12a
0116
(K12a
0116
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 9 10 4 7 1 6 11
Solving Sequence
4,8 1,9,10
11 3 2 5 7 6 12
c
8
c
10
c
3
c
1
c
4
c
7
c
6
c
12
c
2
, c
5
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.89741 × 10
143
u
70
+ 9.51177 × 10
143
u
69
+ ··· + 1.56737 × 10
147
d + 3.91135 × 10
146
,
4.81606 × 10
144
u
70
+ 8.39188 × 10
144
u
69
+ ··· + 4.38864 × 10
148
c − 3.94097 × 10
148
,
8.50193 × 10
145
u
70
+ 2.17599 × 10
146
u
69
+ ··· + 5.03271 × 10
148
b − 4.36186 × 10
148
,
− 1.70391 × 10
145
u
70
− 5.09324 × 10
145
u
69
+ ··· + 5.03271 × 10
148
a + 2.97413 × 10
148
,
u
71
+ 2u
70
+ ··· − 1536u
2
+ 512i
I
u
2
= h984u
8
a
2
+ 450u
8
a + ··· + 2162a − 142, 10u
8
a
2
− 2340u
8
a + ··· + 2307a + 6,
379u
8
a
2
+ 2864u
8
a + ··· + 2660a − 2336, u
8
a + u
8
+ ··· − a − 1,
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
v
1
= hc, d + 1, b, a − v, v
2
− v + 1i
I
v
2
= ha, d, c − 1, b − v − 1, v
2
+ v + 1i
I
v
3
= ha, d + 1, c − a, b + 1, v − 1i
I
v
4
= hc, d + 1, a
2
v
2
− 2cav − v
2
a + c
2
+ cv + v
2
, bv + 1i
* 5 irreducible components of dim
C
= 0, with total 103 representations.
* 1 irreducible components of dim
C
= 1
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
= h4.90×10
143
u
70
+9.51×10
143
u
69
+· · ·+1.57×10
147
d+3.91×10
146
, 4.82×
10
144
u
70
+8.39×10
144
u
69
+· · · + 4.39×10
148
c−3.94×10
148
, 8.50×10
145
u
70
+
2.18 × 10
146
u
69
+ · · · + 5.03 × 10
148
b − 4.36 × 10
148
, −1.70 × 10
145
u
70
− 5.09 ×
10
145
u
69
+ · · · + 5.03 × 10
148
a + 2.97 × 10
148
, u
71
+ 2u
70
+ · · · − 1536u
2
+ 512i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
1
=
0.000338567u
70
+ 0.00101203u
69
+ ··· − 1.54441u − 0.590959
−0.00168933u
70
− 0.00432370u
69
+ ··· + 3.58313u + 0.866702
a
9
=
1
−u
2
a
10
=
−0.000109739u
70
− 0.000191218u
69
+ ··· + 0.195370u + 0.897994
−0.000312460u
70
− 0.000606862u
69
+ ··· + 0.402802u − 0.249548
a
11
=
−0.00183569u
70
− 0.00101807u
69
+ ··· − 0.404520u − 0.815831
0.000206711u
70
− 0.00283529u
69
+ ··· + 2.05506u + 2.78231
a
3
=
−u
u
a
2
=
−0.000272969u
70
+ 0.000824654u
69
+ ··· − 2.23600u − 0.903349
−0.00107780u
70
− 0.00413632u
69
+ ··· + 4.27473u + 1.17909
a
5
=
0.00135077u
70
+ 0.00331167u
69
+ ··· − 2.03873u − 0.275743
−0.00107780u
70
− 0.00413632u
69
+ ··· + 4.27473u + 1.17909
a
7
=
−0.000109739u
70
− 0.000191218u
69
+ ··· + 0.195370u + 0.897994
0.000398397u
70
+ 0.000736742u
69
+ ··· − 0.458988u + 0.264017
a
6
=
−0.000422199u
70
− 0.000798080u
69
+ ··· + 0.598171u + 0.648446
0.000578173u
70
+ 0.000945600u
69
+ ··· − 0.618968u + 0.273263
a
12
=
−0.00163584u
70
− 0.00127944u
69
+ ··· − 0.420031u − 1.00282
−0.000707113u
70
− 0.00441555u
69
+ ··· + 2.78684u + 2.81850
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000644196u
70
− 0.0111115u
69
+ ··· + 0.863041u + 15.1191
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 30u
70
+ ··· + 4640u + 256
c
2
, c
4
u
71
− 8u
70
+ ··· + 56u − 16
c
3
, c
8
u
71
− 2u
70
+ ··· + 1536u
2
− 512
c
5
, c
11
u
71
+ 2u
70
+ ··· − 5u
2
− 4
c
6
, c
7
, c
9
u
71
+ 8u
70
+ ··· + 56u − 16
c
10
, c
12
u
71
+ 24u
70
+ ··· − 40u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 30y
70
+ ··· + 5022208y − 65536
c
2
, c
4
y
71
− 30y
70
+ ··· + 4640y − 256
c
3
, c
8
y
71
− 30y
70
+ ··· + 1572864y − 262144
c
5
, c
11
y
71
+ 24y
70
+ ··· − 40y − 16
c
6
, c
7
, c
9
y
71
− 70y
70
+ ··· − 1504y − 256
c
10
, c
12
y
71
+ 48y
70
+ ··· − 6880y − 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.372595 + 0.922213I
a = 0.231527 + 0.248876I
b = 0.846890 − 0.552313I
c = 0.779729 − 0.752305I
d = 0.335802 − 0.640838I
−0.206074 − 1.106620I 1.82615 + 2.10157I
u = 0.372595 − 0.922213I
a = 0.231527 − 0.248876I
b = 0.846890 + 0.552313I
c = 0.779729 + 0.752305I
d = 0.335802 + 0.640838I
−0.206074 + 1.106620I 1.82615 − 2.10157I
u = −0.661751 + 0.731261I
a = −1.22188 + 0.76837I
b = −0.172678 − 1.098140I
c = 0.700653 + 0.489800I
d = 0.041277 + 0.670208I
−5.31233 + 1.23150I −6.16629 − 0.79467I
u = −0.661751 − 0.731261I
a = −1.22188 − 0.76837I
b = −0.172678 + 1.098140I
c = 0.700653 − 0.489800I
d = 0.041277 − 0.670208I
−5.31233 − 1.23150I −6.16629 + 0.79467I
u = −0.216094 + 0.961248I
a = 0.0234029 − 0.1065430I
b = −0.945678 − 0.148881I
c = 0.432999 − 0.019039I
d = −1.305020 − 0.101353I
2.60149 + 2.06138I 6.60052 − 3.22142I
u = −0.216094 − 0.961248I
a = 0.0234029 + 0.1065430I
b = −0.945678 + 0.148881I
c = 0.432999 + 0.019039I
d = −1.305020 + 0.101353I
2.60149 − 2.06138I 6.60052 + 3.22142I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.510340 + 0.919175I
a = 0.422439 + 0.636543I
b = 0.777623 − 0.912598I
c = 0.433850 + 0.046431I
d = −1.278840 + 0.243884I
−1.22762 − 4.53498I −0.48837 + 4.83158I
u = 0.510340 − 0.919175I
a = 0.422439 − 0.636543I
b = 0.777623 + 0.912598I
c = 0.433850 − 0.046431I
d = −1.278840 − 0.243884I
−1.22762 + 4.53498I −0.48837 − 4.83158I
u = −0.843761 + 0.417994I
a = −2.34521 + 0.64153I
b = 0.679972 − 0.889234I
c = 0.642763 + 0.309103I
d = −0.263568 + 0.607646I
−1.74336 − 3.95563I 0.57229 + 6.63484I
u = −0.843761 − 0.417994I
a = −2.34521 − 0.64153I
b = 0.679972 + 0.889234I
c = 0.642763 − 0.309103I
d = −0.263568 − 0.607646I
−1.74336 + 3.95563I 0.57229 − 6.63484I
u = 0.980094 + 0.401535I
a = 0.396858 + 0.104153I
b = −0.149301 − 1.202720I
c = 0.587267 − 0.304226I
d = −0.342522 − 0.695475I
0.13020 + 4.00402I 4.41276 − 6.69495I
u = 0.980094 − 0.401535I
a = 0.396858 − 0.104153I
b = −0.149301 + 1.202720I
c = 0.587267 + 0.304226I
d = −0.342522 + 0.695475I
0.13020 − 4.00402I 4.41276 + 6.69495I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482781 + 0.984718I
a = −0.188094 + 0.642789I
b = −0.975231 − 0.875039I
c = 0.678408 + 0.703356I
d = 0.289585 + 0.736539I
−0.99233 + 6.45679I 0.34368 − 6.97496I
u = −0.482781 − 0.984718I
a = −0.188094 − 0.642789I
b = −0.975231 + 0.875039I
c = 0.678408 − 0.703356I
d = 0.289585 − 0.736539I
−0.99233 − 6.45679I 0.34368 + 6.97496I
u = −0.777198 + 0.427799I
a = −0.190894 + 0.697004I
b = −0.24801 − 1.87626I
c = 0.674459 + 0.312849I
d = −0.220144 + 0.565966I
−1.94652 + 0.34051I −0.37051 + 3.03065I
u = −0.777198 − 0.427799I
a = −0.190894 − 0.697004I
b = −0.24801 + 1.87626I
c = 0.674459 − 0.312849I
d = −0.220144 − 0.565966I
−1.94652 − 0.34051I −0.37051 − 3.03065I
u = −1.127060 + 0.152551I
a = 0.892844 + 0.350255I
b = −0.849674 + 0.379750I
c = −2.51225 − 0.47372I
d = 1.384380 − 0.072480I
4.50468 + 2.47836I 7.49354 − 3.38416I
u = −1.127060 − 0.152551I
a = 0.892844 − 0.350255I
b = −0.849674 − 0.379750I
c = −2.51225 + 0.47372I
d = 1.384380 + 0.072480I
4.50468 − 2.47836I 7.49354 + 3.38416I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.982347 + 0.611518I
a = −1.043830 + 0.376477I
b = 0.83985 − 1.62811I
c = 0.577038 + 0.381219I
d = −0.206434 + 0.797028I
−4.29573 − 6.37313I −3.00781 + 7.19219I
u = −0.982347 − 0.611518I
a = −1.043830 − 0.376477I
b = 0.83985 + 1.62811I
c = 0.577038 − 0.381219I
d = −0.206434 − 0.797028I
−4.29573 + 6.37313I −3.00781 − 7.19219I
u = −1.173990 + 0.222972I
a = 1.082200 + 0.369743I
b = −0.979927 + 0.355538I
c = 0.478067 − 0.168003I
d = −0.861829 − 0.654286I
5.09577 − 1.83902I 8.24819 + 0.I
u = −1.173990 − 0.222972I
a = 1.082200 − 0.369743I
b = −0.979927 − 0.355538I
c = 0.478067 + 0.168003I
d = −0.861829 + 0.654286I
5.09577 + 1.83902I 8.24819 + 0.I
u = 1.203430 + 0.094057I
a = −0.832154 + 0.565988I
b = 0.782311 + 0.231668I
c = 0.487795 + 0.191279I
d = −0.776824 + 0.696746I
5.36659 − 3.89584I 8.41567 + 5.55146I
u = 1.203430 − 0.094057I
a = −0.832154 − 0.565988I
b = 0.782311 − 0.231668I
c = 0.487795 − 0.191279I
d = −0.776824 − 0.696746I
5.36659 + 3.89584I 8.41567 − 5.55146I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.117530 + 0.478181I
a = 1.42291 − 0.12389I
b = −1.194070 + 0.739062I
c = −1.92995 − 1.17457I
d = 1.378100 − 0.230112I
3.15531 − 5.12152I 0
u = −1.117530 − 0.478181I
a = 1.42291 + 0.12389I
b = −1.194070 − 0.739062I
c = −1.92995 + 1.17457I
d = 1.378100 + 0.230112I
3.15531 + 5.12152I 0
u = 1.137650 + 0.460214I
a = 0.741192 − 0.324271I
b = −0.613390 − 0.807893I
c = −1.94441 + 1.10888I
d = 1.388080 + 0.221318I
3.19656 + 2.55854I 0
u = 1.137650 − 0.460214I
a = 0.741192 + 0.324271I
b = −0.613390 + 0.807893I
c = −1.94441 − 1.10888I
d = 1.388080 − 0.221318I
3.19656 − 2.55854I 0
u = 0.725491 + 0.260568I
a = 2.45954 + 0.18676I
b = −0.615456 − 0.467489I
c = 0.687076 − 0.223450I
d = −0.316229 − 0.428062I
−1.09934 − 1.05821I 3.09814 − 1.72718I
u = 0.725491 − 0.260568I
a = 2.45954 − 0.18676I
b = −0.615456 + 0.467489I
c = 0.687076 + 0.223450I
d = −0.316229 + 0.428062I
−1.09934 + 1.05821I 3.09814 + 1.72718I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.247645 + 1.226350I
a = 0.445696 − 1.201150I
b = −1.18878 + 1.33643I
c = 0.410272 + 0.019958I
d = −1.43165 + 0.11829I
6.94619 + 1.12108I 0
u = 0.247645 − 1.226350I
a = 0.445696 + 1.201150I
b = −1.18878 − 1.33643I
c = 0.410272 − 0.019958I
d = −1.43165 − 0.11829I
6.94619 − 1.12108I 0
u = −0.464983 + 0.581438I
a = 0.467028 − 0.609266I
b = −0.226473 + 0.762464I
c = 0.469417 − 0.045212I
d = −1.110720 − 0.203295I
1.011140 + 0.938516I 3.66296 + 0.79830I
u = −0.464983 − 0.581438I
a = 0.467028 + 0.609266I
b = −0.226473 − 0.762464I
c = 0.469417 + 0.045212I
d = −1.110720 + 0.203295I
1.011140 − 0.938516I 3.66296 − 0.79830I
u = −0.368570 + 1.210560I
a = −0.22498 − 1.41639I
b = 0.91974 + 1.60894I
c = 0.410382 − 0.029911I
d = −1.42388 − 0.17667I
6.42018 + 4.68044I 0
u = −0.368570 − 1.210560I
a = −0.22498 + 1.41639I
b = 0.91974 − 1.60894I
c = 0.410382 + 0.029911I
d = −1.42388 + 0.17667I
6.42018 − 4.68044I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.248660 + 0.306382I
a = −1.35825 + 0.40426I
b = 1.185690 + 0.329456I
c = −2.03698 + 0.67503I
d = 1.44235 + 0.14659I
7.51654 + 1.91781I 0
u = 1.248660 − 0.306382I
a = −1.35825 − 0.40426I
b = 1.185690 − 0.329456I
c = −2.03698 − 0.67503I
d = 1.44235 − 0.14659I
7.51654 − 1.91781I 0
u = −0.504947 + 1.215580I
a = 0.553982 + 0.970050I
b = −1.71071 − 1.04995I
c = 0.408022 − 0.040917I
d = −1.42645 − 0.24333I
5.42990 + 4.32973I 0
u = −0.504947 − 1.215580I
a = 0.553982 − 0.970050I
b = −1.71071 + 1.04995I
c = 0.408022 + 0.040917I
d = −1.42645 + 0.24333I
5.42990 − 4.32973I 0
u = 1.152900 + 0.667545I
a = 1.49225 − 0.13001I
b = −1.39286 − 1.11846I
c = −1.51029 + 1.23782I
d = 1.39607 + 0.32462I
0.80414 + 10.42400I 0
u = 1.152900 − 0.667545I
a = 1.49225 + 0.13001I
b = −1.39286 + 1.11846I
c = −1.51029 − 1.23782I
d = 1.39607 − 0.32462I
0.80414 − 10.42400I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.185800 + 0.609579I
a = 1.321700 − 0.330477I
b = −1.23211 − 0.88467I
c = 0.512898 − 0.362376I
d = −0.300514 − 0.918848I
2.33908 + 6.73341I 0
u = 1.185800 − 0.609579I
a = 1.321700 + 0.330477I
b = −1.23211 + 0.88467I
c = 0.512898 + 0.362376I
d = −0.300514 + 0.918848I
2.33908 − 6.73341I 0
u = 0.593784 + 1.208600I
a = −0.434729 + 1.290470I
b = 1.63973 − 1.36961I
c = 0.406921 + 0.048241I
d = −1.42342 + 0.28730I
4.48821 − 10.17210I 0
u = 0.593784 − 1.208600I
a = −0.434729 − 1.290470I
b = 1.63973 + 1.36961I
c = 0.406921 − 0.048241I
d = −1.42342 − 0.28730I
4.48821 + 10.17210I 0
u = −1.233000 + 0.545251I
a = −1.135370 − 0.579184I
b = 1.066230 − 0.598971I
c = −1.68270 − 1.01731I
d = 1.43521 − 0.26312I
5.82408 − 7.48275I 0
u = −1.233000 − 0.545251I
a = −1.135370 + 0.579184I
b = 1.066230 + 0.598971I
c = −1.68270 + 1.01731I
d = 1.43521 + 0.26312I
5.82408 + 7.48275I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.176438 + 0.617781I
a = 0.569269 − 0.700050I
b = 0.224168 − 0.149459I
c = 0.464689 + 0.015931I
d = −1.149450 + 0.073691I
0.42738 + 1.60074I 0.77404 − 2.18898I
u = 0.176438 − 0.617781I
a = 0.569269 + 0.700050I
b = 0.224168 + 0.149459I
c = 0.464689 − 0.015931I
d = −1.149450 − 0.073691I
0.42738 − 1.60074I 0.77404 + 2.18898I
u = −1.181300 + 0.680585I
a = −1.58235 − 0.21766I
b = 1.49849 − 1.03336I
c = 0.507502 + 0.382227I
d = −0.257265 + 0.946913I
1.22414 − 12.55690I 0
u = −1.181300 − 0.680585I
a = −1.58235 + 0.21766I
b = 1.49849 + 1.03336I
c = 0.507502 − 0.382227I
d = −0.257265 − 0.946913I
1.22414 + 12.55690I 0
u = −0.010891 + 0.626888I
a = 0.061320 − 0.678183I
b = 0.075286 + 0.237093I
c = 2.55566 − 0.55082I
d = 0.626081 − 0.080591I
0.65592 − 2.35939I 1.51759 + 4.85897I
u = −0.010891 − 0.626888I
a = 0.061320 + 0.678183I
b = 0.075286 − 0.237093I
c = 2.55566 + 0.55082I
d = 0.626081 + 0.080591I
0.65592 + 2.35939I 1.51759 − 4.85897I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.617428 + 0.085193I
a = −0.811434 + 0.311389I
b = 1.63829 − 0.79430I
c = 0.704538 − 0.093715I
d = −0.394694 − 0.185518I
−0.93328 + 2.67780I 3.99337 − 7.95500I
u = 0.617428 − 0.085193I
a = −0.811434 − 0.311389I
b = 1.63829 + 0.79430I
c = 0.704538 + 0.093715I
d = −0.394694 + 0.185518I
−0.93328 − 2.67780I 3.99337 + 7.95500I
u = −0.591164
a = 0.615382
b = −0.924859
c = 0.583091
d = −0.714998
1.02886 10.5160
u = 0.282782 + 0.492299I
a = 1.18279 − 0.79051I
b = 0.068443 − 0.284824I
c = 1.051110 − 0.331574I
d = 0.134725 − 0.272953I
−1.67984 − 0.60130I −3.90300 + 0.33160I
u = 0.282782 − 0.492299I
a = 1.18279 + 0.79051I
b = 0.068443 + 0.284824I
c = 1.051110 + 0.331574I
d = 0.134725 + 0.272953I
−1.67984 + 0.60130I −3.90300 − 0.33160I
u = 1.33133 + 0.61244I
a = −2.12188 − 0.10102I
b = 1.78141 + 0.79853I
c = −1.50521 + 0.91788I
d = 1.48428 + 0.29531I
10.54930 + 5.35435I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33133 − 0.61244I
a = −2.12188 + 0.10102I
b = 1.78141 − 0.79853I
c = −1.50521 − 0.91788I
d = 1.48428 − 0.29531I
10.54930 − 5.35435I 0
u = −1.29995 + 0.68416I
a = 2.14975 − 0.35038I
b = −1.78132 + 1.02145I
c = −1.42200 − 1.00239I
d = 1.46979 − 0.33117I
9.4739 − 11.4004I 0
u = −1.29995 − 0.68416I
a = 2.14975 + 0.35038I
b = −1.78132 − 1.02145I
c = −1.42200 + 1.00239I
d = 1.46979 + 0.33117I
9.4739 + 11.4004I 0
u = −1.27239 + 0.75883I
a = −2.02990 − 0.46254I
b = 1.99508 − 0.81285I
c = −1.32486 − 1.06843I
d = 1.45735 − 0.36883I
7.95427 − 11.37060I 0
u = −1.27239 − 0.75883I
a = −2.02990 + 0.46254I
b = 1.99508 + 0.81285I
c = −1.32486 + 1.06843I
d = 1.45735 + 0.36883I
7.95427 + 11.37060I 0
u = 1.24401 + 0.80606I
a = 2.17907 − 0.26765I
b = −2.13805 − 1.02984I
c = −1.26249 + 1.11762I
d = 1.44408 + 0.39312I
6.6365 + 17.3722I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24401 − 0.80606I
a = 2.17907 + 0.26765I
b = −2.13805 + 1.02984I
c = −1.26249 − 1.11762I
d = 1.44408 − 0.39312I
6.6365 − 17.3722I 0
u = 1.51788 + 0.06429I
a = −0.63883 − 1.65996I
b = 0.502635 + 0.680323I
c = −1.74732 + 0.09337I
d = 1.57068 + 0.03050I
13.78050 + 0.08878I 0
u = 1.51788 − 0.06429I
a = −0.63883 + 1.65996I
b = 0.502635 − 0.680323I
c = −1.74732 − 0.09337I
d = 1.57068 − 0.03050I
13.78050 − 0.08878I 0
u = −1.51414 + 0.16464I
a = 0.25635 − 1.72702I
b = −0.145703 + 0.706687I
c = −1.72459 − 0.23680I
d = 1.56912 − 0.07814I
13.6007 − 6.3599I 0
u = −1.51414 − 0.16464I
a = 0.25635 + 1.72702I
b = −0.145703 − 0.706687I
c = −1.72459 + 0.23680I
d = 1.56912 + 0.07814I
13.6007 + 6.3599I 0
16
II. I
u
2
= h984a
2
u
8
+ 450au
8
+ · · · + 2162a − 142, 10a
2
u
8
− 2340au
8
+ · · · +
2307a + 6, 379a
2
u
8
+ 2864au
8
+ · · · + 2660a − 2336, u
8
a + u
8
+ · · · − a −
1, u
9
− u
8
+ · · · − u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
1
=
a
−0.206991a
2
u
8
− 1.56417au
8
+ ··· − 1.45276a + 1.27581
a
9
=
1
−u
2
a
10
=
−0.00546150a
2
u
8
+ 1.27799au
8
+ ··· − 1.25997a − 0.00327690
−0.537411a
2
u
8
− 0.245767au
8
+ ··· − 1.18078a + 0.0775532
a
11
=
−0.00546150a
2
u
8
+ 1.27799au
8
+ ··· − 1.25997a − 0.00327690
−0.436920a
2
u
8
+ 0.239214au
8
+ ··· − 0.797378a − 0.262152
a
3
=
−u
u
a
2
=
0.208629a
2
u
8
+ 1.18078au
8
+ ··· + 1.73075a − 1.07482
−0.415620a
2
u
8
− 2.74495au
8
+ ··· − 2.18351a + 2.35063
a
5
=
0.206991a
2
u
8
+ 1.56417au
8
+ ··· + 0.452758a − 1.27581
−0.415620a
2
u
8
− 2.74495au
8
+ ··· − 2.18351a + 2.35063
a
7
=
−0.00546150a
2
u
8
+ 1.27799au
8
+ ··· − 1.25997a − 0.00327690
0.637903a
2
u
8
+ 0.730748au
8
+ ··· + 1.56417a − 0.417258
a
6
=
−0.542873a
2
u
8
+ 1.03222au
8
+ ··· − 2.44074a + 0.0742764
0.926270a
2
u
8
+ 1.25287au
8
+ ··· + 2.49044a − 1.04424
a
12
=
−0.171491a
2
u
8
+ 0.128891au
8
+ ··· − 0.762971a + 0.297105
−0.926270a
2
u
8
− 1.25287au
8
+ ··· − 2.49044a + 1.04424
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 8u
5
− 4u
4
− 8u
3
+ 4u
2
− 4u + 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 18u
26
+ ··· + 5u + 1
c
2
, c
4
, c
6
c
7
, c
9
u
27
− 9u
25
+ ··· − u + 1
c
3
, c
8
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
c
5
, c
11
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
c
10
, c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 18y
26
+ ··· − 15y − 1
c
2
, c
4
, c
6
c
7
, c
9
y
27
− 18y
26
+ ··· + 5y − 1
c
3
, c
8
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
c
5
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
c
10
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −0.875705 − 0.477936I
b = 0.681130 + 0.860855I
c = 0.675016 − 0.354446I
d = −0.161261 − 0.609769I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = 0.772920 + 0.510351I
a = 0.410374 + 0.842624I
b = −0.01297 − 2.10540I
c = 0.473784 + 0.085898I
d = −1.043500 + 0.370490I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = 0.772920 + 0.510351I
a = 2.01117 + 0.65601I
b = −0.412038 − 0.965972I
c = −2.06450 + 2.41256I
d = 1.204760 + 0.239279I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = 0.772920 − 0.510351I
a = −0.875705 + 0.477936I
b = 0.681130 − 0.860855I
c = 0.675016 + 0.354446I
d = −0.161261 + 0.609769I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = 0.772920 − 0.510351I
a = 0.410374 − 0.842624I
b = −0.01297 + 2.10540I
c = 0.473784 − 0.085898I
d = −1.043500 − 0.370490I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = 0.772920 − 0.510351I
a = 2.01117 − 0.65601I
b = −0.412038 + 0.965972I
c = −2.06450 − 2.41256I
d = 1.204760 − 0.239279I
−1.78344 − 2.09337I −0.51499 + 4.16283I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.825933
a = 0.566697 + 0.073493I
b = −0.840182 − 0.678317I
c = 0.580888 − 0.143767I
d = −0.622141 − 0.401472I
1.19845 8.65230
u = −0.825933
a = 0.566697 − 0.073493I
b = −0.840182 + 0.678317I
c = 0.580888 + 0.143767I
d = −0.622141 + 0.401472I
1.19845 8.65230
u = −0.825933
a = −2.78526
b = 0.910725
c = −4.09362
d = 1.24428
1.19845 8.65230
u = −1.173910 + 0.391555I
a = −0.542704 − 0.501634I
b = 0.438594 − 0.586599I
c = 0.459000 − 0.147401I
d = −0.974973 − 0.634235I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = −1.173910 + 0.391555I
a = 1.393210 + 0.120134I
b = −1.198840 + 0.548367I
c = 0.525422 + 0.301815I
d = −0.431041 + 0.822025I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = −1.173910 + 0.391555I
a = −3.19833 + 1.16461I
b = 1.57493 − 1.25625I
c = −2.02893 − 0.93842I
d = 1.40601 − 0.18779I
4.37135 − 1.33617I 7.28409 + 0.70175I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.173910 − 0.391555I
a = −0.542704 + 0.501634I
b = 0.438594 + 0.586599I
c = 0.459000 + 0.147401I
d = −0.974973 + 0.634235I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = −1.173910 − 0.391555I
a = 1.393210 − 0.120134I
b = −1.198840 − 0.548367I
c = 0.525422 − 0.301815I
d = −0.431041 − 0.822025I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = −1.173910 − 0.391555I
a = −3.19833 − 1.16461I
b = 1.57493 + 1.25625I
c = −2.02893 + 0.93842I
d = 1.40601 + 0.18779I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 0.141484 + 0.739668I
a = −0.127412 − 0.662482I
b = −0.274121 + 0.513437I
c = 1.24382 − 0.80550I
d = 0.433577 − 0.366819I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = 0.141484 + 0.739668I
a = 0.313138 − 0.492021I
b = 0.423223 − 0.044379I
c = 1.58042 + 2.09413I
d = 0.770392 + 0.304242I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = 0.141484 + 0.739668I
a = 0.09724 + 2.63384I
b = 0.06688 − 4.55687I
c = 0.453361 + 0.012872I
d = −1.203970 + 0.062577I
0.61694 − 2.45442I 2.32792 + 2.91298I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141484 − 0.739668I
a = −0.127412 + 0.662482I
b = −0.274121 − 0.513437I
c = 1.24382 + 0.80550I
d = 0.433577 + 0.366819I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = 0.141484 − 0.739668I
a = 0.313138 + 0.492021I
b = 0.423223 + 0.044379I
c = 1.58042 − 2.09413I
d = 0.770392 − 0.304242I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = 0.141484 − 0.739668I
a = 0.09724 − 2.63384I
b = 0.06688 + 4.55687I
c = 0.453361 − 0.012872I
d = −1.203970 − 0.062577I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = 1.172470 + 0.500383I
a = 0.912481 − 0.404680I
b = −0.807640 − 0.750845I
c = 0.447551 + 0.136556I
d = −1.044080 + 0.623685I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = 1.172470 + 0.500383I
a = −1.56344 − 0.08945I
b = 1.31021 + 0.73026I
c = 0.523388 − 0.332558I
d = −0.361113 − 0.864843I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = 1.172470 + 0.500383I
a = 2.99591 + 1.49490I
b = −1.40454 − 1.59601I
c = −1.82241 + 1.08463I
d = 1.40520 + 0.24116I
3.59813 + 7.08493I 5.57680 − 5.91335I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.172470 − 0.500383I
a = 0.912481 + 0.404680I
b = −0.807640 + 0.750845I
c = 0.447551 − 0.136556I
d = −1.044080 − 0.623685I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = 1.172470 − 0.500383I
a = −1.56344 + 0.08945I
b = 1.31021 − 0.73026I
c = 0.523388 + 0.332558I
d = −0.361113 + 0.864843I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = 1.172470 − 0.500383I
a = 2.99591 − 1.49490I
b = −1.40454 + 1.59601I
c = −1.82241 − 1.08463I
d = 1.40520 − 0.24116I
3.59813 − 7.08493I 5.57680 + 5.91335I
24
III. I
v
1
= hc, d + 1, b, a − v, v
2
− v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
1
=
v
0
a
9
=
1
0
a
10
=
0
−1
a
11
=
v − 1
−1
a
3
=
v
0
a
2
=
v
0
a
5
=
v
0
a
7
=
1
1
a
6
=
0
1
a
12
=
v − 1
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 7
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
u
2
c
5
, c
10
u
2
− u + 1
c
6
, c
7
(u + 1)
2
c
9
(u − 1)
2
c
11
, c
12
u
2
+ u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
c
6
, c
7
, c
9
(y − 1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 0
c = 0
d = −1.00000
1.64493 − 2.02988I 9.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 0
c = 0
d = −1.00000
1.64493 + 2.02988I 9.00000 − 3.46410I
28
IV. I
v
2
= ha, d, c − 1, b − v − 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
1
=
0
v + 1
a
9
=
1
0
a
10
=
1
0
a
11
=
1
v
a
3
=
v
0
a
2
=
v
v + 1
a
5
=
0
−v − 1
a
7
=
1
0
a
6
=
1
0
a
12
=
v + 1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 1
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
u
2
c
4
(u + 1)
2
c
5
, c
12
u
2
+ u + 1
c
10
, c
11
u
2
− u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
c = 1.00000
d = 0
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
c = 1.00000
d = 0
−1.64493 + 2.02988I −3.00000 − 3.46410I
32
V. I
v
3
= ha, d + 1, c − a, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
1
0
a
1
=
0
−1
a
9
=
1
0
a
10
=
0
−1
a
11
=
0
−1
a
3
=
1
0
a
2
=
1
−1
a
5
=
0
1
a
7
=
1
1
a
6
=
0
1
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
9
u − 1
c
3
, c
5
, c
8
c
10
, c
11
, c
12
u
c
4
, c
6
, c
7
u + 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
9
y − 1
c
3
, c
5
, c
8
c
10
, c
11
, c
12
y
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
c = 0
d = −1.00000
0 0
36
VI. I
v
4
= hc, d + 1, a
2
v
2
− 2cav − v
2
a + c
2
+ cv + v
2
, bv + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
1
=
a
b
a
9
=
1
0
a
10
=
0
−1
a
11
=
a − 1
ba − 1
a
3
=
v
0
a
2
=
a + v
b
a
5
=
−a
−b
a
7
=
1
1
a
6
=
0
1
a
12
=
a − 1
ba − a
(ii) Obstruction class = −1
(iii) Cusp Shapes = −b
2
− v
2
+ 4a
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
37
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
2.02988I 4.09661 + 3.75064I
38
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
3
(u
27
+ 18u
26
+ ··· + 5u + 1)
· (u
71
+ 30u
70
+ ··· + 4640u + 256)
c
2
u
2
(u − 1)
3
(u
27
− 9u
25
+ ··· − u + 1)(u
71
− 8u
70
+ ··· + 56u − 16)
c
3
, c
8
u
5
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
· (u
71
− 2u
70
+ ··· + 1536u
2
− 512)
c
4
u
2
(u + 1)
3
(u
27
− 9u
25
+ ··· − u + 1)(u
71
− 8u
70
+ ··· + 56u − 16)
c
5
, c
11
u(u
2
− u + 1)(u
2
+ u + 1)(u
9
+ u
8
+ ··· + u − 1)
3
· (u
71
+ 2u
70
+ ··· − 5u
2
− 4)
c
6
, c
7
u
2
(u + 1)
3
(u
27
− 9u
25
+ ··· − u + 1)(u
71
+ 8u
70
+ ··· + 56u − 16)
c
9
u
2
(u − 1)
3
(u
27
− 9u
25
+ ··· − u + 1)(u
71
+ 8u
70
+ ··· + 56u − 16)
c
10
u(u
2
− u + 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
· (u
71
+ 24u
70
+ ··· − 40u − 16)
c
12
u(u
2
+ u + 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
· (u
71
+ 24u
70
+ ··· − 40u − 16)
39
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y − 1)
3
(y
27
− 18y
26
+ ··· − 15y − 1)
· (y
71
+ 30y
70
+ ··· + 5022208y − 65536)
c
2
, c
4
y
2
(y − 1)
3
(y
27
− 18y
26
+ ··· + 5y − 1)
· (y
71
− 30y
70
+ ··· + 4640y − 256)
c
3
, c
8
y
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
· (y
71
− 30y
70
+ ··· + 1572864y − 262144)
c
5
, c
11
y(y
2
+ y + 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
· (y
71
+ 24y
70
+ ··· − 40y − 16)
c
6
, c
7
, c
9
y
2
(y − 1)
3
(y
27
− 18y
26
+ ··· + 5y − 1)
· (y
71
− 70y
70
+ ··· − 1504y − 256)
c
10
, c
12
y(y
2
+ y + 1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
· (y
71
+ 48y
70
+ ··· − 6880y − 256)
40
