12a
1097
(K12a
1097
)
A knot diagram
1
Linearized knot diagam
4 7 11 8 12 3 10 1 5 2 6 9
Solving Sequence
2,7 3,11
4 1 6 12 5 10 8 9
c
2
c
3
c
1
c
6
c
11
c
5
c
10
c
7
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3102178454u
24
− 15488927339u
23
+ ··· + 126671695426b − 3208274034,
− 109125500312u
24
+ 169518693654u
23
+ ··· + 126671695426a + 248511754619,
u
25
− u
24
+ ··· − 4u − 1i
I
u
2
= h−3.64244 × 10
488
u
119
− 1.96796 × 10
488
u
118
+ ··· + 1.15571 × 10
490
b − 2.23233 × 10
491
,
2.53470 × 10
491
u
119
+ 1.70055 × 10
491
u
118
+ ··· + 4.31080 × 10
492
a + 3.08118 × 10
494
,
u
120
+ u
119
+ ··· + 3274u + 373i
I
u
3
= h−1.26770 × 10
32
u
33
− 6.32813 × 10
32
u
32
+ ··· + 1.13470 × 10
33
b − 1.22256 × 10
33
,
8.99358 × 10
32
u
33
+ 2.58920 × 10
33
u
32
+ ··· + 7.94293 × 10
33
a − 1.81454 × 10
34
, u
34
+ 4u
33
+ ··· + 10u + 7i
I
u
4
= hu
2
+ b − u + 1, a + u, u
3
− u
2
+ 2u − 1i
* 4 irreducible components of dim
C
= 0, with total 182 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−3.10×10
9
u
24
−1.55×10
10
u
23
+· · ·+1.27×10
11
b−3.21×10
9
, −1.09×
10
11
u
24
+1.70×10
11
u
23
+· · ·+1.27×10
11
a+2.49×10
11
, u
25
−u
24
+· · ·−4u−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
0.861483u
24
− 1.33825u
23
+ ··· − 10.2790u − 1.96186
0.0244899u
24
+ 0.122276u
23
+ ··· + 1.96923u + 0.0253275
a
4
=
−1.24527u
24
+ 1.18630u
23
+ ··· + 4.94727u + 5.83862
0.330003u
24
− 0.336309u
23
+ ··· − 1.60736u − 0.885973
a
1
=
−1.04759u
24
+ 1.71210u
23
+ ··· + 8.80196u + 2.26840
0.0958880u
24
− 0.387211u
23
+ ··· − 0.961789u + 0.417723
a
6
=
u
u
3
+ u
a
12
=
1.20401u
24
− 1.61811u
23
+ ··· − 11.3742u − 2.51518
0.0593353u
24
+ 0.0734059u
23
+ ··· + 1.46726u − 0.465323
a
5
=
−0.889942u
24
+ 0.849149u
23
+ ··· − 1.21154u + 5.82056
0.166699u
24
− 0.468616u
23
+ ··· − 0.00571945u − 1.23391
a
10
=
0.885973u
24
− 1.21598u
23
+ ··· − 8.30975u − 1.93653
0.0244899u
24
+ 0.122276u
23
+ ··· + 1.96923u + 0.0253275
a
8
=
0.417723u
24
− 0.321835u
23
+ ··· + 1.89594u − 2.63268
−0.338923u
24
+ 0.558319u
23
+ ··· + 0.971046u + 0.791762
a
9
=
−0.246780u
24
+ 0.403197u
23
+ ··· + 3.81792u − 1.58508
−0.0476005u
24
+ 0.202824u
23
+ ··· + 0.169772u + 0.695874
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
58456314520
63335847713
u
24
−
118830395739
63335847713
u
23
+ ··· −
1160180780406
63335847713
u −
761638158750
63335847713
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
25
− u
24
+ ··· + 28u + 13
c
2
, c
6
, c
8
c
12
u
25
+ u
24
+ ··· − 4u + 1
c
3
, c
9
u
25
− u
24
+ ··· + 24u + 8
c
4
, c
10
4(4u
25
− 4u
24
+ ··· + 4u + 1)
c
5
, c
11
4(4u
25
− 12u
24
+ ··· − 344u + 40)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
25
+ 21y
24
+ ··· + 4112y −169
c
2
, c
6
, c
8
c
12
y
25
+ 17y
24
+ ··· + 20y −1
c
3
, c
9
y
25
+ 9y
24
+ ··· + 256y −64
c
4
, c
10
16(16y
25
+ 336y
24
+ ··· − 4y −1)
c
5
, c
11
16(16y
25
+ 304y
24
+ ··· + 27776y −1600)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.211687 + 0.985151I
a = 0.054135 − 1.103940I
b = −0.144638 + 0.502780I
2.32892 − 2.20108I −10.08383 + 3.97912I
u = 0.211687 − 0.985151I
a = 0.054135 + 1.103940I
b = −0.144638 − 0.502780I
2.32892 + 2.20108I −10.08383 − 3.97912I
u = 0.531651 + 0.812171I
a = −0.650095 − 0.103642I
b = −0.575312 − 0.511008I
1.67097 − 3.94275I −14.2459 + 7.3928I
u = 0.531651 − 0.812171I
a = −0.650095 + 0.103642I
b = −0.575312 + 0.511008I
1.67097 + 3.94275I −14.2459 − 7.3928I
u = −0.090278 + 1.083730I
a = 0.34542 + 2.11090I
b = 0.55243 − 1.97550I
6.61385 + 1.08919I −3.90952 + 2.05372I
u = −0.090278 − 1.083730I
a = 0.34542 − 2.11090I
b = 0.55243 + 1.97550I
6.61385 − 1.08919I −3.90952 − 2.05372I
u = −0.759076 + 0.841792I
a = 0.983474 − 0.029586I
b = 0.082128 − 0.598891I
4.59853 + 2.71316I −3.58633 − 2.16462I
u = −0.759076 − 0.841792I
a = 0.983474 + 0.029586I
b = 0.082128 + 0.598891I
4.59853 − 2.71316I −3.58633 + 2.16462I
u = −0.795867 + 0.037941I
a = −0.090425 + 0.410318I
b = 0.678970 + 0.915805I
0.07267 − 4.35672I −13.6982 + 5.9671I
u = −0.795867 − 0.037941I
a = −0.090425 − 0.410318I
b = 0.678970 − 0.915805I
0.07267 + 4.35672I −13.6982 − 5.9671I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.130652 + 1.262320I
a = −0.36503 + 2.00469I
b = −0.262641 − 1.153140I
11.96210 + 3.79673I 0.99019 − 1.08851I
u = −0.130652 − 1.262320I
a = −0.36503 − 2.00469I
b = −0.262641 + 1.153140I
11.96210 − 3.79673I 0.99019 + 1.08851I
u = 1.283170 + 0.138278I
a = −0.1264500 + 0.0272136I
b = −0.609786 − 1.030790I
5.09693 − 7.29373I −6.53712 + 7.10526I
u = 1.283170 − 0.138278I
a = −0.1264500 − 0.0272136I
b = −0.609786 + 1.030790I
5.09693 + 7.29373I −6.53712 − 7.10526I
u = −0.324609 + 1.255330I
a = 0.174379 − 1.064750I
b = 0.205309 + 0.235499I
8.79693 + 5.43785I −7.61088 − 4.32634I
u = −0.324609 − 1.255330I
a = 0.174379 + 1.064750I
b = 0.205309 − 0.235499I
8.79693 − 5.43785I −7.61088 + 4.32634I
u = −0.420644 + 1.280190I
a = −0.04988 − 1.77342I
b = −1.01226 + 1.62483I
7.8259 + 13.3271I −5.74524 − 10.07551I
u = −0.420644 − 1.280190I
a = −0.04988 + 1.77342I
b = −1.01226 − 1.62483I
7.8259 − 13.3271I −5.74524 + 10.07551I
u = 0.50923 + 1.46306I
a = 0.08105 − 1.50897I
b = 1.07565 + 1.36286I
15.4595 − 19.6209I −4.50944 + 9.03245I
u = 0.50923 − 1.46306I
a = 0.08105 + 1.50897I
b = 1.07565 − 1.36286I
15.4595 + 19.6209I −4.50944 − 9.03245I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.56756 + 1.47388I
a = −0.495606 + 0.843370I
b = −0.002290 − 1.336230I
14.1477 − 6.4090I −0.73994 + 3.70265I
u = 0.56756 − 1.47388I
a = −0.495606 − 0.843370I
b = −0.002290 + 1.336230I
14.1477 + 6.4090I −0.73994 − 3.70265I
u = 0.303142
a = −0.873492
b = 0.266168
−0.553708 −17.9600
u = −0.233731 + 0.135219I
a = 1.57579 − 3.69840I
b = −0.620642 + 0.604636I
3.94965 + 0.82098I −7.34374 − 4.35501I
u = −0.233731 − 0.135219I
a = 1.57579 + 3.69840I
b = −0.620642 − 0.604636I
3.94965 − 0.82098I −7.34374 + 4.35501I
7
II. I
u
2
= h−3.64 × 10
488
u
119
− 1.97 × 10
488
u
118
+ · · · + 1.16 × 10
490
b − 2.23 ×
10
491
, 2.53 × 10
491
u
119
+ 1.70 × 10
491
u
118
+ · · · + 4.31 × 10
492
a + 3.08 ×
10
494
, u
120
+ u
119
+ · · · + 3274u + 373i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
−0.0587990u
119
− 0.0394486u
118
+ ··· − 331.889u − 71.4760
0.0315169u
119
+ 0.0170282u
118
+ ··· + 82.3482u + 19.3157
a
4
=
0.00530998u
119
− 0.0270182u
118
+ ··· − 221.501u − 36.6777
0.0182302u
119
+ 0.0140764u
118
+ ··· + 116.691u + 21.9513
a
1
=
−0.160110u
119
− 0.129560u
118
+ ··· − 888.759u − 170.800
0.0324386u
119
+ 0.0221919u
118
+ ··· + 236.973u + 50.2961
a
6
=
u
u
3
+ u
a
12
=
−0.0431920u
119
− 0.0375647u
118
+ ··· − 393.968u − 82.1957
0.0191721u
119
+ 0.0140410u
118
+ ··· + 59.3771u + 13.7147
a
5
=
0.00557811u
119
+ 0.0117214u
118
+ ··· − 16.7458u + 0.784071
−0.00709475u
119
− 0.0228846u
118
+ ··· + 16.8580u + 7.18962
a
10
=
−0.0272820u
119
− 0.0224204u
118
+ ··· − 249.541u − 52.1603
0.0315169u
119
+ 0.0170282u
118
+ ··· + 82.3482u + 19.3157
a
8
=
0.0200896u
119
+ 0.0432169u
118
+ ··· + 49.2589u − 5.99909
−0.00989759u
119
− 0.0141728u
118
+ ··· − 7.10394u − 1.44063
a
9
=
0.0982715u
119
+ 0.0637556u
118
+ ··· + 617.329u + 129.828
−0.00409398u
119
− 0.00734538u
118
+ ··· − 21.4414u − 3.91955
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0416181u
119
+ 0.115712u
118
+ ··· + 275.820u + 38.7552
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
120
− 11u
119
+ ··· − 7076832991u + 1201214753
c
2
, c
6
, c
8
c
12
u
120
− u
119
+ ··· − 3274u + 373
c
3
, c
9
u
120
− u
119
+ ··· + 40633750u + 2972977
c
4
, c
10
u
120
+ 5u
119
+ ··· − 257509u + 235151
c
5
, c
11
(u
60
+ 6u
59
+ ··· + 58u + 13)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
120
+ 55y
119
+ ··· + 4.74 × 10
19
y + 1.44 × 10
18
c
2
, c
6
, c
8
c
12
y
120
+ 89y
119
+ ··· − 413086y + 139129
c
3
, c
9
y
120
+ 71y
119
+ ··· + 487658353656878y + 8838592242529
c
4
, c
10
y
120
+ 71y
119
+ ··· + 3045613958149y + 55295992801
c
5
, c
11
(y
60
+ 38y
59
+ ··· − 2298y + 169)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.176278 + 1.003150I
a = −0.26302 + 1.69210I
b = 0.702847 − 0.582113I
−0.45517 + 1.61974I 0
u = −0.176278 − 1.003150I
a = −0.26302 − 1.69210I
b = 0.702847 + 0.582113I
−0.45517 − 1.61974I 0
u = 0.668703 + 0.773478I
a = −1.38571 + 0.91884I
b = −1.082060 + 0.140425I
2.66044 − 2.58613I 0
u = 0.668703 − 0.773478I
a = −1.38571 − 0.91884I
b = −1.082060 − 0.140425I
2.66044 + 2.58613I 0
u = 0.109634 + 1.023630I
a = −0.33741 + 5.27176I
b = −0.63155 − 5.30275I
6.56424 0
u = 0.109634 − 1.023630I
a = −0.33741 − 5.27176I
b = −0.63155 + 5.30275I
6.56424 0
u = −0.333875 + 0.882085I
a = 0.39883 + 1.37895I
b = 1.152120 − 0.113139I
−1.10643 + 1.49905I 0
u = −0.333875 − 0.882085I
a = 0.39883 − 1.37895I
b = 1.152120 + 0.113139I
−1.10643 − 1.49905I 0
u = −0.982492 + 0.426289I
a = 0.0810181 − 0.1157020I
b = −0.598200 + 0.684462I
3.68720 + 3.23259I 0
u = −0.982492 − 0.426289I
a = 0.0810181 + 0.1157020I
b = −0.598200 − 0.684462I
3.68720 − 3.23259I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369669 + 1.016010I
a = 0.952924 + 0.891255I
b = −0.494773 − 0.424758I
4.55693 + 1.81266I 0
u = −0.369669 − 1.016010I
a = 0.952924 − 0.891255I
b = −0.494773 + 0.424758I
4.55693 − 1.81266I 0
u = −0.177852 + 1.071520I
a = 0.49349 − 2.16617I
b = −0.548919 + 0.678340I
4.36703 + 6.35969I 0
u = −0.177852 − 1.071520I
a = 0.49349 + 2.16617I
b = −0.548919 − 0.678340I
4.36703 − 6.35969I 0
u = −0.907570 + 0.044954I
a = 0.263905 − 0.230766I
b = −0.690296 − 0.984161I
3.94962 − 8.58069I 0
u = −0.907570 − 0.044954I
a = 0.263905 + 0.230766I
b = −0.690296 + 0.984161I
3.94962 + 8.58069I 0
u = 0.889684 + 0.126509I
a = −0.272775 − 0.158542I
b = −0.561692 + 0.349545I
−1.90732 + 0.96795I 0
u = 0.889684 − 0.126509I
a = −0.272775 + 0.158542I
b = −0.561692 − 0.349545I
−1.90732 − 0.96795I 0
u = −0.739097 + 0.452145I
a = −0.065041 + 0.389516I
b = 0.953305 − 0.774577I
6.35339 + 3.89468I 0
u = −0.739097 − 0.452145I
a = −0.065041 − 0.389516I
b = 0.953305 + 0.774577I
6.35339 − 3.89468I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.358267 + 1.083930I
a = 0.60263 − 2.41653I
b = 0.594241 + 0.396300I
9.77900 − 9.75690I 0
u = 0.358267 − 1.083930I
a = 0.60263 + 2.41653I
b = 0.594241 − 0.396300I
9.77900 + 9.75690I 0
u = 0.839850 + 0.176934I
a = 0.012982 + 0.295674I
b = 0.674555 + 0.059784I
−0.45517 − 1.61974I 0
u = 0.839850 − 0.176934I
a = 0.012982 − 0.295674I
b = 0.674555 − 0.059784I
−0.45517 + 1.61974I 0
u = −0.246958 + 0.808765I
a = 0.620936 − 1.199770I
b = −0.810037 + 0.310511I
2.63550 − 2.44024I 0
u = −0.246958 − 0.808765I
a = 0.620936 + 1.199770I
b = −0.810037 − 0.310511I
2.63550 + 2.44024I 0
u = −0.027998 + 1.185840I
a = 0.907181 + 0.669202I
b = −1.98408 − 0.46062I
6.84022 − 0.18821I 0
u = −0.027998 − 1.185840I
a = 0.907181 − 0.669202I
b = −1.98408 + 0.46062I
6.84022 + 0.18821I 0
u = 0.726256 + 0.351007I
a = 1.289320 + 0.319498I
b = 0.991531 − 0.524952I
7.61643 + 5.63059I 0
u = 0.726256 − 0.351007I
a = 1.289320 − 0.319498I
b = 0.991531 + 0.524952I
7.61643 − 5.63059I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.187870 + 0.114986I
a = −0.103231 + 0.124022I
b = 0.317569 − 0.956913I
9.31651 + 3.72518I 0
u = −1.187870 − 0.114986I
a = −0.103231 − 0.124022I
b = 0.317569 + 0.956913I
9.31651 − 3.72518I 0
u = −0.051145 + 1.193110I
a = 1.022770 + 0.623977I
b = 0.768749 − 0.460343I
6.35339 + 3.89468I 0
u = −0.051145 − 1.193110I
a = 1.022770 − 0.623977I
b = 0.768749 + 0.460343I
6.35339 − 3.89468I 0
u = 1.204050 + 0.043115I
a = 0.251057 − 0.053187I
b = 0.628299 + 1.077040I
9.59442 − 0.08130I 0
u = 1.204050 − 0.043115I
a = 0.251057 + 0.053187I
b = 0.628299 − 1.077040I
9.59442 + 0.08130I 0
u = 0.001071 + 1.211090I
a = −1.61401 − 1.61052I
b = −0.374800 + 0.609659I
12.5974 + 7.9743I 0
u = 0.001071 − 1.211090I
a = −1.61401 + 1.61052I
b = −0.374800 − 0.609659I
12.5974 − 7.9743I 0
u = 0.259400 + 1.210870I
a = 1.09120 − 1.20780I
b = 0.354610 + 0.770780I
8.15494 − 5.72051I 0
u = 0.259400 − 1.210870I
a = 1.09120 + 1.20780I
b = 0.354610 − 0.770780I
8.15494 + 5.72051I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.235330 + 0.186358I
a = 0.0735251 − 0.0756817I
b = 0.682199 + 1.003610I
10.2333 − 13.5581I 0
u = 1.235330 − 0.186358I
a = 0.0735251 + 0.0756817I
b = 0.682199 − 1.003610I
10.2333 + 13.5581I 0
u = 0.322888 + 1.213660I
a = 0.036213 − 1.280870I
b = 0.284724 + 0.891677I
2.63550 − 2.44024I 0
u = 0.322888 − 1.213660I
a = 0.036213 + 1.280870I
b = 0.284724 − 0.891677I
2.63550 + 2.44024I 0
u = −0.116284 + 1.252440I
a = 0.61299 − 1.76585I
b = 0.177748 + 0.791027I
8.04886 + 2.24498I 0
u = −0.116284 − 1.252440I
a = 0.61299 + 1.76585I
b = 0.177748 − 0.791027I
8.04886 − 2.24498I 0
u = −0.221334 + 1.239270I
a = −0.598567 − 1.051570I
b = −0.140914 + 0.987940I
4.28902 − 0.81320I 0
u = −0.221334 − 1.239270I
a = −0.598567 + 1.051570I
b = −0.140914 − 0.987940I
4.28902 + 0.81320I 0
u = 0.234651 + 1.254290I
a = −0.15584 − 1.79885I
b = 0.86984 + 1.77853I
4.23041 − 2.90929I 0
u = 0.234651 − 1.254290I
a = −0.15584 + 1.79885I
b = 0.86984 − 1.77853I
4.23041 + 2.90929I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.510980 + 0.507008I
a = 0.282339 − 0.343044I
b = −1.184830 + 0.020121I
1.54983 + 5.59559I −11.4093 − 9.5168I
u = −0.510980 − 0.507008I
a = 0.282339 + 0.343044I
b = −1.184830 − 0.020121I
1.54983 − 5.59559I −11.4093 + 9.5168I
u = 0.410538 + 1.224760I
a = −0.20877 + 1.45788I
b = −0.626455 − 0.761944I
1.54983 − 5.59559I 0
u = 0.410538 − 1.224760I
a = −0.20877 − 1.45788I
b = −0.626455 + 0.761944I
1.54983 + 5.59559I 0
u = −0.026828 + 1.293420I
a = −0.48040 − 1.72666I
b = 1.23127 + 1.35058I
12.17540 − 1.45489I 0
u = −0.026828 − 1.293420I
a = −0.48040 + 1.72666I
b = 1.23127 − 1.35058I
12.17540 + 1.45489I 0
u = −0.087316 + 1.306490I
a = −0.88730 + 1.57846I
b = −0.017811 − 0.658565I
12.17540 + 1.45489I 0
u = −0.087316 − 1.306490I
a = −0.88730 − 1.57846I
b = −0.017811 + 0.658565I
12.17540 − 1.45489I 0
u = 0.466149 + 1.229610I
a = −0.337611 + 0.820388I
b = −0.686404 − 0.707875I
2.28986 − 4.46331I 0
u = 0.466149 − 1.229610I
a = −0.337611 − 0.820388I
b = −0.686404 + 0.707875I
2.28986 + 4.46331I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.107992 + 1.313110I
a = −0.92179 + 1.26531I
b = 1.69594 − 1.45548I
14.2470 − 9.6079I 0
u = 0.107992 − 1.313110I
a = −0.92179 − 1.26531I
b = 1.69594 + 1.45548I
14.2470 + 9.6079I 0
u = −0.367619 + 1.275400I
a = −0.00263 + 1.75334I
b = 1.10339 − 1.54209I
3.94962 + 8.58069I 0
u = −0.367619 − 1.275400I
a = −0.00263 − 1.75334I
b = 1.10339 + 1.54209I
3.94962 − 8.58069I 0
u = −0.292279 + 1.296470I
a = −0.03064 − 1.73167I
b = −1.06249 + 1.34745I
8.55784 + 4.02774I 0
u = −0.292279 − 1.296470I
a = −0.03064 + 1.73167I
b = −1.06249 − 1.34745I
8.55784 − 4.02774I 0
u = −0.368618 + 0.550927I
a = −1.90762 + 1.20740I
b = 1.199840 − 0.119486I
6.84022 + 0.18821I −6.49782 + 0.44070I
u = −0.368618 − 0.550927I
a = −1.90762 − 1.20740I
b = 1.199840 + 0.119486I
6.84022 − 0.18821I −6.49782 − 0.44070I
u = −0.420287 + 0.511386I
a = −0.055452 + 0.560232I
b = 1.072910 + 0.178946I
−1.90732 + 0.96795I −12.6888 − 7.3089I
u = −0.420287 − 0.511386I
a = −0.055452 − 0.560232I
b = 1.072910 − 0.178946I
−1.90732 − 0.96795I −12.6888 + 7.3089I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.084057 + 1.359270I
a = 0.75428 − 1.19759I
b = −1.54353 + 1.46157I
9.31651 − 3.72518I 0
u = 0.084057 − 1.359270I
a = 0.75428 + 1.19759I
b = −1.54353 − 1.46157I
9.31651 + 3.72518I 0
u = 1.319240 + 0.347086I
a = 0.014559 + 0.179753I
b = −0.019197 + 0.232157I
−1.10643 − 1.49905I 0
u = 1.319240 − 0.347086I
a = 0.014559 − 0.179753I
b = −0.019197 − 0.232157I
−1.10643 + 1.49905I 0
u = −0.602231 + 0.187253I
a = 0.65282 − 1.57560I
b = −0.530286 − 0.309338I
4.55693 + 1.81266I −10.23887 − 3.85340I
u = −0.602231 − 0.187253I
a = 0.65282 + 1.57560I
b = −0.530286 + 0.309338I
4.55693 − 1.81266I −10.23887 + 3.85340I
u = 0.178252 + 1.383970I
a = 0.53018 + 1.49720I
b = −1.20877 − 1.41432I
8.15494 − 5.72051I 0
u = 0.178252 − 1.383970I
a = 0.53018 − 1.49720I
b = −1.20877 + 1.41432I
8.15494 + 5.72051I 0
u = −0.321741 + 1.370860I
a = 0.672543 + 0.754862I
b = 0.068428 − 0.834427I
8.55784 − 4.02774I 0
u = −0.321741 − 1.370860I
a = 0.672543 − 0.754862I
b = 0.068428 + 0.834427I
8.55784 + 4.02774I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.562722 + 0.173882I
a = −0.382918 + 0.811402I
b = 0.401456 + 0.643541I
0.0322866 −14.4116 + 0.I
u = 0.562722 − 0.173882I
a = −0.382918 − 0.811402I
b = 0.401456 − 0.643541I
0.0322866 −14.4116 + 0.I
u = 0.135642 + 1.405890I
a = −0.718454 + 0.962174I
b = 1.39554 − 1.24527I
13.56410 + 2.81403I 0
u = 0.135642 − 1.405890I
a = −0.718454 − 0.962174I
b = 1.39554 + 1.24527I
13.56410 − 2.81403I 0
u = 0.43667 + 1.35342I
a = −0.161677 − 1.000140I
b = 0.964347 + 0.876399I
4.36703 − 6.35969I 0
u = 0.43667 − 1.35342I
a = −0.161677 + 1.000140I
b = 0.964347 − 0.876399I
4.36703 + 6.35969I 0
u = 0.546337 + 0.150299I
a = 1.43208 + 0.34210I
b = −0.394330 + 1.050910I
4.23041 − 2.90929I −7.65574 + 4.38595I
u = 0.546337 − 0.150299I
a = 1.43208 − 0.34210I
b = −0.394330 − 1.050910I
4.23041 + 2.90929I −7.65574 − 4.38595I
u = −0.533272 + 0.106929I
a = −0.726783 + 0.418703I
b = −0.542752 + 0.957663I
4.28902 + 0.81320I −6.84059 − 3.44170I
u = −0.533272 − 0.106929I
a = −0.726783 − 0.418703I
b = −0.542752 − 0.957663I
4.28902 − 0.81320I −6.84059 + 3.44170I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.50137 + 1.42810I
a = 0.22487 + 1.45201I
b = 0.66035 − 1.40498I
14.2470 + 9.6079I 0
u = −0.50137 − 1.42810I
a = 0.22487 − 1.45201I
b = 0.66035 + 1.40498I
14.2470 − 9.6079I 0
u = 0.54952 + 1.42526I
a = 0.28606 − 1.42124I
b = 1.08934 + 1.23901I
14.2455 − 6.2396I 0
u = 0.54952 − 1.42526I
a = 0.28606 + 1.42124I
b = 1.08934 − 1.23901I
14.2455 + 6.2396I 0
u = −0.42935 + 1.46747I
a = 0.05138 − 1.42612I
b = −0.86569 + 1.29089I
9.55514 + 8.37100I 0
u = −0.42935 − 1.46747I
a = 0.05138 + 1.42612I
b = −0.86569 − 1.29089I
9.55514 − 8.37100I 0
u = −0.33933 + 1.49221I
a = −0.33204 + 1.57954I
b = 1.07078 − 1.32636I
12.5974 + 7.9743I 0
u = −0.33933 − 1.49221I
a = −0.33204 − 1.57954I
b = 1.07078 + 1.32636I
12.5974 − 7.9743I 0
u = 0.52512 + 1.46653I
a = −0.13016 + 1.42578I
b = −1.08764 − 1.33570I
10.2333 − 13.5581I 0
u = 0.52512 − 1.46653I
a = −0.13016 − 1.42578I
b = −1.08764 + 1.33570I
10.2333 + 13.5581I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.58916 + 1.44525I
a = −0.482233 − 0.888641I
b = −0.315692 + 0.988998I
13.56410 + 2.81403I 0
u = −0.58916 − 1.44525I
a = −0.482233 + 0.888641I
b = −0.315692 − 0.988998I
13.56410 − 2.81403I 0
u = −0.156662 + 0.381632I
a = −1.318340 − 0.199824I
b = −0.994983 − 0.538798I
2.28986 − 4.46331I −13.54848 − 2.38688I
u = −0.156662 − 0.381632I
a = −1.318340 + 0.199824I
b = −0.994983 + 0.538798I
2.28986 + 4.46331I −13.54848 + 2.38688I
u = −0.099408 + 0.344856I
a = −3.93423 + 2.15008I
b = −0.273283 + 0.641463I
3.68720 − 3.23259I −8.57639 + 0.86367I
u = −0.099408 − 0.344856I
a = −3.93423 − 2.15008I
b = −0.273283 − 0.641463I
3.68720 + 3.23259I −8.57639 − 0.86367I
u = 0.61596 + 1.56625I
a = 0.358532 − 0.694252I
b = 0.159081 + 1.150580I
9.59442 + 0.08130I 0
u = 0.61596 − 1.56625I
a = 0.358532 + 0.694252I
b = 0.159081 − 1.150580I
9.59442 − 0.08130I 0
u = −0.44050 + 1.62570I
a = 0.296034 − 0.959490I
b = −0.947266 + 0.887890I
9.77900 + 9.75690I 0
u = −0.44050 − 1.62570I
a = 0.296034 + 0.959490I
b = −0.947266 − 0.887890I
9.77900 − 9.75690I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.59552 + 1.58631I
a = 0.081772 + 0.797386I
b = 0.609949 − 0.840431I
7.61643 + 5.63059I 0
u = −0.59552 − 1.58631I
a = 0.081772 − 0.797386I
b = 0.609949 + 0.840431I
7.61643 − 5.63059I 0
u = 0.71220 + 1.56274I
a = −0.411575 + 0.527033I
b = −0.054412 − 0.972081I
14.2455 + 6.2396I 0
u = 0.71220 − 1.56274I
a = −0.411575 − 0.527033I
b = −0.054412 + 0.972081I
14.2455 − 6.2396I 0
u = −1.70848 + 0.30086I
a = 0.0273666 − 0.0484215I
b = −0.126892 + 0.538178I
2.66044 + 2.58613I 0
u = −1.70848 − 0.30086I
a = 0.0273666 + 0.0484215I
b = −0.126892 − 0.538178I
2.66044 − 2.58613I 0
u = 0.182838 + 0.191283I
a = 5.65215 + 1.56451I
b = 0.561663 − 0.789668I
9.55514 − 8.37100I −7.19441 + 2.95709I
u = 0.182838 − 0.191283I
a = 5.65215 − 1.56451I
b = 0.561663 + 0.789668I
9.55514 + 8.37100I −7.19441 − 2.95709I
u = −0.253635 + 0.005888I
a = 0.16209 − 3.79438I
b = 0.463401 + 1.070820I
8.04886 − 2.24498I 2.89013 + 0.81084I
u = −0.253635 − 0.005888I
a = 0.16209 + 3.79438I
b = 0.463401 − 1.070820I
8.04886 + 2.24498I 2.89013 − 0.81084I
22
III. I
u
3
= h−1.27 × 10
32
u
33
− 6.33 × 10
32
u
32
+ · · · + 1.13 × 10
33
b − 1.22 ×
10
33
, 8.99 × 10
32
u
33
+ 2.59 × 10
33
u
32
+ · · · + 7.94 × 10
33
a − 1.81 ×
10
34
, u
34
+ 4u
33
+ · · · + 10u + 7i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
−0.113227u
33
− 0.325975u
32
+ ··· + 5.78776u + 2.28447
0.111720u
33
+ 0.557690u
32
+ ··· + 0.856688u + 1.07742
a
4
=
−0.114547u
33
− 0.658603u
32
+ ··· − 2.86982u + 0.759352
−0.0602019u
33
− 0.0962396u
32
+ ··· + 0.526391u + 1.75711
a
1
=
0.565117u
33
+ 2.32758u
32
+ ··· + 7.38638u + 0.651814
0.168583u
33
+ 0.611282u
32
+ ··· + 3.52947u − 0.296108
a
6
=
u
u
3
+ u
a
12
=
0.00527349u
33
+ 0.145841u
32
+ ··· + 5.46296u + 1.68028
0.137611u
33
+ 0.660271u
32
+ ··· − 0.275746u + 0.488551
a
5
=
−0.265154u
33
− 1.05878u
32
+ ··· + 3.68551u + 3.35256
0.00230147u
33
+ 0.0964240u
32
+ ··· + 5.31222u + 1.30808
a
10
=
−0.00150704u
33
+ 0.231715u
32
+ ··· + 6.64445u + 3.36189
0.111720u
33
+ 0.557690u
32
+ ··· + 0.856688u + 1.07742
a
8
=
0.198698u
33
+ 0.696739u
32
+ ··· − 12.8673u − 6.17754
−0.182505u
33
− 0.773985u
32
+ ··· − 4.39149u − 0.844624
a
9
=
−0.0195368u
33
+ 0.210586u
32
+ ··· − 2.65608u + 1.48406
0.0313226u
33
+ 0.152659u
32
+ ··· + 2.75030u + 2.52166
(ii) Obstruction class = 1
(iii) Cusp Shapes = −0.985932u
33
− 3.78082u
32
+ ··· − 10.9183u + 4.21228
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
34
− 4u
33
+ ··· + 159u + 119
c
2
, c
8
u
34
+ 4u
33
+ ··· + 10u + 7
c
3
, c
9
u
34
+ 10u
32
+ ··· − 272u + 136
c
4
, c
10
68(68u
34
+ 136u
33
+ ··· + u + 1)
c
5
, c
11
68(68u
34
+ 1472u
32
+ ··· + 9742u
2
+ 569)
c
6
, c
12
u
34
− 4u
33
+ ··· − 10u + 7
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
34
+ 12y
33
+ ··· + 154409y + 14161
c
2
, c
6
, c
8
c
12
y
34
+ 18y
33
+ ··· + 866y + 49
c
3
, c
9
y
34
+ 20y
33
+ ··· + 580992y + 18496
c
4
, c
10
4624(4624y
34
+ 12512y
33
+ ··· + 45y + 1)
c
5
, c
11
4624(68y
17
+ 1472y
16
+ ··· + 9742y + 569)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.279146 + 0.955951I
a = 1.90621 − 1.87545I
b = −0.131148 + 0.660855I
10.55050 − 9.11260I −1.11963 + 6.52496I
u = 0.279146 − 0.955951I
a = 1.90621 + 1.87545I
b = −0.131148 − 0.660855I
10.55050 + 9.11260I −1.11963 − 6.52496I
u = −0.593710 + 0.821733I
a = 1.47281 + 1.09599I
b = 0.981736 + 0.011259I
2.41238 + 2.35691I −17.3898 + 5.2155I
u = −0.593710 − 0.821733I
a = 1.47281 − 1.09599I
b = 0.981736 − 0.011259I
2.41238 − 2.35691I −17.3898 − 5.2155I
u = 0.343978 + 0.900440I
a = −0.294188 + 1.352930I
b = −1.232430 − 0.094462I
−0.98061 − 1.49267I 23.0743 − 0.6160I
u = 0.343978 − 0.900440I
a = −0.294188 − 1.352930I
b = −1.232430 + 0.094462I
−0.98061 + 1.49267I 23.0743 + 0.6160I
u = −0.306899 + 1.095080I
a = −1.13557 − 1.08940I
b = 0.594073 + 1.163390I
4.94935 + 0.89260I −5.81523 + 1.42063I
u = −0.306899 − 1.095080I
a = −1.13557 + 1.08940I
b = 0.594073 − 1.163390I
4.94935 − 0.89260I −5.81523 − 1.42063I
u = −0.989294 + 0.605595I
a = −0.0155157 + 0.0835609I
b = 0.654990 − 0.644786I
3.81228 + 4.06379I −7.84851 − 10.27207I
u = −0.989294 − 0.605595I
a = −0.0155157 − 0.0835609I
b = 0.654990 + 0.644786I
3.81228 − 4.06379I −7.84851 + 10.27207I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.354624 + 0.653162I
a = −2.46500 − 0.10060I
b = −0.269932 − 0.586777I
3.81228 − 4.06379I −7.84851 + 10.27207I
u = 0.354624 − 0.653162I
a = −2.46500 + 0.10060I
b = −0.269932 + 0.586777I
3.81228 + 4.06379I −7.84851 − 10.27207I
u = −0.691845 + 0.086261I
a = −0.060198 − 0.728424I
b = −0.625518 + 0.856147I
7.27964 + 2.76701I −6.07911 − 3.96251I
u = −0.691845 − 0.086261I
a = −0.060198 + 0.728424I
b = −0.625518 − 0.856147I
7.27964 − 2.76701I −6.07911 + 3.96251I
u = −0.075854 + 1.321820I
a = 0.366840 − 0.801091I
b = 0.604903 + 0.571060I
7.27964 + 2.76701I −6.07911 − 3.96251I
u = −0.075854 − 1.321820I
a = 0.366840 + 0.801091I
b = 0.604903 − 0.571060I
7.27964 − 2.76701I −6.07911 + 3.96251I
u = −0.141564 + 1.316630I
a = 0.22064 + 1.65081I
b = −0.433215 − 1.164250I
11.5292 −6 − 1.314595 + 0.10I
u = −0.141564 − 1.316630I
a = 0.22064 − 1.65081I
b = −0.433215 + 1.164250I
11.5292 −6 − 1.314595 + 0.10I
u = 0.118646 + 1.325500I
a = −0.574016 − 0.251782I
b = −0.559703 − 0.248060I
12.11980 + 6.93734I −3.36551 − 3.27150I
u = 0.118646 − 1.325500I
a = −0.574016 + 0.251782I
b = −0.559703 + 0.248060I
12.11980 − 6.93734I −3.36551 + 3.27150I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.503608 + 1.244920I
a = −0.386127 + 0.913401I
b = −0.590167 − 0.765565I
2.61769 − 4.83354I −2.88744 + 9.00278I
u = 0.503608 − 1.244920I
a = −0.386127 − 0.913401I
b = −0.590167 + 0.765565I
2.61769 + 4.83354I −2.88744 − 9.00278I
u = 1.38107 + 0.34886I
a = 0.0250048 + 0.0273904I
b = −0.020337 + 0.396343I
−0.98061 − 1.49267I 23.0743 − 0.6160I
u = 1.38107 − 0.34886I
a = 0.0250048 − 0.0273904I
b = −0.020337 − 0.396343I
−0.98061 + 1.49267I 23.0743 + 0.6160I
u = −0.39794 + 1.40404I
a = 0.00217 − 1.63828I
b = −0.84215 + 1.19906I
12.11980 + 6.93734I −3.36551 − 3.27150I
u = −0.39794 − 1.40404I
a = 0.00217 + 1.63828I
b = −0.84215 − 1.19906I
12.11980 − 6.93734I −3.36551 + 3.27150I
u = −0.059587 + 0.533224I
a = 0.076841 − 0.954083I
b = 1.049650 − 0.367339I
2.61769 + 4.83354I −2.88744 − 9.00278I
u = −0.059587 − 0.533224I
a = 0.076841 + 0.954083I
b = 1.049650 + 0.367339I
2.61769 − 4.83354I −2.88744 + 9.00278I
u = 0.239828 + 0.374110I
a = −2.68633 − 0.65658I
b = 0.820885 − 0.880167I
4.94935 − 0.89260I −5.81523 − 1.42063I
u = 0.239828 − 0.374110I
a = −2.68633 + 0.65658I
b = 0.820885 + 0.880167I
4.94935 + 0.89260I −5.81523 + 1.42063I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.40691 + 1.53091I
a = −0.218047 + 1.281380I
b = 0.94449 − 1.22938I
10.55050 + 9.11260I 0
u = −0.40691 − 1.53091I
a = −0.218047 − 1.281380I
b = 0.94449 + 1.22938I
10.55050 − 9.11260I 0
u = −1.55731 + 0.43444I
a = −0.164089 + 0.243091I
b = 0.053877 + 0.238446I
2.41238 + 2.35691I 0
u = −1.55731 − 0.43444I
a = −0.164089 − 0.243091I
b = 0.053877 − 0.238446I
2.41238 − 2.35691I 0
29
IV. I
u
4
= hu
2
+ b − u + 1, a + u, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
−u
−u
2
+ u − 1
a
4
=
u
2
+ 1
u
2
− u + 1
a
1
=
0
−u
a
6
=
u
u
2
− u + 1
a
12
=
−u
−u
2
+ u − 1
a
5
=
u
u
2
− u + 1
a
10
=
−u
2
− 1
−u
2
+ u − 1
a
8
=
−1
0
a
9
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 8u − 20
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
3
+ u
2
− 1
c
2
, c
8
u
3
− u
2
+ 2u − 1
c
3
, c
6
, c
9
c
12
u
3
+ u
2
+ 2u + 1
c
5
, c
11
u
3
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
3
− y
2
+ 2y −1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
y
3
+ 3y
2
+ 2y −1
c
5
, c
11
y
3
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.215080 − 1.307140I
b = 0.877439 + 0.744862I
6.04826 − 5.65624I −4.98049 + 5.95889I
u = 0.215080 − 1.307140I
a = −0.215080 + 1.307140I
b = 0.877439 − 0.744862I
6.04826 + 5.65624I −4.98049 − 5.95889I
u = 0.569840
a = −0.569840
b = −0.754878
−2.22691 −18.0390
33
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
+ u
2
− 1)(u
25
− u
24
+ ··· + 28u + 13)(u
34
− 4u
33
+ ··· + 159u + 119)
· (u
120
− 11u
119
+ ··· − 7076832991u + 1201214753)
c
2
, c
8
(u
3
− u
2
+ 2u − 1)(u
25
+ u
24
+ ··· − 4u + 1)(u
34
+ 4u
33
+ ··· + 10u + 7)
· (u
120
− u
119
+ ··· − 3274u + 373)
c
3
, c
9
(u
3
+ u
2
+ 2u + 1)(u
25
− u
24
+ ··· + 24u + 8)
· (u
34
+ 10u
32
+ ··· − 272u + 136)
· (u
120
− u
119
+ ··· + 40633750u + 2972977)
c
4
, c
10
272(u
3
+ u
2
− 1)(4u
25
− 4u
24
+ ··· + 4u + 1)
· (68u
34
+ 136u
33
+ ··· + u + 1)
· (u
120
+ 5u
119
+ ··· − 257509u + 235151)
c
5
, c
11
272u
3
(4u
25
− 12u
24
+ ··· − 344u + 40)
· (68u
34
+ 1472u
32
+ ··· + 9742u
2
+ 569)
· (u
60
+ 6u
59
+ ··· + 58u + 13)
2
c
6
, c
12
(u
3
+ u
2
+ 2u + 1)(u
25
+ u
24
+ ··· − 4u + 1)(u
34
− 4u
33
+ ··· − 10u + 7)
· (u
120
− u
119
+ ··· − 3274u + 373)
34
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
3
− y
2
+ 2y −1)(y
25
+ 21y
24
+ ··· + 4112y −169)
· (y
34
+ 12y
33
+ ··· + 154409y + 14161)
· (y
120
+ 55y
119
+ ··· + 4.74 × 10
19
y + 1.44 × 10
18
)
c
2
, c
6
, c
8
c
12
(y
3
+ 3y
2
+ 2y −1)(y
25
+ 17y
24
+ ··· + 20y −1)
· (y
34
+ 18y
33
+ ··· + 866y + 49)
· (y
120
+ 89y
119
+ ··· − 413086y + 139129)
c
3
, c
9
(y
3
+ 3y
2
+ 2y −1)(y
25
+ 9y
24
+ ··· + 256y −64)
· (y
34
+ 20y
33
+ ··· + 580992y + 18496)
· (y
120
+ 71y
119
+ ··· + 487658353656878y + 8838592242529)
c
4
, c
10
73984(y
3
− y
2
+ 2y −1)(16y
25
+ 336y
24
+ ··· − 4y −1)
· (4624y
34
+ 12512y
33
+ ··· + 45y + 1)
· (y
120
+ 71y
119
+ ··· + 3045613958149y + 55295992801)
c
5
, c
11
73984y
3
(68y
17
+ 1472y
16
+ ··· + 9742y + 569)
2
· (16y
25
+ 304y
24
+ ··· + 27776y −1600)
· (y
60
+ 38y
59
+ ··· − 2298y + 169)
2
35
