12a
0756
(K12a
0756
)
A knot diagram
1
Linearized knot diagam
3 8 10 11 9 12 2 6 1 4 7 5
Solving Sequence
3,10
4 11
5,8
2 1 7 12 6 9
c
3
c
10
c
4
c
2
c
1
c
7
c
11
c
6
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.63385 × 10
330
u
124
− 1.41764 × 10
330
u
123
+ ··· + 1.29035 × 10
328
b + 9.70787 × 10
330
,
6.48012 × 10
331
u
124
+ 5.24624 × 10
331
u
123
+ ··· + 1.29035 × 10
328
a − 3.36479 × 10
332
, u
125
+ u
124
+ ··· − 39u − 1i
I
u
2
= h469u
31
− 142u
30
+ ··· + 293b + 474, −1355u
31
+ 717u
30
+ ··· + 293a − 2414,
u
32
− 18u
30
+ ··· − 4u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 157 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−1.63 × 10
330
u
124
− 1.42 × 10
330
u
123
+ · · · + 1.29 × 10
328
b + 9.71 ×
10
330
, 6.48 × 10
331
u
124
+ 5.25 × 10
331
u
123
+ · · · + 1.29 × 10
328
a − 3.36 ×
10
332
, u
125
+ u
124
+ · · · − 39u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
11
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
−5021.98u
124
− 4065.74u
123
+ ··· + 883332.u + 26076.5
126.621u
124
+ 109.865u
123
+ ··· − 25537.3u − 752.343
a
2
=
−4001.75u
124
− 3223.53u
123
+ ··· + 698858.u + 20642.5
−37.9296u
124
− 8.33395u
123
+ ··· − 10819.9u − 389.924
a
1
=
−4039.68u
124
− 3231.87u
123
+ ··· + 688038.u + 20252.5
−37.9296u
124
− 8.33395u
123
+ ··· − 10819.9u − 389.924
a
7
=
−1453.38u
124
− 1154.59u
123
+ ··· + 246407.u + 7265.27
471.963u
124
+ 369.067u
123
+ ··· − 66258.7u − 1840.77
a
12
=
−3723.02u
124
− 2997.80u
123
+ ··· + 649734.u + 19189.7
−82.0694u
124
− 41.9836u
123
+ ··· − 4543.04u − 212.025
a
6
=
−5194.57u
124
− 4244.77u
123
+ ··· + 953249.u + 28426.4
−69.1566u
124
− 74.0379u
123
+ ··· + 28810.1u + 944.086
a
9
=
3626.15u
124
+ 3080.15u
123
+ ··· − 754222.u − 22905.4
523.574u
124
+ 441.914u
123
+ ··· − 104441.u − 3131.93
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10077.2u
124
− 8235.08u
123
+ ··· + 1.77727 × 10
6
u + 52146.8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
125
+ 49u
124
+ ··· + 9905408u + 295936
c
2
, c
7
u
125
+ u
124
+ ··· − 1072u − 544
c
3
, c
4
, c
10
u
125
+ u
124
+ ··· − 39u − 1
c
5
, c
8
u
125
− 2u
124
+ ··· − 10915u + 1369
c
6
, c
11
u
125
+ u
124
+ ··· − 614u − 129
c
9
u
125
− 7u
124
+ ··· − 597974523u + 137487799
c
12
u
125
− 5u
124
+ ··· + 2718423u − 646429
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
125
+ 71y
124
+ ··· − 2183472283648y −87578116096
c
2
, c
7
y
125
− 49y
124
+ ··· + 9905408y −295936
c
3
, c
4
, c
10
y
125
− 129y
124
+ ··· + 123y −1
c
5
, c
8
y
125
+ 76y
124
+ ··· − 60105945y −1874161
c
6
, c
11
y
125
+ 67y
124
+ ··· − 1021106y −16641
c
9
y
125
− 53y
124
+ ··· + 628976017143595697y −18902894873864401
c
12
y
125
− 25y
124
+ ··· + 4561628210455y −417870452041
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.560070 + 0.830618I
a = 0.005726 + 0.557264I
b = 0.638215 − 0.682382I
−0.99708 − 2.04417I 0
u = −0.560070 − 0.830618I
a = 0.005726 − 0.557264I
b = 0.638215 + 0.682382I
−0.99708 + 2.04417I 0
u = −0.522093 + 0.835666I
a = 0.868028 − 1.000420I
b = 0.675904 + 0.675750I
2.86252 + 2.82941I 0
u = −0.522093 − 0.835666I
a = 0.868028 + 1.000420I
b = 0.675904 − 0.675750I
2.86252 − 2.82941I 0
u = −0.766804 + 0.684858I
a = −0.75095 + 1.45806I
b = −0.793488 − 0.543772I
−0.41768 − 3.51081I 0
u = −0.766804 − 0.684858I
a = −0.75095 − 1.45806I
b = −0.793488 + 0.543772I
−0.41768 + 3.51081I 0
u = 0.952983 + 0.413336I
a = 0.56168 − 1.41133I
b = −1.023360 + 0.155541I
−1.25962 − 2.31481I 0
u = 0.952983 − 0.413336I
a = 0.56168 + 1.41133I
b = −1.023360 − 0.155541I
−1.25962 + 2.31481I 0
u = 0.526064 + 0.898950I
a = −0.683296 − 1.126120I
b = −1.095740 + 0.689568I
1.40579 + 13.87260I 0
u = 0.526064 − 0.898950I
a = −0.683296 + 1.126120I
b = −1.095740 − 0.689568I
1.40579 − 13.87260I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.574092 + 0.756910I
a = 0.177973 − 0.420259I
b = −0.528567 + 0.876131I
3.11164 − 8.07591I 0
u = −0.574092 − 0.756910I
a = 0.177973 + 0.420259I
b = −0.528567 − 0.876131I
3.11164 + 8.07591I 0
u = 0.470946 + 0.980198I
a = 0.557346 + 1.056750I
b = 1.005970 − 0.651704I
−2.09362 + 7.24326I 0
u = 0.470946 − 0.980198I
a = 0.557346 − 1.056750I
b = 1.005970 + 0.651704I
−2.09362 − 7.24326I 0
u = 0.716743 + 0.877059I
a = −0.116982 − 0.199348I
b = 0.990435 + 0.643096I
1.90273 − 7.96364I 0
u = 0.716743 − 0.877059I
a = −0.116982 + 0.199348I
b = 0.990435 − 0.643096I
1.90273 + 7.96364I 0
u = 0.584208 + 0.610604I
a = −0.554282 + 0.009632I
b = 0.686207 + 0.758646I
5.48584 + 2.08617I 0
u = 0.584208 − 0.610604I
a = −0.554282 − 0.009632I
b = 0.686207 − 0.758646I
5.48584 − 2.08617I 0
u = −1.145640 + 0.206937I
a = −1.157130 + 0.045348I
b = −0.507097 − 0.326991I
3.88412 − 5.25444I 0
u = −1.145640 − 0.206937I
a = −1.157130 − 0.045348I
b = −0.507097 + 0.326991I
3.88412 + 5.25444I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.165430 + 0.091842I
a = 0.728158 − 0.555600I
b = 1.101850 + 0.466236I
0.33460 − 5.32985I 0
u = −1.165430 − 0.091842I
a = 0.728158 + 0.555600I
b = 1.101850 − 0.466236I
0.33460 + 5.32985I 0
u = −0.749603 + 0.352544I
a = 0.337914 + 1.263390I
b = 0.471834 − 0.145078I
−1.55105 − 1.59703I 0
u = −0.749603 − 0.352544I
a = 0.337914 − 1.263390I
b = 0.471834 + 0.145078I
−1.55105 + 1.59703I 0
u = −0.666409 + 0.452542I
a = −0.94981 + 1.66830I
b = −0.842878 − 0.409913I
−0.39342 − 3.59527I 0
u = −0.666409 − 0.452542I
a = −0.94981 − 1.66830I
b = −0.842878 + 0.409913I
−0.39342 + 3.59527I 0
u = −0.445649 + 0.668121I
a = 1.35812 − 1.35621I
b = 0.987473 + 0.682486I
4.57341 − 7.56022I 0
u = −0.445649 − 0.668121I
a = 1.35812 + 1.35621I
b = 0.987473 − 0.682486I
4.57341 + 7.56022I 0
u = 0.318208 + 0.730456I
a = −0.680030 − 0.855887I
b = −0.849369 + 0.756483I
4.68328 + 2.26812I 0
u = 0.318208 − 0.730456I
a = −0.680030 + 0.855887I
b = −0.849369 − 0.756483I
4.68328 − 2.26812I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.117992 + 0.778543I
a = −0.745560 + 0.488532I
b = −1.044850 − 0.052298I
−5.84195 + 1.29047I 0
u = 0.117992 − 0.778543I
a = −0.745560 − 0.488532I
b = −1.044850 + 0.052298I
−5.84195 − 1.29047I 0
u = 0.929508 + 0.812838I
a = 0.304121 + 0.383870I
b = −0.907528 − 0.588471I
−0.789159 − 1.059320I 0
u = 0.929508 − 0.812838I
a = 0.304121 − 0.383870I
b = −0.907528 + 0.588471I
−0.789159 + 1.059320I 0
u = −0.681221 + 0.250791I
a = 0.391398 − 0.974536I
b = 1.145420 + 0.617855I
−0.01058 − 5.49855I 0
u = −0.681221 − 0.250791I
a = 0.391398 + 0.974536I
b = 1.145420 − 0.617855I
−0.01058 + 5.49855I 0
u = −0.114227 + 0.716514I
a = −0.985080 + 0.777489I
b = −0.877419 + 0.522652I
−2.38804 + 2.09884I 0
u = −0.114227 − 0.716514I
a = −0.985080 − 0.777489I
b = −0.877419 − 0.522652I
−2.38804 − 2.09884I 0
u = −0.366763 + 0.612661I
a = −0.263955 − 0.210363I
b = −0.881588 + 0.774174I
4.60862 + 3.48554I 0
u = −0.366763 − 0.612661I
a = −0.263955 + 0.210363I
b = −0.881588 − 0.774174I
4.60862 − 3.48554I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.684821 + 0.192674I
a = 0.191778 + 0.641827I
b = 0.189140 − 0.835048I
2.75381 − 0.24097I 0
u = 0.684821 − 0.192674I
a = 0.191778 − 0.641827I
b = 0.189140 + 0.835048I
2.75381 + 0.24097I 0
u = 1.171860 + 0.550693I
a = −0.113413 + 1.195930I
b = 0.889439 − 0.246879I
−2.73540 + 3.43854I 0
u = 1.171860 − 0.550693I
a = −0.113413 − 1.195930I
b = 0.889439 + 0.246879I
−2.73540 − 3.43854I 0
u = −1.300470 + 0.054758I
a = −0.503238 + 1.222800I
b = −1.173770 − 0.449089I
0.52150 − 2.48167I 0
u = −1.300470 − 0.054758I
a = −0.503238 − 1.222800I
b = −1.173770 + 0.449089I
0.52150 + 2.48167I 0
u = −0.563295 + 0.410456I
a = −0.73797 + 1.46376I
b = −1.130870 − 0.461304I
−1.01038 − 3.73149I 0
u = −0.563295 − 0.410456I
a = −0.73797 − 1.46376I
b = −1.130870 + 0.461304I
−1.01038 + 3.73149I 0
u = 1.295980 + 0.276425I
a = −0.104844 + 0.406230I
b = 0.667351 + 0.431985I
1.97854 + 1.51991I 0
u = 1.295980 − 0.276425I
a = −0.104844 − 0.406230I
b = 0.667351 − 0.431985I
1.97854 − 1.51991I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.321440 + 0.252713I
a = 0.229971 − 0.530094I
b = −0.991752 − 0.302605I
2.20410 + 2.63018I 0
u = 1.321440 − 0.252713I
a = 0.229971 + 0.530094I
b = −0.991752 + 0.302605I
2.20410 − 2.63018I 0
u = −1.334000 + 0.230857I
a = −0.010917 − 0.275692I
b = 1.206230 + 0.109276I
−1.31497 − 4.81685I 0
u = −1.334000 − 0.230857I
a = −0.010917 + 0.275692I
b = 1.206230 − 0.109276I
−1.31497 + 4.81685I 0
u = 0.207239 + 0.608895I
a = 0.887015 − 0.326481I
b = 1.270940 − 0.040167I
−3.49592 + 5.99439I 0
u = 0.207239 − 0.608895I
a = 0.887015 + 0.326481I
b = 1.270940 + 0.040167I
−3.49592 − 5.99439I 0
u = −0.160001 + 0.619308I
a = 1.139030 − 0.725126I
b = 1.062110 − 0.364198I
−2.40336 + 0.58212I 0
u = −0.160001 − 0.619308I
a = 1.139030 + 0.725126I
b = 1.062110 + 0.364198I
−2.40336 − 0.58212I 0
u = 1.36461
a = −0.201345
b = −1.09759
2.85484 0
u = −1.386170 + 0.008339I
a = 0.44783 + 2.17065I
b = −0.913799 − 0.669271I
2.83268 − 1.28287I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.386170 − 0.008339I
a = 0.44783 − 2.17065I
b = −0.913799 + 0.669271I
2.83268 + 1.28287I 0
u = −1.388640 + 0.024356I
a = −1.04296 + 2.29329I
b = 0.722162 − 0.581090I
4.76840 − 3.49617I 0
u = −1.388640 − 0.024356I
a = −1.04296 − 2.29329I
b = 0.722162 + 0.581090I
4.76840 + 3.49617I 0
u = 1.390110 + 0.044785I
a = 0.409417 − 0.865522I
b = −0.202973 + 0.810809I
3.62840 + 2.12031I 0
u = 1.390110 − 0.044785I
a = 0.409417 + 0.865522I
b = −0.202973 − 0.810809I
3.62840 − 2.12031I 0
u = −1.399420 + 0.045549I
a = −0.54545 − 1.88034I
b = 1.11231 + 0.99003I
8.51763 − 4.17105I 0
u = −1.399420 − 0.045549I
a = −0.54545 + 1.88034I
b = 1.11231 − 0.99003I
8.51763 + 4.17105I 0
u = 0.574493 + 0.157884I
a = 0.606746 + 0.361121I
b = −0.421532 − 0.396092I
1.011430 + 0.226694I 0
u = 0.574493 − 0.157884I
a = 0.606746 − 0.361121I
b = −0.421532 + 0.396092I
1.011430 − 0.226694I 0
u = −1.41252 + 0.17057I
a = 0.437694 + 0.475558I
b = −1.49767 − 0.14692I
1.71323 − 8.66640I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41252 − 0.17057I
a = 0.437694 − 0.475558I
b = −1.49767 + 0.14692I
1.71323 + 8.66640I 0
u = 1.42990 + 0.04798I
a = 0.517785 + 0.550231I
b = 1.107380 − 0.031310I
5.93415 + 3.76410I 0
u = 1.42990 − 0.04798I
a = 0.517785 − 0.550231I
b = 1.107380 + 0.031310I
5.93415 − 3.76410I 0
u = 1.45024 + 0.09542I
a = 1.17413 − 1.64301I
b = −0.793055 + 0.649275I
3.21590 + 3.84758I 0
u = 1.45024 − 0.09542I
a = 1.17413 + 1.64301I
b = −0.793055 − 0.649275I
3.21590 − 3.84758I 0
u = 1.45433 + 0.12436I
a = −0.90741 + 2.22612I
b = 0.971525 − 0.584749I
3.95800 + 8.15493I 0
u = 1.45433 − 0.12436I
a = −0.90741 − 2.22612I
b = 0.971525 + 0.584749I
3.95800 − 8.15493I 0
u = 1.46094 + 0.02460I
a = −0.62291 + 1.58596I
b = 0.67639 − 1.27596I
9.83186 + 3.67940I 0
u = 1.46094 − 0.02460I
a = −0.62291 − 1.58596I
b = 0.67639 + 1.27596I
9.83186 − 3.67940I 0
u = −1.46482 + 0.34435I
a = 0.01966 − 1.80520I
b = 0.935755 + 0.825465I
10.29070 − 6.34764I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46482 − 0.34435I
a = 0.01966 + 1.80520I
b = 0.935755 − 0.825465I
10.29070 + 6.34764I 0
u = 1.49090 + 0.24676I
a = −0.25178 − 1.91311I
b = −1.092470 + 0.701219I
10.8627 + 10.9335I 0
u = 1.49090 − 0.24676I
a = −0.25178 + 1.91311I
b = −1.092470 − 0.701219I
10.8627 − 10.9335I 0
u = 1.48613 + 0.28135I
a = −0.826003 − 1.017160I
b = 0.863483 + 0.870070I
10.53280 + 0.06582I 0
u = 1.48613 − 0.28135I
a = −0.826003 + 1.017160I
b = 0.863483 − 0.870070I
10.53280 − 0.06582I 0
u = 0.031279 + 0.484384I
a = 1.29261 − 0.70808I
b = −0.059153 − 0.541656I
0.65818 + 2.61281I 0
u = 0.031279 − 0.484384I
a = 1.29261 + 0.70808I
b = −0.059153 + 0.541656I
0.65818 − 2.61281I 0
u = −1.53360 + 0.19563I
a = 0.901457 − 0.881586I
b = −0.577297 + 0.890051I
12.45140 − 5.03884I 0
u = −1.53360 − 0.19563I
a = 0.901457 + 0.881586I
b = −0.577297 − 0.890051I
12.45140 + 5.03884I 0
u = 1.54095 + 0.12837I
a = −0.35724 + 1.54219I
b = 1.215550 − 0.602561I
6.00078 + 5.72659I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54095 − 0.12837I
a = −0.35724 − 1.54219I
b = 1.215550 + 0.602561I
6.00078 − 5.72659I 0
u = 1.54379 + 0.09192I
a = 0.60093 − 1.49709I
b = −1.28320 + 0.84650I
7.28577 + 6.85904I 0
u = 1.54379 − 0.09192I
a = 0.60093 + 1.49709I
b = −1.28320 − 0.84650I
7.28577 − 6.85904I 0
u = −0.284654 + 0.350194I
a = −0.56372 + 3.72614I
b = −1.073340 − 0.462416I
−1.82555 − 6.40335I 0. + 12.56791I
u = −0.284654 − 0.350194I
a = −0.56372 − 3.72614I
b = −1.073340 + 0.462416I
−1.82555 + 6.40335I 0. − 12.56791I
u = 1.53448 + 0.21454I
a = 0.03631 + 1.77056I
b = 1.040570 − 0.636265I
6.77922 + 6.58251I 0
u = 1.53448 − 0.21454I
a = 0.03631 − 1.77056I
b = 1.040570 + 0.636265I
6.77922 − 6.58251I 0
u = −1.55767 + 0.01776I
a = 0.15615 + 1.48985I
b = −0.259787 − 1.171730I
10.25640 − 0.32613I 0
u = −1.55767 − 0.01776I
a = 0.15615 − 1.48985I
b = −0.259787 + 1.171730I
10.25640 + 0.32613I 0
u = −1.55722 + 0.10507I
a = −0.711336 + 1.014210I
b = 0.506428 − 0.739167I
8.30090 − 1.37345I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55722 − 0.10507I
a = −0.711336 − 1.014210I
b = 0.506428 + 0.739167I
8.30090 + 1.37345I 0
u = 1.53801 + 0.27214I
a = 0.764294 + 1.117260I
b = −0.627234 − 0.900488I
5.83514 + 5.99338I 0
u = 1.53801 − 0.27214I
a = 0.764294 − 1.117260I
b = −0.627234 + 0.900488I
5.83514 − 5.99338I 0
u = 1.54556 + 0.25935I
a = −0.782113 − 1.163170I
b = 0.558374 + 1.055100I
10.0370 + 11.8102I 0
u = 1.54556 − 0.25935I
a = −0.782113 + 1.163170I
b = 0.558374 − 1.055100I
10.0370 − 11.8102I 0
u = −1.55007 + 0.32187I
a = −0.03780 − 1.81800I
b = 1.158870 + 0.755891I
8.1406 − 18.3342I 0
u = −1.55007 − 0.32187I
a = −0.03780 + 1.81800I
b = 1.158870 − 0.755891I
8.1406 + 18.3342I 0
u = −1.54543 + 0.34619I
a = 0.04293 + 1.78974I
b = −1.075140 − 0.732250I
4.45255 − 12.03210I 0
u = −1.54543 − 0.34619I
a = 0.04293 − 1.78974I
b = −1.075140 + 0.732250I
4.45255 + 12.03210I 0
u = 1.57451 + 0.28056I
a = −0.18047 − 1.55731I
b = −0.912835 + 0.670428I
9.79840 + 1.34406I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57451 − 0.28056I
a = −0.18047 + 1.55731I
b = −0.912835 − 0.670428I
9.79840 − 1.34406I 0
u = −0.129864 + 0.337557I
a = 2.18916 − 0.20050I
b = 0.834121 − 0.293543I
−1.36503 + 0.96077I −2.26477 − 0.76917I
u = −0.129864 − 0.337557I
a = 2.18916 + 0.20050I
b = 0.834121 + 0.293543I
−1.36503 − 0.96077I −2.26477 + 0.76917I
u = −0.284448 + 0.208008I
a = −2.38495 − 2.92243I
b = 0.964406 + 0.463082I
−2.58416 − 2.59005I −0.96655 + 4.26055I
u = −0.284448 − 0.208008I
a = −2.38495 + 2.92243I
b = 0.964406 − 0.463082I
−2.58416 + 2.59005I −0.96655 − 4.26055I
u = −1.66079 + 0.04111I
a = −0.765492 + 0.775809I
b = 0.605364 − 0.404140I
8.65952 − 1.61792I 0
u = −1.66079 − 0.04111I
a = −0.765492 − 0.775809I
b = 0.605364 + 0.404140I
8.65952 + 1.61792I 0
u = −1.67909 + 0.20352I
a = 0.669467 − 0.807013I
b = −0.799147 + 0.656332I
10.15450 + 3.80654I 0
u = −1.67909 − 0.20352I
a = 0.669467 + 0.807013I
b = −0.799147 − 0.656332I
10.15450 − 3.80654I 0
u = −0.208967 + 0.119445I
a = −2.46111 + 2.48479I
b = 0.544639 + 0.424569I
−1.46307 − 1.24235I −0.09926 + 3.49057I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.208967 − 0.119445I
a = −2.46111 − 2.48479I
b = 0.544639 − 0.424569I
−1.46307 + 1.24235I −0.09926 − 3.49057I
u = −0.185898 + 0.065034I
a = 0.35462 + 1.40565I
b = −0.814308 + 1.000220I
4.08748 + 3.55759I 20.3705 − 11.4990I
u = −0.185898 − 0.065034I
a = 0.35462 − 1.40565I
b = −0.814308 − 1.000220I
4.08748 − 3.55759I 20.3705 + 11.4990I
u = −0.180834 + 0.014822I
a = −6.96058 + 7.53634I
b = −0.705849 + 0.105967I
0.42093 − 3.22495I −2.01065 + 9.42270I
u = −0.180834 − 0.014822I
a = −6.96058 − 7.53634I
b = −0.705849 − 0.105967I
0.42093 + 3.22495I −2.01065 − 9.42270I
17
II. I
u
2
= h469u
31
− 142u
30
+ · · · + 293b + 474, −1355u
31
+ 717u
30
+ · · · +
293a − 2414, u
32
− 18u
30
+ · · · − 4u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
11
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
4.62457u
31
− 2.44710u
30
+ ··· − 20.2116u + 8.23891
−1.60068u
31
+ 0.484642u
30
+ ··· + 2.06143u − 1.61775
a
2
=
−6.93857u
31
+ 2.38225u
30
+ ··· + 26.4710u − 11.4027
1.13311u
31
− 0.505119u
30
+ ··· − 7.97952u + 3.46075
a
1
=
−5.80546u
31
+ 1.87713u
30
+ ··· + 18.4915u − 7.94198
1.13311u
31
− 0.505119u
30
+ ··· − 7.97952u + 3.46075
a
7
=
−3.09215u
31
+ 1.42662u
30
+ ··· + 15.2935u − 8.39590
2.80205u
31
− 2.45392u
30
+ ··· − 12.1843u + 4.85324
a
12
=
−5.80546u
31
+ 1.87713u
30
+ ··· + 17.4915u − 7.94198
1.13311u
31
− 0.505119u
30
+ ··· − 6.97952u + 3.46075
a
6
=
−2.95563u
31
+ 0.498294u
30
+ ··· + 14.0068u − 6.84642
0.416382u
31
− 2.63140u
30
+ ··· + 0.525597u + 0.825939
a
9
=
0.365188u
31
− 0.283276u
30
+ ··· + 5.13311u − 0.505119
2.87713u
31
− 2.76451u
30
+ ··· − 8.94198u + 5.80546
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2531
293
u
31
−
838
293
u
30
+ ··· +
12142
293
u −
5448
293
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
− 16u
31
+ ··· − 19u + 1
c
2
u
32
− 8u
30
+ ··· + u + 1
c
3
, c
4
u
32
− 18u
30
+ ··· − 4u
2
+ 1
c
5
u
32
− 3u
31
+ ··· + 10u
2
+ 1
c
6
u
32
+ 12u
30
+ ··· − u + 1
c
7
u
32
− 8u
30
+ ··· − u + 1
c
8
u
32
+ 3u
31
+ ··· + 10u
2
+ 1
c
9
u
32
− 2u
30
+ ··· − 3u
2
+ 1
c
10
u
32
− 18u
30
+ ··· − 4u
2
+ 1
c
11
u
32
+ 12u
30
+ ··· + u + 1
c
12
u
32
− 9u
29
+ ··· + 8u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
+ 16y
31
+ ··· + 17y + 1
c
2
, c
7
y
32
− 16y
31
+ ··· − 19y + 1
c
3
, c
4
, c
10
y
32
− 36y
31
+ ··· − 8y + 1
c
5
, c
8
y
32
+ 17y
31
+ ··· + 20y + 1
c
6
, c
11
y
32
+ 24y
31
+ ··· + 29y + 1
c
9
y
32
− 4y
31
+ ··· − 6y + 1
c
12
y
32
+ 2y
30
+ ··· + 16y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.823229 + 0.573526I
a = 0.230051 − 1.193660I
b = 1.001010 + 0.496794I
−2.09021 − 5.00508I 0.32029 + 7.36848I
u = −0.823229 − 0.573526I
a = 0.230051 + 1.193660I
b = 1.001010 − 0.496794I
−2.09021 + 5.00508I 0.32029 − 7.36848I
u = −0.905331 + 0.410272I
a = 0.637023 − 0.634846I
b = −1.030370 + 0.490351I
−2.15241 + 1.03931I −0.740501 − 0.627183I
u = −0.905331 − 0.410272I
a = 0.637023 + 0.634846I
b = −1.030370 − 0.490351I
−2.15241 − 1.03931I −0.740501 + 0.627183I
u = 0.886661 + 0.571779I
a = 0.277016 − 0.483095I
b = 0.686227 + 0.474422I
−1.00963 + 0.99283I 2.87836 + 2.32450I
u = 0.886661 − 0.571779I
a = 0.277016 + 0.483095I
b = 0.686227 − 0.474422I
−1.00963 − 0.99283I 2.87836 − 2.32450I
u = 0.960413 + 0.497111I
a = −0.30409 − 1.84527I
b = −0.655739 + 0.511334I
−0.86909 + 3.07016I −1.325078 − 0.355339I
u = 0.960413 − 0.497111I
a = −0.30409 + 1.84527I
b = −0.655739 − 0.511334I
−0.86909 − 3.07016I −1.325078 + 0.355339I
u = 1.226110 + 0.132661I
a = −1.16737 − 1.05240I
b = −0.739922 − 0.151475I
3.21909 + 4.21288I 2.38672 − 4.46762I
u = 1.226110 − 0.132661I
a = −1.16737 + 1.05240I
b = −0.739922 + 0.151475I
3.21909 − 4.21288I 2.38672 + 4.46762I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.250750 + 0.066354I
a = −0.073988 − 0.215665I
b = −1.152920 − 0.317190I
1.41682 − 6.19666I 4.72969 + 6.81735I
u = −1.250750 − 0.066354I
a = −0.073988 + 0.215665I
b = −1.152920 + 0.317190I
1.41682 + 6.19666I 4.72969 − 6.81735I
u = −1.284700 + 0.159063I
a = 0.941075 − 0.385333I
b = 1.054270 + 0.306052I
0.19355 − 3.89178I 2.00000 + 2.50362I
u = −1.284700 − 0.159063I
a = 0.941075 + 0.385333I
b = 1.054270 − 0.306052I
0.19355 + 3.89178I 2.00000 − 2.50362I
u = 1.331670 + 0.231893I
a = −0.422062 + 0.851905I
b = 0.823576 + 0.245895I
1.14054 + 1.60622I −2.50242 + 0.I
u = 1.331670 − 0.231893I
a = −0.422062 − 0.851905I
b = 0.823576 − 0.245895I
1.14054 − 1.60622I −2.50242 + 0.I
u = −0.109844 + 0.592866I
a = −1.00351 + 1.39190I
b = −0.921703 + 0.346676I
−3.36734 + 1.41923I −6.06389 − 0.47143I
u = −0.109844 − 0.592866I
a = −1.00351 − 1.39190I
b = −0.921703 − 0.346676I
−3.36734 − 1.41923I −6.06389 + 0.47143I
u = 0.501084 + 0.247454I
a = −0.46279 + 3.56984I
b = 0.647644 − 0.228760I
0.68591 − 2.77162I 5.96833 − 2.65828I
u = 0.501084 − 0.247454I
a = −0.46279 − 3.56984I
b = 0.647644 + 0.228760I
0.68591 + 2.77162I 5.96833 + 2.65828I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44081 + 0.14512I
a = −0.48645 + 1.82864I
b = 1.06820 − 0.96421I
8.61139 + 5.32683I 7.34287 − 6.36655I
u = 1.44081 − 0.14512I
a = −0.48645 − 1.82864I
b = 1.06820 + 0.96421I
8.61139 − 5.32683I 7.34287 + 6.36655I
u = −0.464219 + 0.029319I
a = −1.04008 + 2.30995I
b = 1.131700 − 0.427011I
−1.36908 + 5.66549I 1.76337 − 5.56166I
u = −0.464219 − 0.029319I
a = −1.04008 − 2.30995I
b = 1.131700 + 0.427011I
−1.36908 − 5.66549I 1.76337 + 5.56166I
u = −1.54390 + 0.08683I
a = −0.437146 + 1.308350I
b = 0.571375 − 1.007390I
9.97917 + 1.85409I 0
u = −1.54390 − 0.08683I
a = −0.437146 − 1.308350I
b = 0.571375 + 1.007390I
9.97917 − 1.85409I 0
u = 1.55180 + 0.09269I
a = 0.49340 − 1.57704I
b = −1.185780 + 0.630177I
5.90343 + 6.49247I 0
u = 1.55180 − 0.09269I
a = 0.49340 + 1.57704I
b = −1.185780 − 0.630177I
5.90343 − 6.49247I 0
u = 0.121239 + 0.343078I
a = −0.823676 + 0.494341I
b = −0.847913 − 0.952252I
3.85757 − 3.46773I −10.92260 − 0.41543I
u = 0.121239 − 0.343078I
a = −0.823676 − 0.494341I
b = −0.847913 + 0.952252I
3.85757 + 3.46773I −10.92260 + 0.41543I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63782 + 0.00403I
a = 0.642615 + 0.909308I
b = −0.449660 − 0.347435I
8.74898 + 2.00355I 0
u = −1.63782 − 0.00403I
a = 0.642615 − 0.909308I
b = −0.449660 + 0.347435I
8.74898 − 2.00355I 0
24
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
32
− 16u
31
+ ··· − 19u + 1)
· (u
125
+ 49u
124
+ ··· + 9905408u + 295936)
c
2
(u
32
− 8u
30
+ ··· + u + 1)(u
125
+ u
124
+ ··· − 1072u − 544)
c
3
, c
4
(u
32
− 18u
30
+ ··· − 4u
2
+ 1)(u
125
+ u
124
+ ··· − 39u − 1)
c
5
(u
32
− 3u
31
+ ··· + 10u
2
+ 1)(u
125
− 2u
124
+ ··· − 10915u + 1369)
c
6
(u
32
+ 12u
30
+ ··· − u + 1)(u
125
+ u
124
+ ··· − 614u − 129)
c
7
(u
32
− 8u
30
+ ··· − u + 1)(u
125
+ u
124
+ ··· − 1072u − 544)
c
8
(u
32
+ 3u
31
+ ··· + 10u
2
+ 1)(u
125
− 2u
124
+ ··· − 10915u + 1369)
c
9
(u
32
− 2u
30
+ ··· − 3u
2
+ 1)
· (u
125
− 7u
124
+ ··· − 597974523u + 137487799)
c
10
(u
32
− 18u
30
+ ··· − 4u
2
+ 1)(u
125
+ u
124
+ ··· − 39u − 1)
c
11
(u
32
+ 12u
30
+ ··· + u + 1)(u
125
+ u
124
+ ··· − 614u − 129)
c
12
(u
32
− 9u
29
+ ··· + 8u
2
+ 1)(u
125
− 5u
124
+ ··· + 2718423u − 646429)
25
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
32
+ 16y
31
+ ··· + 17y + 1)
· (y
125
+ 71y
124
+ ··· − 2183472283648y −87578116096)
c
2
, c
7
(y
32
− 16y
31
+ ··· − 19y + 1)
· (y
125
− 49y
124
+ ··· + 9905408y −295936)
c
3
, c
4
, c
10
(y
32
− 36y
31
+ ··· − 8y + 1)(y
125
− 129y
124
+ ··· + 123y −1)
c
5
, c
8
(y
32
+ 17y
31
+ ··· + 20y + 1)
· (y
125
+ 76y
124
+ ··· − 60105945y −1874161)
c
6
, c
11
(y
32
+ 24y
31
+ ··· + 29y + 1)
· (y
125
+ 67y
124
+ ··· − 1021106y −16641)
c
9
(y
32
− 4y
31
+ ··· − 6y + 1)
· (y
125
− 53y
124
+ ··· + 628976017143595697y −18902894873864401)
c
12
(y
32
+ 2y
30
+ ··· + 16y + 1)
· (y
125
− 25y
124
+ ··· + 4561628210455y −417870452041)
26
