12a
0925
(K12a
0925
)
A knot diagram
1
Linearized knot diagam
4 6 9 11 2 12 10 3 1 7 5 8
Solving Sequence
3,9 4,6
2 1 5 8 12 7 11 10
c
3
c
2
c
1
c
5
c
8
c
12
c
6
c
11
c
10
c
4
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.37208 × 10
955
u
174
5.29428 × 10
954
u
173
+ ··· + 1.52887 × 10
955
b + 1.80446 × 10
959
,
6.40167 × 10
959
u
174
5.34264 × 10
958
u
173
+ ··· + 4.00718 × 10
958
a + 1.81672 × 10
963
,
u
175
+ u
174
+ ··· 2853u 2621i
I
u
2
= h3.32259 × 10
40
u
52
2.34870 × 10
40
u
51
+ ··· + 1.43120 × 10
38
b + 4.37472 × 10
40
,
1.47911 × 10
41
u
52
+ 8.39026 × 10
40
u
51
+ ··· + 1.43120 × 10
38
a 1.72574 × 10
41
,
u
53
14u
51
+ ··· 11u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 228 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−6.37 × 10
955
u
174
5.29 × 10
954
u
173
+ · · · + 1.53 × 10
955
b + 1.80 ×
10
959
, 6.40 × 10
959
u
174
5.34 × 10
958
u
173
+ · · · + 4.01 × 10
958
a + 1.82 ×
10
963
, u
175
+ u
174
+ · · · 2853u 2621i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
6
=
15.9755u
174
+ 1.33327u
173
+ ··· 36.3411u 45336.5
4.16783u
174
+ 0.346286u
173
+ ··· 35.5749u 11802.5
a
2
=
7.11073u
174
0.574352u
173
+ ··· 66.0517u + 20079.5
0.176273u
174
+ 0.265217u
173
+ ··· + 849.646u 407.719
a
1
=
1.19707u
174
+ 0.161818u
173
+ ··· + 772.531u + 2539.92
4.37966u
174
+ 0.848427u
173
+ ··· + 1577.97u 13977.9
a
5
=
13.0539u
174
+ 0.606725u
173
+ ··· 1662.11u 35463.6
9.15087u
174
+ 0.394872u
173
+ ··· 1353.36u 24800.8
a
8
=
u
u
a
12
=
5.51568u
174
0.379165u
173
+ ··· + 107.438u + 15356.9
0.0610535u
174
+ 0.307444u
173
+ ··· + 912.877u 1160.90
a
7
=
1.37797u
174
0.870688u
173
+ ··· 3364.65u 674.753
5.18568u
174
0.184804u
173
+ ··· 2096.15u 12781.4
a
11
=
0.476362u
174
+ 0.160489u
173
+ ··· + 766.812u + 911.061
6.49332u
174
0.319529u
173
+ ··· + 879.629u + 17886.6
a
10
=
13.6307u
174
1.30945u
173
+ ··· 209.392u + 39302.5
7.00162u
174
0.711508u
173
+ ··· 27.9154u + 20160.6
(ii) Obstruction class = 1
(iii) Cusp Shapes = 32.4777u
174
3.37563u
173
+ ··· 2284.15u + 94315.5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
175
8u
174
+ ··· + 1890868908462u 280537441299
c
2
, c
5
u
175
+ 4u
174
+ ··· + 417270u + 63403
c
3
, c
8
u
175
+ u
174
+ ··· 2853u 2621
c
4
, c
11
u
175
+ u
174
+ ··· 21401u + 1549
c
6
u
175
2u
174
+ ··· 657105u + 475777
c
7
, c
10
u
175
+ 6u
174
+ ··· 343340u 23572
c
9
u
175
6u
174
+ ··· + 4627516764u + 594875704
c
12
u
175
+ 2u
174
+ ··· 218568u + 5697
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
175
52y
174
+ ··· + 3.27 × 10
24
y 7.87 × 10
22
c
2
, c
5
y
175
96y
174
+ ··· + 241757138316y 4019940409
c
3
, c
8
y
175
107y
174
+ ··· + 304239221y 6869641
c
4
, c
11
y
175
87y
174
+ ··· + 251496317y 2399401
c
6
y
175
+ 18y
174
+ ··· 12874725123895y 226363753729
c
7
, c
10
y
175
+ 122y
174
+ ··· 6061106160y 555639184
c
9
y
175
+ 62y
174
+ ··· 2.61 × 10
19
y 3.54 × 10
17
c
12
y
175
+ 62y
174
+ ··· 12813231636y 32455809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.008340 + 0.114977I
a = 0.06770 + 2.00673I
b = 0.639902 0.509941I
0.72811 + 5.24649I 0
u = 1.008340 0.114977I
a = 0.06770 2.00673I
b = 0.639902 + 0.509941I
0.72811 5.24649I 0
u = 0.052380 + 0.983705I
a = 0.271367 + 0.895018I
b = 0.175627 1.046830I
0.09640 + 8.25979I 0
u = 0.052380 0.983705I
a = 0.271367 0.895018I
b = 0.175627 + 1.046830I
0.09640 8.25979I 0
u = 0.969775 + 0.092941I
a = 0.404042 + 1.238470I
b = 0.56097 + 1.30163I
0.779150 0.881346I 0
u = 0.969775 0.092941I
a = 0.404042 1.238470I
b = 0.56097 1.30163I
0.779150 + 0.881346I 0
u = 0.894099 + 0.360744I
a = 0.117949 + 0.659180I
b = 0.740112 0.004916I
6.23141 + 0.57035I 0
u = 0.894099 0.360744I
a = 0.117949 0.659180I
b = 0.740112 + 0.004916I
6.23141 0.57035I 0
u = 0.731796 + 0.610840I
a = 0.568517 + 0.583153I
b = 1.120150 + 0.353376I
1.57326 1.76025I 0
u = 0.731796 0.610840I
a = 0.568517 0.583153I
b = 1.120150 0.353376I
1.57326 + 1.76025I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.918709 + 0.237229I
a = 0.270110 0.894702I
b = 0.536386 + 0.661275I
2.86322 1.32931I 0
u = 0.918709 0.237229I
a = 0.270110 + 0.894702I
b = 0.536386 0.661275I
2.86322 + 1.32931I 0
u = 1.055870 + 0.100541I
a = 0.402174 + 0.029672I
b = 0.529728 + 0.479846I
6.48509 + 0.71958I 0
u = 1.055870 0.100541I
a = 0.402174 0.029672I
b = 0.529728 0.479846I
6.48509 0.71958I 0
u = 1.058450 + 0.124315I
a = 2.55497 0.49443I
b = 1.283910 + 0.415138I
3.02613 + 1.59757I 0
u = 1.058450 0.124315I
a = 2.55497 + 0.49443I
b = 1.283910 0.415138I
3.02613 1.59757I 0
u = 0.923940 + 0.062597I
a = 1.118240 + 0.104649I
b = 0.819568 + 1.135490I
0.99939 + 1.70499I 0
u = 0.923940 0.062597I
a = 1.118240 0.104649I
b = 0.819568 1.135490I
0.99939 1.70499I 0
u = 0.815324 + 0.429136I
a = 0.19301 1.45744I
b = 1.034920 + 0.535439I
1.35633 + 5.98085I 0
u = 0.815324 0.429136I
a = 0.19301 + 1.45744I
b = 1.034920 0.535439I
1.35633 5.98085I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.912619 + 0.122850I
a = 0.227881 1.307120I
b = 0.102478 1.254120I
1.44152 3.97683I 0
u = 0.912619 0.122850I
a = 0.227881 + 1.307120I
b = 0.102478 + 1.254120I
1.44152 + 3.97683I 0
u = 0.857554 + 0.331513I
a = 0.75497 + 1.63777I
b = 1.030800 0.444653I
1.97267 9.14333I 0
u = 0.857554 0.331513I
a = 0.75497 1.63777I
b = 1.030800 + 0.444653I
1.97267 + 9.14333I 0
u = 0.766214 + 0.499618I
a = 0.91660 1.50789I
b = 1.133460 0.201915I
1.82975 + 5.58360I 0
u = 0.766214 0.499618I
a = 0.91660 + 1.50789I
b = 1.133460 + 0.201915I
1.82975 5.58360I 0
u = 0.681198 + 0.607884I
a = 0.341632 + 0.617565I
b = 0.713431 + 0.601410I
1.43546 3.18285I 0
u = 0.681198 0.607884I
a = 0.341632 0.617565I
b = 0.713431 0.601410I
1.43546 + 3.18285I 0
u = 1.055600 + 0.262250I
a = 2.41064 + 0.62625I
b = 1.359230 0.365500I
6.00895 5.26943I 0
u = 1.055600 0.262250I
a = 2.41064 0.62625I
b = 1.359230 + 0.365500I
6.00895 + 5.26943I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.983587 + 0.477897I
a = 1.267250 0.165255I
b = 0.727556 + 0.809995I
1.49248 2.13116I 0
u = 0.983587 0.477897I
a = 1.267250 + 0.165255I
b = 0.727556 0.809995I
1.49248 + 2.13116I 0
u = 0.890066 + 0.167770I
a = 0.478732 + 0.037537I
b = 0.565199 0.581016I
1.47170 + 0.87487I 0
u = 0.890066 0.167770I
a = 0.478732 0.037537I
b = 0.565199 + 0.581016I
1.47170 0.87487I 0
u = 0.750069 + 0.798108I
a = 0.599263 0.776735I
b = 0.714467 0.072197I
0.409841 + 0.584531I 0
u = 0.750069 0.798108I
a = 0.599263 + 0.776735I
b = 0.714467 + 0.072197I
0.409841 0.584531I 0
u = 1.110910 + 0.016667I
a = 2.93249 + 0.41183I
b = 1.149250 0.374540I
7.32014 + 1.45894I 0
u = 1.110910 0.016667I
a = 2.93249 0.41183I
b = 1.149250 + 0.374540I
7.32014 1.45894I 0
u = 0.885283 + 0.024542I
a = 4.60948 1.59603I
b = 0.758385 0.020744I
0.05882 4.46982I 0
u = 0.885283 0.024542I
a = 4.60948 + 1.59603I
b = 0.758385 + 0.020744I
0.05882 + 4.46982I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.077380 + 0.293356I
a = 2.45114 + 0.40387I
b = 1.48414 0.56183I
3.80384 + 10.36360I 0
u = 1.077380 0.293356I
a = 2.45114 0.40387I
b = 1.48414 + 0.56183I
3.80384 10.36360I 0
u = 0.882540
a = 4.88625
b = 0.757507
3.90842 0
u = 1.061440 + 0.363688I
a = 1.55159 + 0.32538I
b = 0.917976 0.612189I
1.40636 + 2.81522I 0
u = 1.061440 0.363688I
a = 1.55159 0.32538I
b = 0.917976 + 0.612189I
1.40636 2.81522I 0
u = 1.104410 + 0.224190I
a = 2.09979 0.37926I
b = 1.30053 + 0.77145I
1.80068 6.55713I 0
u = 1.104410 0.224190I
a = 2.09979 + 0.37926I
b = 1.30053 0.77145I
1.80068 + 6.55713I 0
u = 0.313944 + 0.808747I
a = 0.103102 + 0.433947I
b = 0.850043 0.444944I
1.81980 + 0.11582I 0
u = 0.313944 0.808747I
a = 0.103102 0.433947I
b = 0.850043 + 0.444944I
1.81980 0.11582I 0
u = 1.126140 + 0.168539I
a = 1.54899 + 1.33006I
b = 0.986495 0.615170I
7.60050 + 5.26863I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.126140 0.168539I
a = 1.54899 1.33006I
b = 0.986495 + 0.615170I
7.60050 5.26863I 0
u = 1.101550 + 0.327879I
a = 0.601592 0.264941I
b = 0.463340 + 0.801709I
1.11431 4.04608I 0
u = 1.101550 0.327879I
a = 0.601592 + 0.264941I
b = 0.463340 0.801709I
1.11431 + 4.04608I 0
u = 0.294355 + 1.111750I
a = 0.089913 + 0.361865I
b = 1.46643 0.36244I
5.19682 3.12832I 0
u = 0.294355 1.111750I
a = 0.089913 0.361865I
b = 1.46643 + 0.36244I
5.19682 + 3.12832I 0
u = 0.555505 + 1.007470I
a = 0.056272 + 0.654668I
b = 1.065360 0.663216I
4.41497 0.27045I 0
u = 0.555505 1.007470I
a = 0.056272 0.654668I
b = 1.065360 + 0.663216I
4.41497 + 0.27045I 0
u = 1.050050 + 0.493222I
a = 0.510811 + 0.751441I
b = 0.648656 0.018944I
5.54541 + 6.77031I 0
u = 1.050050 0.493222I
a = 0.510811 0.751441I
b = 0.648656 + 0.018944I
5.54541 6.77031I 0
u = 1.061500 + 0.473801I
a = 0.148639 0.686284I
b = 0.394648 0.169968I
0.57205 4.46548I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.061500 0.473801I
a = 0.148639 + 0.686284I
b = 0.394648 + 0.169968I
0.57205 + 4.46548I 0
u = 0.130560 + 0.823512I
a = 0.590084 + 0.629492I
b = 0.096768 0.484498I
2.76466 3.57057I 0
u = 0.130560 0.823512I
a = 0.590084 0.629492I
b = 0.096768 + 0.484498I
2.76466 + 3.57057I 0
u = 0.140766 + 0.807970I
a = 0.59109 1.62492I
b = 0.088000 + 0.863080I
5.30870 1.78531I 0
u = 0.140766 0.807970I
a = 0.59109 + 1.62492I
b = 0.088000 0.863080I
5.30870 + 1.78531I 0
u = 0.148594 + 1.173010I
a = 0.407767 + 0.518930I
b = 1.282450 0.593367I
3.3301 14.1176I 0
u = 0.148594 1.173010I
a = 0.407767 0.518930I
b = 1.282450 + 0.593367I
3.3301 + 14.1176I 0
u = 1.157350 + 0.257215I
a = 0.137219 + 0.951199I
b = 0.277699 + 0.698109I
3.62656 + 4.64520I 0
u = 1.157350 0.257215I
a = 0.137219 0.951199I
b = 0.277699 0.698109I
3.62656 4.64520I 0
u = 0.764638 + 0.280136I
a = 0.137922 0.343939I
b = 0.161390 0.992421I
1.47080 + 1.90539I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.764638 0.280136I
a = 0.137922 + 0.343939I
b = 0.161390 + 0.992421I
1.47080 1.90539I 0
u = 0.619257 + 0.514956I
a = 0.66997 + 1.96532I
b = 0.934962 0.523006I
3.97045 4.40481I 0
u = 0.619257 0.514956I
a = 0.66997 1.96532I
b = 0.934962 + 0.523006I
3.97045 + 4.40481I 0
u = 0.640063 + 0.469754I
a = 1.268060 0.484721I
b = 1.026780 + 0.705633I
1.34087 + 7.56322I 0
u = 0.640063 0.469754I
a = 1.268060 + 0.484721I
b = 1.026780 0.705633I
1.34087 7.56322I 0
u = 0.018313 + 0.788627I
a = 0.695905 + 0.160230I
b = 1.312860 + 0.110976I
5.42053 0.73784I 0
u = 0.018313 0.788627I
a = 0.695905 0.160230I
b = 1.312860 0.110976I
5.42053 + 0.73784I 0
u = 0.068963 + 1.210180I
a = 0.609750 + 0.396868I
b = 1.159300 0.409788I
5.77869 + 7.27147I 0
u = 0.068963 1.210180I
a = 0.609750 0.396868I
b = 1.159300 + 0.409788I
5.77869 7.27147I 0
u = 1.174220 + 0.406921I
a = 2.56128 0.72573I
b = 1.227910 + 0.245565I
8.17152 7.99853I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.174220 0.406921I
a = 2.56128 + 0.72573I
b = 1.227910 0.245565I
8.17152 + 7.99853I 0
u = 0.245489 + 1.220510I
a = 0.554382 0.267502I
b = 1.155370 + 0.256181I
1.92129 1.96501I 0
u = 0.245489 1.220510I
a = 0.554382 + 0.267502I
b = 1.155370 0.256181I
1.92129 + 1.96501I 0
u = 0.619235 + 0.424388I
a = 0.730260 0.027654I
b = 0.138368 0.650286I
1.32344 + 1.75688I 0
u = 0.619235 0.424388I
a = 0.730260 + 0.027654I
b = 0.138368 + 0.650286I
1.32344 1.75688I 0
u = 0.499157 + 0.558083I
a = 1.17487 0.96889I
b = 0.829562 + 0.095388I
3.85851 2.55091I 0
u = 0.499157 0.558083I
a = 1.17487 + 0.96889I
b = 0.829562 0.095388I
3.85851 + 2.55091I 0
u = 1.226400 + 0.318205I
a = 2.44179 + 0.60903I
b = 1.166520 0.436983I
3.35407 + 7.74672I 0
u = 1.226400 0.318205I
a = 2.44179 0.60903I
b = 1.166520 + 0.436983I
3.35407 7.74672I 0
u = 1.117490 + 0.599149I
a = 1.51665 + 1.46224I
b = 1.002940 0.072372I
6.93585 + 0.03498I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.117490 0.599149I
a = 1.51665 1.46224I
b = 1.002940 + 0.072372I
6.93585 0.03498I 0
u = 1.254460 + 0.223040I
a = 2.65308 0.66422I
b = 1.135600 + 0.530534I
6.13100 9.36045I 0
u = 1.254460 0.223040I
a = 2.65308 + 0.66422I
b = 1.135600 0.530534I
6.13100 + 9.36045I 0
u = 1.087070 + 0.683942I
a = 0.272679 + 0.266678I
b = 0.843710 + 0.265451I
0.002842 + 1.006490I 0
u = 1.087070 0.683942I
a = 0.272679 0.266678I
b = 0.843710 0.265451I
0.002842 1.006490I 0
u = 0.661990 + 0.268164I
a = 0.688289 0.333784I
b = 0.839786 0.696152I
0.56526 5.07278I 0
u = 0.661990 0.268164I
a = 0.688289 + 0.333784I
b = 0.839786 + 0.696152I
0.56526 + 5.07278I 0
u = 0.335407 + 1.244040I
a = 1.266040 0.155532I
b = 0.717952 + 0.021782I
3.71341 3.52873I 0
u = 0.335407 1.244040I
a = 1.266040 + 0.155532I
b = 0.717952 0.021782I
3.71341 + 3.52873I 0
u = 1.191900 + 0.500396I
a = 0.157852 0.714867I
b = 0.636888 0.475720I
0.98080 4.93698I 0
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.191900 0.500396I
a = 0.157852 + 0.714867I
b = 0.636888 + 0.475720I
0.98080 + 4.93698I 0
u = 0.638722 + 1.126880I
a = 0.377501 0.675726I
b = 1.081380 + 0.332470I
1.67900 + 5.40673I 0
u = 0.638722 1.126880I
a = 0.377501 + 0.675726I
b = 1.081380 0.332470I
1.67900 5.40673I 0
u = 1.261520 + 0.301281I
a = 0.579930 + 0.064910I
b = 0.304684 + 1.160470I
1.08964 3.91173I 0
u = 1.261520 0.301281I
a = 0.579930 0.064910I
b = 0.304684 1.160470I
1.08964 + 3.91173I 0
u = 0.647164 + 0.262298I
a = 0.33760 + 1.75787I
b = 0.739546 + 0.278175I
5.12039 + 4.35071I 0
u = 0.647164 0.262298I
a = 0.33760 1.75787I
b = 0.739546 0.278175I
5.12039 4.35071I 0
u = 1.231500 + 0.453162I
a = 2.08904 0.92007I
b = 1.49855 + 0.17664I
9.09985 + 5.23913I 0
u = 1.231500 0.453162I
a = 2.08904 + 0.92007I
b = 1.49855 0.17664I
9.09985 5.23913I 0
u = 0.221710 + 1.307120I
a = 0.285676 0.469695I
b = 1.28686 + 0.60598I
1.42759 + 7.54557I 0
15
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.221710 1.307120I
a = 0.285676 + 0.469695I
b = 1.28686 0.60598I
1.42759 7.54557I 0
u = 1.230740 + 0.511440I
a = 1.74491 + 1.14224I
b = 1.368610 0.170839I
8.76679 3.97759I 0
u = 1.230740 0.511440I
a = 1.74491 1.14224I
b = 1.368610 + 0.170839I
8.76679 + 3.97759I 0
u = 1.161600 + 0.654083I
a = 0.249946 0.007995I
b = 0.796581 0.849957I
5.49836 0.49981I 0
u = 1.161600 0.654083I
a = 0.249946 + 0.007995I
b = 0.796581 + 0.849957I
5.49836 + 0.49981I 0
u = 1.254300 + 0.476731I
a = 0.305065 0.131370I
b = 0.036167 0.925380I
6.25848 + 8.38918I 0
u = 1.254300 0.476731I
a = 0.305065 + 0.131370I
b = 0.036167 + 0.925380I
6.25848 8.38918I 0
u = 1.332760 + 0.251941I
a = 1.53065 0.17190I
b = 1.36195 0.43879I
10.53900 3.28777I 0
u = 1.332760 0.251941I
a = 1.53065 + 0.17190I
b = 1.36195 + 0.43879I
10.53900 + 3.28777I 0
u = 0.276801 + 0.570508I
a = 0.286998 + 0.049882I
b = 0.444883 + 0.822005I
0.37927 1.97711I 0
16
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.276801 0.570508I
a = 0.286998 0.049882I
b = 0.444883 0.822005I
0.37927 + 1.97711I 0
u = 0.375201 + 0.492490I
a = 0.744863 0.250786I
b = 0.166968 + 0.139307I
1.114590 + 0.401874I 0
u = 0.375201 0.492490I
a = 0.744863 + 0.250786I
b = 0.166968 0.139307I
1.114590 0.401874I 0
u = 0.085429 + 0.591958I
a = 1.91604 + 1.08934I
b = 0.442090 0.675980I
3.00195 4.31106I 0
u = 0.085429 0.591958I
a = 1.91604 1.08934I
b = 0.442090 + 0.675980I
3.00195 + 4.31106I 0
u = 1.301550 + 0.522330I
a = 0.439028 0.363167I
b = 0.282008 1.239440I
3.7589 13.6502I 0
u = 1.301550 0.522330I
a = 0.439028 + 0.363167I
b = 0.282008 + 1.239440I
3.7589 + 13.6502I 0
u = 0.150731 + 0.572727I
a = 0.235175 + 0.122498I
b = 0.594135 0.567255I
1.74023 + 0.39935I 0
u = 0.150731 0.572727I
a = 0.235175 0.122498I
b = 0.594135 + 0.567255I
1.74023 0.39935I 0
u = 0.330324 + 0.481603I
a = 0.620211 0.426795I
b = 1.098310 0.449362I
3.99697 + 2.30639I 0
17
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.330324 0.481603I
a = 0.620211 + 0.426795I
b = 1.098310 + 0.449362I
3.99697 2.30639I 0
u = 1.37512 + 0.36567I
a = 1.61474 0.50797I
b = 1.62668 0.20347I
10.64380 + 7.96001I 0
u = 1.37512 0.36567I
a = 1.61474 + 0.50797I
b = 1.62668 + 0.20347I
10.64380 7.96001I 0
u = 1.42368 + 0.05365I
a = 1.92968 0.59993I
b = 1.007090 0.305244I
9.73211 0.72862I 0
u = 1.42368 0.05365I
a = 1.92968 + 0.59993I
b = 1.007090 + 0.305244I
9.73211 + 0.72862I 0
u = 1.34316 + 0.47875I
a = 0.540948 + 0.003445I
b = 0.169189 1.158220I
4.17992 3.09056I 0
u = 1.34316 0.47875I
a = 0.540948 0.003445I
b = 0.169189 + 1.158220I
4.17992 + 3.09056I 0
u = 1.38981 + 0.33380I
a = 1.74926 + 0.39755I
b = 1.383630 0.033651I
7.78454 3.02046I 0
u = 1.38981 0.33380I
a = 1.74926 0.39755I
b = 1.383630 + 0.033651I
7.78454 + 3.02046I 0
u = 1.37065 + 0.41141I
a = 2.08744 + 0.48751I
b = 0.943955 0.351472I
1.84180 + 8.35189I 0
18
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.37065 0.41141I
a = 2.08744 0.48751I
b = 0.943955 + 0.351472I
1.84180 8.35189I 0
u = 0.10147 + 1.43531I
a = 0.077662 1.057210I
b = 0.30045 + 1.43856I
5.08012 1.04482I 0
u = 0.10147 1.43531I
a = 0.077662 + 1.057210I
b = 0.30045 1.43856I
5.08012 + 1.04482I 0
u = 1.34660 + 0.53135I
a = 0.302884 + 0.299279I
b = 0.440339 + 1.295460I
0.59625 + 7.19814I 0
u = 1.34660 0.53135I
a = 0.302884 0.299279I
b = 0.440339 1.295460I
0.59625 7.19814I 0
u = 1.34014 + 0.60969I
a = 1.65962 + 0.99269I
b = 1.32556 0.68118I
7.0959 + 20.3913I 0
u = 1.34014 0.60969I
a = 1.65962 0.99269I
b = 1.32556 + 0.68118I
7.0959 20.3913I 0
u = 1.35716 + 0.60958I
a = 1.55427 0.87412I
b = 1.268760 + 0.442159I
5.64483 + 8.45646I 0
u = 1.35716 0.60958I
a = 1.55427 + 0.87412I
b = 1.268760 0.442159I
5.64483 8.45646I 0
u = 1.47733 + 0.19605I
a = 1.403440 + 0.140394I
b = 1.36593 + 0.44138I
5.36633 2.05046I 0
19
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.47733 0.19605I
a = 1.403440 0.140394I
b = 1.36593 0.44138I
5.36633 + 2.05046I 0
u = 1.37551 + 0.58206I
a = 1.67685 + 0.84959I
b = 1.262590 0.516035I
9.9360 13.5352I 0
u = 1.37551 0.58206I
a = 1.67685 0.84959I
b = 1.262590 + 0.516035I
9.9360 + 13.5352I 0
u = 1.37676 + 0.58869I
a = 1.74311 0.68706I
b = 0.914411 + 0.204323I
0.07993 3.14611I 0
u = 1.37676 0.58869I
a = 1.74311 + 0.68706I
b = 0.914411 0.204323I
0.07993 + 3.14611I 0
u = 1.38162 + 0.58756I
a = 1.44313 + 0.89154I
b = 1.50726 0.43510I
8.81779 3.38404I 0
u = 1.38162 0.58756I
a = 1.44313 0.89154I
b = 1.50726 + 0.43510I
8.81779 + 3.38404I 0
u = 1.36377 + 0.63586I
a = 1.51294 0.92796I
b = 1.30941 + 0.72075I
2.3490 14.2732I 0
u = 1.36377 0.63586I
a = 1.51294 + 0.92796I
b = 1.30941 0.72075I
2.3490 + 14.2732I 0
u = 1.52541 + 0.05793I
a = 1.59016 + 0.44216I
b = 0.878284 + 0.146429I
8.89709 + 1.21364I 0
20
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.52541 0.05793I
a = 1.59016 0.44216I
b = 0.878284 0.146429I
8.89709 1.21364I 0
u = 1.32888 + 0.76202I
a = 1.18883 + 1.04197I
b = 1.20462 0.80755I
6.72128 + 7.21119I 0
u = 1.32888 0.76202I
a = 1.18883 1.04197I
b = 1.20462 + 0.80755I
6.72128 7.21119I 0
u = 0.463129 + 0.037953I
a = 0.591795 0.376644I
b = 0.886324 0.307856I
1.46629 + 0.61331I 6.68087 + 1.30735I
u = 0.463129 0.037953I
a = 0.591795 + 0.376644I
b = 0.886324 + 0.307856I
1.46629 0.61331I 6.68087 1.30735I
u = 0.039278 + 0.434058I
a = 2.29975 + 0.71426I
b = 0.977335 + 0.298452I
4.89990 + 4.37822I 1.92116 6.85769I
u = 0.039278 0.434058I
a = 2.29975 0.71426I
b = 0.977335 0.298452I
4.89990 4.37822I 1.92116 + 6.85769I
u = 1.52942 + 0.34829I
a = 1.315230 0.277888I
b = 1.34392 0.44415I
9.04257 + 8.37334I 0
u = 1.52942 0.34829I
a = 1.315230 + 0.277888I
b = 1.34392 + 0.44415I
9.04257 8.37334I 0
u = 1.54856 + 0.41904I
a = 1.43565 0.23882I
b = 1.183120 0.194524I
11.18890 1.08010I 0
21
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.54856 0.41904I
a = 1.43565 + 0.23882I
b = 1.183120 + 0.194524I
11.18890 + 1.08010I 0
u = 0.326506 + 0.179382I
a = 1.70122 0.83343I
b = 1.203310 0.622332I
1.62999 7.81122I 3.69855 + 4.30402I
u = 0.326506 0.179382I
a = 1.70122 + 0.83343I
b = 1.203310 + 0.622332I
1.62999 + 7.81122I 3.69855 4.30402I
u = 0.244239 + 0.209836I
a = 1.74084 0.44589I
b = 0.981116 0.608112I
0.59753 5.00515I 1.10628 + 2.34393I
u = 0.244239 0.209836I
a = 1.74084 + 0.44589I
b = 0.981116 + 0.608112I
0.59753 + 5.00515I 1.10628 2.34393I
22
II. I
u
2
= h3.32 × 10
40
u
52
2.35 × 10
40
u
51
+ · · · + 1.43 × 10
38
b + 4.37 ×
10
40
, 1.48 × 10
41
u
52
+ 8.39 × 10
40
u
51
+ · · · + 1.43 × 10
38
a 1.73 ×
10
41
, u
53
14u
51
+ · · · 11u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
6
=
1033.47u
52
586.239u
51
+ ··· 2034.70u + 1205.80
232.154u
52
+ 164.107u
51
+ ··· + 392.787u 305.668
a
2
=
759.826u
52
495.375u
51
+ ··· 1526.02u + 1012.14
598.451u
52
+ 397.853u
51
+ ··· + 1082.59u 726.395
a
1
=
215.060u
52
+ 146.327u
51
+ ··· + 316.395u 209.630
1114.17u
52
+ 736.678u
51
+ ··· + 2057.47u 1368.10
a
5
=
387.513u
52
216.690u
51
+ ··· 768.298u + 432.814
716.532u
52
530.992u
51
+ ··· 1375.06u + 978.824
a
8
=
u
u
a
12
=
248.772u
52
156.582u
51
+ ··· 582.712u + 380.721
650.335u
52
+ 433.769u
51
+ ··· + 1158.37u 777.746
a
7
=
546.571u
52
+ 377.064u
51
+ ··· + 1061.69u 754.703
351.767u
52
+ 224.351u
51
+ ··· + 754.487u 536.484
a
11
=
52.9636u
52
105.670u
51
+ ··· 87.6800u + 204.640
430.934u
52
311.679u
51
+ ··· 856.757u + 660.094
a
10
=
703.420u
52
+ 455.534u
51
+ ··· + 1343.06u 886.322
1439.52u
52
+ 949.093u
51
+ ··· + 2690.94u 1793.54
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3884.37u
52
2682.08u
51
+ ··· 7739.45u + 5487.07
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
53
9u
52
+ ··· + 195u 11
c
2
u
53
+ 3u
52
+ ··· + 3u + 1
c
3
u
53
14u
51
+ ··· 11u
2
+ 1
c
4
u
53
14u
51
+ ··· + 19u
2
1
c
5
u
53
3u
52
+ ··· + 3u 1
c
6
u
53
u
52
+ ··· + 36u 1
c
7
u
53
+ 7u
52
+ ··· + 32u + 4
c
8
u
53
14u
51
+ ··· + 11u
2
1
c
9
u
53
+ u
52
+ ··· 8u 1
c
10
u
53
7u
52
+ ··· + 32u 4
c
11
u
53
14u
51
+ ··· 19u
2
+ 1
c
12
u
53
u
52
+ ··· + 7u + 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
y
52
+ ··· 40955y 121
c
2
, c
5
y
53
25y
52
+ ··· + 41y 1
c
3
, c
8
y
53
28y
52
+ ··· + 22y 1
c
4
, c
11
y
53
28y
52
+ ··· + 38y 1
c
6
y
53
+ 9y
52
+ ··· + 274y 1
c
7
, c
10
y
53
+ 37y
52
+ ··· 368y 16
c
9
y
53
+ 13y
52
+ ··· 34y 1
c
12
y
53
+ 33y
52
+ ··· 59y 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.752844 + 0.713687I
a = 0.198059 0.480468I
b = 0.914130 0.339042I
0.09340 + 1.65159I 0
u = 0.752844 0.713687I
a = 0.198059 + 0.480468I
b = 0.914130 + 0.339042I
0.09340 1.65159I 0
u = 0.299078 + 1.026960I
a = 0.393358 + 0.613280I
b = 1.140540 0.485752I
1.34681 6.32629I 0
u = 0.299078 1.026960I
a = 0.393358 0.613280I
b = 1.140540 + 0.485752I
1.34681 + 6.32629I 0
u = 1.059390 + 0.320455I
a = 1.290580 0.016665I
b = 0.727852 1.003420I
0.12206 + 2.81902I 0
u = 1.059390 0.320455I
a = 1.290580 + 0.016665I
b = 0.727852 + 1.003420I
0.12206 2.81902I 0
u = 0.819880 + 0.298094I
a = 0.722650 + 0.495336I
b = 0.947182 0.712365I
0.27515 5.80106I 0. + 9.09280I
u = 0.819880 0.298094I
a = 0.722650 0.495336I
b = 0.947182 + 0.712365I
0.27515 + 5.80106I 0. 9.09280I
u = 1.030080 + 0.471732I
a = 0.415358 0.419386I
b = 0.624176 + 0.253691I
5.40111 + 7.24256I 0
u = 1.030080 0.471732I
a = 0.415358 + 0.419386I
b = 0.624176 0.253691I
5.40111 7.24256I 0
28
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.095380 + 0.356719I
a = 0.223666 0.310574I
b = 0.151815 0.857240I
0.17444 5.06362I 0
u = 1.095380 0.356719I
a = 0.223666 + 0.310574I
b = 0.151815 + 0.857240I
0.17444 + 5.06362I 0
u = 0.260655 + 0.769473I
a = 0.298108 0.749014I
b = 1.188530 + 0.204645I
5.11094 + 2.19227I 1.08190 2.25516I
u = 0.260655 0.769473I
a = 0.298108 + 0.749014I
b = 1.188530 0.204645I
5.11094 2.19227I 1.08190 + 2.25516I
u = 0.629209 + 0.510184I
a = 0.773759 0.759289I
b = 1.004930 + 0.404428I
5.17858 + 2.02235I 2.59548 3.49504I
u = 0.629209 0.510184I
a = 0.773759 + 0.759289I
b = 1.004930 0.404428I
5.17858 2.02235I 2.59548 + 3.49504I
u = 0.797683 + 0.111339I
a = 0.466604 0.948576I
b = 0.639151 1.191020I
1.51765 0.97300I 9.68105 1.37819I
u = 0.797683 0.111339I
a = 0.466604 + 0.948576I
b = 0.639151 + 1.191020I
1.51765 + 0.97300I 9.68105 + 1.37819I
u = 0.794471 + 0.121913I
a = 0.563563 1.291760I
b = 0.251719 1.118650I
1.70258 + 3.06326I 5.81290 2.73140I
u = 0.794471 0.121913I
a = 0.563563 + 1.291760I
b = 0.251719 + 1.118650I
1.70258 3.06326I 5.81290 + 2.73140I
29
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.991191 + 0.675691I
a = 0.424392 0.523521I
b = 0.708148 + 0.720515I
4.71573 + 1.55508I 0
u = 0.991191 0.675691I
a = 0.424392 + 0.523521I
b = 0.708148 0.720515I
4.71573 1.55508I 0
u = 1.165290 + 0.336388I
a = 0.71543 1.76538I
b = 0.571523 0.095423I
1.59579 6.35701I 0
u = 1.165290 0.336388I
a = 0.71543 + 1.76538I
b = 0.571523 + 0.095423I
1.59579 + 6.35701I 0
u = 0.411876 + 1.152010I
a = 1.174370 + 0.130403I
b = 0.633482 0.149689I
3.91392 + 3.35036I 0
u = 0.411876 1.152010I
a = 1.174370 0.130403I
b = 0.633482 + 0.149689I
3.91392 3.35036I 0
u = 1.141410 + 0.462340I
a = 1.91918 1.28362I
b = 1.104120 + 0.578790I
5.49466 6.54899I 0
u = 1.141410 0.462340I
a = 1.91918 + 1.28362I
b = 1.104120 0.578790I
5.49466 + 6.54899I 0
u = 1.214970 + 0.215579I
a = 2.50327 + 0.14853I
b = 1.252620 0.440926I
4.78145 + 8.92871I 0
u = 1.214970 0.215579I
a = 2.50327 0.14853I
b = 1.252620 + 0.440926I
4.78145 8.92871I 0
30
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.726895 + 0.011194I
a = 0.92003 1.45073I
b = 1.173500 + 0.560834I
2.47355 + 8.00979I 5.29973 6.12277I
u = 0.726895 0.011194I
a = 0.92003 + 1.45073I
b = 1.173500 0.560834I
2.47355 8.00979I 5.29973 + 6.12277I
u = 0.525289 + 0.501536I
a = 1.03635 + 1.25446I
b = 0.795025 + 0.150056I
3.87787 3.22018I 0. + 5.52484I
u = 0.525289 0.501536I
a = 1.03635 1.25446I
b = 0.795025 0.150056I
3.87787 + 3.22018I 0. 5.52484I
u = 0.708618 + 0.119698I
a = 3.70903 + 1.70788I
b = 0.522684 0.189476I
0.50284 + 4.33535I 8.51434 0.68763I
u = 0.708618 0.119698I
a = 3.70903 1.70788I
b = 0.522684 + 0.189476I
0.50284 4.33535I 8.51434 + 0.68763I
u = 1.175600 + 0.528767I
a = 1.050890 + 0.713469I
b = 0.529417 0.234138I
0.83195 + 2.49544I 0
u = 1.175600 0.528767I
a = 1.050890 0.713469I
b = 0.529417 + 0.234138I
0.83195 2.49544I 0
u = 1.224470 + 0.408994I
a = 2.12820 + 0.72335I
b = 1.45549 0.05041I
9.22566 6.14828I 0
u = 1.224470 0.408994I
a = 2.12820 0.72335I
b = 1.45549 + 0.05041I
9.22566 + 6.14828I 0
31
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.658241
a = 4.15037
b = 0.417329
4.44579 13.6430
u = 0.028280 + 1.387320I
a = 0.052279 + 1.089990I
b = 0.24874 1.39671I
5.12796 + 0.95282I 0
u = 0.028280 1.387320I
a = 0.052279 1.089990I
b = 0.24874 + 1.39671I
5.12796 0.95282I 0
u = 1.293790 + 0.538796I
a = 1.61599 1.03387I
b = 1.49779 + 0.33300I
8.18982 + 3.34786I 0
u = 1.293790 0.538796I
a = 1.61599 + 1.03387I
b = 1.49779 0.33300I
8.18982 3.34786I 0
u = 0.515235 + 0.205408I
a = 1.39548 2.24020I
b = 1.041340 + 0.290147I
4.99057 3.63097I 5.49740 + 2.27793I
u = 0.515235 0.205408I
a = 1.39548 + 2.24020I
b = 1.041340 0.290147I
4.99057 + 3.63097I 5.49740 2.27793I
u = 1.46902 + 0.06627I
a = 2.01781 + 0.22433I
b = 0.962652 + 0.218339I
9.29019 + 0.18307I 0
u = 1.46902 0.06627I
a = 2.01781 0.22433I
b = 0.962652 0.218339I
9.29019 0.18307I 0
u = 1.46774 + 0.12916I
a = 1.46035 + 0.55805I
b = 0.958796 + 0.218988I
9.27640 + 1.59820I 0
32
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.46774 0.12916I
a = 1.46035 0.55805I
b = 0.958796 0.218988I
9.27640 1.59820I 0
u = 0.080303 + 0.512048I
a = 0.426879 + 1.243660I
b = 0.991593 0.288651I
0.736838 + 0.952251I 3.21681 1.98889I
u = 0.080303 0.512048I
a = 0.426879 1.243660I
b = 0.991593 + 0.288651I
0.736838 0.952251I 3.21681 + 1.98889I
33
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
53
9u
52
+ ··· + 195u 11)
· (u
175
8u
174
+ ··· + 1890868908462u 280537441299)
c
2
(u
53
+ 3u
52
+ ··· + 3u + 1)(u
175
+ 4u
174
+ ··· + 417270u + 63403)
c
3
(u
53
14u
51
+ ··· 11u
2
+ 1)(u
175
+ u
174
+ ··· 2853u 2621)
c
4
(u
53
14u
51
+ ··· + 19u
2
1)(u
175
+ u
174
+ ··· 21401u + 1549)
c
5
(u
53
3u
52
+ ··· + 3u 1)(u
175
+ 4u
174
+ ··· + 417270u + 63403)
c
6
(u
53
u
52
+ ··· + 36u 1)(u
175
2u
174
+ ··· 657105u + 475777)
c
7
(u
53
+ 7u
52
+ ··· + 32u + 4)(u
175
+ 6u
174
+ ··· 343340u 23572)
c
8
(u
53
14u
51
+ ··· + 11u
2
1)(u
175
+ u
174
+ ··· 2853u 2621)
c
9
(u
53
+ u
52
+ ··· 8u 1)
· (u
175
6u
174
+ ··· + 4627516764u + 594875704)
c
10
(u
53
7u
52
+ ··· + 32u 4)(u
175
+ 6u
174
+ ··· 343340u 23572)
c
11
(u
53
14u
51
+ ··· 19u
2
+ 1)(u
175
+ u
174
+ ··· 21401u + 1549)
c
12
(u
53
u
52
+ ··· + 7u + 1)(u
175
+ 2u
174
+ ··· 218568u + 5697)
34
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
53
y
52
+ ··· 40955y 121)
· (y
175
52y
174
+ ··· + 3.27 × 10
24
y 7.87 × 10
22
)
c
2
, c
5
(y
53
25y
52
+ ··· + 41y 1)
· (y
175
96y
174
+ ··· + 241757138316y 4019940409)
c
3
, c
8
(y
53
28y
52
+ ··· + 22y 1)
· (y
175
107y
174
+ ··· + 304239221y 6869641)
c
4
, c
11
(y
53
28y
52
+ ··· + 38y 1)
· (y
175
87y
174
+ ··· + 251496317y 2399401)
c
6
(y
53
+ 9y
52
+ ··· + 274y 1)
· (y
175
+ 18y
174
+ ··· 12874725123895y 226363753729)
c
7
, c
10
(y
53
+ 37y
52
+ ··· 368y 16)
· (y
175
+ 122y
174
+ ··· 6061106160y 555639184)
c
9
(y
53
+ 13y
52
+ ··· 34y 1)
· (y
175
+ 62y
174
+ ··· 2.61 × 10
19
y 3.54 × 10
17
)
c
12
(y
53
+ 33y
52
+ ··· 59y 1)
· (y
175
+ 62y
174
+ ··· 12813231636y 32455809)
35