 + 7.75829I −8.00000 − 5.56536I
u = 0.334120 − 0.773008I
a = 1.40358 − 1.52546I
b = −0.539106 + 1.066420I
−0.13905 − 7.75829I −8.00000 + 5.56536I
u = 1.046770 + 0.497215I
a = 0.791526 + 0.842867I
b = −0.762222 − 0.692209I
1.80098 − 1.90056I 0
u = 1.046770 − 0.497215I
a = 0.791526 − 0.842867I
b = −0.762222 + 0.692209I
1.80098 + 1.90056I 0
u = −1.119360 + 0.356705I
a = 1.22102 − 0.85606I
b = −0.91575 − 1.13866I
2.84057 + 5.30163I 0
u = −1.119360 − 0.356705I
a = 1.22102 + 0.85606I
b = −0.91575 + 1.13866I
2.84057 − 5.30163I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.721814 + 0.398847I
a = 1.72578 + 0.44649I
b = −0.770308 − 0.842569I
4.77173 − 1.29519I −6.57252 + 4.54515I
u = 0.721814 − 0.398847I
a = 1.72578 − 0.44649I
b = −0.770308 + 0.842569I
4.77173 + 1.29519I −6.57252 − 4.54515I
u = 0.802326 + 0.169310I
a = −0.492490 − 0.106042I
b = 0.680281
−1.20551 −8.00000 + 0.I
u = 0.802326 − 0.169310I
a = −0.492490 + 0.106042I
b = 0.680281
−1.20551 −8.00000 + 0.I
u = −1.099200 + 0.460843I
a = −0.910873 + 0.992427I
b = 0.855566 − 0.509496I
−0.71762 + 7.20372I 0
u = −1.099200 − 0.460843I
a = −0.910873 − 0.992427I
b = 0.855566 + 0.509496I
−0.71762 − 7.20372I 0
u = −1.194500 + 0.031721I
a = 1.182540 − 0.474576I
b = −0.649638 + 0.235121I
−1.38772 − 4.38785I 0
u = −1.194500 − 0.031721I
a = 1.182540 + 0.474576I
b = −0.649638 − 0.235121I
−1.38772 + 4.38785I 0
u = 0.612226 + 0.510027I
a = −1.97383 + 0.36189I
b = 0.866328 − 0.908971I
5.88425 − 3.20070I −2.16616 + 0.89919I
u = 0.612226 − 0.510027I
a = −1.97383 − 0.36189I
b = 0.866328 + 0.908971I
5.88425 + 3.20070I −2.16616 − 0.89919I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.043950 + 0.601459I
a = 0.360306 − 0.207444I
b = −0.653736 + 0.265939I
2.01949 + 3.27741I 0
u = −1.043950 − 0.601459I
a = 0.360306 + 0.207444I
b = −0.653736 − 0.265939I
2.01949 − 3.27741I 0
u = −1.211760 + 0.175745I
a = −0.697257 + 1.066010I
b = 0.248597 + 0.964510I
−4.34575 + 2.86126I 0
u = −1.211760 − 0.175745I
a = −0.697257 − 1.066010I
b = 0.248597 − 0.964510I
−4.34575 − 2.86126I 0
u = −1.244220 + 0.184328I
a = −0.537397 − 0.339553I
b = 0.443016 − 1.223900I
−4.94120 − 4.54649I 0
u = −1.244220 − 0.184328I
a = −0.537397 + 0.339553I
b = 0.443016 + 1.223900I
−4.94120 + 4.54649I 0
u = −0.593600 + 0.440238I
a = −1.42250 + 1.05012I
b = 0.866328 − 0.908971I
5.88425 − 3.20070I −2.16616 + 0.89919I
u = −0.593600 − 0.440238I
a = −1.42250 − 1.05012I
b = 0.866328 + 0.908971I
5.88425 + 3.20070I −2.16616 − 0.89919I
u = −0.972857 + 0.815922I
a = 1.90153 − 0.46848I
b = −0.478202 − 1.054340I
−4.00386 + 7.55816I 0
u = −0.972857 − 0.815922I
a = 1.90153 + 0.46848I
b = −0.478202 + 1.054340I
−4.00386 − 7.55816I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.141660 + 0.581775I
a = −1.99002 − 0.20402I
b = 0.670725 − 1.105940I
−2.52024 − 12.89480I 0
u = 1.141660 − 0.581775I
a = −1.99002 + 0.20402I
b = 0.670725 + 1.105940I
−2.52024 + 12.89480I 0
u = 1.140890 + 0.584969I
a = −0.339649 − 0.579400I
b = 0.855566 + 0.509496I
−0.71762 − 7.20372I 0
u = 1.140890 − 0.584969I
a = −0.339649 + 0.579400I
b = 0.855566 − 0.509496I
−0.71762 + 7.20372I 0
u = 0.684343 + 0.206798I
a = 0.521770 + 0.152717I
b = −0.91575 − 1.13866I
2.84057 + 5.30163I −7.85801 + 1.01717I
u = 0.684343 − 0.206798I
a = 0.521770 − 0.152717I
b = −0.91575 + 1.13866I
2.84057 − 5.30163I −7.85801 − 1.01717I
u = −0.383891 + 1.239540I
a = −0.996825 + 0.585339I
b = 0.671974 − 1.108810I
3.84347 − 12.89570I 0
u = −0.383891 − 1.239540I
a = −0.996825 − 0.585339I
b = 0.671974 + 1.108810I
3.84347 + 12.89570I 0
u = −1.166690 + 0.569532I
a = 1.82870 − 0.28405I
b = −0.679085 − 0.979076I
0.92368 + 7.36867I 0
u = −1.166690 − 0.569532I
a = 1.82870 + 0.28405I
b = −0.679085 + 0.979076I
0.92368 − 7.36867I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.117430 + 0.729568I
a = −0.260752 − 0.387052I
b = −0.301144 + 0.693334I
1.79885 + 3.99008I 0
u = −1.117430 − 0.729568I
a = −0.260752 + 0.387052I
b = −0.301144 − 0.693334I
1.79885 − 3.99008I 0
u = 0.045675 + 0.662245I
a = −2.29878 + 1.46807I
b = 0.567925 − 0.761675I
4.01439 − 2.26335I −4.34155 + 5.25549I
u = 0.045675 − 0.662245I
a = −2.29878 − 1.46807I
b = 0.567925 + 0.761675I
4.01439 + 2.26335I −4.34155 − 5.25549I
u = −1.192030 + 0.614794I
a = −1.252570 + 0.434769I
b = 0.443016 + 1.223900I
−4.94120 + 4.54649I 0
u = −1.192030 − 0.614794I
a = −1.252570 − 0.434769I
b = 0.443016 − 1.223900I
−4.94120 − 4.54649I 0
u = 1.226470 + 0.560558I
a = 0.131618 + 0.653166I
b = 0.037214 + 1.116100I
−0.48936 − 5.43427I 0
u = 1.226470 − 0.560558I
a = 0.131618 − 0.653166I
b = 0.037214 − 1.116100I
−0.48936 + 5.43427I 0
u = 1.295390 + 0.424903I
a = 1.353430 + 0.074875I
b = −0.423320 + 1.145930I
−4.25004 + 0.23491I 0
u = 1.295390 − 0.424903I
a = 1.353430 − 0.074875I
b = −0.423320 − 1.145930I
−4.25004 − 0.23491I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.041349 + 0.626266I
a = 1.90603 + 1.22179I
b = −0.653736 − 0.265939I
2.01949 − 3.27741I −3.11199 + 1.77350I
u = −0.041349 − 0.626266I
a = 1.90603 − 1.22179I
b = −0.653736 + 0.265939I
2.01949 + 3.27741I −3.11199 − 1.77350I
u = 1.326420 + 0.359373I
a = 0.551420 + 0.312235I
b = 0.073870 + 1.235250I
−6.67841 − 5.00577I 0
u = 1.326420 − 0.359373I
a = 0.551420 − 0.312235I
b = 0.073870 − 1.235250I
−6.67841 + 5.00577I 0
u = −1.253890 + 0.572111I
a = −1.49618 + 0.78283I
b = 0.670725 + 1.105940I
−2.52024 + 12.89480I 0
u = −1.253890 − 0.572111I
a = −1.49618 − 0.78283I
b = 0.670725 − 1.105940I
−2.52024 − 12.89480I 0
u = −0.607530 + 0.100261I
a = 4.30314 − 3.15216I
b = −0.301144 − 0.693334I
1.79885 − 3.99008I −11.95183 − 3.89656I
u = −0.607530 − 0.100261I
a = 4.30314 + 3.15216I
b = −0.301144 + 0.693334I
1.79885 + 3.99008I −11.95183 + 3.89656I
u = 1.268700 + 0.558221I
a = 1.21224 + 0.85304I
b = −0.539106 + 1.066420I
−0.13905 − 7.75829I 0
u = 1.268700 − 0.558221I
a = 1.21224 − 0.85304I
b = −0.539106 − 1.066420I
−0.13905 + 7.75829I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.322080 + 0.463901I
a = 0.775597 + 0.493532I
b = −0.453771 + 1.302660I
−0.99839 − 6.78751I 0
u = 1.322080 − 0.463901I
a = 0.775597 − 0.493532I
b = −0.453771 − 1.302660I
−0.99839 + 6.78751I 0
u = −1.180370 + 0.771323I
a = −0.707864 + 0.647021I
b = 0.883774 − 0.518629I
5.65528 + 7.13741I 0
u = −1.180370 − 0.771323I
a = −0.707864 − 0.647021I
b = 0.883774 + 0.518629I
5.65528 − 7.13741I 0
u = −0.548467 + 0.044788I
a = 1.17874 − 3.02344I
b = −0.453771 − 1.302660I
−0.99839 + 6.78751I −6.07550 − 0.00937I
u = −0.548467 − 0.044788I
a = 1.17874 + 3.02344I
b = −0.453771 + 1.302660I
−0.99839 − 6.78751I −6.07550 + 0.00937I
u = 1.26837 + 0.80392I
a = −1.63403 − 0.42395I
b = 0.671974 − 1.108810I
3.84347 − 12.89570I 0
u = 1.26837 − 0.80392I
a = −1.63403 + 0.42395I
b = 0.671974 + 1.108810I
3.84347 + 12.89570I 0
u = −1.54109 + 0.22738I
a = 0.291738 + 0.789229I
b = −0.327524 + 0.686330I
−2.49314 + 4.00946I 0
u = −1.54109 − 0.22738I
a = 0.291738 − 0.789229I
b = −0.327524 − 0.686330I
−2.49314 − 4.00946I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.66116 + 0.03445I
a = 0.397291 − 0.311952I
b = −0.478202 − 1.054340I
−4.00386 + 7.55816I 0
u = 1.66116 − 0.03445I
a = 0.397291 + 0.311952I
b = −0.478202 + 1.054340I
−4.00386 − 7.55816I 0
u = −0.137331 + 0.227372I
a = 0.65218 − 1.64356I
b = 0.248597 − 0.964510I
−4.34575 − 2.86126I −14.9194 + 5.6525I
u = −0.137331 − 0.227372I
a = 0.65218 + 1.64356I
b = 0.248597 + 0.964510I
−4.34575 + 2.86126I −14.9194 − 5.6525I
22
III.
I
u
3
= h2.88 × 10
16
u
39
+ 2.47 × 10
16
u
38
+ · · · + 5.40 × 10
14
b − 1.88 × 10
16
, 5.04 ×
10
15
u
39
−1.85×10
15
u
38
+· · ·+4.91×10
13
a+5.20×10
15
, u
40
−13u
38
+· · ·+u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
8
=
−102.688u
39
+ 37.7644u
38
+ ··· + 123.687u − 105.951
−53.3826u
39
− 45.7958u
38
+ ··· + 154.242u + 34.8899
a
11
=
−u
−u
3
+ u
a
2
=
23.4545u
39
+ 10.0606u
38
+ ··· − 97.9184u − 124.580
88.4793u
39
− 130.550u
38
+ ··· − 95.5678u + 260.797
a
9
=
94.6296u
39
− 22.3052u
38
+ ··· − 129.156u + 53.8107
−118.215u
39
+ 7.52827u
38
+ ··· + 19.5197u − 126.477
a
1
=
111.934u
39
− 120.489u
38
+ ··· − 193.486u + 136.217
88.4793u
39
− 130.550u
38
+ ··· − 95.5678u + 260.797
a
5
=
−116.925u
39
+ 13.4192u
38
+ ··· + 222.814u − 49.2814
−4.54813u
39
+ 41.3023u
38
+ ··· + 29.8254u − 89.6280
a
6
=
−94.1953u
39
+ 2.86623u
38
+ ··· + 182.666u − 7.43989
−15.8610u
39
+ 56.1581u
38
+ ··· + 57.7962u − 120.916
a
12
=
−41.9674u
39
− 21.6822u
38
+ ··· − 22.7763u + 4.31586
−126.949u
39
+ 10.4832u
38
+ ··· + 197.913u − 74.7568
a
7
=
−46.0649u
39
+ 59.8349u
38
+ ··· + 134.934u − 104.640
124.240u
39
− 60.7324u
38
+ ··· − 129.631u + 114.774
(ii) Obstruction class = 1
(iii) Cusp Shapes =
−
163221859693865844
540031743483991
u
39
+
237015301458847729
540031743483991
u
38
+···+
123031965042997292
540031743483991
u−
580439103264460885
540031743483991
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
− 10u
19
+ ··· − 14u + 1)
2
c
2
(u
20
+ 5u
18
+ ··· + 7u
2
+ 1)
2
c
3
, c
11
u
40
− 13u
38
+ ··· + u + 1
c
4
, c
9
u
40
+ 3u
39
+ ··· + 13u
2
+ 1
c
5
u
40
+ 56u
34
+ ··· − 141720u
2
+ 128321
c
6
, c
12
u
40
− 3u
39
+ ··· + 13u
2
+ 1
c
7
, c
10
u
40
− 13u
38
+ ··· − u + 1
c
8
(u
20
+ 5u
18
+ ··· + 7u
2
+ 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 10y
19
+ ··· − 6y + 1)
2
c
2
, c
8
(y
20
+ 10y
19
+ ··· + 14y + 1)
2
c
3
, c
7
, c
10
c
11
y
40
− 26y
39
+ ··· − 29y + 1
c
4
, c
6
, c
9
c
12
y
40
+ 29y
39
+ ··· + 26y + 1
c
5
(y
20
+ 56y
17
+ ··· − 141720y + 128321)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.854018 + 0.464184I
a = −0.542777 + 0.722282I
b = −0.743220 − 0.511653I
4.62575 + 0.35522I −6.19616 + 1.21819I
u = 0.854018 − 0.464184I
a = −0.542777 − 0.722282I
b = −0.743220 + 0.511653I
4.62575 − 0.35522I −6.19616 − 1.21819I
u = −0.685463 + 0.816677I
a = 0.568457 − 0.911720I
b = −0.123891 + 0.748791I
−2.97635 + 4.30562I −16.0544 − 7.4345I
u = −0.685463 − 0.816677I
a = 0.568457 + 0.911720I
b = −0.123891 − 0.748791I
−2.97635 − 4.30562I −16.0544 + 7.4345I
u = 0.815757 + 0.332932I
a = −1.351770 − 0.076566I
b = 1.071900 − 0.836081I
4.90554 − 3.79001I −7.80691 + 4.95342I
u = 0.815757 − 0.332932I
a = −1.351770 + 0.076566I
b = 1.071900 + 0.836081I
4.90554 + 3.79001I −7.80691 − 4.95342I
u = 0.835982 + 0.268041I
a = −0.555181 − 0.851378I
b = 0.433646 + 0.812077I
−5.04942 + 1.77007I −17.5948 − 2.0908I
u = 0.835982 − 0.268041I
a = −0.555181 + 0.851378I
b = 0.433646 − 0.812077I
−5.04942 − 1.77007I −17.5948 + 2.0908I
u = −1.117170 + 0.322020I
a = 1.20118 − 0.99970I
b = −0.869042 − 1.107020I
2.82540 + 5.97720I 0. − 9.61899I
u = −1.117170 − 0.322020I
a = 1.20118 + 0.99970I
b = −0.869042 + 1.107020I
2.82540 − 5.97720I 0. + 9.61899I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.037248 + 0.826043I
a = 2.52741 + 1.59723I
b = −0.430743 − 0.838149I
4.79201 + 1.80579I 3.52157 − 1.81881I
u = 0.037248 − 0.826043I
a = 2.52741 − 1.59723I
b = −0.430743 + 0.838149I
4.79201 − 1.80579I 3.52157 + 1.81881I
u = −1.176210 + 0.186112I
a = −1.32993 + 1.14946I
b = 0.433646 + 0.812077I
−5.04942 + 1.77007I 0
u = −1.176210 − 0.186112I
a = −1.32993 − 1.14946I
b = 0.433646 − 0.812077I
−5.04942 − 1.77007I 0
u = 0.726107 + 0.295735I
a = −1.63217 − 2.27014I
b = 0.452190 − 1.262780I
−1.19875 − 7.32970I −11.0543 + 12.2739I
u = 0.726107 − 0.295735I
a = −1.63217 + 2.27014I
b = 0.452190 + 1.262780I
−1.19875 + 7.32970I −11.0543 − 12.2739I
u = 1.028220 + 0.660995I
a = 1.29507 + 0.72228I
b = −0.269579 + 1.157740I
−4.73788 − 5.97724I 0
u = 1.028220 − 0.660995I
a = 1.29507 − 0.72228I
b = −0.269579 − 1.157740I
−4.73788 + 5.97724I 0
u = 1.176120 + 0.407437I
a = −0.409481 + 0.212734I
b = 0.297808 + 0.967308I
−5.19899 + 1.23996I 0
u = 1.176120 − 0.407437I
a = −0.409481 − 0.212734I
b = 0.297808 − 0.967308I
−5.19899 − 1.23996I 0
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.208932 + 1.295110I
a = 0.575730 − 0.103623I
b = −0.430743 + 0.838149I
4.79201 − 1.80579I 0
u = 0.208932 − 1.295110I
a = 0.575730 + 0.103623I
b = −0.430743 − 0.838149I
4.79201 + 1.80579I 0
u = 1.108480 + 0.708142I
a = 0.411122 + 0.011766I
b = 0.180933 + 0.514277I
2.01270 − 4.40791I 0
u = 1.108480 − 0.708142I
a = 0.411122 − 0.011766I
b = 0.180933 − 0.514277I
2.01270 + 4.40791I 0
u = −0.660772 + 0.106155I
a = −0.114626 + 0.950462I
b = 1.071900 − 0.836081I
4.90554 − 3.79001I −7.80691 + 4.95342I
u = −0.660772 − 0.106155I
a = −0.114626 − 0.950462I
b = 1.071900 + 0.836081I
4.90554 + 3.79001I −7.80691 − 4.95342I
u = −1.270490 + 0.496547I
a = −1.312060 + 0.288118I
b = 0.297808 + 0.967308I
−5.19899 + 1.23996I 0
u = −1.270490 − 0.496547I
a = −1.312060 − 0.288118I
b = 0.297808 − 0.967308I
−5.19899 − 1.23996I 0
u = 0.563923 + 0.256895I
a = −0.531115 − 1.075650I
b = −0.743220 + 0.511653I
4.62575 − 0.35522I −6.19616 − 1.21819I
u = 0.563923 − 0.256895I
a = −0.531115 + 1.075650I
b = −0.743220 − 0.511653I
4.62575 + 0.35522I −6.19616 + 1.21819I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.602461 + 0.070349I
a = 1.34248 − 0.64273I
b = −0.869042 − 1.107020I
2.82540 + 5.97720I −8.53563 − 9.61899I
u = −0.602461 − 0.070349I
a = 1.34248 + 0.64273I
b = −0.869042 + 1.107020I
2.82540 − 5.97720I −8.53563 + 9.61899I
u = −1.35990 + 0.40030I
a = −0.643683 + 0.517695I
b = 0.452190 + 1.262780I
−1.19875 + 7.32970I 0
u = −1.35990 − 0.40030I
a = −0.643683 − 0.517695I
b = 0.452190 − 1.262780I
−1.19875 − 7.32970I 0
u = 1.42905 + 0.08950I
a = 0.595484 + 0.144916I
b = −0.269579 + 1.157740I
−4.73788 − 5.97724I 0
u = 1.42905 − 0.08950I
a = 0.595484 − 0.144916I
b = −0.269579 − 1.157740I
−4.73788 + 5.97724I 0
u = −1.43398 + 0.21210I
a = 0.444256 + 1.038960I
b = −0.123891 + 0.748791I
−2.97635 + 4.30562I 0
u = −1.43398 − 0.21210I
a = 0.444256 − 1.038960I
b = −0.123891 − 0.748791I
−2.97635 − 4.30562I 0
u = −0.477388 + 0.216837I
a = 2.46160 + 4.64703I
b = 0.180933 − 0.514277I
2.01270 + 4.40791I −3.71756 − 11.02130I
u = −0.477388 − 0.216837I
a = 2.46160 − 4.64703I
b = 0.180933 + 0.514277I
2.01270 − 4.40791I −3.71756 + 11.02130I
29
IV. I
u
4
=
h−u
5
−u
3
+u
2
+b+u, u
7
−u
6
+2u
5
−3u
4
−u
2
+a−u+2, u
8
+u
6
−u
5
−2u
4
+u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
8
=
−u
7
+ u
6
− 2u
5
+ 3u
4
+ u
2
+ u − 2
u
5
+ u
3
− u
2
− u
a
11
=
−u
−u
3
+ u
a
2
=
2u
7
+ 2u
5
− 2u
4
− 3u
3
+ 2
−u
7
− u
5
+ u
4
+ u
3
− u − 1
a
9
=
−u
7
+ u
6
− 2u
5
+ 2u
4
− u
2
+ 2u − 1
−u
6
+ u
5
− u
4
+ 2u
3
+ u
2
− u
a
1
=
u
7
+ u
5
− u
4
− 2u
3
− u + 1
−u
7
− u
5
+ u
4
+ u
3
− u − 1
a
5
=
−u
7
+ u
6
− u
5
+ 2u
4
+ u
3
− 2u
2
− 1
u
7
− u
6
+ u
5
− 2u
4
− u
3
+ 2u
2
a
6
=
−u
7
+ u
6
− u
5
+ 2u
4
+ u
3
− 2u
2
− 1
u
7
− u
6
+ u
5
− 2u
4
− u
3
+ 2u
2
a
12
=
2u
7
− u
6
+ 3u
5
− 3u
4
− 2u
3
+ u
2
− 3u + 2
−u
7
+ u
6
− 2u
5
+ 2u
4
− u
3
− u
2
+ u − 1
a
7
=
−2u
7
+ 2u
6
− 3u
5
+ 5u
4
+ u
3
− 2u
2
+ u − 4
u
7
− u
6
+ 2u
5
− 3u
4
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
7
+ 4u
6
+ 4u
5
− 2u
4
− 4u
3
− 10u
2
− u − 4
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 4u
7
+ 10u
6
− 16u
5
+ 19u
4
− 15u
3
+ 8u
2
− 3u + 1
c
2
u
8
+ 2u
6
+ 3u
4
+ u
3
+ 2u
2
+ u + 1
c
3
, c
11
u
8
+ u
6
− u
5
− 2u
4
+ u + 1
c
4
, c
9
u
8
+ u
7
− 2u
4
− u
3
+ u
2
+ 1
c
5
u
8
c
6
, c
12
u
8
− u
7
− 2u
4
+ u
3
+ u
2
+ 1
c
7
, c
10
u
8
+ u
6
+ u
5
− 2u
4
− u + 1
c
8
u
8
+ 2u
6
+ 3u
4
− u
3
+ 2u
2
− u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 4y
7
+ 10y
6
+ 20y
5
+ 19y
4
+ 3y
3
+ 12y
2
+ 7y + 1
c
2
, c
8
y
8
+ 4y
7
+ 10y
6
+ 16y
5
+ 19y
4
+ 15y
3
+ 8y
2
+ 3y + 1
c
3
, c
7
, c
10
c
11
y
8
+ 2y
7
− 3y
6
− 5y
5
+ 6y
4
+ 4y
3
− 4y
2
− y + 1
c
4
, c
6
, c
9
c
12
y
8
− y
7
− 4y
6
+ 4y
5
+ 6y
4
− 5y
3
− 3y
2
+ 2y + 1
c
5
y
8
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024220 + 0.223225I
a = 1.45783 + 1.08401I
b = −0.497664 + 1.123000I
−5.60402 − 3.77609I −16.1882 + 2.9305I
u = 1.024220 − 0.223225I
a = 1.45783 − 1.08401I
b = −0.497664 − 1.123000I
−5.60402 + 3.77609I −16.1882 − 2.9305I
u = −0.085673 + 0.857175I
a = −1.40103 + 0.55770I
b = 0.774658 − 0.904481I
6.36547 − 2.93267I −0.21388 + 2.83534I
u = −0.085673 − 0.857175I
a = −1.40103 − 0.55770I
b = 0.774658 + 0.904481I
6.36547 + 2.93267I −0.21388 − 2.83534I
u = −0.789263 + 0.118455I
a = −0.43102 − 1.57027I
b = −0.516141 + 0.507737I
−3.52853 − 0.48963I −8.65015 + 1.75654I
u = −0.789263 − 0.118455I
a = −0.43102 + 1.57027I
b = −0.516141 − 0.507737I
−3.52853 + 0.48963I −8.65015 − 1.75654I
u = −0.149281 + 1.379480I
a = −1.125780 − 0.299104I
b = 0.239148 + 0.913430I
2.76707 + 1.04226I −14.9478 − 4.2014I
u = −0.149281 − 1.379480I
a = −1.125780 + 0.299104I
b = 0.239148 − 0.913430I
2.76707 − 1.04226I −14.9478 + 4.2014I
33
V. I
u
5
= h4.02 × 10
5
u
23
+ 1.34 × 10
5
u
22
+ · · · + 8.45 × 10
5
b − 3.82 × 10
6
, 1.30 ×
10
9
u
23
+8.29×10
8
u
22
+· · ·+9.56×10
8
a−5.35×10
9
, u
24
−4u
22
+· · ·−14u+4i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
8
=
−1.35682u
23
− 0.866980u
22
+ ··· − 18.8198u + 5.60068
−0.476038u
23
− 0.159161u
22
+ ··· − 6.10638u + 4.51695
a
11
=
−u
−u
3
+ u
a
2
=
0.680533u
23
− 0.0955877u
22
+ ··· + 7.93509u − 11.7983
−0.476038u
23
− 0.159161u
22
+ ··· − 6.10638u + 3.51695
a
9
=
0.204495u
23
− 0.254749u
22
+ ··· + 1.82871u − 8.28134
−0.476038u
23
− 0.159161u
22
+ ··· − 6.10638u + 3.51695
a
1
=
0.204495u
23
− 0.254749u
22
+ ··· + 1.82871u − 8.28134
−0.476038u
23
− 0.159161u
22
+ ··· − 6.10638u + 3.51695
a
5
=
1.82096u
23
+ 1.09707u
22
+ ··· + 25.9792u − 13.8916
−0.0221995u
23
− 0.164055u
22
+ ··· − 0.604064u − 1.04903
a
6
=
1.57779u
23
+ 0.899999u
22
+ ··· + 22.0974u − 11.2707
0.184281u
23
− 0.00847915u
22
+ ··· + 1.49132u − 2.88168
a
12
=
0.569618u
23
+ 0.0154414u
22
+ ··· + 10.6995u − 10.0556
−0.227426u
23
+ 0.0561493u
22
+ ··· − 2.08654u + 1.39931
a
7
=
−0.820652u
23
− 0.0760856u
22
+ ··· − 11.0031u + 6.53629
−0.133229u
23
− 0.121509u
22
+ ··· − 0.793912u + 0.507308
(ii) Obstruction class = −1
(iii) Cusp Shapes =
402075
211157
u
23
+
134432
211157
u
22
+ ··· +
5157618
211157
u −
5082086
211157
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
(u
2
+ u + 1)
12
c
3
, c
7
, c
10
c
11
u
24
− 4u
22
+ ··· + 14u + 4
c
4
, c
6
, c
9
c
12
u
24
+ 4u
22
+ ··· + 2u + 4
c
5
(u
12
+ 2u
9
− 10u
8
+ 3u
6
− 10u
5
+ 25u
4
+ 2u
3
+ 5u
2
+ 1)
2
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
8
(y
2
+ y + 1)
12
c
3
, c
7
, c
10
c
11
y
24
− 8y
23
+ ··· − 188y + 16
c
4
, c
6
, c
9
c
12
y
24
+ 8y
23
+ ··· + 196y + 16
c
5
(y
12
− 20y
10
+ ··· + 10y + 1)
2
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.336524 + 0.943089I
a = −0.558710 − 0.481647I
b = 0.500000 + 0.866025I
3.94784 + 2.02988I −8.00000 − 3.46410I
u = −0.336524 − 0.943089I
a = −0.558710 + 0.481647I
b = 0.500000 − 0.866025I
3.94784 − 2.02988I −8.00000 + 3.46410I
u = −0.963851 + 0.277395I
a = −2.21509 + 1.42859I
b = 0.500000 + 0.866025I
−3.94784 + 2.02988I −8.00000 − 3.46410I
u = −0.963851 − 0.277395I
a = −2.21509 − 1.42859I
b = 0.500000 − 0.866025I
−3.94784 − 2.02988I −8.00000 + 3.46410I
u = −0.868413 + 0.571698I
a = −0.996744 + 0.470368I
b = 0.500000 − 0.866025I
−3.94784 − 2.02988I −8.00000 + 3.46410I
u = −0.868413 − 0.571698I
a = −0.996744 − 0.470368I
b = 0.500000 + 0.866025I
−3.94784 + 2.02988I −8.00000 − 3.46410I
u = 0.976086 + 0.384626I
a = −1.43647 − 2.16007I
b = 0.500000 − 0.866025I
3.94784 − 2.02988I −8.00000 + 3.46410I
u = 0.976086 − 0.384626I
a = −1.43647 + 2.16007I
b = 0.500000 + 0.866025I
3.94784 + 2.02988I −8.00000 − 3.46410I
u = −0.925307 + 0.645118I
a = 0.375494 + 1.166280I
b = 0.500000 − 0.866025I
3.94784 − 2.02988I −8.00000 + 3.46410I
u = −0.925307 − 0.645118I
a = 0.375494 − 1.166280I
b = 0.500000 + 0.866025I
3.94784 + 2.02988I −8.00000 − 3.46410I
37
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154221 + 1.132760I
a = −1.58405 + 0.85717I
b = 0.500000 − 0.866025I
3.94784 − 2.02988I −8.00000 + 3.46410I
u = −0.154221 − 1.132760I
a = −1.58405 − 0.85717I
b = 0.500000 + 0.866025I
3.94784 + 2.02988I −8.00000 − 3.46410I
u = 0.656880 + 0.339024I
a = −0.33446 − 2.05538I
b = 0.500000 + 0.866025I
−3.94784 + 2.02988I −8.00000 − 3.46410I
u = 0.656880 − 0.339024I
a = −0.33446 + 2.05538I
b = 0.500000 − 0.866025I
−3.94784 − 2.02988I −8.00000 + 3.46410I
u = 1.151420 + 0.675427I
a = −1.70413 − 0.00361I
b = 0.500000 − 0.866025I
−3.94784 − 2.02988I −8.00000 + 3.46410I
u = 1.151420 − 0.675427I
a = −1.70413 + 0.00361I
b = 0.500000 + 0.866025I
−3.94784 + 2.02988I −8.00000 − 3.46410I
u = −0.009837 + 1.364810I
a = −0.815468 − 0.099784I
b = 0.500000 + 0.866025I
3.94784 + 2.02988I −8.00000 − 3.46410I
u = −0.009837 − 1.364810I
a = −0.815468 + 0.099784I
b = 0.500000 − 0.866025I
3.94784 − 2.02988I −8.00000 + 3.46410I
u = −1.44219 + 0.20589I
a = −0.668063 + 0.703047I
b = 0.500000 + 0.866025I
−3.94784 + 2.02988I −8.00000 − 3.46410I
u = −1.44219 − 0.20589I
a = −0.668063 − 0.703047I
b = 0.500000 − 0.866025I
−3.94784 − 2.02988I −8.00000 + 3.46410I
38
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46615 + 0.42481I
a = −0.213473 + 0.288288I
b = 0.500000 + 0.866025I
−3.94784 + 2.02988I −8.00000 − 3.46410I
u = 1.46615 − 0.42481I
a = −0.213473 − 0.288288I
b = 0.500000 − 0.866025I
−3.94784 − 2.02988I −8.00000 + 3.46410I
u = 0.449802 + 0.145401I
a = −4.34884 − 2.27908I
b = 0.500000 − 0.866025I
3.94784 − 2.02988I −8.00000 + 3.46410I
u = 0.449802 − 0.145401I
a = −4.34884 + 2.27908I
b = 0.500000 + 0.866025I
3.94784 + 2.02988I −8.00000 − 3.46410I
39
VI. I
u
6
= hb, a + 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
−1
a
4
=
1
1
a
8
=
−1
0
a
11
=
1
0
a
2
=
1
0
a
9
=
−1
0
a
1
=
1
0
a
5
=
0
1
a
6
=
−1
1
a
12
=
1
−1
a
7
=
−2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
u
c
3
, c
5
, c
7
c
10
, c
11
u − 1
c
4
, c
6
, c
9
c
12
u + 1
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
8
y
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y −1
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−4.93480 −18.0000
43
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
+ u + 1)
12
(u
8
− 4u
7
+ ··· − 3u + 1)
· ((u
20
− 10u
19
+ ··· − 14u + 1)
2
)(u
31
+ 13u
30
+ ··· − 5076u − 1296)
· (u
52
+ 22u
51
+ ··· + 7092u + 1296)
2
c
2
u(u
2
+ u + 1)
12
(u
8
+ 2u
6
+ 3u
4
+ u
3
+ 2u
2
+ u + 1)
· ((u
20
+ 5u
18
+ ··· + 7u
2
+ 1)
2
)(u
31
− u
30
+ ··· − 54u + 36)
· (u
52
− 6u
51
+ ··· − 222u + 36)
2
c
3
, c
11
(u − 1)(u
8
+ u
6
+ ··· + u + 1)(u
24
− 4u
22
+ ··· + 14u + 4)
· (u
31
+ u
30
+ ··· − 4u
2
+ 1)(u
40
− 13u
38
+ ··· + u + 1)
· (u
104
− u
103
+ ··· − 1113u + 179)
c
4
, c
9
(u + 1)(u
8
+ u
7
+ ··· + u
2
+ 1)(u
24
+ 4u
22
+ ··· + 2u + 4)
· (u
31
− 2u
30
+ ··· + 3u + 1)(u
40
+ 3u
39
+ ··· + 13u
2
+ 1)
· (u
104
− 2u
103
+ ··· − 854u + 101)
c
5
u
8
(u − 1)(u
12
+ 2u
9
− 10u
8
+ 3u
6
− 10u
5
+ 25u
4
+ 2u
3
+ 5u
2
+ 1)
2
· (u
31
+ 6u
30
+ ··· + 6656u + 1024)
· (u
40
+ 56u
34
+ ··· − 141720u
2
+ 128321)
· (u
52
− 2u
51
+ ··· − 2u + 1)
2
c
6
, c
12
(u + 1)(u
8
− u
7
+ ··· + u
2
+ 1)(u
24
+ 4u
22
+ ··· + 2u + 4)
· (u
31
− 2u
30
+ ··· + 3u + 1)(u
40
− 3u
39
+ ··· + 13u
2
+ 1)
· (u
104
− 2u
103
+ ··· − 854u + 101)
c
7
, c
10
(u − 1)(u
8
+ u
6
+ ··· − u + 1)(u
24
− 4u
22
+ ··· + 14u + 4)
· (u
31
+ u
30
+ ··· − 4u
2
+ 1)(u
40
− 13u
38
+ ··· − u + 1)
· (u
104
− u
103
+ ··· − 1113u + 179)
c
8
u(u
2
+ u + 1)
12
(u
8
+ 2u
6
+ 3u
4
− u
3
+ 2u
2
− u + 1)
· ((u
20
+ 5u
18
+ ··· + 7u
2
+ 1)
2
)(u
31
− u
30
+ ··· − 54u + 36)
· (u
52
− 6u
51
+ ··· − 222u + 36)
2
44
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
12
(y
8
+ 4y
7
+ ··· + 7y + 1)
· (y
20
+ 10y
19
+ ··· − 6y + 1)
2
· (y
31
+ 13y
30
+ ··· + 17064432y −1679616)
· (y
52
+ 22y
51
+ ··· − 195696y + 1679616)
2
c
2
, c
8
y(y
2
+ y + 1)
12
(y
8
+ 4y
7
+ ··· + 3y + 1)
· ((y
20
+ 10y
19
+ ··· + 14y + 1)
2
)(y
31
+ 13y
30
+ ··· − 5076y −1296)
· (y
52
+ 22y
51
+ ··· + 7092y + 1296)
2
c
3
, c
7
, c
10
c
11
(y −1)(y
8
+ 2y
7
− 3y
6
− 5y
5
+ 6y
4
+ 4y
3
− 4y
2
− y + 1)
· (y
24
− 8y
23
+ ··· − 188y + 16)(y
31
− 11y
30
+ ··· + 8y −1)
· (y
40
− 26y
39
+ ··· − 29y + 1)(y
104
− 59y
103
+ ··· − 398901y + 32041)
c
4
, c
6
, c
9
c
12
(y −1)(y
8
− y
7
− 4y
6
+ 4y
5
+ 6y
4
− 5y
3
− 3y
2
+ 2y + 1)
· (y
24
+ 8y
23
+ ··· + 196y + 16)(y
31
+ 18y
30
+ ··· + 13y −1)
· (y
40
+ 29y
39
+ ··· + 26y + 1)(y
104
+ 68y
103
+ ··· + 541870y + 10201)
c
5
y
8
(y −1)(y
12
− 20y
10
+ ··· + 10y + 1)
2
· (y
20
+ 56y
17
+ ··· − 141720y + 128321)
2
· (y
31
+ 2y
30
+ ··· − 1310720y −1048576)
· (y
52
+ 2y
51
+ ··· + 88y + 1)
2
45
