12a
0271
(K12a
0271
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 11 2 9 4 12 1 5 10
Solving Sequence
9,12
10 1
4,11
8 3 2 7 5 6
c
9
c
12
c
10
c
8
c
3
c
1
c
7
c
4
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.23243 × 10
129
u
108
+ 1.55838 × 10
130
u
107
+ ··· + 3.15285 × 10
126
b + 9.10169 × 10
128
,
6.10588 × 10
129
u
108
+ 7.74537 × 10
130
u
107
+ ··· + 6.30570 × 10
126
a + 4.64339 × 10
129
,
u
109
+ 14u
108
+ ··· + 7u + 1i
I
u
2
= h23a
8
+ 230a
7
+ 849a
6
+ 1550a
5
+ 2020a
4
+ 2255a
3
+ 1022a
2
+ 145b + 663a − 205,
a
9
+ 7a
8
+ 17a
7
+ 26a
6
+ 42a
5
+ 30a
4
+ 34a
3
+ 9a
2
+ 8a − 1, u − 1i
I
u
3
= h−134a
3
u + 33a
3
− 58a
2
u − 279a
2
− 52au + 1310b − 476a + 52u − 834,
a
4
+ 2a
3
u + 4a
3
+ 6a
2
u + 13a
2
+ 14au + 22a + 30u + 52, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 126 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
= h1.23 × 10
129
u
108
+ 1.56 × 10
130
u
107
+ · · · + 3.15 × 10
126
b + 9.10 ×
10
128
, 6.11 × 10
129
u
108
+ 7.75 × 10
130
u
107
+ · · · + 6.31 × 10
126
a + 4.64 ×
10
129
, u
109
+ 14u
108
+ · · · + 7u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−968.311u
108
− 12283.1u
107
+ ··· − 4584.18u − 736.380
−390.893u
108
− 4942.78u
107
+ ··· − 1804.94u − 288.681
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
−929.018u
108
− 11751.3u
107
+ ··· − 4271.39u − 682.333
−735.325u
108
− 9383.18u
107
+ ··· − 3627.78u − 583.409
a
3
=
−244.974u
108
− 3068.45u
107
+ ··· − 1003.44u − 164.812
679.242u
108
+ 8687.50u
107
+ ··· + 3444.28u + 556.251
a
2
=
328.541u
108
+ 4085.82u
107
+ ··· + 1244.91u + 200.212
29.4565u
108
+ 399.793u
107
+ ··· + 227.612u + 39.0444
a
7
=
−193.693u
108
− 2368.15u
107
+ ··· − 643.610u − 98.9239
−735.325u
108
− 9383.18u
107
+ ··· − 3627.78u − 583.409
a
5
=
763.605u
108
+ 9680.35u
107
+ ··· + 3621.10u + 578.034
−1957.98u
108
− 24889.9u
107
+ ··· − 9485.41u − 1525.65
a
6
=
−13.8716u
108
− 155.907u
107
+ ··· + 8.72015u + 0.253671
−1586.38u
108
− 20163.0u
107
+ ··· − 7667.22u − 1232.67
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1327.30u
108
+ 16843.2u
107
+ ··· + 6329.93u + 1019.14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
109
+ 56u
108
+ ··· − 5688u − 1296
c
2
, c
6
u
109
− 2u
108
+ ··· + 72u − 36
c
3
, c
8
u
109
− 2u
108
+ ··· + 15u − 9
c
4
u
109
− 6u
108
+ ··· + 1068687u − 322299
c
5
, c
11
u
109
+ u
108
+ ··· − 6144u − 512
c
7
u
109
− 52u
108
+ ··· − 189u − 81
c
9
, c
10
, c
12
u
109
− 14u
108
+ ··· + 7u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
109
+ 4y
108
+ ··· + 86720544y −1679616
c
2
, c
6
y
109
+ 56y
108
+ ··· − 5688y −1296
c
3
, c
8
y
109
− 52y
108
+ ··· − 189y −81
c
4
y
109
+ 20y
108
+ ··· − 3429890229501y −103876645401
c
5
, c
11
y
109
+ 69y
108
+ ··· + 11272192y −262144
c
7
y
109
+ 16y
108
+ ··· + 363123y −6561
c
9
, c
10
, c
12
y
109
− 108y
108
+ ··· + 63y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.016630 + 0.004269I
a = 8.13325 + 5.59186I
b = 0.837596 − 0.489489I
−3.33980 − 2.03615I 0
u = 1.016630 − 0.004269I
a = 8.13325 − 5.59186I
b = 0.837596 + 0.489489I
−3.33980 + 2.03615I 0
u = 0.404790 + 0.937368I
a = −0.90874 − 1.47581I
b = 1.124360 − 0.589303I
−0.76763 − 12.89190I 0
u = 0.404790 − 0.937368I
a = −0.90874 + 1.47581I
b = 1.124360 + 0.589303I
−0.76763 + 12.89190I 0
u = 0.411108 + 0.884965I
a = 0.521196 + 0.355803I
b = 0.369946 + 0.793260I
−3.00544 − 7.70749I 0
u = 0.411108 − 0.884965I
a = 0.521196 − 0.355803I
b = 0.369946 − 0.793260I
−3.00544 + 7.70749I 0
u = 1.016580 + 0.274813I
a = 0.484768 + 0.857560I
b = 0.012958 + 0.405942I
−1.93065 − 0.92430I 0
u = 1.016580 − 0.274813I
a = 0.484768 − 0.857560I
b = 0.012958 − 0.405942I
−1.93065 + 0.92430I 0
u = 0.786470 + 0.711560I
a = −0.139650 − 0.997227I
b = 0.385614 − 0.697857I
−4.16608 + 2.27907I 0
u = 0.786470 − 0.711560I
a = −0.139650 + 0.997227I
b = 0.385614 + 0.697857I
−4.16608 − 2.27907I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.912194 + 0.564468I
a = 0.124511 − 0.334015I
b = −1.052250 − 0.499335I
0.05579 + 2.65712I 0
u = 0.912194 − 0.564468I
a = 0.124511 + 0.334015I
b = −1.052250 + 0.499335I
0.05579 − 2.65712I 0
u = 0.320133 + 0.851289I
a = 1.19396 + 1.23612I
b = −1.114450 + 0.552127I
1.84711 − 7.63939I 0
u = 0.320133 − 0.851289I
a = 1.19396 − 1.23612I
b = −1.114450 − 0.552127I
1.84711 + 7.63939I 0
u = 0.301149 + 0.854421I
a = 1.006620 + 0.099668I
b = −1.140280 − 0.181677I
1.90970 − 5.11227I 0
u = 0.301149 − 0.854421I
a = 1.006620 − 0.099668I
b = −1.140280 + 0.181677I
1.90970 + 5.11227I 0
u = 0.943762 + 0.586540I
a = 0.532799 + 1.247840I
b = −1.044820 + 0.255463I
−0.0247817 + 0.0796703I 0
u = 0.943762 − 0.586540I
a = 0.532799 − 1.247840I
b = −1.044820 − 0.255463I
−0.0247817 − 0.0796703I 0
u = 0.849998 + 0.764802I
a = −0.009634 + 0.635203I
b = 1.093690 + 0.562163I
−2.10039 + 7.13248I 0
u = 0.849998 − 0.764802I
a = −0.009634 − 0.635203I
b = 1.093690 − 0.562163I
−2.10039 − 7.13248I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.567153 + 0.640929I
a = 1.006030 − 0.275954I
b = 0.493383 + 0.632986I
−4.68801 + 0.41176I 0
u = 0.567153 − 0.640929I
a = 1.006030 + 0.275954I
b = 0.493383 − 0.632986I
−4.68801 − 0.41176I 0
u = 0.454957 + 0.721916I
a = 0.137567 − 0.733744I
b = 0.611030 − 0.716852I
−4.29347 − 5.01697I 0
u = 0.454957 − 0.721916I
a = 0.137567 + 0.733744I
b = 0.611030 + 0.716852I
−4.29347 + 5.01697I 0
u = 0.345213 + 0.752658I
a = −0.349887 − 0.087687I
b = −0.320749 − 0.709497I
−0.44649 − 2.81276I 0
u = 0.345213 − 0.752658I
a = −0.349887 + 0.087687I
b = −0.320749 + 0.709497I
−0.44649 + 2.81276I 0
u = 0.623603 + 0.494487I
a = 0.307659 + 0.731604I
b = −0.554457 + 0.508718I
−1.54674 − 1.43755I 0
u = 0.623603 − 0.494487I
a = 0.307659 − 0.731604I
b = −0.554457 − 0.508718I
−1.54674 + 1.43755I 0
u = 0.428746 + 0.651403I
a = −2.05459 − 1.82233I
b = 1.042280 − 0.549995I
−3.06677 − 4.24362I 0
u = 0.428746 − 0.651403I
a = −2.05459 + 1.82233I
b = 1.042280 + 0.549995I
−3.06677 + 4.24362I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.142100 + 0.435495I
a = −0.41213 − 1.72843I
b = 1.064570 − 0.391803I
0.71816 − 4.11005I 0
u = 1.142100 − 0.435495I
a = −0.41213 + 1.72843I
b = 1.064570 + 0.391803I
0.71816 + 4.11005I 0
u = 0.463780 + 0.617736I
a = −0.527069 + 1.057310I
b = 0.976057 + 0.625465I
−3.21393 + 0.11148I 0
u = 0.463780 − 0.617736I
a = −0.527069 − 1.057310I
b = 0.976057 − 0.625465I
−3.21393 − 0.11148I 0
u = −1.249550 + 0.003143I
a = −0.283939 + 0.688479I
b = 1.234130 + 0.398669I
1.78465 + 1.35351I 0
u = −1.249550 − 0.003143I
a = −0.283939 − 0.688479I
b = 1.234130 − 0.398669I
1.78465 − 1.35351I 0
u = 1.206400 + 0.327884I
a = −0.389297 + 0.143393I
b = −1.037800 − 0.324158I
0.50722 + 1.42907I 0
u = 1.206400 − 0.327884I
a = −0.389297 − 0.143393I
b = −1.037800 + 0.324158I
0.50722 − 1.42907I 0
u = 0.148361 + 0.734114I
a = −1.44030 + 0.28159I
b = 1.111060 + 0.271317I
3.73455 − 0.07956I 0
u = 0.148361 − 0.734114I
a = −1.44030 − 0.28159I
b = 1.111060 − 0.271317I
3.73455 + 0.07956I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.251330 + 0.110567I
a = 0.310557 − 1.114140I
b = −1.219260 − 0.473681I
1.25854 + 7.78889I 0
u = −1.251330 − 0.110567I
a = 0.310557 + 1.114140I
b = −1.219260 + 0.473681I
1.25854 − 7.78889I 0
u = −1.295240 + 0.056218I
a = −0.164026 + 0.829289I
b = −0.067094 + 0.861154I
−2.25141 + 3.00990I 0
u = −1.295240 − 0.056218I
a = −0.164026 − 0.829289I
b = −0.067094 − 0.861154I
−2.25141 − 3.00990I 0
u = −0.082194 + 0.675232I
a = 0.899320 − 0.233825I
b = −1.134390 + 0.407127I
4.49085 − 5.11092I 0
u = −0.082194 − 0.675232I
a = 0.899320 + 0.233825I
b = −1.134390 − 0.407127I
4.49085 + 5.11092I 0
u = 1.325510 + 0.015098I
a = −0.68029 + 2.85029I
b = −1.011680 + 0.589449I
−5.19776 − 2.18585I 0
u = 1.325510 − 0.015098I
a = −0.68029 − 2.85029I
b = −1.011680 − 0.589449I
−5.19776 + 2.18585I 0
u = 1.329390 + 0.112204I
a = 1.13368 + 1.20869I
b = 0.402859 + 0.628401I
−3.01364 − 0.75193I 0
u = 1.329390 − 0.112204I
a = 1.13368 − 1.20869I
b = 0.402859 − 0.628401I
−3.01364 + 0.75193I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.373420 + 0.042297I
a = −1.41682 + 1.56257I
b = −0.553024 + 0.689823I
−6.55401 − 2.75061I 0
u = 1.373420 − 0.042297I
a = −1.41682 − 1.56257I
b = −0.553024 − 0.689823I
−6.55401 + 2.75061I 0
u = −0.460518 + 0.401129I
a = 0.33891 − 2.30443I
b = −1.140320 − 0.523300I
2.81375 + 7.97265I 6.75785 − 7.76688I
u = −0.460518 − 0.401129I
a = 0.33891 + 2.30443I
b = −1.140320 + 0.523300I
2.81375 − 7.97265I 6.75785 + 7.76688I
u = 1.383490 + 0.198811I
a = 0.27751 − 2.31980I
b = 1.078330 − 0.543261I
−1.04938 − 5.38156I 0
u = 1.383490 − 0.198811I
a = 0.27751 + 2.31980I
b = 1.078330 + 0.543261I
−1.04938 + 5.38156I 0
u = 1.380860 + 0.221289I
a = 0.651853 − 0.050411I
b = 1.079270 + 0.187980I
−1.05843 − 2.88175I 0
u = 1.380860 − 0.221289I
a = 0.651853 + 0.050411I
b = 1.079270 − 0.187980I
−1.05843 + 2.88175I 0
u = −0.270752 + 0.530344I
a = −0.257115 + 0.691543I
b = 1.134540 − 0.317097I
4.20308 + 0.05931I 8.59381 + 0.I
u = −0.270752 − 0.530344I
a = −0.257115 − 0.691543I
b = 1.134540 + 0.317097I
4.20308 − 0.05931I 8.59381 + 0.I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.380480 + 0.266205I
a = −0.080388 + 0.259982I
b = 1.200820 − 0.191115I
−1.15287 + 3.63290I 0
u = −1.380480 − 0.266205I
a = −0.080388 − 0.259982I
b = 1.200820 + 0.191115I
−1.15287 − 3.63290I 0
u = −0.267350 + 0.518380I
a = −1.09999 + 2.03371I
b = 1.126850 + 0.452815I
4.19677 + 2.70080I 8.69742 − 1.85620I
u = −0.267350 − 0.518380I
a = −1.09999 − 2.03371I
b = 1.126850 − 0.452815I
4.19677 − 2.70080I 8.69742 + 1.85620I
u = −1.42886 + 0.12570I
a = 0.624904 − 0.307615I
b = −1.108450 + 0.263345I
−7.14836 − 0.04349I 0
u = −1.42886 − 0.12570I
a = 0.624904 + 0.307615I
b = −1.108450 − 0.263345I
−7.14836 + 0.04349I 0
u = −1.45766 + 0.09362I
a = −0.66552 + 1.42703I
b = −0.918640 + 0.694553I
−7.56134 − 1.77744I 0
u = −1.45766 − 0.09362I
a = −0.66552 − 1.42703I
b = −0.918640 − 0.694553I
−7.56134 + 1.77744I 0
u = 1.45706 + 0.14043I
a = −0.99668 − 1.44033I
b = −0.389827 − 0.753821I
−5.72245 − 5.15147I 0
u = 1.45706 − 0.14043I
a = −0.99668 + 1.44033I
b = −0.389827 + 0.753821I
−5.72245 + 5.15147I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47452 + 0.15767I
a = −0.49541 − 1.54608I
b = −0.693140 − 0.745975I
−8.21597 + 3.64315I 0
u = −1.47452 − 0.15767I
a = −0.49541 + 1.54608I
b = −0.693140 + 0.745975I
−8.21597 − 3.64315I 0
u = −1.44827 + 0.33097I
a = −0.053983 − 0.394503I
b = −1.207320 + 0.135353I
−3.69746 + 9.38157I 0
u = −1.44827 − 0.33097I
a = −0.053983 + 0.394503I
b = −1.207320 − 0.135353I
−3.69746 − 9.38157I 0
u = −1.45770 + 0.28932I
a = −0.893306 + 0.858668I
b = −0.342996 + 0.833291I
−6.25498 + 6.61355I 0
u = −1.45770 − 0.28932I
a = −0.893306 − 0.858668I
b = −0.342996 − 0.833291I
−6.25498 − 6.61355I 0
u = −1.47125 + 0.23991I
a = −0.61335 + 2.09178I
b = 1.115140 + 0.563775I
−9.20098 + 7.51308I 0
u = −1.47125 − 0.23991I
a = −0.61335 − 2.09178I
b = 1.115140 − 0.563775I
−9.20098 − 7.51308I 0
u = −1.47703 + 0.22116I
a = 0.73960 − 1.38654I
b = 1.001020 − 0.698022I
−9.48577 + 2.96099I 0
u = −1.47703 − 0.22116I
a = 0.73960 + 1.38654I
b = 1.001020 + 0.698022I
−9.48577 − 2.96099I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45794 + 0.33062I
a = 0.27434 − 2.04142I
b = −1.145410 − 0.593691I
−3.86036 + 11.90930I 0
u = −1.45794 − 0.33062I
a = 0.27434 + 2.04142I
b = −1.145410 + 0.593691I
−3.86036 − 11.90930I 0
u = 1.49360 + 0.16926I
a = −0.51766 + 2.19626I
b = −1.105820 + 0.581728I
−3.61148 − 10.21280I 0
u = 1.49360 − 0.16926I
a = −0.51766 − 2.19626I
b = −1.105820 − 0.581728I
−3.61148 + 10.21280I 0
u = −0.078882 + 0.490309I
a = 0.817776 − 0.190481I
b = 0.033791 − 0.647762I
1.23015 − 1.32761I 4.63192 + 3.39563I
u = −0.078882 − 0.490309I
a = 0.817776 + 0.190481I
b = 0.033791 + 0.647762I
1.23015 + 1.32761I 4.63192 − 3.39563I
u = −0.345451 + 0.355207I
a = −1.20883 + 0.84661I
b = −0.235515 + 0.725816I
0.19256 + 3.25530I 3.54040 − 3.77477I
u = −0.345451 − 0.355207I
a = −1.20883 − 0.84661I
b = −0.235515 − 0.725816I
0.19256 − 3.25530I 3.54040 + 3.77477I
u = −1.48934 + 0.25765I
a = 0.45244 + 1.60841I
b = 0.630174 + 0.807266I
−10.59110 + 8.58055I 0
u = −1.48934 − 0.25765I
a = 0.45244 − 1.60841I
b = 0.630174 − 0.807266I
−10.59110 − 8.58055I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50605 + 0.20053I
a = 0.971598 − 0.547193I
b = 0.346235 − 0.727850I
−11.44530 + 2.58672I 0
u = −1.50605 − 0.20053I
a = 0.971598 + 0.547193I
b = 0.346235 + 0.727850I
−11.44530 − 2.58672I 0
u = −1.50267 + 0.33676I
a = 0.998701 − 0.957933I
b = 0.389482 − 0.855808I
−9.1719 + 12.1476I 0
u = −1.50267 − 0.33676I
a = 0.998701 + 0.957933I
b = 0.389482 + 0.855808I
−9.1719 − 12.1476I 0
u = −1.50887 + 0.36177I
a = −0.15566 + 2.15597I
b = 1.139470 + 0.617419I
−6.9159 + 17.6040I 0
u = −1.50887 − 0.36177I
a = −0.15566 − 2.15597I
b = 1.139470 − 0.617419I
−6.9159 − 17.6040I 0
u = −1.61741 + 0.14592I
a = 0.36078 + 1.47913I
b = 0.539268 + 0.620370I
−12.38970 + 0.73229I 0
u = −1.61741 − 0.14592I
a = 0.36078 − 1.47913I
b = 0.539268 − 0.620370I
−12.38970 − 0.73229I 0
u = 0.213705 + 0.270030I
a = 5.47530 + 0.91762I
b = −0.938716 − 0.391710I
−1.65195 + 1.59364I 4.83512 + 0.49899I
u = 0.213705 − 0.270030I
a = 5.47530 − 0.91762I
b = −0.938716 + 0.391710I
−1.65195 − 1.59364I 4.83512 − 0.49899I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.67589 + 0.02232I
a = −0.507389 − 1.223280I
b = −0.914844 − 0.395620I
−9.62956 + 1.60028I 0
u = −1.67589 − 0.02232I
a = −0.507389 + 1.223280I
b = −0.914844 + 0.395620I
−9.62956 − 1.60028I 0
u = −1.67218 + 0.12795I
a = 0.66697 − 1.25834I
b = 1.020840 − 0.549982I
−10.95800 − 3.88953I 0
u = −1.67218 − 0.12795I
a = 0.66697 + 1.25834I
b = 1.020840 + 0.549982I
−10.95800 + 3.88953I 0
u = 0.199122 + 0.115978I
a = 1.28671 − 1.95913I
b = −0.834445 + 0.576923I
−1.68477 − 2.29240I 4.69113 + 5.69052I
u = 0.199122 − 0.115978I
a = 1.28671 + 1.95913I
b = −0.834445 − 0.576923I
−1.68477 + 2.29240I 4.69113 − 5.69052I
u = −0.164063
a = 3.46287
b = 0.724134
0.959322 11.2500
u = −0.0898438 + 0.0819134I
a = −2.63908 − 6.71038I
b = −0.731105 − 0.544483I
−1.85092 + 2.17150I 2.55964 − 3.90051I
u = −0.0898438 − 0.0819134I
a = −2.63908 + 6.71038I
b = −0.731105 + 0.544483I
−1.85092 − 2.17150I 2.55964 + 3.90051I
15
II. I
u
2
= h23a
8
+ 145b + · · · + 663a − 205, a
9
+ 7a
8
+ · · · + 8a − 1, u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
1
a
10
=
1
1
a
1
=
−1
0
a
4
=
a
−0.158621a
8
− 1.58621a
7
+ ··· − 4.57241a + 1.41379
a
11
=
0
1
a
8
=
−0.475862a
8
− 3.15862a
7
+ ··· + 2.68276a + 0.841379
−0.972414a
8
− 6.92414a
7
+ ··· − 2.04828a + 1.07586
a
3
=
0.275862a
8
+ 1.55862a
7
+ ··· − 3.28276a − 0.441379
0.565517a
8
+ 3.05517a
7
+ ··· − 7.48966a + 1.05517
a
2
=
0.275862a
8
+ 1.55862a
7
+ ··· − 3.28276a − 0.441379
−0.179310a
8
− 1.59310a
7
+ ··· − 3.58621a + 0.406897
a
7
=
0.496552a
8
+ 3.76552a
7
+ ··· + 4.73103a − 0.234483
−0.972414a
8
− 6.92414a
7
+ ··· − 2.04828a + 1.07586
a
5
=
0
−0.406897a
8
− 2.66897a
7
+ ··· + 3.26207a + 0.331034
a
6
=
0
−0.406897a
8
− 2.66897a
7
+ ··· + 3.26207a + 0.331034
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
303
145
a
8
−
2247
145
a
7
−
5744
145
a
6
−
8116
145
a
5
−
2392
29
a
4
−
1889
29
a
3
−
6157
145
a
2
−
2841
145
a +
653
145
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
2
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
3
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
, c
11
u
9
c
6
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
7
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
8
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
9
, c
10
(u − 1)
9
c
12
(u + 1)
9
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
2
, c
6
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
3
, c
8
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
5
, c
11
y
9
c
7
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
9
, c
10
, c
12
(y −1)
9
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.217279 + 0.962736I
b = −0.141484 + 0.739668I
−1.02799 + 2.45442I −0.10038 − 1.90984I
u = 1.00000
a = −0.217279 − 0.962736I
b = −0.141484 − 0.739668I
−1.02799 − 2.45442I −0.10038 + 1.90984I
u = 1.00000
a = 0.038112 + 1.195250I
b = −1.172470 + 0.500383I
1.95319 − 7.08493I 3.23178 + 2.93209I
u = 1.00000
a = 0.038112 − 1.195250I
b = −1.172470 − 0.500383I
1.95319 + 7.08493I 3.23178 − 2.93209I
u = 1.00000
a = −0.121911 + 0.782086I
b = 1.173910 + 0.391555I
2.72642 + 1.33617I 6.61905 − 0.64999I
u = 1.00000
a = −0.121911 − 0.782086I
b = 1.173910 − 0.391555I
2.72642 − 1.33617I 6.61905 + 0.64999I
u = 1.00000
a = 0.106533
b = 0.825933
−0.446489 1.84400
u = 1.00000
a = −3.25219 + 0.42284I
b = −0.772920 − 0.510351I
−3.42837 + 2.09337I −12.6725 − 14.2088I
u = 1.00000
a = −3.25219 − 0.42284I
b = −0.772920 + 0.510351I
−3.42837 − 2.09337I −12.6725 + 14.2088I
19
III. I
u
3
=
h−134a
3
u − 58a
2
u + · · · − 476a − 834, 2a
3
u + 6a
2
u + · · · + 22a + 52, u
2
+ u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u + 1
a
1
=
−u
−u + 1
a
4
=
a
0.102290a
3
u + 0.0442748a
2
u + ··· + 0.363359a + 0.636641
a
11
=
u
u
a
8
=
−0.109924a
3
u − 0.525191a
2
u + ··· − 0.241221a − 0.758779
−0.112977a
3
u − 0.317557a
2
u + ··· − 0.192366a + 0.192366
a
3
=
0.0748092a
3
u − 0.0870229a
2
u + ··· − 0.196947a − 1.80305
0.197710a
3
u + 0.0557252a
2
u + ··· − 0.163359a + 0.163359
a
2
=
0.0748092a
3
u − 0.0870229a
2
u + ··· − 0.196947a − 1.80305
0.197710a
3
u + 0.0557252a
2
u + ··· − 0.163359a + 1.16336
a
7
=
0.00305344a
3
u − 0.207634a
2
u + ··· − 0.0488550a − 0.951145
−0.112977a
3
u − 0.317557a
2
u + ··· − 0.192366a + 0.192366
a
5
=
−0.0954198a
3
u − 0.0114504a
2
u + ··· + 0.526718a + 0.473282
0
a
6
=
0.145038a
3
u + 0.137405a
2
u + ··· − 0.320611a + 0.320611
0.240458a
3
u + 0.148855a
2
u + ··· − 0.847328a − 0.152672
(ii) Obstruction class = 1
(iii) Cusp Shapes =
296
655
a
3
u −
112
655
a
3
+
832
655
a
2
u −
244
655
a
2
+
1288
655
au +
504
655
a +
1332
655
u −
3124
655
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
c
2
, c
6
(u
2
+ 1)
4
c
3
, c
4
, c
8
(u
4
− u
2
+ 1)
2
c
5
, c
11
(u
4
+ 3u
2
+ 1)
2
c
7
(u
2
+ u + 1)
4
c
9
, c
10
(u
2
+ u − 1)
4
c
12
(u
2
− u − 1)
4
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
c
2
, c
6
(y + 1)
8
c
3
, c
4
, c
8
(y
2
− y + 1)
4
c
5
, c
11
(y
2
+ 3y + 1)
4
c
7
(y
2
+ y + 1)
4
c
9
, c
10
, c
12
(y
2
− 3y + 1)
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.09224 + 2.45827I
b = −0.866025 + 0.500000I
−2.63189 − 2.02988I −6.00000 + 3.46410I
u = 0.618034
a = 0.09224 − 2.45827I
b = −0.866025 − 0.500000I
−2.63189 + 2.02988I −6.00000 − 3.46410I
u = 0.618034
a = −2.71028 + 2.07630I
b = 0.866025 − 0.500000I
−2.63189 − 2.02988I −6.00000 + 3.46410I
u = 0.618034
a = −2.71028 − 2.07630I
b = 0.866025 + 0.500000I
−2.63189 + 2.02988I −6.00000 − 3.46410I
u = −1.61803
a = 0.344250 + 0.978225I
b = 0.866025 + 0.500000I
−10.52760 + 2.02988I −6.00000 − 3.46410I
u = −1.61803
a = 0.344250 − 0.978225I
b = 0.866025 − 0.500000I
−10.52760 − 2.02988I −6.00000 + 3.46410I
u = −1.61803
a = −0.72622 + 1.63981I
b = −0.866025 + 0.500000I
−10.52760 − 2.02988I −6.00000 + 3.46410I
u = −1.61803
a = −0.72622 − 1.63981I
b = −0.866025 − 0.500000I
−10.52760 + 2.02988I −6.00000 − 3.46410I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
9
− 3u
8
+ ··· + u + 1)
· (u
109
+ 56u
108
+ ··· − 5688u − 1296)
c
2
(u
2
+ 1)
4
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
109
− 2u
108
+ ··· + 72u − 36)
c
3
(u
4
− u
2
+ 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
109
− 2u
108
+ ··· + 15u − 9)
c
4
(u
4
− u
2
+ 1)
2
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
109
− 6u
108
+ ··· + 1068687u − 322299)
c
5
, c
11
u
9
(u
4
+ 3u
2
+ 1)
2
(u
109
+ u
108
+ ··· − 6144u − 512)
c
6
(u
2
+ 1)
4
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
109
− 2u
108
+ ··· + 72u − 36)
c
7
((u
2
+ u + 1)
4
)(u
9
+ 5u
8
+ ··· + u + 1)
· (u
109
− 52u
108
+ ··· − 189u − 81)
c
8
(u
4
− u
2
+ 1)
2
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
109
− 2u
108
+ ··· + 15u − 9)
c
9
, c
10
((u − 1)
9
)(u
2
+ u − 1)
4
(u
109
− 14u
108
+ ··· + 7u − 1)
c
12
((u + 1)
9
)(u
2
− u − 1)
4
(u
109
− 14u
108
+ ··· + 7u − 1)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
109
+ 4y
108
+ ··· + 86720544y −1679616)
c
2
, c
6
((y + 1)
8
)(y
9
+ 3y
8
+ ··· + y −1)
· (y
109
+ 56y
108
+ ··· − 5688y −1296)
c
3
, c
8
((y
2
− y + 1)
4
)(y
9
− 5y
8
+ ··· + y −1)
· (y
109
− 52y
108
+ ··· − 189y −81)
c
4
((y
2
− y + 1)
4
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
109
+ 20y
108
+ ··· − 3429890229501y −103876645401)
c
5
, c
11
y
9
(y
2
+ 3y + 1)
4
(y
109
+ 69y
108
+ ··· + 1.12722 × 10
7
y −262144)
c
7
(y
2
+ y + 1)
4
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
109
+ 16y
108
+ ··· + 363123y −6561)
c
9
, c
10
, c
12
((y −1)
9
)(y
2
− 3y + 1)
4
(y
109
− 108y
108
+ ··· + 63y −1)
25
