12a
0429
(K12a
0429
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 5 11 1 12 7 4 9
Solving Sequence
9,12
10
1,4
3 2 8 5 11 7 6
c
9
c
12
c
3
c
1
c
8
c
4
c
11
c
7
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.05234 × 10
155
u
99
+ 7.99874 × 10
155
u
98
+ ··· + 1.26559 × 10
156
b − 4.31298 × 10
155
,
− 6.46036 × 10
154
u
99
+ 2.42368 × 10
155
u
98
+ ··· + 4.21862 × 10
155
a − 2.87887 × 10
155
,
u
100
− 4u
99
+ ··· − 2u + 2i
I
u
2
= h9b
3
+ 6b
2
u + 3b
2
− 6b − 2u − 1, a, u
2
+ u + 1i
I
u
3
= hb + 1, 2a + u, u
2
+ 2i
I
v
1
= ha, b − 1, v −1i
* 4 irreducible components of dim
C
= 0, with total 109 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−2.05 × 10
155
u
99
+ 8.00 × 10
155
u
98
+ · · · + 1.27 × 10
156
b − 4.31 ×
10
155
, −6.46 × 10
154
u
99
+ 2.42 × 10
155
u
98
+ · · · + 4.22 × 10
155
a − 2.88 ×
10
155
, u
100
− 4u
99
+ · · · − 2u + 2i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u
2
a
1
=
u
u
a
4
=
0.153139u
99
− 0.574519u
98
+ ··· − 8.03232u + 0.682420
0.162165u
99
− 0.632019u
98
+ ··· − 5.73442u + 0.340789
a
3
=
−0.0302022u
99
+ 0.163017u
98
+ ··· − 2.06770u + 0.417704
0.179404u
99
− 0.709755u
98
+ ··· − 6.10945u + 0.349133
a
2
=
−0.173099u
99
+ 0.676163u
98
+ ··· + 4.89191u + 0.906950
0.0182730u
99
− 0.0469571u
98
+ ··· + 4.00425u − 1.14662
a
8
=
u
2
+ 1
u
2
a
5
=
0.0703189u
99
− 0.177839u
98
+ ··· − 1.91494u + 0.223572
0.202770u
99
− 0.766671u
98
+ ··· − 5.41230u + 0.265518
a
11
=
0.0494285u
99
− 0.0313702u
98
+ ··· + 1.20145u + 0.366829
0.00688276u
99
+ 0.0220776u
98
+ ··· − 2.07197u + 0.512273
a
7
=
0.0425457u
99
− 0.0534478u
98
+ ··· + 3.27342u − 0.145444
−0.00688276u
99
− 0.0220776u
98
+ ··· + 2.07197u − 0.512273
a
6
=
0.138863u
99
− 0.465578u
98
+ ··· − 1.24267u − 0.857682
−0.0184998u
99
+ 0.0344608u
98
+ ··· − 0.833055u + 0.461735
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.15224u
99
− 4.78283u
98
+ ··· − 86.7199u + 10.7919
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
100
+ 34u
99
+ ··· + 925u + 81
c
2
, c
5
u
100
+ 6u
99
+ ··· + 59u + 9
c
3
27(27u
100
− 234u
99
+ ··· − 3357967u − 461099)
c
4
27(27u
100
+ 45u
99
+ ··· − 4549965u + 518603)
c
7
, c
10
u
100
+ 5u
99
+ ··· − 38u − 3
c
8
, c
9
, c
12
u
100
+ 4u
99
+ ··· + 2u + 2
c
11
u
100
− 4u
99
+ ··· − 12960u − 5184
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
100
+ 70y
99
+ ··· − 377077y + 6561
c
2
, c
5
y
100
− 34y
99
+ ··· − 925y + 81
c
3
729
· (729y
100
+ 11502y
99
+ ··· − 1559280610721y + 212612287801)
c
4
729
· (729y
100
− 27135y
99
+ ··· − 3345262023807y + 268949071609)
c
7
, c
10
y
100
− 53y
99
+ ··· − 658y + 9
c
8
, c
9
, c
12
y
100
+ 94y
99
+ ··· − 60y + 4
c
11
y
100
+ 32y
99
+ ··· + 414305280y + 26873856
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679869 + 0.748107I
a = −0.295432 − 1.043560I
b = −0.528057 − 0.396540I
0.57702 − 2.41824I 0
u = 0.679869 − 0.748107I
a = −0.295432 + 1.043560I
b = −0.528057 + 0.396540I
0.57702 + 2.41824I 0
u = −0.936181 + 0.398524I
a = −0.806021 + 0.540723I
b = −0.497698 − 0.087674I
3.87531 − 7.09723I 0
u = −0.936181 − 0.398524I
a = −0.806021 − 0.540723I
b = −0.497698 + 0.087674I
3.87531 + 7.09723I 0
u = −0.344981 + 0.919122I
a = −0.224263 − 0.488787I
b = −0.173178 − 0.412785I
−0.77026 − 2.23336I 0
u = −0.344981 − 0.919122I
a = −0.224263 + 0.488787I
b = −0.173178 + 0.412785I
−0.77026 + 2.23336I 0
u = 0.849871 + 0.454924I
a = 1.30719 + 0.64935I
b = 0.877707 − 0.222614I
0.55952 + 13.49860I 0
u = 0.849871 − 0.454924I
a = 1.30719 − 0.64935I
b = 0.877707 + 0.222614I
0.55952 − 13.49860I 0
u = −0.898112 + 0.334651I
a = 0.868301 − 0.554620I
b = 0.482624 + 0.101398I
4.50393 − 1.41421I 0
u = −0.898112 − 0.334651I
a = 0.868301 + 0.554620I
b = 0.482624 − 0.101398I
4.50393 + 1.41421I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.732409 + 0.617249I
a = −0.681387 + 0.294463I
b = −0.437220 − 0.022316I
−1.18132 − 2.64358I 0
u = −0.732409 − 0.617249I
a = −0.681387 − 0.294463I
b = −0.437220 + 0.022316I
−1.18132 + 2.64358I 0
u = 0.758120 + 0.731071I
a = 0.266524 + 1.044920I
b = 0.488342 + 0.372478I
−0.23831 − 8.08349I 0
u = 0.758120 − 0.731071I
a = 0.266524 − 1.044920I
b = 0.488342 − 0.372478I
−0.23831 + 8.08349I 0
u = 0.820796 + 0.415357I
a = −1.33445 − 0.70691I
b = −0.838028 + 0.244297I
1.56962 + 7.53478I 0
u = 0.820796 − 0.415357I
a = −1.33445 + 0.70691I
b = −0.838028 − 0.244297I
1.56962 − 7.53478I 0
u = 0.739811 + 0.488405I
a = 0.236103 + 1.139040I
b = 0.383295 + 0.485386I
−5.36950 − 2.86567I 0
u = 0.739811 − 0.488405I
a = 0.236103 − 1.139040I
b = 0.383295 − 0.485386I
−5.36950 + 2.86567I 0
u = 0.685574 + 0.521881I
a = 1.54529 + 0.54023I
b = 0.773480 − 0.091899I
−5.53789 + 7.57635I 0
u = 0.685574 − 0.521881I
a = 1.54529 − 0.54023I
b = 0.773480 + 0.091899I
−5.53789 − 7.57635I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.773853 + 0.126658I
a = 0.073723 + 1.239840I
b = 0.112212 + 0.588993I
−2.85478 + 2.28442I 0
u = 0.773853 − 0.126658I
a = 0.073723 − 1.239840I
b = 0.112212 − 0.588993I
−2.85478 − 2.28442I 0
u = −0.742950 + 0.971442I
a = −0.379885 + 0.450207I
b = −0.443297 + 0.208112I
2.25943 + 1.26483I 0
u = −0.742950 − 0.971442I
a = −0.379885 − 0.450207I
b = −0.443297 − 0.208112I
2.25943 − 1.26483I 0
u = 0.021499 + 1.227650I
a = −0.999611 − 0.389930I
b = −2.86921 − 0.22184I
0.82547 − 1.32524I 0
u = 0.021499 − 1.227650I
a = −0.999611 + 0.389930I
b = −2.86921 + 0.22184I
0.82547 + 1.32524I 0
u = −0.682650 + 1.028010I
a = 0.314081 − 0.478465I
b = 0.411579 − 0.285935I
2.53530 − 4.11578I 0
u = −0.682650 − 1.028010I
a = 0.314081 + 0.478465I
b = 0.411579 + 0.285935I
2.53530 + 4.11578I 0
u = 0.089185 + 1.254450I
a = 1.090420 + 0.281507I
b = 3.13638 + 0.17745I
0.54484 + 5.05920I 0
u = 0.089185 − 1.254450I
a = 1.090420 − 0.281507I
b = 3.13638 − 0.17745I
0.54484 − 5.05920I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.129409 + 1.287930I
a = −0.441936 − 0.858037I
b = −1.209260 − 0.582559I
0.097636 − 0.577860I 0
u = 0.129409 − 1.287930I
a = −0.441936 + 0.858037I
b = −1.209260 + 0.582559I
0.097636 + 0.577860I 0
u = 0.591401 + 0.372296I
a = −1.78322 − 0.87172I
b = −0.608394 + 0.173490I
−1.51260 + 4.59124I −1.18190 − 7.08838I
u = 0.591401 − 0.372296I
a = −1.78322 + 0.87172I
b = −0.608394 − 0.173490I
−1.51260 − 4.59124I −1.18190 + 7.08838I
u = −0.188206 + 1.312440I
a = −0.000149 − 1.118010I
b = 0.03449 − 1.53600I
−1.31735 − 3.54814I 0
u = −0.188206 − 1.312440I
a = −0.000149 + 1.118010I
b = 0.03449 + 1.53600I
−1.31735 + 3.54814I 0
u = −0.049713 + 1.345270I
a = 0.51133 + 1.49541I
b = 1.17296 + 2.41695I
−7.10395 − 1.14182I 0
u = −0.049713 − 1.345270I
a = 0.51133 − 1.49541I
b = 1.17296 − 2.41695I
−7.10395 + 1.14182I 0
u = 0.136745 + 1.361250I
a = 0.439945 + 0.800424I
b = 1.351600 + 0.407360I
−0.81482 + 5.24891I 0
u = 0.136745 − 1.361250I
a = 0.439945 − 0.800424I
b = 1.351600 − 0.407360I
−0.81482 − 5.24891I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.277514 + 1.363830I
a = 0.760070 − 0.073241I
b = 1.46420 + 0.87101I
−6.81470 + 1.22350I 0
u = 0.277514 − 1.363830I
a = 0.760070 + 0.073241I
b = 1.46420 − 0.87101I
−6.81470 − 1.22350I 0
u = −0.089485 + 1.389530I
a = 0.090696 − 0.485921I
b = −0.94839 + 2.04503I
−4.19619 + 2.34737I 0
u = −0.089485 − 1.389530I
a = 0.090696 + 0.485921I
b = −0.94839 − 2.04503I
−4.19619 − 2.34737I 0
u = −0.548947 + 0.259031I
a = −1.30165 − 1.81150I
b = −0.262516 + 0.230241I
2.18117 − 6.47618I −0.36986 + 8.71363I
u = −0.548947 − 0.259031I
a = −1.30165 + 1.81150I
b = −0.262516 − 0.230241I
2.18117 + 6.47618I −0.36986 − 8.71363I
u = −0.583366 + 0.156368I
a = 1.51729 + 1.42250I
b = 0.302065 − 0.186011I
3.23926 − 0.72911I 2.75290 + 2.73531I
u = −0.583366 − 0.156368I
a = 1.51729 − 1.42250I
b = 0.302065 + 0.186011I
3.23926 + 0.72911I 2.75290 − 2.73531I
u = −0.188664 + 1.389350I
a = −0.177107 + 1.219500I
b = −0.42888 + 1.77705I
−3.06032 − 9.15441I 0
u = −0.188664 − 1.389350I
a = −0.177107 − 1.219500I
b = −0.42888 − 1.77705I
−3.06032 + 9.15441I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.526193 + 0.244659I
a = 1.331340 − 0.219705I
b = 0.414062 + 0.073402I
1.090210 − 0.801985I 5.31856 + 2.50411I
u = −0.526193 − 0.244659I
a = 1.331340 + 0.219705I
b = 0.414062 − 0.073402I
1.090210 + 0.801985I 5.31856 − 2.50411I
u = 0.406757 + 0.405711I
a = −0.429280 − 1.280950I
b = −0.568191 − 0.723482I
−1.89883 − 1.20494I −2.45244 − 0.57004I
u = 0.406757 − 0.405711I
a = −0.429280 + 1.280950I
b = −0.568191 + 0.723482I
−1.89883 + 1.20494I −2.45244 + 0.57004I
u = −0.17361 + 1.42113I
a = −0.773205 − 0.392754I
b = −2.26968 − 0.26907I
−4.31361 − 3.27424I 0
u = −0.17361 − 1.42113I
a = −0.773205 + 0.392754I
b = −2.26968 + 0.26907I
−4.31361 + 3.27424I 0
u = −0.08217 + 1.43290I
a = 0.012161 + 0.479575I
b = 1.47788 − 1.81226I
−4.33040 − 2.95362I 0
u = −0.08217 − 1.43290I
a = 0.012161 − 0.479575I
b = 1.47788 + 1.81226I
−4.33040 + 2.95362I 0
u = 0.369359 + 0.423465I
a = 2.63371 + 0.41174I
b = 0.439230 + 0.012251I
−4.52529 + 0.64236I −8.88416 − 5.33505I
u = 0.369359 − 0.423465I
a = 2.63371 − 0.41174I
b = 0.439230 − 0.012251I
−4.52529 − 0.64236I −8.88416 + 5.33505I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04013 + 1.43787I
a = 0.368603 + 0.074688I
b = 3.17675 + 1.32808I
−7.42832 + 0.17125I 0
u = 0.04013 − 1.43787I
a = 0.368603 − 0.074688I
b = 3.17675 − 1.32808I
−7.42832 − 0.17125I 0
u = 0.34785 + 1.41208I
a = −0.798393 + 0.009874I
b = −1.51058 − 0.70211I
−7.81342 + 6.46103I 0
u = 0.34785 − 1.41208I
a = −0.798393 − 0.009874I
b = −1.51058 + 0.70211I
−7.81342 − 6.46103I 0
u = 0.15166 + 1.45394I
a = −1.341240 + 0.389661I
b = −3.44448 + 0.51105I
−10.59050 + 2.67643I 0
u = 0.15166 − 1.45394I
a = −1.341240 − 0.389661I
b = −3.44448 − 0.51105I
−10.59050 − 2.67643I 0
u = 0.21401 + 1.44731I
a = 1.165350 − 0.332979I
b = 3.24423 − 0.33629I
−7.38327 + 7.53531I 0
u = 0.21401 − 1.44731I
a = 1.165350 + 0.332979I
b = 3.24423 + 0.33629I
−7.38327 − 7.53531I 0
u = −0.04327 + 1.46569I
a = 0.612952 + 0.425075I
b = 2.22983 + 0.27823I
−7.08799 + 0.13600I 0
u = −0.04327 − 1.46569I
a = 0.612952 − 0.425075I
b = 2.22983 − 0.27823I
−7.08799 − 0.13600I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514435 + 0.029790I
a = −0.62541 + 1.82321I
b = −0.248771 − 0.638119I
4.13023 − 2.87256I 2.80596 + 5.41221I
u = 0.514435 − 0.029790I
a = −0.62541 − 1.82321I
b = −0.248771 + 0.638119I
4.13023 + 2.87256I 2.80596 − 5.41221I
u = −0.189126 + 0.472524I
a = −1.170830 − 0.682908I
b = −1.90042 − 0.09678I
1.62783 − 1.86935I −4.71859 + 9.09029I
u = −0.189126 − 0.472524I
a = −1.170830 + 0.682908I
b = −1.90042 + 0.09678I
1.62783 + 1.86935I −4.71859 − 9.09029I
u = −0.33202 + 1.46447I
a = −0.812027 − 0.326676I
b = −2.22023 − 0.19560I
−1.27736 − 5.80994I 0
u = −0.33202 − 1.46447I
a = −0.812027 + 0.326676I
b = −2.22023 + 0.19560I
−1.27736 + 5.80994I 0
u = −0.282682 + 0.397129I
a = 1.30656 + 0.57839I
b = 2.05135 + 0.16180I
1.30774 + 3.73013I −2.74021 + 5.37610I
u = −0.282682 − 0.397129I
a = 1.30656 − 0.57839I
b = 2.05135 − 0.16180I
1.30774 − 3.73013I −2.74021 − 5.37610I
u = 0.30445 + 1.48923I
a = 0.995764 − 0.381668I
b = 3.00560 − 0.23025I
−4.57444 + 11.61720I 0
u = 0.30445 − 1.48923I
a = 0.995764 + 0.381668I
b = 3.00560 + 0.23025I
−4.57444 − 11.61720I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.464839 + 0.113252I
a = 0.27220 − 1.70926I
b = 0.123712 + 0.765459I
3.88141 + 3.13960I 1.64371 − 0.37863I
u = 0.464839 − 0.113252I
a = 0.27220 + 1.70926I
b = 0.123712 − 0.765459I
3.88141 − 3.13960I 1.64371 + 0.37863I
u = 0.23746 + 1.50791I
a = −1.085810 + 0.439549I
b = −3.05401 + 0.40388I
−12.1325 + 10.9448I 0
u = 0.23746 − 1.50791I
a = −1.085810 − 0.439549I
b = −3.05401 − 0.40388I
−12.1325 − 10.9448I 0
u = 0.08480 + 1.53234I
a = 0.596803 + 0.147459I
b = 2.21447 + 0.68075I
−7.40992 − 0.00114I 0
u = 0.08480 − 1.53234I
a = 0.596803 − 0.147459I
b = 2.21447 − 0.68075I
−7.40992 + 0.00114I 0
u = −0.22585 + 1.52169I
a = 0.765917 + 0.329597I
b = 2.21047 + 0.25037I
−8.11266 − 6.00339I 0
u = −0.22585 − 1.52169I
a = 0.765917 − 0.329597I
b = 2.21047 − 0.25037I
−8.11266 + 6.00339I 0
u = −0.34530 + 1.50016I
a = 0.808150 + 0.315217I
b = 2.20445 + 0.19663I
−2.24324 − 11.70050I 0
u = −0.34530 − 1.50016I
a = 0.808150 − 0.315217I
b = 2.20445 − 0.19663I
−2.24324 + 11.70050I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.31293 + 1.51066I
a = −0.979232 + 0.406327I
b = −2.95400 + 0.23722I
−5.7917 + 17.7278I 0
u = 0.31293 − 1.51066I
a = −0.979232 − 0.406327I
b = −2.95400 − 0.23722I
−5.7917 − 17.7278I 0
u = 0.24997 + 1.52779I
a = −0.716417 − 0.060866I
b = −1.78953 − 0.69898I
−11.99200 + 0.79354I 0
u = 0.24997 − 1.52779I
a = −0.716417 + 0.060866I
b = −1.78953 + 0.69898I
−11.99200 − 0.79354I 0
u = 0.13806 + 1.60905I
a = −0.679385 − 0.144169I
b = −2.01284 − 0.57418I
−8.37514 − 4.86967I 0
u = 0.13806 − 1.60905I
a = −0.679385 + 0.144169I
b = −2.01284 + 0.57418I
−8.37514 + 4.86967I 0
u = −0.313657
a = −5.14324
b = −0.161887
−2.86791 11.2900
u = 0.054224 + 0.273579I
a = −1.10118 − 1.39810I
b = −0.515038 + 0.369932I
−1.295400 + 0.319885I −8.06448 + 0.00737I
u = 0.054224 − 0.273579I
a = −1.10118 + 1.39810I
b = −0.515038 − 0.369932I
−1.295400 − 0.319885I −8.06448 − 0.00737I
u = −0.203756
a = 2.23736
b = 2.72642
−3.01291 42.4150
14
II. I
u
2
= h9b
3
+ 6b
2
u + 3b
2
− 6b − 2u − 1, a, u
2
+ u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u + 1
a
1
=
u
u
a
4
=
0
b
a
3
=
−b
−bu
a
2
=
−2b
2
u − b
2
+ u
b
2
u + 2b
2
+ u
a
8
=
−u
−u − 1
a
5
=
bu + b
2b
a
11
=
0
u
a
7
=
−u
−u
a
6
=
b
2
u − b
2
− u
4b
2
u + 2b
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 17b
2
u + 30b
2
+ 11bu + b − 5u − 15
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
27(27u
6
− 27u
4
+ 6u
2
+ 1)
c
4
27(27u
6
− 27u
5
+ 27u
4
− 18u
3
+ 15u
2
− 6u + 1)
c
5
(u
3
− u
2
+ 1)
2
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
12
(u
2
− u + 1)
3
c
8
, c
9
, c
10
(u
2
+ u + 1)
3
c
11
u
6
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
(y
3
− y
2
+ 2y −1)
2
c
3
729(27y
3
− 27y
2
+ 6y + 1)
2
c
4
729(729y
6
+ 729y
5
+ 567y
4
+ 216y
3
+ 63y
2
− 6y + 1)
c
7
, c
8
, c
9
c
10
, c
12
(y
2
+ y + 1)
3
c
11
y
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = 0.754678 − 0.124176I
3.02413 − 4.85801I −0.04017 + 7.54626I
u = −0.500000 + 0.866025I
a = 0
b = −0.754678 − 0.124176I
3.02413 + 0.79824I 1.23319 + 1.22705I
u = −0.500000 + 0.866025I
a = 0
b = − 0.328997I
−1.11345 − 2.02988I −11.69302 − 4.44318I
u = −0.500000 − 0.866025I
a = 0
b = 0.754678 + 0.124176I
3.02413 + 4.85801I −0.04017 − 7.54626I
u = −0.500000 − 0.866025I
a = 0
b = −0.754678 + 0.124176I
3.02413 − 0.79824I 1.23319 − 1.22705I
u = −0.500000 − 0.866025I
a = 0
b = 0.328997I
−1.11345 + 2.02988I −11.69302 + 4.44318I
18
III. I
u
3
= hb + 1, 2a + u, u
2
+ 2i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
2
a
1
=
u
u
a
4
=
−
1
2
u
−1
a
3
=
−
3
2
u + 1
−2u + 1
a
2
=
−
1
2
u + 1
−u + 1
a
8
=
−1
−2
a
5
=
−
3
2
u + 1
−2u + 1
a
11
=
1
2
u
u + 1
a
7
=
1
2
u − 1
u − 1
a
6
=
−u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
(u − 1)
2
c
3
u
2
− 2u + 3
c
4
u
2
+ 2u + 3
c
5
, c
6
, c
7
c
11
(u + 1)
2
c
8
, c
9
, c
12
u
2
+ 2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
(y −1)
2
c
3
, c
4
y
2
+ 2y + 9
c
8
, c
9
, c
12
(y + 2)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = − 0.707107I
b = −1.00000
−8.22467 −12.0000
u = − 1.414210I
a = 0.707107I
b = −1.00000
−8.22467 −12.0000
22
IV. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
1
0
a
10
=
1
0
a
1
=
1
0
a
4
=
0
1
a
3
=
−1
1
a
2
=
0
1
a
8
=
1
0
a
5
=
−1
1
a
11
=
1
1
a
7
=
0
−1
a
6
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
u − 1
c
3
, c
4
, c
5
c
6
, c
10
u + 1
c
8
, c
9
, c
12
u
24
(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
7
, c
10
, c
11
y −1
c
8
, c
9
, c
12
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
3
− u
2
+ 2u − 1)
2
(u
100
+ 34u
99
+ ··· + 925u + 81)
c
2
((u − 1)
3
)(u
3
+ u
2
− 1)
2
(u
100
+ 6u
99
+ ··· + 59u + 9)
c
3
729(u + 1)(u
2
− 2u + 3)(27u
6
− 27u
4
+ 6u
2
+ 1)
· (27u
100
− 234u
99
+ ··· − 3357967u − 461099)
c
4
729(u + 1)(u
2
+ 2u + 3)(27u
6
− 27u
5
+ ··· − 6u + 1)
· (27u
100
+ 45u
99
+ ··· − 4549965u + 518603)
c
5
((u + 1)
3
)(u
3
− u
2
+ 1)
2
(u
100
+ 6u
99
+ ··· + 59u + 9)
c
6
((u + 1)
3
)(u
3
+ u
2
+ 2u + 1)
2
(u
100
+ 34u
99
+ ··· + 925u + 81)
c
7
(u − 1)(u + 1)
2
(u
2
− u + 1)
3
(u
100
+ 5u
99
+ ··· − 38u − 3)
c
8
, c
9
u(u
2
+ 2)(u
2
+ u + 1)
3
(u
100
+ 4u
99
+ ··· + 2u + 2)
c
10
((u − 1)
2
)(u + 1)(u
2
+ u + 1)
3
(u
100
+ 5u
99
+ ··· − 38u − 3)
c
11
u
6
(u − 1)(u + 1)
2
(u
100
− 4u
99
+ ··· − 12960u − 5184)
c
12
u(u
2
+ 2)(u
2
− u + 1)
3
(u
100
+ 4u
99
+ ··· + 2u + 2)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y −1)
3
)(y
3
+ 3y
2
+ 2y −1)
2
(y
100
+ 70y
99
+ ··· − 377077y + 6561)
c
2
, c
5
((y −1)
3
)(y
3
− y
2
+ 2y −1)
2
(y
100
− 34y
99
+ ··· − 925y + 81)
c
3
531441(y −1)(y
2
+ 2y + 9)(27y
3
− 27y
2
+ 6y + 1)
2
· (729y
100
+ 11502y
99
+ ··· − 1559280610721y + 212612287801)
c
4
531441(y −1)(y
2
+ 2y + 9)
· (729y
6
+ 729y
5
+ 567y
4
+ 216y
3
+ 63y
2
− 6y + 1)
· (729y
100
− 27135y
99
+ ··· − 3345262023807y + 268949071609)
c
7
, c
10
((y −1)
3
)(y
2
+ y + 1)
3
(y
100
− 53y
99
+ ··· − 658y + 9)
c
8
, c
9
, c
12
y(y + 2)
2
(y
2
+ y + 1)
3
(y
100
+ 94y
99
+ ··· − 60y + 4)
c
11
y
6
(y −1)
3
(y
100
+ 32y
99
+ ··· + 4.14305 × 10
8
y + 2.68739 × 10
7
)
28
