12a
0588
(K12a
0588
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 12 2 11 6 1 5 8 4
Solving Sequence
8,11
12
2,7
3 1 6 9 5 10 4
c
11
c
7
c
2
c
1
c
6
c
8
c
5
c
10
c
4
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.06111 × 10
773
u
166
+ 1.98874 × 10
774
u
165
+ ··· + 4.70005 × 10
772
b − 5.06349 × 10
777
,
− 2.89028 × 10
777
u
166
+ 8.09192 × 10
777
u
165
+ ··· + 2.74812 × 10
776
a − 2.11200 × 10
781
,
u
167
− 2u
166
+ ··· + 46140u + 5847i
I
u
2
= h9.18102 × 10
17
u
38
− 1.34409 × 10
19
u
37
+ ··· + 9.06237 × 10
15
b − 3.91149 × 10
19
,
− 1.28417 × 10
19
u
38
+ 4.98704 × 10
19
u
37
+ ··· + 9.06237 × 10
15
a − 3.71425 × 10
18
, u
39
− 5u
38
+ ··· − 9u + 1i
I
u
3
= hb − a − 1, a
2
− 3a + 1, u + 1i
I
v
1
= ha, b + 1, v −1i
* 4 irreducible components of dim
C
= 0, with total 209 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−7.06 × 10
773
u
166
+ 1.99 × 10
774
u
165
+ · · · + 4.70 × 10
772
b − 5.06 ×
10
777
, −2.89 × 10
777
u
166
+ 8.09 × 10
777
u
165
+ · · · + 2.75 × 10
776
a − 2.11 ×
10
781
, u
167
− 2u
166
+ · · · + 46140u + 5847i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
2
=
10.5173u
166
− 29.4453u
165
+ ··· + 510485.u + 76852.5
15.0235u
166
− 42.3132u
165
+ ··· + 717941.u + 107733.
a
7
=
u
u
a
3
=
7.22247u
166
− 20.0391u
165
+ ··· + 358938.u + 54309.3
11.7287u
166
− 32.9070u
165
+ ··· + 566395.u + 85189.5
a
1
=
39.2230u
166
− 111.042u
165
+ ··· + 1.84559 × 10
6
u + 275964.
18.7469u
166
− 53.1149u
165
+ ··· + 880172.u + 131530.
a
6
=
0.661216u
166
− 2.29430u
165
+ ··· + 11316.9u + 1043.92
−12.4536u
166
+ 34.9983u
165
+ ··· − 598548.u − 89946.7
a
9
=
−79.9532u
166
+ 226.459u
165
+ ··· − 3.75759 × 10
6
u − 561688.
−57.9512u
166
+ 164.085u
165
+ ··· − 2.72593 × 10
6
u − 407523.
a
5
=
14.2566u
166
− 40.7929u
165
+ ··· + 650841.u + 96673.1
−3.04496u
166
+ 8.35531u
165
+ ··· − 156295.u − 23829.6
a
10
=
−53.0429u
166
+ 150.311u
165
+ ··· − 2.48802 × 10
6
u − 371738.
−51.4081u
166
+ 145.510u
165
+ ··· − 2.41953 × 10
6
u − 361765.
a
4
=
−6.89637u
166
+ 16.0888u
165
+ ··· − 483395.u − 77477.5
6.82176u
166
− 21.7442u
165
+ ··· + 209405.u + 27717.5
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −1337.96u
166
+ 3790.87u
165
+ ··· − 6.28006 × 10
7
u − 9.38419 × 10
6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
167
+ 71u
166
+ ··· + 2794905u + 88209
c
2
, c
6
u
167
− 3u
166
+ ··· − 1611u − 297
c
3
u
167
− u
166
+ ··· + 9u − 1
c
4
, c
10
u
167
+ u
166
+ ··· + 286094u + 26963
c
5
u
167
− 4u
166
+ ··· − 98117u + 118061
c
7
, c
11
u
167
− 2u
166
+ ··· + 46140u + 5847
c
8
u
167
− 5u
166
+ ··· − 30593750u + 2687500
c
9
u
167
+ 9u
166
+ ··· − 1286138u − 711596
c
12
u
167
+ 17u
166
+ ··· − 36u − 12
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
167
+ 53y
166
+ ··· − 16946980639767y −7780827681
c
2
, c
6
y
167
− 71y
166
+ ··· + 2794905y −88209
c
3
y
167
+ 19y
166
+ ··· + 903y −1
c
4
, c
10
y
167
− 109y
166
+ ··· + 67092980862y −727003369
c
5
y
167
+ 16y
166
+ ··· − 734586387985y −13938399721
c
7
, c
11
y
167
− 86y
166
+ ··· + 1156461642y −34187409
c
8
y
167
− 17y
166
+ ··· + 606399335937500y −7222656250000
c
9
y
167
+ 55y
166
+ ··· − 11009677597860y −506368867216
c
12
y
167
− 29y
166
+ ··· + 6408y −144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.972662 + 0.230057I
a = −0.714704 + 0.054338I
b = −0.629457 + 0.206535I
−1.74998 + 0.43329I 0
u = −0.972662 − 0.230057I
a = −0.714704 − 0.054338I
b = −0.629457 − 0.206535I
−1.74998 − 0.43329I 0
u = 0.821125 + 0.560089I
a = 0.457294 − 0.470633I
b = 1.66147 − 0.32360I
4.79609 − 5.26583I 0
u = 0.821125 − 0.560089I
a = 0.457294 + 0.470633I
b = 1.66147 + 0.32360I
4.79609 + 5.26583I 0
u = 0.039794 + 0.986024I
a = 0.18398 − 1.64651I
b = 0.817154 − 0.578261I
0.11929 + 8.53958I 0
u = 0.039794 − 0.986024I
a = 0.18398 + 1.64651I
b = 0.817154 + 0.578261I
0.11929 − 8.53958I 0
u = −0.894406 + 0.414575I
a = −0.467639 + 0.689638I
b = 0.505608 + 0.092764I
5.21083 − 0.90333I 0
u = −0.894406 − 0.414575I
a = −0.467639 − 0.689638I
b = 0.505608 − 0.092764I
5.21083 + 0.90333I 0
u = 0.801414 + 0.625750I
a = −0.474913 + 0.949506I
b = −0.261128 − 0.222516I
4.85064 + 0.68988I 0
u = 0.801414 − 0.625750I
a = −0.474913 − 0.949506I
b = −0.261128 + 0.222516I
4.85064 − 0.68988I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.942240 + 0.252531I
a = −1.13569 − 1.23380I
b = −2.34372 − 0.69387I
2.20316 + 4.25845I 0
u = −0.942240 − 0.252531I
a = −1.13569 + 1.23380I
b = −2.34372 + 0.69387I
2.20316 − 4.25845I 0
u = 0.864699 + 0.448507I
a = 0.57238 + 1.37555I
b = −0.606818 + 1.182450I
4.25327 − 10.46020I 0
u = 0.864699 − 0.448507I
a = 0.57238 − 1.37555I
b = −0.606818 − 1.182450I
4.25327 + 10.46020I 0
u = 0.872923 + 0.539032I
a = −0.028634 − 0.661713I
b = −0.814435 − 0.686233I
−2.00357 − 3.87173I 0
u = 0.872923 − 0.539032I
a = −0.028634 + 0.661713I
b = −0.814435 + 0.686233I
−2.00357 + 3.87173I 0
u = 0.764718 + 0.593333I
a = −0.224352 + 0.611378I
b = 0.003174 − 0.502837I
4.86027 + 0.57727I 0
u = 0.764718 − 0.593333I
a = −0.224352 − 0.611378I
b = 0.003174 + 0.502837I
4.86027 − 0.57727I 0
u = 0.807662 + 0.525764I
a = −0.109429 − 0.467702I
b = 1.103770 − 0.284116I
4.72818 − 5.02734I 0
u = 0.807662 − 0.525764I
a = −0.109429 + 0.467702I
b = 1.103770 + 0.284116I
4.72818 + 5.02734I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.03726
a = 3.68109
b = 4.54373
−3.13749 0
u = −0.897317 + 0.347194I
a = 1.41904 − 0.00440I
b = 2.79934 − 0.20867I
3.47117 + 10.13850I 0
u = −0.897317 − 0.347194I
a = 1.41904 + 0.00440I
b = 2.79934 + 0.20867I
3.47117 − 10.13850I 0
u = 1.018550 + 0.259841I
a = 0.071552 + 0.245607I
b = −0.609424 − 0.451865I
−2.58602 − 3.93355I 0
u = 1.018550 − 0.259841I
a = 0.071552 − 0.245607I
b = −0.609424 + 0.451865I
−2.58602 + 3.93355I 0
u = 0.878831 + 0.341393I
a = 1.05330 − 2.00228I
b = 0.565038 − 0.965512I
4.72304 − 4.97410I 0
u = 0.878831 − 0.341393I
a = 1.05330 + 2.00228I
b = 0.565038 + 0.965512I
4.72304 + 4.97410I 0
u = −1.025650 + 0.269556I
a = −2.30755 + 0.91685I
b = −3.16643 + 0.41485I
−5.43574 + 0.32299I 0
u = −1.025650 − 0.269556I
a = −2.30755 − 0.91685I
b = −3.16643 − 0.41485I
−5.43574 − 0.32299I 0
u = 0.777394 + 0.493312I
a = 0.720123 + 0.423177I
b = 0.20264 + 1.47698I
4.51945 + 6.57191I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.777394 − 0.493312I
a = 0.720123 − 0.423177I
b = 0.20264 − 1.47698I
4.51945 − 6.57191I 0
u = 0.187205 + 0.889090I
a = 0.03570 + 2.05620I
b = −0.330273 + 0.835028I
0.92581 + 6.07862I 0
u = 0.187205 − 0.889090I
a = 0.03570 − 2.05620I
b = −0.330273 − 0.835028I
0.92581 − 6.07862I 0
u = −0.021949 + 1.093140I
a = 0.26200 − 1.66572I
b = 0.270816 − 0.551047I
−0.45503 − 6.15957I 0
u = −0.021949 − 1.093140I
a = 0.26200 + 1.66572I
b = 0.270816 + 0.551047I
−0.45503 + 6.15957I 0
u = 0.765199 + 0.480119I
a = −0.33579 + 1.43118I
b = −0.005294 + 0.173701I
4.82252 + 0.90757I 0
u = 0.765199 − 0.480119I
a = −0.33579 − 1.43118I
b = −0.005294 − 0.173701I
4.82252 − 0.90757I 0
u = −1.016800 + 0.443199I
a = −0.644176 + 0.375189I
b = −0.369034 + 1.056070I
−2.16138 + 1.67808I 0
u = −1.016800 − 0.443199I
a = −0.644176 − 0.375189I
b = −0.369034 − 1.056070I
−2.16138 − 1.67808I 0
u = −0.351162 + 1.053340I
a = −0.0276257 + 0.1218040I
b = −0.935297 − 0.078163I
6.01572 − 8.10134I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351162 − 1.053340I
a = −0.0276257 − 0.1218040I
b = −0.935297 + 0.078163I
6.01572 + 8.10134I 0
u = −0.852820 + 0.226205I
a = 1.019270 + 0.598571I
b = 0.292599 − 0.596293I
2.55823 − 2.10130I 0
u = −0.852820 − 0.226205I
a = 1.019270 − 0.598571I
b = 0.292599 + 0.596293I
2.55823 + 2.10130I 0
u = 1.122420 + 0.040813I
a = −1.050590 − 0.673726I
b = −2.09129 − 0.10135I
−4.84462 + 2.01205I 0
u = 1.122420 − 0.040813I
a = −1.050590 + 0.673726I
b = −2.09129 + 0.10135I
−4.84462 − 2.01205I 0
u = 0.398803 + 0.780172I
a = −0.676907 + 0.558220I
b = −0.0453966 − 0.1333240I
2.71184 + 2.00711I 0
u = 0.398803 − 0.780172I
a = −0.676907 − 0.558220I
b = −0.0453966 + 0.1333240I
2.71184 − 2.00711I 0
u = 0.824347 + 0.289882I
a = −2.62081 + 0.89290I
b = −3.67138 + 0.60920I
4.99211 + 2.13455I 0
u = 0.824347 − 0.289882I
a = −2.62081 − 0.89290I
b = −3.67138 − 0.60920I
4.99211 − 2.13455I 0
u = 0.092978 + 0.867549I
a = 0.314473 − 0.607042I
b = −0.627542 + 0.003275I
1.35564 + 3.10692I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.092978 − 0.867549I
a = 0.314473 + 0.607042I
b = −0.627542 − 0.003275I
1.35564 − 3.10692I 0
u = −0.792901 + 0.355099I
a = −0.26167 − 1.82672I
b = 0.518383 − 0.533921I
3.80719 − 7.07343I 0
u = −0.792901 − 0.355099I
a = −0.26167 + 1.82672I
b = 0.518383 + 0.533921I
3.80719 + 7.07343I 0
u = −0.788640 + 0.339798I
a = −1.47249 − 0.51463I
b = −0.895767 + 0.050514I
−1.85499 + 0.29361I 0
u = −0.788640 − 0.339798I
a = −1.47249 + 0.51463I
b = −0.895767 − 0.050514I
−1.85499 − 0.29361I 0
u = 1.091310 + 0.405083I
a = −0.001384 + 0.328024I
b = 0.018709 − 0.539674I
0.86485 − 3.58498I 0
u = 1.091310 − 0.405083I
a = −0.001384 − 0.328024I
b = 0.018709 + 0.539674I
0.86485 + 3.58498I 0
u = −1.087430 + 0.415532I
a = −0.128643 − 0.308564I
b = −0.597632 − 0.988389I
−0.912275 − 0.937931I 0
u = −1.087430 − 0.415532I
a = −0.128643 + 0.308564I
b = −0.597632 + 0.988389I
−0.912275 + 0.937931I 0
u = −0.724392 + 0.412992I
a = 1.12167 + 1.41576I
b = 0.248043 + 1.093250I
−4.11167 + 2.24501I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724392 − 0.412992I
a = 1.12167 − 1.41576I
b = 0.248043 − 1.093250I
−4.11167 − 2.24501I 0
u = −0.831820 + 0.017037I
a = 2.33554 − 3.06965I
b = 1.26334 − 2.18652I
1.81851 + 2.85219I 0
u = −0.831820 − 0.017037I
a = 2.33554 + 3.06965I
b = 1.26334 + 2.18652I
1.81851 − 2.85219I 0
u = 0.344357 + 0.753523I
a = −0.492546 + 0.258225I
b = 0.282513 + 0.131141I
2.55307 + 1.66800I 0
u = 0.344357 − 0.753523I
a = −0.492546 − 0.258225I
b = 0.282513 − 0.131141I
2.55307 − 1.66800I 0
u = 1.095270 + 0.416653I
a = −1.54064 − 0.99695I
b = −2.42748 − 0.40304I
−4.08354 − 3.20236I 0
u = 1.095270 − 0.416653I
a = −1.54064 + 0.99695I
b = −2.42748 + 0.40304I
−4.08354 + 3.20236I 0
u = −1.17213
a = −0.922587
b = −1.73912
−2.83879 0
u = −0.826385
a = −0.917377
b = −2.75477
−0.705957 0
u = −0.407511 + 1.106390I
a = 0.529226 − 0.143879I
b = 1.270910 − 0.032384I
6.61099 + 1.46475I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.407511 − 1.106390I
a = 0.529226 + 0.143879I
b = 1.270910 + 0.032384I
6.61099 − 1.46475I 0
u = −1.098180 + 0.447252I
a = 2.34715 + 0.76754I
b = 3.31921 + 0.63775I
−3.43399 + 6.32250I 0
u = −1.098180 − 0.447252I
a = 2.34715 − 0.76754I
b = 3.31921 − 0.63775I
−3.43399 − 6.32250I 0
u = −0.307719 + 0.745452I
a = 0.50216 + 1.92220I
b = 0.016544 + 0.780195I
−4.08290 + 2.57720I 0
u = −0.307719 − 0.745452I
a = 0.50216 − 1.92220I
b = 0.016544 − 0.780195I
−4.08290 − 2.57720I 0
u = −1.204090 + 0.039093I
a = 1.44148 + 1.52259I
b = 2.08490 + 1.30733I
−2.95281 + 0.67247I 0
u = −1.204090 − 0.039093I
a = 1.44148 − 1.52259I
b = 2.08490 − 1.30733I
−2.95281 − 0.67247I 0
u = 0.713714 + 0.342186I
a = 1.36260 − 1.29521I
b = 2.58306 − 0.99547I
5.13802 − 4.71471I 0
u = 0.713714 − 0.342186I
a = 1.36260 + 1.29521I
b = 2.58306 + 0.99547I
5.13802 + 4.71471I 0
u = 1.074270 + 0.570781I
a = −1.49456 − 0.84545I
b = −2.00878 − 0.22597I
−2.83698 − 0.68862I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.074270 − 0.570781I
a = −1.49456 + 0.84545I
b = −2.00878 + 0.22597I
−2.83698 + 0.68862I 0
u = −1.171690 + 0.339206I
a = 0.479015 + 0.777736I
b = 0.868747 + 0.476023I
−2.94382 + 0.96462I 0
u = −1.171690 − 0.339206I
a = 0.479015 − 0.777736I
b = 0.868747 − 0.476023I
−2.94382 − 0.96462I 0
u = −0.366444 + 1.164790I
a = 0.36161 + 1.76843I
b = 0.625432 + 0.738449I
4.2665 − 13.9116I 0
u = −0.366444 − 1.164790I
a = 0.36161 − 1.76843I
b = 0.625432 − 0.738449I
4.2665 + 13.9116I 0
u = 0.917100 + 0.807092I
a = −1.13593 + 1.11590I
b = −0.929625 + 0.348672I
−1.51643 − 0.92743I 0
u = 0.917100 − 0.807092I
a = −1.13593 − 1.11590I
b = −0.929625 − 0.348672I
−1.51643 + 0.92743I 0
u = −1.088940 + 0.560207I
a = 1.61092 + 0.88655I
b = 2.51985 + 0.90599I
−3.20452 + 3.95476I 0
u = −1.088940 − 0.560207I
a = 1.61092 − 0.88655I
b = 2.51985 − 0.90599I
−3.20452 − 3.95476I 0
u = −1.176440 + 0.365393I
a = −0.154254 − 0.460357I
b = −0.757170 + 0.469133I
2.18325 + 7.21707I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.176440 − 0.365393I
a = −0.154254 + 0.460357I
b = −0.757170 − 0.469133I
2.18325 − 7.21707I 0
u = −0.682130 + 0.352918I
a = 0.317815 − 0.020147I
b = 0.168107 + 1.249880I
5.87369 + 4.34128I 0
u = −0.682130 − 0.352918I
a = 0.317815 + 0.020147I
b = 0.168107 − 1.249880I
5.87369 − 4.34128I 0
u = 1.095280 + 0.579401I
a = 0.231558 − 0.424823I
b = 0.647454 − 0.755009I
0.64781 − 7.09781I 0
u = 1.095280 − 0.579401I
a = 0.231558 + 0.424823I
b = 0.647454 + 0.755009I
0.64781 + 7.09781I 0
u = 1.118200 + 0.548382I
a = −0.0060452 − 0.0355583I
b = −0.095778 − 0.615914I
0.25306 − 6.57486I 0
u = 1.118200 − 0.548382I
a = −0.0060452 + 0.0355583I
b = −0.095778 + 0.615914I
0.25306 + 6.57486I 0
u = −1.238610 + 0.271155I
a = −1.017820 + 0.563393I
b = −1.99341 + 0.13579I
−2.85298 + 0.64390I 0
u = −1.238610 − 0.271155I
a = −1.017820 − 0.563393I
b = −1.99341 − 0.13579I
−2.85298 − 0.64390I 0
u = −1.227170 + 0.344099I
a = −2.27737 − 0.42570I
b = −3.08426 − 0.18927I
−1.30612 + 3.53496I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.227170 − 0.344099I
a = −2.27737 + 0.42570I
b = −3.08426 + 0.18927I
−1.30612 − 3.53496I 0
u = 0.012707 + 0.720570I
a = 0.60416 + 1.54109I
b = −0.258429 + 0.159699I
2.09377 + 4.82413I 0
u = 0.012707 − 0.720570I
a = 0.60416 − 1.54109I
b = −0.258429 − 0.159699I
2.09377 − 4.82413I 0
u = 1.28122
a = −1.38634
b = −2.48042
−5.67652 0
u = 1.026020 + 0.798036I
a = 1.64787 − 0.96510I
b = 2.45767 − 1.06110I
−1.85216 − 5.28971I 0
u = 1.026020 − 0.798036I
a = 1.64787 + 0.96510I
b = 2.45767 + 1.06110I
−1.85216 + 5.28971I 0
u = 1.253590 + 0.345646I
a = 1.93694 + 0.33452I
b = 2.84400 + 0.12698I
−8.61590 − 6.29433I 0
u = 1.253590 − 0.345646I
a = 1.93694 − 0.33452I
b = 2.84400 − 0.12698I
−8.61590 + 6.29433I 0
u = 0.551471 + 1.181840I
a = −0.507872 − 0.319245I
b = −1.191230 + 0.067118I
5.51074 − 0.68657I 0
u = 0.551471 − 1.181840I
a = −0.507872 + 0.319245I
b = −1.191230 − 0.067118I
5.51074 + 0.68657I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.211830 + 0.494684I
a = 0.154240 − 0.059774I
b = 0.012165 + 0.721490I
−2.00966 − 7.97299I 0
u = 1.211830 − 0.494684I
a = 0.154240 + 0.059774I
b = 0.012165 − 0.721490I
−2.00966 + 7.97299I 0
u = 1.308990 + 0.086760I
a = 0.245930 − 0.640665I
b = 0.448222 + 0.007371I
−0.46214 + 4.41042I 0
u = 1.308990 − 0.086760I
a = 0.245930 + 0.640665I
b = 0.448222 − 0.007371I
−0.46214 − 4.41042I 0
u = −1.290030 + 0.287728I
a = −1.65547 + 0.48423I
b = −2.32068 + 0.04081I
−3.90405 − 1.98704I 0
u = −1.290030 − 0.287728I
a = −1.65547 − 0.48423I
b = −2.32068 − 0.04081I
−3.90405 + 1.98704I 0
u = 0.279869 + 0.616788I
a = −0.699436 + 0.686480I
b = 0.659738 + 0.266091I
3.12930 − 0.37154I 0
u = 0.279869 − 0.616788I
a = −0.699436 − 0.686480I
b = 0.659738 − 0.266091I
3.12930 + 0.37154I 0
u = 1.203670 + 0.552576I
a = 2.17894 − 0.16451I
b = 3.11524 − 0.12905I
−2.11962 − 11.30150I 0
u = 1.203670 − 0.552576I
a = 2.17894 + 0.16451I
b = 3.11524 + 0.12905I
−2.11962 + 11.30150I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.234800 + 0.486824I
a = 1.65067 − 0.31367I
b = 2.64316 − 0.17948I
−1.50103 − 9.35073I 0
u = 1.234800 − 0.486824I
a = 1.65067 + 0.31367I
b = 2.64316 + 0.17948I
−1.50103 + 9.35073I 0
u = 0.243949 + 1.305120I
a = 0.88825 + 1.47403I
b = 1.29692 + 0.96572I
4.21291 + 0.50576I 0
u = 0.243949 − 1.305120I
a = 0.88825 − 1.47403I
b = 1.29692 − 0.96572I
4.21291 − 0.50576I 0
u = −0.523891 + 0.420043I
a = −1.109200 + 0.842834I
b = 0.343578 + 0.954743I
−0.70512 + 2.01041I 0
u = −0.523891 − 0.420043I
a = −1.109200 − 0.842834I
b = 0.343578 − 0.954743I
−0.70512 − 2.01041I 0
u = 0.473620 + 1.282640I
a = 0.52904 − 1.82862I
b = 0.710791 − 1.085310I
5.40830 + 3.98730I 0
u = 0.473620 − 1.282640I
a = 0.52904 + 1.82862I
b = 0.710791 + 1.085310I
5.40830 − 3.98730I 0
u = 1.265470 + 0.517748I
a = −2.00987 + 0.56643I
b = −2.93999 + 0.39718I
−3.6237 − 13.8044I 0
u = 1.265470 − 0.517748I
a = −2.00987 − 0.56643I
b = −2.93999 − 0.39718I
−3.6237 + 13.8044I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.300020 + 0.465588I
a = 1.68103 + 1.34936I
b = 2.19774 + 1.00780I
−0.04586 − 6.47494I 0
u = 1.300020 − 0.465588I
a = 1.68103 − 1.34936I
b = 2.19774 − 1.00780I
−0.04586 + 6.47494I 0
u = −1.230910 + 0.643789I
a = 0.272720 + 0.217535I
b = 0.256950 − 0.600005I
3.2289 + 14.1873I 0
u = −1.230910 − 0.643789I
a = 0.272720 − 0.217535I
b = 0.256950 + 0.600005I
3.2289 − 14.1873I 0
u = 0.120763 + 1.387720I
a = −0.38831 + 1.41511I
b = −0.652403 + 0.625650I
3.06862 + 4.02525I 0
u = 0.120763 − 1.387720I
a = −0.38831 − 1.41511I
b = −0.652403 − 0.625650I
3.06862 − 4.02525I 0
u = −1.298750 + 0.516850I
a = 1.63367 − 0.30995I
b = 2.56653 − 0.03819I
−4.48105 + 11.69190I 0
u = −1.298750 − 0.516850I
a = 1.63367 + 0.30995I
b = 2.56653 + 0.03819I
−4.48105 − 11.69190I 0
u = 1.207060 + 0.714555I
a = 0.161680 − 0.448181I
b = −0.050290 + 0.212292I
3.22888 − 6.01975I 0
u = 1.207060 − 0.714555I
a = 0.161680 + 0.448181I
b = −0.050290 − 0.212292I
3.22888 + 6.01975I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.253070 + 0.646797I
a = −0.235848 − 0.479252I
b = −0.270872 + 0.331856I
3.79785 + 4.81113I 0
u = −1.253070 − 0.646797I
a = −0.235848 + 0.479252I
b = −0.270872 − 0.331856I
3.79785 − 4.81113I 0
u = −1.27339 + 0.64989I
a = −1.82198 − 0.05193I
b = −2.56866 − 0.24143I
−6.54719 + 3.14760I 0
u = −1.27339 − 0.64989I
a = −1.82198 + 0.05193I
b = −2.56866 + 0.24143I
−6.54719 − 3.14760I 0
u = −1.26670 + 0.68313I
a = −1.89994 − 0.47253I
b = −2.83664 − 0.40349I
1.3708 + 20.4475I 0
u = −1.26670 − 0.68313I
a = −1.89994 + 0.47253I
b = −2.83664 + 0.40349I
1.3708 − 20.4475I 0
u = −0.53085 + 1.34755I
a = −0.33148 − 1.58673I
b = −0.439544 − 0.688030I
4.41501 − 3.86776I 0
u = −0.53085 − 1.34755I
a = −0.33148 + 1.58673I
b = −0.439544 + 0.688030I
4.41501 + 3.86776I 0
u = −1.39962 + 0.37548I
a = 1.13546 − 0.92302I
b = 1.71784 − 0.37281I
−4.57607 − 3.35241I 0
u = −1.39962 − 0.37548I
a = 1.13546 + 0.92302I
b = 1.71784 + 0.37281I
−4.57607 + 3.35241I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46469 + 0.01323I
a = 1.42838 − 0.61391I
b = 2.20866 − 0.23716I
−3.18044 − 9.46852I 0
u = 1.46469 − 0.01323I
a = 1.42838 + 0.61391I
b = 2.20866 + 0.23716I
−3.18044 + 9.46852I 0
u = 1.29332 + 0.70894I
a = −2.04321 + 0.46120I
b = −2.81009 + 0.39990I
2.54670 − 10.98520I 0
u = 1.29332 − 0.70894I
a = −2.04321 − 0.46120I
b = −2.81009 − 0.39990I
2.54670 + 10.98520I 0
u = −0.290043 + 0.437666I
a = −0.70552 − 2.82250I
b = −0.670446 − 0.733525I
−1.12363 − 2.51826I 0
u = −0.290043 − 0.437666I
a = −0.70552 + 2.82250I
b = −0.670446 + 0.733525I
−1.12363 + 2.51826I 0
u = −1.29382 + 0.74799I
a = 1.66716 + 0.41933I
b = 2.58668 + 0.38500I
1.69980 + 11.17630I 0
u = −1.29382 − 0.74799I
a = 1.66716 − 0.41933I
b = 2.58668 − 0.38500I
1.69980 − 11.17630I 0
u = −1.49814
a = −1.05233
b = −2.26146
−3.57692 0
u = 1.50073 + 0.30730I
a = −1.56109 + 0.14111I
b = −2.46137 + 0.18035I
−5.68281 + 0.50897I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50073 − 0.30730I
a = −1.56109 − 0.14111I
b = −2.46137 − 0.18035I
−5.68281 − 0.50897I 0
u = 0.413681
a = 1.17546
b = −1.57045
−1.68445 −5.87110
u = 0.029948 + 0.382068I
a = −1.206370 − 0.356686I
b = 0.001172 + 0.400612I
−0.149131 + 1.319240I −1.86986 − 5.03740I
u = 0.029948 − 0.382068I
a = −1.206370 + 0.356686I
b = 0.001172 − 0.400612I
−0.149131 − 1.319240I −1.86986 + 5.03740I
u = −0.117535 + 0.252253I
a = −1.54475 + 0.54235I
b = 0.48065 − 1.44244I
5.25829 − 4.17203I 6.61357 + 8.01980I
u = −0.117535 − 0.252253I
a = −1.54475 − 0.54235I
b = 0.48065 + 1.44244I
5.25829 + 4.17203I 6.61357 − 8.01980I
u = −0.225749
a = −4.58336
b = −0.611591
−1.68303 −4.96990
21
II.
I
u
2
= h9.18×10
17
u
38
−1.34×10
19
u
37
+· · ·+9.06×10
15
b−3.91×10
19
, −1.28×
10
19
u
38
+4.99×10
19
u
37
+· · ·+9.06×10
15
a−3.71×10
18
, u
39
−5u
38
+· · ·−9u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
2
=
1417.04u
38
− 5503.02u
37
+ ··· + 3313.37u + 409.854
−101.309u
38
+ 1483.15u
37
+ ··· − 21944.4u + 4316.19
a
7
=
u
u
a
3
=
1672.55u
38
− 6652.10u
37
+ ··· + 7245.12u − 195.711
154.203u
38
+ 334.074u
37
+ ··· − 18012.6u + 3710.62
a
1
=
−6028.69u
38
+ 27194.1u
37
+ ··· − 85705.9u + 12281.3
−19626.0u
38
+ 89034.5u
37
+ ··· − 288221.u + 41765.0
a
6
=
9317.72u
38
− 41268.0u
37
+ ··· + 116538.u − 15918.4
13957.7u
38
− 62051.3u
37
+ ··· + 178722.u − 24480.5
a
9
=
−34297.2u
38
+ 154375.u
37
+ ··· − 477938.u + 67924.1
−25809.4u
38
+ 116867.u
37
+ ··· − 373807.u + 53904.3
a
5
=
−1623.45u
38
+ 7364.96u
37
+ ··· − 23617.2u + 3241.46
10662.2u
38
− 47331.4u
37
+ ··· + 135007.u − 18407.6
a
10
=
45853.7u
38
− 207137.u
37
+ ··· + 655551.u − 93993.3
10529.3u
38
− 47691.1u
37
+ ··· + 153327.u − 22129.9
a
4
=
−3555.55u
38
+ 16760.9u
37
+ ··· − 71534.6u + 11256.4
−9390.03u
38
+ 41903.9u
37
+ ··· − 128358.u + 17968.8
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
389178706152018704476
9062374718835497
u
38
+
1773907411422215220288
9062374718835497
u
37
+ ··· −
6037733369173327592722
9062374718835497
u +
885315973119248416826
9062374718835497
22
(iv) u-Polynomials at the component
23
Crossings u-Polynomials at each crossing
c
1
u
39
− 21u
38
+ ··· + 16u − 1
c
2
u
39
+ u
38
+ ··· + 2u − 1
c
3
u
39
− 2u
38
+ ··· + u − 1
c
4
u
39
− 2u
38
+ ··· − 6u
2
− 1
c
5
u
39
− 2u
38
+ ··· − 2u + 1
c
6
u
39
− u
38
+ ··· + 2u + 1
c
7
u
39
+ 5u
38
+ ··· − 9u − 1
c
8
u
39
+ 8u
38
+ ··· + 13u + 1
c
9
u
39
+ 11u
37
+ ··· − 14u + 1
c
10
u
39
+ 2u
38
+ ··· + 6u
2
+ 1
c
11
u
39
− 5u
38
+ ··· − 9u + 1
c
12
u
39
− 4u
38
+ ··· + u − 5
24
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
− 5y
38
+ ··· − 16y −1
c
2
, c
6
y
39
− 21y
38
+ ··· + 16y −1
c
3
y
39
+ 22y
38
+ ··· + 21y −1
c
4
, c
10
y
39
− 18y
38
+ ··· − 12y −1
c
5
y
39
− 2y
38
+ ··· − 46y −1
c
7
, c
11
y
39
− 15y
38
+ ··· + 31y −1
c
8
y
39
+ 10y
38
+ ··· + 127y −1
c
9
y
39
+ 22y
38
+ ··· + 32y −1
c
12
y
39
− 20y
38
+ ··· − 2749y −25
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.141338 + 0.971193I
a = 0.359164 + 1.304700I
b = 0.894031 + 0.163396I
4.64157 − 2.47258I 0
u = −0.141338 − 0.971193I
a = 0.359164 − 1.304700I
b = 0.894031 − 0.163396I
4.64157 + 2.47258I 0
u = 0.155284 + 0.968762I
a = −0.370469 + 0.980702I
b = −0.935460 + 0.157066I
5.66797 + 2.80150I 0
u = 0.155284 − 0.968762I
a = −0.370469 − 0.980702I
b = −0.935460 − 0.157066I
5.66797 − 2.80150I 0
u = 0.802024 + 0.682544I
a = −0.36849 + 1.57650I
b = 0.260672 + 1.137170I
−2.98362 − 2.92262I 0
u = 0.802024 − 0.682544I
a = −0.36849 − 1.57650I
b = 0.260672 − 1.137170I
−2.98362 + 2.92262I 0
u = −0.882146 + 0.588152I
a = 1.32712 + 0.72292I
b = 0.955867 − 0.035979I
−3.36110 + 0.54468I 0
u = −0.882146 − 0.588152I
a = 1.32712 − 0.72292I
b = 0.955867 + 0.035979I
−3.36110 − 0.54468I 0
u = −0.879366 + 0.191337I
a = −1.36217 + 0.84104I
b = −0.642259 + 1.035880I
−2.32189 + 0.38514I −27.2636 + 7.9694I
u = −0.879366 − 0.191337I
a = −1.36217 − 0.84104I
b = −0.642259 − 1.035880I
−2.32189 − 0.38514I −27.2636 − 7.9694I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.840362 + 0.247653I
a = −0.648425 − 0.010014I
b = 0.346685 − 0.484292I
−2.61620 + 3.22051I −10.02369 − 1.21631I
u = −0.840362 − 0.247653I
a = −0.648425 + 0.010014I
b = 0.346685 + 0.484292I
−2.61620 − 3.22051I −10.02369 + 1.21631I
u = −0.817321 + 0.012496I
a = 2.29214 − 2.92454I
b = 1.20520 − 2.02239I
1.83275 + 2.84642I 196.907 + 95.064I
u = −0.817321 − 0.012496I
a = 2.29214 + 2.92454I
b = 1.20520 + 2.02239I
1.83275 − 2.84642I 196.907 − 95.064I
u = −1.180080 + 0.228160I
a = 1.45182 − 0.72290I
b = 2.20504 − 0.22444I
−4.15330 − 1.11756I 0
u = −1.180080 − 0.228160I
a = 1.45182 + 0.72290I
b = 2.20504 + 0.22444I
−4.15330 + 1.11756I 0
u = −1.063620 + 0.594929I
a = −1.87108 − 0.96000I
b = −2.74609 − 0.99291I
−3.99639 + 4.40950I 0
u = −1.063620 − 0.594929I
a = −1.87108 + 0.96000I
b = −2.74609 + 0.99291I
−3.99639 − 4.40950I 0
u = 1.148470 + 0.410713I
a = 0.117858 − 0.619202I
b = 0.679130 + 0.077509I
2.33675 − 6.79577I 0
u = 1.148470 − 0.410713I
a = 0.117858 + 0.619202I
b = 0.679130 − 0.077509I
2.33675 + 6.79577I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.108230 + 0.524742I
a = 1.81964 + 0.56691I
b = 2.59101 + 0.07948I
−4.25674 − 2.07764I 0
u = 1.108230 − 0.524742I
a = 1.81964 − 0.56691I
b = 2.59101 − 0.07948I
−4.25674 + 2.07764I 0
u = 0.723231
a = 0.424055
b = 2.41556
−0.426246 9.90700
u = 0.371912 + 1.237760I
a = −0.695008 − 1.019350I
b = −1.151100 − 0.609012I
4.51382 + 0.80773I 0
u = 0.371912 − 1.237760I
a = −0.695008 + 1.019350I
b = −1.151100 + 0.609012I
4.51382 − 0.80773I 0
u = 1.182380 + 0.569998I
a = −0.545919 − 0.277864I
b = −0.753269 + 0.152826I
1.42160 − 6.76295I 0
u = 1.182380 − 0.569998I
a = −0.545919 + 0.277864I
b = −0.753269 − 0.152826I
1.42160 + 6.76295I 0
u = 0.585363 + 0.165989I
a = −0.710101 − 0.918474I
b = −0.41486 − 1.98531I
4.81841 + 3.85595I −6.08635 + 0.91025I
u = 0.585363 − 0.165989I
a = −0.710101 + 0.918474I
b = −0.41486 + 1.98531I
4.81841 − 3.85595I −6.08635 − 0.91025I
u = 1.304940 + 0.539231I
a = −1.87452 + 0.09300I
b = −2.77139 + 0.03406I
−0.92374 − 11.08000I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.304940 − 0.539231I
a = −1.87452 − 0.09300I
b = −2.77139 − 0.03406I
−0.92374 + 11.08000I 0
u = 0.30461 + 1.40894I
a = 0.27126 − 1.65775I
b = 0.441333 − 0.860845I
3.07969 + 4.56052I 0
u = 0.30461 − 1.40894I
a = 0.27126 + 1.65775I
b = 0.441333 + 0.860845I
3.07969 − 4.56052I 0
u = 1.46886
a = 1.02985
b = 2.27927
−3.63763 0
u = −1.49431
a = 1.54404
b = 2.46779
−5.18675 0
u = 0.497810 + 0.063527I
a = 0.87402 + 1.99616I
b = −1.37070 + 0.92345I
3.89177 − 8.53814I −3.62373 + 7.72914I
u = 0.497810 − 0.063527I
a = 0.87402 − 1.99616I
b = −1.37070 − 0.92345I
3.89177 + 8.53814I −3.62373 − 7.72914I
u = 0.494312 + 0.040027I
a = 2.43418 + 0.46723I
b = 1.124850 − 0.800183I
5.25863 + 3.20086I −1.28928 − 2.92765I
u = 0.494312 − 0.040027I
a = 2.43418 − 0.46723I
b = 1.124850 + 0.800183I
5.25863 − 3.20086I −1.28928 + 2.92765I
30
III. I
u
3
= hb − a − 1, a
2
− 3a + 1, u + 1i
(i) Arc colorings
a
8
=
0
−1
a
11
=
1
0
a
12
=
1
1
a
2
=
a
a + 1
a
7
=
−1
−1
a
3
=
a − 1
a
a
1
=
1
1
a
6
=
a − 1
a
a
9
=
a
2a − 2
a
5
=
a − 2
a − 1
a
10
=
2
a
a
4
=
−a
−a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
(u − 1)
2
c
3
, c
4
u
2
+ u − 1
c
5
, c
6
, c
11
(u + 1)
2
c
8
, c
9
, c
10
u
2
− u − 1
c
12
u
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
11
(y −1)
2
c
3
, c
4
, c
8
c
9
, c
10
y
2
− 3y + 1
c
12
y
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.381966
b = 1.38197
−3.28987 −17.0000
u = −1.00000
a = 2.61803
b = 3.61803
−3.28987 −17.0000
34
IV. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
1
0
a
12
=
1
0
a
2
=
0
−1
a
7
=
1
0
a
3
=
1
−1
a
1
=
−1
0
a
6
=
1
−1
a
9
=
0
1
a
5
=
2
−1
a
10
=
−1
1
a
4
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
10
u + 1
c
7
, c
11
, c
12
u
c
9
u − 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
9
, c
10
y −1
c
7
, c
11
, c
12
y
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
−1.64493 −6.00000
38
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u + 1)(u
39
− 21u
38
+ ··· + 16u − 1)
· (u
167
+ 71u
166
+ ··· + 2794905u + 88209)
c
2
((u − 1)
2
)(u + 1)(u
39
+ u
38
+ ··· + 2u − 1)
· (u
167
− 3u
166
+ ··· − 1611u − 297)
c
3
(u + 1)(u
2
+ u − 1)(u
39
− 2u
38
+ ··· + u − 1)(u
167
− u
166
+ ··· + 9u − 1)
c
4
(u + 1)(u
2
+ u − 1)(u
39
− 2u
38
+ ··· − 6u
2
− 1)
· (u
167
+ u
166
+ ··· + 286094u + 26963)
c
5
((u + 1)
3
)(u
39
− 2u
38
+ ··· − 2u + 1)
· (u
167
− 4u
166
+ ··· − 98117u + 118061)
c
6
((u + 1)
3
)(u
39
− u
38
+ ··· + 2u + 1)(u
167
− 3u
166
+ ··· − 1611u − 297)
c
7
u(u − 1)
2
(u
39
+ 5u
38
+ ··· − 9u − 1)
· (u
167
− 2u
166
+ ··· + 46140u + 5847)
c
8
(u + 1)(u
2
− u − 1)(u
39
+ 8u
38
+ ··· + 13u + 1)
· (u
167
− 5u
166
+ ··· − 30593750u + 2687500)
c
9
(u − 1)(u
2
− u − 1)(u
39
+ 11u
37
+ ··· − 14u + 1)
· (u
167
+ 9u
166
+ ··· − 1286138u − 711596)
c
10
(u + 1)(u
2
− u − 1)(u
39
+ 2u
38
+ ··· + 6u
2
+ 1)
· (u
167
+ u
166
+ ··· + 286094u + 26963)
c
11
u(u + 1)
2
(u
39
− 5u
38
+ ··· − 9u + 1)
· (u
167
− 2u
166
+ ··· + 46140u + 5847)
c
12
u
3
(u
39
− 4u
38
+ ··· + u − 5)(u
167
+ 17u
166
+ ··· − 36u − 12)
39
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
3
)(y
39
− 5y
38
+ ··· − 16y −1)
· (y
167
+ 53y
166
+ ··· − 16946980639767y −7780827681)
c
2
, c
6
((y −1)
3
)(y
39
− 21y
38
+ ··· + 16y −1)
· (y
167
− 71y
166
+ ··· + 2794905y −88209)
c
3
(y −1)(y
2
− 3y + 1)(y
39
+ 22y
38
+ ··· + 21y −1)
· (y
167
+ 19y
166
+ ··· + 903y −1)
c
4
, c
10
(y −1)(y
2
− 3y + 1)(y
39
− 18y
38
+ ··· − 12y −1)
· (y
167
− 109y
166
+ ··· + 67092980862y −727003369)
c
5
((y −1)
3
)(y
39
− 2y
38
+ ··· − 46y −1)
· (y
167
+ 16y
166
+ ··· − 734586387985y −13938399721)
c
7
, c
11
y(y −1)
2
(y
39
− 15y
38
+ ··· + 31y −1)
· (y
167
− 86y
166
+ ··· + 1156461642y −34187409)
c
8
(y −1)(y
2
− 3y + 1)(y
39
+ 10y
38
+ ··· + 127y −1)
· (y
167
− 17y
166
+ ··· + 606399335937500y −7222656250000)
c
9
(y −1)(y
2
− 3y + 1)(y
39
+ 22y
38
+ ··· + 32y −1)
· (y
167
+ 55y
166
+ ··· − 11009677597860y −506368867216)
c
12
y
3
(y
39
− 20y
38
+ ··· − 2749y −25)(y
167
− 29y
166
+ ··· + 6408y −144)
40
