12a
0070
(K12a
0070
)
A knot diagram
1
Linearized knot diagam
3 5 7 9 2 10 12 11 6 4 1 8
Solving Sequence
2,5
3
6,9
10 7 1 4 11 8 12
c
2
c
5
c
9
c
6
c
1
c
4
c
10
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.73994 × 10
281
u
121
+ 1.62267 × 10
282
u
120
+ ··· + 4.12994 × 10
281
b + 5.77778 × 10
282
,
− 2.42748 × 10
282
u
121
+ 8.21343 × 10
282
u
120
+ ··· + 2.06497 × 10
282
a + 9.97461 × 10
282
,
u
122
− 4u
121
+ ··· + 199u + 25i
I
u
2
= h−10a
2
+ 13au + 5b − 5a + u + 1, 5a
3
− 4a
2
u − au − a − 1, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 128 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−4.74 × 10
281
u
121
+ 1.62 × 10
282
u
120
+ · · · + 4.13 × 10
281
b + 5.78 ×
10
282
, −2.43 × 10
282
u
121
+ 8.21 × 10
282
u
120
+ · · · + 2.06 × 10
282
a + 9.97 ×
10
282
, u
122
− 4u
121
+ · · · + 199u + 25i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
9
=
1.17555u
121
− 3.97750u
120
+ ··· − 47.5754u − 4.83038
1.14770u
121
− 3.92903u
120
+ ··· − 111.438u − 13.9900
a
10
=
0.869037u
121
− 3.13754u
120
+ ··· − 34.3561u − 3.25714
0.841186u
121
− 3.08907u
120
+ ··· − 98.2189u − 12.4167
a
7
=
1.25220u
121
− 4.99677u
120
+ ··· − 279.917u − 36.4053
1.16763u
121
− 2.48554u
120
+ ··· + 149.063u + 13.0091
a
1
=
u
2
+ 1
−u
4
a
4
=
0.134051u
121
+ 0.485797u
120
+ ··· + 72.7723u + 10.5439
−1.71953u
121
+ 6.19096u
120
+ ··· + 223.156u + 28.4621
a
11
=
−0.0930748u
121
+ 0.186740u
120
+ ··· − 25.6459u − 1.79576
0.0179185u
121
− 0.626037u
120
+ ··· − 119.121u − 13.9132
a
8
=
−0.823254u
121
+ 3.23286u
120
+ ··· + 200.194u + 26.4359
−0.969644u
121
+ 2.62640u
120
+ ··· − 8.27264u + 1.68771
a
12
=
−0.622433u
121
+ 2.11008u
120
+ ··· + 58.1543u + 8.71432
−0.615775u
121
+ 1.57164u
120
+ ··· − 49.5573u − 4.66944
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.314772u
121
+ 1.38514u
120
+ ··· + 51.9020u + 17.1153
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
122
+ 44u
121
+ ··· − 11251u + 625
c
2
, c
5
u
122
+ 4u
121
+ ··· − 199u + 25
c
3
25(25u
122
− 110u
121
+ ··· − 2.01822 × 10
8
u + 2.90241 × 10
7
)
c
4
25(25u
122
+ 285u
121
+ ··· + 1.39320 × 10
8
u − 4.70438 × 10
8
)
c
6
, c
9
u
122
− 3u
121
+ ··· + 6u − 1
c
7
, c
12
u
122
− 3u
121
+ ··· + 2u − 1
c
8
u
122
− 9u
121
+ ··· + 464382u − 40851
c
10
u
122
− 3u
121
+ ··· − 64800u + 8000
c
11
u
122
− 61u
121
+ ··· − 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
122
+ 72y
121
+ ··· − 671351251y + 390625
c
2
, c
5
y
122
+ 44y
121
+ ··· − 11251y + 625
c
3
625(625y
122
+ 33050y
121
+ ··· + 9.83882 × 10
15
y + 8.42397 × 10
14
)
c
4
625(625y
122
− 37825y
121
+ ··· − 5.31980 × 10
18
y + 2.21312 × 10
17
)
c
6
, c
9
y
122
− 77y
121
+ ··· − 6y + 1
c
7
, c
12
y
122
− 61y
121
+ ··· − 6y + 1
c
8
y
122
+ 55y
121
+ ··· − 105170828166y + 1668804201
c
10
y
122
− 35y
121
+ ··· − 1976960000y + 64000000
c
11
y
122
+ 3y
121
+ ··· − 26y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.326285 + 0.942418I
a = 0.692847 + 0.187568I
b = 1.78757 + 0.05136I
−3.66042 + 5.13633I 0
u = 0.326285 − 0.942418I
a = 0.692847 − 0.187568I
b = 1.78757 − 0.05136I
−3.66042 − 5.13633I 0
u = −0.572010 + 0.816257I
a = 0.507803 − 0.572524I
b = 0.260550 − 0.686004I
0.73647 − 2.28933I 0
u = −0.572010 − 0.816257I
a = 0.507803 + 0.572524I
b = 0.260550 + 0.686004I
0.73647 + 2.28933I 0
u = 0.553016 + 0.850381I
a = −0.437624 + 0.409552I
b = −1.53016 − 0.57476I
−2.78287 − 0.75215I 0
u = 0.553016 − 0.850381I
a = −0.437624 − 0.409552I
b = −1.53016 + 0.57476I
−2.78287 + 0.75215I 0
u = 0.218439 + 0.992336I
a = −0.799538 − 0.333829I
b = −1.69967 − 0.12677I
−4.61287 + 0.09185I 0
u = 0.218439 − 0.992336I
a = −0.799538 + 0.333829I
b = −1.69967 + 0.12677I
−4.61287 − 0.09185I 0
u = 0.795450 + 0.578520I
a = 0.373619 − 1.026800I
b = 0.839001 − 0.103657I
4.78667 − 7.85752I 0
u = 0.795450 − 0.578520I
a = 0.373619 + 1.026800I
b = 0.839001 + 0.103657I
4.78667 + 7.85752I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.529652 + 0.820417I
a = −1.76543 + 3.76659I
b = −2.39046 + 2.84255I
1.90583 − 1.93557I 0
u = −0.529652 − 0.820417I
a = −1.76543 − 3.76659I
b = −2.39046 − 2.84255I
1.90583 + 1.93557I 0
u = 0.749029 + 0.701395I
a = 0.469358 − 0.870420I
b = 1.055920 + 0.011491I
6.29582 + 1.05570I 0
u = 0.749029 − 0.701395I
a = 0.469358 + 0.870420I
b = 1.055920 − 0.011491I
6.29582 − 1.05570I 0
u = −0.510762 + 0.914144I
a = −3.17676 − 1.26449I
b = −3.73598 − 2.07584I
1.59606 − 2.27047I 0
u = −0.510762 − 0.914144I
a = −3.17676 + 1.26449I
b = −3.73598 + 2.07584I
1.59606 + 2.27047I 0
u = 0.779251 + 0.539024I
a = 0.58932 − 1.31309I
b = −0.381525 − 0.131833I
3.36722 − 6.19016I 0
u = 0.779251 − 0.539024I
a = 0.58932 + 1.31309I
b = −0.381525 + 0.131833I
3.36722 + 6.19016I 0
u = 0.724387 + 0.597756I
a = −0.332312 + 0.938470I
b = −0.850470 − 0.028516I
1.82069 − 2.81316I 0
u = 0.724387 − 0.597756I
a = −0.332312 − 0.938470I
b = −0.850470 + 0.028516I
1.82069 + 2.81316I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.242829 + 1.033120I
a = 0.789327 + 0.692107I
b = 1.194330 + 0.413124I
0.308045 + 0.406265I 0
u = −0.242829 − 1.033120I
a = 0.789327 − 0.692107I
b = 1.194330 − 0.413124I
0.308045 − 0.406265I 0
u = 0.559214 + 0.903189I
a = 0.571243 − 0.340975I
b = 1.71545 + 0.36241I
−2.96199 + 5.17216I 0
u = 0.559214 − 0.903189I
a = 0.571243 + 0.340975I
b = 1.71545 − 0.36241I
−2.96199 − 5.17216I 0
u = 0.026443 + 1.069990I
a = −0.909170 − 0.542272I
b = −1.56204 − 0.29348I
−3.43542 − 1.88104I 0
u = 0.026443 − 1.069990I
a = −0.909170 + 0.542272I
b = −1.56204 + 0.29348I
−3.43542 + 1.88104I 0
u = 0.681014 + 0.619625I
a = −0.438429 + 1.272400I
b = 0.446348 − 0.085207I
2.94385 − 1.10084I 0
u = 0.681014 − 0.619625I
a = −0.438429 − 1.272400I
b = 0.446348 + 0.085207I
2.94385 + 1.10084I 0
u = 0.078954 + 1.079210I
a = −0.314714 − 0.213547I
b = −0.711670 − 1.188950I
−1.82843 − 0.11722I 0
u = 0.078954 − 1.079210I
a = −0.314714 + 0.213547I
b = −0.711670 + 1.188950I
−1.82843 + 0.11722I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.713590 + 0.819160I
a = −0.549865 + 0.433932I
b = −1.82136 + 0.96114I
8.11043 − 1.78541I 0
u = 0.713590 − 0.819160I
a = −0.549865 − 0.433932I
b = −1.82136 − 0.96114I
8.11043 + 1.78541I 0
u = 0.691033 + 0.838832I
a = −0.458451 + 0.897802I
b = 0.058154 − 0.460882I
5.24954 + 1.80028I 0
u = 0.691033 − 0.838832I
a = −0.458451 − 0.897802I
b = 0.058154 + 0.460882I
5.24954 − 1.80028I 0
u = −0.912021
a = −1.22780
b = 0.0961263
5.29705 0
u = −0.425723 + 0.799219I
a = −1.38513 − 4.06579I
b = −0.84055 − 2.95736I
3.93682 + 1.93972I 0
u = −0.425723 − 0.799219I
a = −1.38513 + 4.06579I
b = −0.84055 + 2.95736I
3.93682 − 1.93972I 0
u = −0.433038 + 1.007040I
a = −0.496728 − 0.724378I
b = −0.773503 − 0.549607I
−0.87402 − 2.91759I 0
u = −0.433038 − 1.007040I
a = −0.496728 + 0.724378I
b = −0.773503 + 0.549607I
−0.87402 + 2.91759I 0
u = 0.689166 + 0.869505I
a = 0.662720 − 0.365295I
b = 1.90462 − 0.97010I
5.15598 + 3.50593I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.689166 − 0.869505I
a = 0.662720 + 0.365295I
b = 1.90462 + 0.97010I
5.15598 − 3.50593I 0
u = 0.957418 + 0.574316I
a = 0.71742 − 1.26333I
b = −0.137405 − 0.288808I
6.71552 − 7.89088I 0
u = 0.957418 − 0.574316I
a = 0.71742 + 1.26333I
b = −0.137405 + 0.288808I
6.71552 + 7.89088I 0
u = −0.501781 + 0.723894I
a = −2.66535 + 0.96560I
b = −2.19693 + 1.68940I
4.16095 − 5.28585I 0
u = −0.501781 − 0.723894I
a = −2.66535 − 0.96560I
b = −2.19693 − 1.68940I
4.16095 + 5.28585I 0
u = 0.777934 + 0.809289I
a = 0.577136 − 0.989100I
b = −0.008776 + 0.238221I
10.29660 − 1.59255I 0
u = 0.777934 − 0.809289I
a = 0.577136 + 0.989100I
b = −0.008776 − 0.238221I
10.29660 + 1.59255I 0
u = 0.699861 + 0.892444I
a = 0.514457 − 0.817381I
b = 0.086762 + 0.498270I
7.88589 + 7.19296I 0
u = 0.699861 − 0.892444I
a = 0.514457 + 0.817381I
b = 0.086762 − 0.498270I
7.88589 − 7.19296I 0
u = −0.020184 + 1.138770I
a = 0.965921 + 0.597820I
b = 1.55915 + 0.39430I
−1.16117 − 6.62977I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.020184 − 1.138770I
a = 0.965921 − 0.597820I
b = 1.55915 − 0.39430I
−1.16117 + 6.62977I 0
u = 0.953494 + 0.635428I
a = −0.72314 + 1.21847I
b = 0.067037 + 0.220763I
11.22670 − 4.20625I 0
u = 0.953494 − 0.635428I
a = −0.72314 − 1.21847I
b = 0.067037 − 0.220763I
11.22670 + 4.20625I 0
u = −0.571594 + 0.994383I
a = −0.149444 − 0.907016I
b = −0.433310 − 0.836597I
0.08551 − 3.09844I 0
u = −0.571594 − 0.994383I
a = −0.149444 + 0.907016I
b = −0.433310 + 0.836597I
0.08551 + 3.09844I 0
u = 0.995946 + 0.569704I
a = −0.74153 + 1.27175I
b = 0.104011 + 0.338940I
9.5742 − 12.9639I 0
u = 0.995946 − 0.569704I
a = −0.74153 − 1.27175I
b = 0.104011 − 0.338940I
9.5742 + 12.9639I 0
u = −0.653324 + 0.960248I
a = −0.084653 + 1.054180I
b = 0.227226 + 1.025350I
3.22768 + 0.36125I 0
u = −0.653324 − 0.960248I
a = −0.084653 − 1.054180I
b = 0.227226 − 1.025350I
3.22768 − 0.36125I 0
u = 0.743559 + 0.916319I
a = −0.780882 + 0.492500I
b = −1.92101 + 1.06915I
9.96690 + 7.32303I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.743559 − 0.916319I
a = −0.780882 − 0.492500I
b = −1.92101 − 1.06915I
9.96690 − 7.32303I 0
u = −0.011779 + 1.182160I
a = 0.452481 + 0.351888I
b = 0.83058 + 1.24696I
−2.50939 − 4.58346I 0
u = −0.011779 − 1.182160I
a = 0.452481 − 0.351888I
b = 0.83058 − 1.24696I
−2.50939 + 4.58346I 0
u = −0.875105 + 0.803170I
a = 0.149464 − 0.598556I
b = 0.928365 + 0.020905I
4.50074 − 3.19439I 0
u = −0.875105 − 0.803170I
a = 0.149464 + 0.598556I
b = 0.928365 − 0.020905I
4.50074 + 3.19439I 0
u = 0.693464 + 0.978885I
a = −0.834108 + 0.544061I
b = −1.62142 − 0.02779I
5.46282 + 4.43629I 0
u = 0.693464 − 0.978885I
a = −0.834108 − 0.544061I
b = −1.62142 + 0.02779I
5.46282 − 4.43629I 0
u = −0.457721 + 0.655697I
a = 1.62774 − 0.29982I
b = 1.23330 − 0.88799I
1.17158 − 1.37282I 0
u = −0.457721 − 0.655697I
a = 1.62774 + 0.29982I
b = 1.23330 + 0.88799I
1.17158 + 1.37282I 0
u = 0.645820 + 1.012120I
a = 1.041090 − 0.252556I
b = 2.08578 − 1.01278I
1.77974 + 6.27141I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.645820 − 1.012120I
a = 1.041090 + 0.252556I
b = 2.08578 + 1.01278I
1.77974 − 6.27141I 0
u = −0.593737 + 0.532852I
a = −1.37729 + 0.86342I
b = −0.756077 + 1.075050I
4.19754 − 5.34475I 0
u = −0.593737 − 0.532852I
a = −1.37729 − 0.86342I
b = −0.756077 − 1.075050I
4.19754 + 5.34475I 0
u = −0.503368 + 0.610247I
a = −2.27049 − 0.13633I
b = −1.85631 + 0.60038I
4.19470 + 2.54550I 0
u = −0.503368 − 0.610247I
a = −2.27049 + 0.13633I
b = −1.85631 − 0.60038I
4.19470 − 2.54550I 0
u = −0.614406 + 1.041270I
a = 0.174033 + 1.088120I
b = 0.489999 + 1.019260I
2.74814 − 7.31758I 0
u = −0.614406 − 1.041270I
a = 0.174033 − 1.088120I
b = 0.489999 − 1.019260I
2.74814 + 7.31758I 0
u = 0.656841 + 1.024640I
a = 0.891513 − 0.450024I
b = 1.70916 + 0.04238I
0.56417 + 8.12101I 0
u = 0.656841 − 1.024640I
a = 0.891513 + 0.450024I
b = 1.70916 − 0.04238I
0.56417 − 8.12101I 0
u = −1.116760 + 0.485850I
a = −0.597238 − 0.318389I
b = 0.337151 + 0.046329I
5.65832 − 1.89007I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.116760 − 0.485850I
a = −0.597238 + 0.318389I
b = 0.337151 − 0.046329I
5.65832 + 1.89007I 0
u = 0.664030 + 1.057230I
a = −1.156050 + 0.319791I
b = −2.13165 + 1.05308I
1.85276 + 11.64830I 0
u = 0.664030 − 1.057230I
a = −1.156050 − 0.319791I
b = −2.13165 − 1.05308I
1.85276 − 11.64830I 0
u = 0.677240 + 1.051660I
a = −0.950846 + 0.470654I
b = −1.72762 − 0.00115I
3.37832 + 13.41190I 0
u = 0.677240 − 1.051660I
a = −0.950846 − 0.470654I
b = −1.72762 + 0.00115I
3.37832 − 13.41190I 0
u = −0.072612 + 0.715576I
a = 0.798310 + 0.776198I
b = 1.356260 − 0.019710I
0.537586 + 0.056581I 7.50385 + 0.I
u = −0.072612 − 0.715576I
a = 0.798310 − 0.776198I
b = 1.356260 + 0.019710I
0.537586 − 0.056581I 7.50385 + 0.I
u = −1.218330 + 0.404273I
a = 0.672627 + 0.192179I
b = −0.248140 − 0.081316I
8.92181 + 2.07048I 0
u = −1.218330 − 0.404273I
a = 0.672627 − 0.192179I
b = −0.248140 + 0.081316I
8.92181 − 2.07048I 0
u = −0.596675 + 1.156060I
a = 0.899024 + 0.398696I
b = 1.42676 + 1.09731I
2.02198 − 5.17207I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.596675 − 1.156060I
a = 0.899024 − 0.398696I
b = 1.42676 − 1.09731I
2.02198 + 5.17207I 0
u = 0.753335 + 1.085870I
a = 1.187310 − 0.556416I
b = 2.12414 − 1.18059I
9.8172 + 10.4510I 0
u = 0.753335 − 1.085870I
a = 1.187310 + 0.556416I
b = 2.12414 + 1.18059I
9.8172 − 10.4510I 0
u = −0.153694 + 1.313130I
a = 0.617355 + 0.477053I
b = 0.98972 + 1.27926I
−0.92102 − 5.87396I 0
u = −0.153694 − 1.313130I
a = 0.617355 − 0.477053I
b = 0.98972 − 1.27926I
−0.92102 + 5.87396I 0
u = −1.206020 + 0.560336I
a = 0.509477 + 0.205574I
b = −0.347031 − 0.145978I
8.74939 − 6.05779I 0
u = −1.206020 − 0.560336I
a = 0.509477 − 0.205574I
b = −0.347031 + 0.145978I
8.74939 + 6.05779I 0
u = 0.729094 + 1.112350I
a = −1.262590 + 0.511220I
b = −2.17153 + 1.16295I
5.0449 + 14.0548I 0
u = 0.729094 − 1.112350I
a = −1.262590 − 0.511220I
b = −2.17153 − 1.16295I
5.0449 − 14.0548I 0
u = −0.297528 + 1.305940I
a = −0.667993 − 0.561744I
b = −1.07985 − 1.31993I
2.89346 − 2.86957I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.297528 − 1.305940I
a = −0.667993 + 0.561744I
b = −1.07985 + 1.31993I
2.89346 + 2.86957I 0
u = 0.740307 + 1.130060I
a = 1.298890 − 0.547578I
b = 2.18914 − 1.18710I
7.8209 + 19.2722I 0
u = 0.740307 − 1.130060I
a = 1.298890 + 0.547578I
b = 2.18914 + 1.18710I
7.8209 − 19.2722I 0
u = −0.369678 + 0.527243I
a = 1.42430 − 0.57175I
b = 0.642330 − 1.116470I
1.16813 − 1.35653I 6.09677 + 4.56023I
u = −0.369678 − 0.527243I
a = 1.42430 + 0.57175I
b = 0.642330 + 1.116470I
1.16813 + 1.35653I 6.09677 − 4.56023I
u = −0.165478 + 1.382290I
a = −0.668460 − 0.472612I
b = −1.02244 − 1.25149I
1.60319 − 10.55180I 0
u = −0.165478 − 1.382290I
a = −0.668460 + 0.472612I
b = −1.02244 + 1.25149I
1.60319 + 10.55180I 0
u = −0.187260 + 0.574208I
a = −1.60794 − 2.72382I
b = −0.996029 − 0.814349I
3.72913 − 4.62245I 8.61256 + 6.77564I
u = −0.187260 − 0.574208I
a = −1.60794 + 2.72382I
b = −0.996029 + 0.814349I
3.72913 + 4.62245I 8.61256 − 6.77564I
u = −0.498350 + 0.331849I
a = −1.78519 + 0.75335I
b = −0.836764 + 0.929097I
4.26111 + 2.58560I 9.74178 − 0.06925I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498350 − 0.331849I
a = −1.78519 − 0.75335I
b = −0.836764 − 0.929097I
4.26111 − 2.58560I 9.74178 + 0.06925I
u = −0.82132 + 1.16633I
a = 0.569140 + 0.173431I
b = 1.137980 + 0.782970I
3.61094 − 5.00772I 0
u = −0.82132 − 1.16633I
a = 0.569140 − 0.173431I
b = 1.137980 − 0.782970I
3.61094 + 5.00772I 0
u = −0.92261 + 1.13281I
a = −0.401577 − 0.115397I
b = −0.996486 − 0.685874I
7.03734 − 1.38824I 0
u = −0.92261 − 1.13281I
a = −0.401577 + 0.115397I
b = −0.996486 + 0.685874I
7.03734 + 1.38824I 0
u = −0.85763 + 1.23391I
a = −0.500717 − 0.266840I
b = −1.047550 − 0.852973I
6.45296 − 9.37183I 0
u = −0.85763 − 1.23391I
a = −0.500717 + 0.266840I
b = −1.047550 + 0.852973I
6.45296 + 9.37183I 0
u = 0.479337 + 0.129610I
a = 0.083018 + 1.272890I
b = −0.116490 − 0.155795I
−1.50913 − 2.14084I 2.75911 + 4.53321I
u = 0.479337 − 0.129610I
a = 0.083018 − 1.272890I
b = −0.116490 + 0.155795I
−1.50913 + 2.14084I 2.75911 − 4.53321I
u = −0.220613 + 0.234043I
a = 3.21386 + 2.90701I
b = 0.651078 + 0.309476I
1.98893 − 0.45223I 4.53206 + 0.87147I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220613 − 0.234043I
a = 3.21386 − 2.90701I
b = 0.651078 − 0.309476I
1.98893 + 0.45223I 4.53206 − 0.87147I
u = −0.150736
a = 3.16545
b = 0.528544
0.958244 11.0420
17
II.
I
u
2
= h−10a
2
+ 13au + 5b − 5a + u + 1, 5a
3
− 4a
2
u − au − a − 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
9
=
a
2a
2
−
13
5
au + a −
1
5
u −
1
5
a
10
=
−2a
2
u − 2a
2
−
8
5
a +
1
5
u
−2a
2
u −
13
5
au −
8
5
a −
1
5
a
7
=
−a + 2u
−a
2
−
6
5
au − a +
3
5
u −
7
5
a
1
=
−u
−u
a
4
=
−a
2
u
−2a
2
u − a
2
+
1
5
a +
3
5
u
a
11
=
−2a
2
u − 2a
2
−
8
5
a +
1
5
u
−2a
2
u −
13
5
au −
8
5
a −
1
5
a
8
=
3a
2
u + 3a
2
+
17
5
a +
1
5
u
3a
2
u +
7
5
au +
17
5
a −
1
5
a
12
=
−4a
2
u − 4a
2
−
21
5
a +
2
5
u
−4a
2
u −
13
5
au + ··· −
21
5
a −
1
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 19a
2
u + 13a
2
−
61
5
au +
27
5
a −
41
5
u −
7
5
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
25(25u
6
− 55u
5
+ 91u
4
− 56u
3
+ 25u
2
− 6u + 1)
c
4
25(25u
6
− 20u
5
+ 11u
4
+ 6u
3
− 3u
2
− u + 1)
c
6
, c
11
(u
3
+ u
2
+ 2u + 1)
2
c
7
(u
3
− u
2
+ 1)
2
c
8
(u
3
− 3u
2
+ 2u + 1)
2
c
9
(u
3
− u
2
+ 2u − 1)
2
c
10
u
6
c
12
(u
3
+ u
2
− 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
3
c
3
625(625y
6
+ 1525y
5
+ 3371y
4
+ 804y
3
+ 135y
2
+ 14y + 1)
c
4
625(625y
6
+ 150y
5
+ 211y
4
− 92y
3
+ 43y
2
− 7y + 1)
c
6
, c
9
, c
11
(y
3
+ 3y
2
+ 2y − 1)
2
c
7
, c
12
(y
3
− y
2
+ 2y − 1)
2
c
8
(y
3
− 5y
2
+ 10y − 1)
2
c
10
y
6
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.421928 + 0.730800I
b = −0.137007 + 1.224300I
1.11345 − 2.02988I 14.4703 − 2.2563I
u = −0.500000 + 0.866025I
a = 0.432147 + 0.224180I
b = 1.67170 − 0.24313I
−3.02413 − 4.85801I 7.32782 − 6.16510I
u = −0.500000 + 0.866025I
a = −0.410219 − 0.262160I
b = −1.43470 + 0.57768I
−3.02413 + 0.79824I −7.97807 − 3.39120I
u = −0.500000 − 0.866025I
a = −0.421928 − 0.730800I
b = −0.137007 − 1.224300I
1.11345 + 2.02988I 14.4703 + 2.2563I
u = −0.500000 − 0.866025I
a = 0.432147 − 0.224180I
b = 1.67170 + 0.24313I
−3.02413 + 4.85801I 7.32782 + 6.16510I
u = −0.500000 − 0.866025I
a = −0.410219 + 0.262160I
b = −1.43470 − 0.57768I
−3.02413 − 0.79824I −7.97807 + 3.39120I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
122
+ 44u
121
+ ··· − 11251u + 625)
c
2
((u
2
+ u + 1)
3
)(u
122
+ 4u
121
+ ··· − 199u + 25)
c
3
625(25u
6
− 55u
5
+ 91u
4
− 56u
3
+ 25u
2
− 6u + 1)
· (25u
122
− 110u
121
+ ··· − 201821590u + 29024081)
c
4
625(25u
6
− 20u
5
+ 11u
4
+ 6u
3
− 3u
2
− u + 1)
· (25u
122
+ 285u
121
+ ··· + 139320349u − 470437783)
c
5
((u
2
− u + 1)
3
)(u
122
+ 4u
121
+ ··· − 199u + 25)
c
6
((u
3
+ u
2
+ 2u + 1)
2
)(u
122
− 3u
121
+ ··· + 6u − 1)
c
7
((u
3
− u
2
+ 1)
2
)(u
122
− 3u
121
+ ··· + 2u − 1)
c
8
((u
3
− 3u
2
+ 2u + 1)
2
)(u
122
− 9u
121
+ ··· + 464382u − 40851)
c
9
((u
3
− u
2
+ 2u − 1)
2
)(u
122
− 3u
121
+ ··· + 6u − 1)
c
10
u
6
(u
122
− 3u
121
+ ··· − 64800u + 8000)
c
11
((u
3
+ u
2
+ 2u + 1)
2
)(u
122
− 61u
121
+ ··· − 6u + 1)
c
12
((u
3
+ u
2
− 1)
2
)(u
122
− 3u
121
+ ··· + 2u − 1)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
122
+ 72y
121
+ ··· − 6.71351 × 10
8
y + 390625)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
122
+ 44y
121
+ ··· − 11251y + 625)
c
3
390625(625y
6
+ 1525y
5
+ 3371y
4
+ 804y
3
+ 135y
2
+ 14y + 1)
· (625y
122
+ 3.31 × 10
4
y
121
+ ··· + 9.84 × 10
15
y + 8.42 × 10
14
)
c
4
390625(625y
6
+ 150y
5
+ 211y
4
− 92y
3
+ 43y
2
− 7y + 1)
· (625y
122
− 3.78 × 10
4
y
121
+ ··· − 5.32 × 10
18
y + 2.21 × 10
17
)
c
6
, c
9
((y
3
+ 3y
2
+ 2y − 1)
2
)(y
122
− 77y
121
+ ··· − 6y + 1)
c
7
, c
12
((y
3
− y
2
+ 2y − 1)
2
)(y
122
− 61y
121
+ ··· − 6y + 1)
c
8
(y
3
− 5y
2
+ 10y − 1)
2
· (y
122
+ 55y
121
+ ··· − 105170828166y + 1668804201)
c
10
y
6
(y
122
− 35y
121
+ ··· − 1.97696 × 10
9
y + 6.40000 × 10
7
)
c
11
((y
3
+ 3y
2
+ 2y − 1)
2
)(y
122
+ 3y
121
+ ··· − 26y + 1)
23
