12a
1056
(K12a
1056
)
A knot diagram
1
Linearized knot diagam
4 7 9 10 1 11 3 12 2 5 8 6
Solving Sequence
8,11
12
3,9
4 7 2 6 1 5 10
c
11
c
8
c
3
c
7
c
2
c
6
c
12
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.20589 × 10
861
u
169
− 1.68317 × 10
862
u
168
+ ··· + 3.92119 × 10
861
b − 1.07359 × 10
864
,
− 2.08380 × 10
863
u
169
− 1.48692 × 10
864
u
168
+ ··· + 8.66583 × 10
863
a − 5.10383 × 10
865
,
u
170
+ 8u
169
+ ··· − 715u + 221i
I
u
2
= h2.87441 × 10
31
u
46
+ 1.04633 × 10
32
u
45
+ ··· + 3.67466 × 10
29
b − 6.08288 × 10
31
,
1.01354 × 10
31
u
46
+ 3.82828 × 10
31
u
45
+ ··· + 3.67466 × 10
29
a − 1.99417 × 10
31
, u
47
+ 3u
46
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 217 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−2.21 × 10
861
u
169
− 1.68 × 10
862
u
168
+ · · · + 3.92 × 10
861
b − 1.07 ×
10
864
, −2.08 × 10
863
u
169
− 1.49 × 10
864
u
168
+ · · · + 8.67 × 10
863
a − 5.10 ×
10
865
, u
170
+ 8u
169
+ · · · − 715u + 221i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
3
=
0.240462u
169
+ 1.71584u
168
+ ··· − 213.145u + 58.8960
0.562557u
169
+ 4.29249u
168
+ ··· − 1443.71u + 273.792
a
9
=
−u
−u
3
+ u
a
4
=
0.345473u
169
+ 2.53056u
168
+ ··· − 549.544u + 119.828
0.451916u
169
+ 3.44659u
168
+ ··· − 1148.66u + 218.467
a
7
=
0.0758536u
169
+ 0.482857u
168
+ ··· + 31.9502u + 1.29112
0.0670230u
169
+ 0.611089u
168
+ ··· − 518.273u + 88.7818
a
2
=
1.29316u
169
+ 9.38618u
168
+ ··· − 1589.87u + 368.013
0.647019u
169
+ 4.85787u
168
+ ··· − 1368.07u + 269.970
a
6
=
0.142877u
169
+ 1.09395u
168
+ ··· − 486.322u + 90.0730
0.0670230u
169
+ 0.611089u
168
+ ··· − 518.273u + 88.7818
a
1
=
3.05118u
169
+ 22.3493u
168
+ ··· − 4601.86u + 988.759
1.73028u
169
+ 12.7494u
168
+ ··· − 2868.52u + 600.253
a
5
=
0.317412u
169
+ 2.17686u
168
+ ··· − 245.983u + 62.9293
−1.04715u
169
− 7.63752u
168
+ ··· + 1595.46u − 335.601
a
10
=
−0.896039u
169
− 6.43983u
168
+ ··· + 1252.55u − 271.632
−0.841413u
169
− 6.23424u
168
+ ··· + 1470.83u − 307.080
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.513757u
169
− 3.30789u
168
+ ··· − 410.609u + 24.5051
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
170
− 14u
169
+ ··· + 18u − 1
c
2
, c
7
u
170
+ u
169
+ ··· − 42944u + 1984
c
3
u
170
− u
169
+ ··· − 276535005u − 23926117
c
4
, c
10
u
170
+ u
169
+ ··· + 60040u − 6379
c
5
, c
12
u
170
+ 2u
169
+ ··· + 6420u − 35591
c
6
u
170
− u
169
+ ··· + 9130974u + 5572759
c
8
, c
11
u
170
+ 8u
169
+ ··· − 715u + 221
c
9
u
170
+ 3u
169
+ ··· + 811454u + 271819
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
170
+ 6y
169
+ ··· − 760y + 1
c
2
, c
7
y
170
− 93y
169
+ ··· − 827236352y + 3936256
c
3
y
170
− 41y
169
+ ··· − 46800698030178335y + 572459074697689
c
4
, c
10
y
170
− 113y
169
+ ··· − 1618495822y + 40691641
c
5
, c
12
y
170
+ 118y
169
+ ··· + 25027873906y + 1266719281
c
6
y
170
− 9y
169
+ ··· + 1788240547802984y + 31055642872081
c
8
, c
11
y
170
− 88y
169
+ ··· + 1304511y + 48841
c
9
y
170
+ 43y
169
+ ··· + 6707969409918y + 73885568761
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.806491 + 0.602217I
a = −0.642128 + 0.983618I
b = 0.19143 − 1.76020I
7.48922 − 0.81335I 0
u = 0.806491 − 0.602217I
a = −0.642128 − 0.983618I
b = 0.19143 + 1.76020I
7.48922 + 0.81335I 0
u = −0.923484 + 0.347149I
a = 1.12852 − 1.00215I
b = −0.674725 + 0.109848I
−5.16258 − 1.55018I 0
u = −0.923484 − 0.347149I
a = 1.12852 + 1.00215I
b = −0.674725 − 0.109848I
−5.16258 + 1.55018I 0
u = 0.141671 + 0.976038I
a = −0.488385 + 1.125170I
b = −0.03831 − 1.42440I
3.36613 + 3.99327I 0
u = 0.141671 − 0.976038I
a = −0.488385 − 1.125170I
b = −0.03831 + 1.42440I
3.36613 − 3.99327I 0
u = 0.956886 + 0.364577I
a = 1.035210 − 0.734016I
b = −0.30003 + 2.40004I
2.92615 − 8.39267I 0
u = 0.956886 − 0.364577I
a = 1.035210 + 0.734016I
b = −0.30003 − 2.40004I
2.92615 + 8.39267I 0
u = 0.798269 + 0.554483I
a = −1.29539 + 0.66106I
b = −0.907230 − 0.822265I
7.53091 − 3.76031I 0
u = 0.798269 − 0.554483I
a = −1.29539 − 0.66106I
b = −0.907230 + 0.822265I
7.53091 + 3.76031I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.831602 + 0.494310I
a = −1.48201 − 0.73010I
b = −0.840353 + 1.057020I
4.31538 + 8.41906I 0
u = −0.831602 − 0.494310I
a = −1.48201 + 0.73010I
b = −0.840353 − 1.057020I
4.31538 − 8.41906I 0
u = −0.338787 + 0.978329I
a = −0.007267 − 0.513671I
b = −0.80769 + 1.41151I
3.70858 + 2.48023I 0
u = −0.338787 − 0.978329I
a = −0.007267 + 0.513671I
b = −0.80769 − 1.41151I
3.70858 − 2.48023I 0
u = −0.802710 + 0.530461I
a = −0.947896 − 1.022750I
b = 0.15648 + 1.76490I
4.38227 − 4.26234I 0
u = −0.802710 − 0.530461I
a = −0.947896 + 1.022750I
b = 0.15648 − 1.76490I
4.38227 + 4.26234I 0
u = −1.044890 + 0.163904I
a = −0.738916 − 0.484622I
b = −0.99773 + 1.59669I
−1.66846 + 0.48444I 0
u = −1.044890 − 0.163904I
a = −0.738916 + 0.484622I
b = −0.99773 − 1.59669I
−1.66846 − 0.48444I 0
u = −0.414758 + 0.845908I
a = 0.183797 − 1.029530I
b = 0.40704 + 1.83699I
0.96077 + 6.50241I 0
u = −0.414758 − 0.845908I
a = 0.183797 + 1.029530I
b = 0.40704 − 1.83699I
0.96077 − 6.50241I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.158664 + 1.046010I
a = −0.605569 − 1.030360I
b = 0.236176 + 1.351120I
−0.85216 − 7.75918I 0
u = −0.158664 − 1.046010I
a = −0.605569 + 1.030360I
b = 0.236176 − 1.351120I
−0.85216 + 7.75918I 0
u = 0.834299 + 0.650852I
a = −0.098909 + 1.187020I
b = −1.35369 − 1.59644I
−3.52491 − 5.82721I 0
u = 0.834299 − 0.650852I
a = −0.098909 − 1.187020I
b = −1.35369 + 1.59644I
−3.52491 + 5.82721I 0
u = −1.018280 + 0.313229I
a = 0.828726 + 0.572675I
b = −1.02081 − 1.92324I
4.88864 + 3.76517I 0
u = −1.018280 − 0.313229I
a = 0.828726 − 0.572675I
b = −1.02081 + 1.92324I
4.88864 − 3.76517I 0
u = 0.224394 + 0.906655I
a = −0.559436 − 0.349460I
b = 0.096076 + 0.954016I
4.22731 + 2.52538I 0
u = 0.224394 − 0.906655I
a = −0.559436 + 0.349460I
b = 0.096076 − 0.954016I
4.22731 − 2.52538I 0
u = 1.036580 + 0.282285I
a = −0.811496 + 0.728701I
b = −1.43074 − 1.60823I
−6.33389 − 5.42778I 0
u = 1.036580 − 0.282285I
a = −0.811496 − 0.728701I
b = −1.43074 + 1.60823I
−6.33389 + 5.42778I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.366311 + 1.028260I
a = −0.601079 − 0.608587I
b = −0.376946 + 0.702967I
1.11850 + 2.49775I 0
u = −0.366311 − 1.028260I
a = −0.601079 + 0.608587I
b = −0.376946 − 0.702967I
1.11850 − 2.49775I 0
u = 0.955413 + 0.535542I
a = −1.031710 − 0.527843I
b = 0.492943 − 0.739556I
−4.00039 + 1.13083I 0
u = 0.955413 − 0.535542I
a = −1.031710 + 0.527843I
b = 0.492943 + 0.739556I
−4.00039 − 1.13083I 0
u = 1.085970 + 0.244696I
a = 0.996060 + 0.557928I
b = −0.051939 + 0.187299I
−2.66025 + 2.54993I 0
u = 1.085970 − 0.244696I
a = 0.996060 − 0.557928I
b = −0.051939 − 0.187299I
−2.66025 − 2.54993I 0
u = 0.874696 + 0.133073I
a = 0.774374 + 1.094520I
b = −0.046872 − 0.469309I
−1.30487 + 1.72427I 0
u = 0.874696 − 0.133073I
a = 0.774374 − 1.094520I
b = −0.046872 + 0.469309I
−1.30487 − 1.72427I 0
u = −0.497941 + 0.729795I
a = 1.165820 + 0.629819I
b = 0.006520 − 0.998511I
−2.03235 − 1.15583I 0
u = −0.497941 − 0.729795I
a = 1.165820 − 0.629819I
b = 0.006520 + 0.998511I
−2.03235 + 1.15583I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.061980 + 0.362119I
a = −0.528626 − 0.797838I
b = 0.149722 + 0.444329I
−2.90057 − 3.69809I 0
u = 1.061980 − 0.362119I
a = −0.528626 + 0.797838I
b = 0.149722 − 0.444329I
−2.90057 + 3.69809I 0
u = −1.002390 + 0.507253I
a = −0.775875 − 0.405924I
b = 0.36366 + 1.97753I
2.66744 + 2.88124I 0
u = −1.002390 − 0.507253I
a = −0.775875 + 0.405924I
b = 0.36366 − 1.97753I
2.66744 − 2.88124I 0
u = 1.039130 + 0.442035I
a = −0.012302 − 0.813686I
b = 0.719743 + 1.063800I
−4.03539 − 3.56778I 0
u = 1.039130 − 0.442035I
a = −0.012302 + 0.813686I
b = 0.719743 − 1.063800I
−4.03539 + 3.56778I 0
u = −1.090030 + 0.319356I
a = −0.276890 + 0.948683I
b = 0.701189 − 0.427324I
−4.85761 + 3.45164I 0
u = −1.090030 − 0.319356I
a = −0.276890 − 0.948683I
b = 0.701189 + 0.427324I
−4.85761 − 3.45164I 0
u = −1.078490 + 0.389234I
a = −0.787230 + 0.880471I
b = 0.048133 − 0.220752I
−6.77478 + 6.50412I 0
u = −1.078490 − 0.389234I
a = −0.787230 − 0.880471I
b = 0.048133 + 0.220752I
−6.77478 − 6.50412I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264729 + 0.810062I
a = −0.919199 + 0.505820I
b = 0.468141 − 0.933035I
−0.28815 − 8.54272I 0
u = −0.264729 − 0.810062I
a = −0.919199 − 0.505820I
b = 0.468141 + 0.933035I
−0.28815 + 8.54272I 0
u = 1.074410 + 0.405058I
a = −0.271488 − 0.968396I
b = 0.076752 + 0.262131I
−1.51684 − 6.06281I 0
u = 1.074410 − 0.405058I
a = −0.271488 + 0.968396I
b = 0.076752 − 0.262131I
−1.51684 + 6.06281I 0
u = 0.770082 + 0.363667I
a = 1.69569 − 0.51875I
b = 1.41698 + 1.21974I
3.56946 + 5.26691I 0
u = 0.770082 − 0.363667I
a = 1.69569 + 0.51875I
b = 1.41698 − 1.21974I
3.56946 − 5.26691I 0
u = −1.087010 + 0.390708I
a = 0.564034 + 1.103930I
b = 0.049728 − 0.981981I
1.73688 + 5.19821I 0
u = −1.087010 − 0.390708I
a = 0.564034 − 1.103930I
b = 0.049728 + 0.981981I
1.73688 − 5.19821I 0
u = −1.014070 + 0.566273I
a = 0.511883 + 1.128890I
b = 0.85240 − 1.71737I
−3.51186 + 6.09555I 0
u = −1.014070 − 0.566273I
a = 0.511883 − 1.128890I
b = 0.85240 + 1.71737I
−3.51186 − 6.09555I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.085820 + 0.418233I
a = 0.798553 − 1.006530I
b = 0.222149 + 1.264500I
1.81434 − 3.63679I 0
u = 1.085820 − 0.418233I
a = 0.798553 + 1.006530I
b = 0.222149 − 1.264500I
1.81434 + 3.63679I 0
u = 1.032740 + 0.540789I
a = −0.639624 + 0.255097I
b = 0.64336 − 1.81774I
3.05780 − 1.58165I 0
u = 1.032740 − 0.540789I
a = −0.639624 − 0.255097I
b = 0.64336 + 1.81774I
3.05780 + 1.58165I 0
u = −1.172030 + 0.110315I
a = 0.546361 − 0.282163I
b = 0.338652 − 0.023447I
−1.85244 − 0.13124I 0
u = −1.172030 − 0.110315I
a = 0.546361 + 0.282163I
b = 0.338652 + 0.023447I
−1.85244 + 0.13124I 0
u = 0.206943 + 0.792165I
a = −0.77995 + 1.43503I
b = −0.23213 − 1.55337I
3.35332 + 3.66686I 0
u = 0.206943 − 0.792165I
a = −0.77995 − 1.43503I
b = −0.23213 + 1.55337I
3.35332 − 3.66686I 0
u = 1.073230 + 0.497941I
a = 0.718078 − 0.898766I
b = 0.56627 + 1.47951I
1.19048 − 4.34256I 0
u = 1.073230 − 0.497941I
a = 0.718078 + 0.898766I
b = 0.56627 − 1.47951I
1.19048 + 4.34256I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.386200 + 0.716926I
a = −1.23518 − 1.03634I
b = −0.09588 + 1.72609I
1.62100 − 4.92629I 0
u = −0.386200 − 0.716926I
a = −1.23518 + 1.03634I
b = −0.09588 − 1.72609I
1.62100 + 4.92629I 0
u = −1.087760 + 0.478529I
a = −0.398562 + 0.536807I
b = −0.090742 + 0.198724I
1.11222 + 2.21408I 0
u = −1.087760 − 0.478529I
a = −0.398562 − 0.536807I
b = −0.090742 − 0.198724I
1.11222 − 2.21408I 0
u = 0.720394 + 0.363656I
a = 0.1003940 − 0.0876140I
b = 0.09773 + 1.62111I
−4.26294 − 3.88455I 0
u = 0.720394 − 0.363656I
a = 0.1003940 + 0.0876140I
b = 0.09773 − 1.62111I
−4.26294 + 3.88455I 0
u = −0.751811 + 0.261150I
a = 1.67265 + 0.26483I
b = 1.79961 − 0.35379I
5.89546 − 1.20354I 0
u = −0.751811 − 0.261150I
a = 1.67265 − 0.26483I
b = 1.79961 + 0.35379I
5.89546 + 1.20354I 0
u = 1.077970 + 0.559514I
a = 0.528140 − 0.647463I
b = 1.59630 + 1.38440I
−5.68088 − 0.47001I 0
u = 1.077970 − 0.559514I
a = 0.528140 + 0.647463I
b = 1.59630 − 1.38440I
−5.68088 + 0.47001I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.141460 + 0.436982I
a = 0.719505 − 0.582562I
b = 1.79355 + 2.15528I
−2.77969 − 9.91991I 0
u = 1.141460 − 0.436982I
a = 0.719505 + 0.582562I
b = 1.79355 − 2.15528I
−2.77969 + 9.91991I 0
u = −0.412691 + 1.159020I
a = 0.751366 + 0.779719I
b = 0.13006 − 1.68933I
2.83336 − 13.74430I 0
u = −0.412691 − 1.159020I
a = 0.751366 − 0.779719I
b = 0.13006 + 1.68933I
2.83336 + 13.74430I 0
u = −0.759159 + 0.077930I
a = 0.27620 + 1.61746I
b = 0.358040 − 0.701749I
−4.43746 + 4.02048I 0
u = −0.759159 − 0.077930I
a = 0.27620 − 1.61746I
b = 0.358040 + 0.701749I
−4.43746 − 4.02048I 0
u = 1.218450 + 0.215306I
a = −0.492939 + 0.554272I
b = −1.21497 − 1.07752I
−5.11241 + 5.14848I 0
u = 1.218450 − 0.215306I
a = −0.492939 − 0.554272I
b = −1.21497 + 1.07752I
−5.11241 − 5.14848I 0
u = −1.103990 + 0.569699I
a = −0.767471 − 0.982847I
b = −1.20004 + 2.17363I
−0.49000 + 9.86610I 0
u = −1.103990 − 0.569699I
a = −0.767471 + 0.982847I
b = −1.20004 − 2.17363I
−0.49000 − 9.86610I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.453656 + 1.178900I
a = −0.531767 + 0.782266I
b = −0.08702 − 1.78565I
5.39447 + 4.87671I 0
u = 0.453656 − 1.178900I
a = −0.531767 − 0.782266I
b = −0.08702 + 1.78565I
5.39447 − 4.87671I 0
u = −0.730425
a = 0.666694
b = 0.382456
−1.46358 0
u = −1.086450 + 0.664366I
a = 0.482956 + 0.569224I
b = 0.96455 − 1.58617I
−1.16037 + 2.89712I 0
u = −1.086450 − 0.664366I
a = 0.482956 − 0.569224I
b = 0.96455 + 1.58617I
−1.16037 − 2.89712I 0
u = 0.499069 + 0.527627I
a = −0.88297 + 1.37264I
b = −1.43447 − 0.40397I
4.65459 − 2.82623I 0
u = 0.499069 − 0.527627I
a = −0.88297 − 1.37264I
b = −1.43447 + 0.40397I
4.65459 + 2.82623I 0
u = −1.161360 + 0.525226I
a = 0.754007 + 0.654124I
b = 0.688330 − 1.215040I
−0.390599 + 1.111860I 0
u = −1.161360 − 0.525226I
a = 0.754007 − 0.654124I
b = 0.688330 + 1.215040I
−0.390599 − 1.111860I 0
u = −0.608042 + 0.394118I
a = −1.44804 − 1.10655I
b = −1.46064 + 0.72845I
3.98560 + 1.07651I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.608042 − 0.394118I
a = −1.44804 + 1.10655I
b = −1.46064 − 0.72845I
3.98560 − 1.07651I 0
u = 1.151370 + 0.560793I
a = −0.779456 + 0.840590I
b = −0.89795 − 2.16549I
0.68066 − 8.67829I 0
u = 1.151370 − 0.560793I
a = −0.779456 − 0.840590I
b = −0.89795 + 2.16549I
0.68066 + 8.67829I 0
u = −1.158310 + 0.565107I
a = 0.651043 − 0.728404I
b = −0.379605 + 0.088246I
−2.91077 + 13.64960I 0
u = −1.158310 − 0.565107I
a = 0.651043 + 0.728404I
b = −0.379605 − 0.088246I
−2.91077 − 13.64960I 0
u = −0.259853 + 1.266720I
a = 0.080496 + 0.743006I
b = 0.08175 − 1.53457I
2.98324 + 4.47610I 0
u = −0.259853 − 1.266720I
a = 0.080496 − 0.743006I
b = 0.08175 + 1.53457I
2.98324 − 4.47610I 0
u = −0.420304 + 1.229010I
a = 0.408093 + 0.560897I
b = 0.63897 − 1.98417I
2.83986 + 2.69706I 0
u = −0.420304 − 1.229010I
a = 0.408093 − 0.560897I
b = 0.63897 + 1.98417I
2.83986 − 2.69706I 0
u = 1.308170 + 0.087102I
a = −0.422502 − 0.416698I
b = 0.371850 + 0.107744I
−7.93701 − 1.01267I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.308170 − 0.087102I
a = −0.422502 + 0.416698I
b = 0.371850 − 0.107744I
−7.93701 + 1.01267I 0
u = 1.176760 + 0.579739I
a = 0.569992 + 0.583963I
b = −0.188102 − 0.147284I
1.43457 − 7.87964I 0
u = 1.176760 − 0.579739I
a = 0.569992 − 0.583963I
b = −0.188102 + 0.147284I
1.43457 + 7.87964I 0
u = 0.663821 + 0.163673I
a = 1.47918 + 0.96656I
b = 0.116724 − 1.086720I
0.37077 + 3.23302I 0
u = 0.663821 − 0.163673I
a = 1.47918 − 0.96656I
b = 0.116724 + 1.086720I
0.37077 − 3.23302I 0
u = 0.285135 + 0.610380I
a = 0.92416 − 1.60790I
b = −0.050637 + 0.924680I
3.32659 + 0.00720I 0
u = 0.285135 − 0.610380I
a = 0.92416 + 1.60790I
b = −0.050637 − 0.924680I
3.32659 − 0.00720I 0
u = 0.489942 + 1.238200I
a = 0.662960 − 0.648185I
b = 0.32328 + 1.65794I
6.77832 + 6.88044I 0
u = 0.489942 − 1.238200I
a = 0.662960 + 0.648185I
b = 0.32328 − 1.65794I
6.77832 − 6.88044I 0
u = −0.224321 + 0.627904I
a = −0.015286 − 0.524588I
b = −0.697858 − 0.367055I
1.46936 + 3.06749I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.224321 − 0.627904I
a = −0.015286 + 0.524588I
b = −0.697858 + 0.367055I
1.46936 − 3.06749I 0
u = −1.239430 + 0.548102I
a = 0.594663 + 0.527662I
b = 1.28662 − 1.99516I
−0.44375 + 3.54352I 0
u = −1.239430 − 0.548102I
a = 0.594663 − 0.527662I
b = 1.28662 + 1.99516I
−0.44375 − 3.54352I 0
u = 1.237470 + 0.568808I
a = −0.627057 + 0.775924I
b = −0.73911 − 1.78795I
0.06510 − 9.48183I 0
u = 1.237470 − 0.568808I
a = −0.627057 − 0.775924I
b = −0.73911 + 1.78795I
0.06510 + 9.48183I 0
u = −0.793060 + 1.121730I
a = −0.603634 − 0.489180I
b = −0.30687 + 1.65575I
5.39327 + 0.10507I 0
u = −0.793060 − 1.121730I
a = −0.603634 + 0.489180I
b = −0.30687 − 1.65575I
5.39327 − 0.10507I 0
u = 0.082693 + 0.619395I
a = 1.330360 − 0.139633I
b = −0.567613 + 0.202043I
−1.43472 − 0.22373I −6.30972 + 0.I
u = 0.082693 − 0.619395I
a = 1.330360 + 0.139633I
b = −0.567613 − 0.202043I
−1.43472 + 0.22373I −6.30972 + 0.I
u = −1.339410 + 0.321709I
a = 0.442287 − 0.111362I
b = 0.236354 + 0.185662I
−1.88503 + 0.69044I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.339410 − 0.321709I
a = 0.442287 + 0.111362I
b = 0.236354 − 0.185662I
−1.88503 − 0.69044I 0
u = −0.596396 + 0.171044I
a = 2.62171 − 0.18103I
b = 0.374303 + 0.234488I
3.70485 − 2.31607I 8.00942 + 10.51133I
u = −0.596396 − 0.171044I
a = 2.62171 + 0.18103I
b = 0.374303 − 0.234488I
3.70485 + 2.31607I 8.00942 − 10.51133I
u = −1.126100 + 0.806514I
a = −0.486449 − 0.786512I
b = −1.14253 + 1.78471I
4.11605 + 6.88628I 0
u = −1.126100 − 0.806514I
a = −0.486449 + 0.786512I
b = −1.14253 − 1.78471I
4.11605 − 6.88628I 0
u = −1.257770 + 0.586925I
a = −0.594375 − 0.866892I
b = −0.84456 + 1.64543I
−4.2304 + 13.5113I 0
u = −1.257770 − 0.586925I
a = −0.594375 + 0.866892I
b = −0.84456 − 1.64543I
−4.2304 − 13.5113I 0
u = −0.602834 + 0.059909I
a = 1.236460 − 0.344801I
b = 0.54829 + 2.39941I
3.83155 + 1.06583I −4.00000 + 2.27970I
u = −0.602834 − 0.059909I
a = 1.236460 + 0.344801I
b = 0.54829 − 2.39941I
3.83155 − 1.06583I −4.00000 − 2.27970I
u = −1.358310 + 0.338934I
a = −0.645718 + 0.311033I
b = −0.788077 − 0.481250I
−2.67108 − 0.80743I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.358310 − 0.338934I
a = −0.645718 − 0.311033I
b = −0.788077 + 0.481250I
−2.67108 + 0.80743I 0
u = −1.41244 + 0.09773I
a = −0.540708 − 0.306582I
b = −0.025817 + 0.713256I
−1.86249 + 2.87351I 0
u = −1.41244 − 0.09773I
a = −0.540708 + 0.306582I
b = −0.025817 − 0.713256I
−1.86249 − 2.87351I 0
u = 1.37826 + 0.32789I
a = 0.455189 + 0.134338I
b = −0.486035 − 0.133376I
−4.44501 − 6.89655I 0
u = 1.37826 − 0.32789I
a = 0.455189 − 0.134338I
b = −0.486035 + 0.133376I
−4.44501 + 6.89655I 0
u = 1.22258 + 0.71942I
a = −0.621398 + 0.775987I
b = −1.07203 − 1.78504I
2.89560 − 11.55240I 0
u = 1.22258 − 0.71942I
a = −0.621398 − 0.775987I
b = −1.07203 + 1.78504I
2.89560 + 11.55240I 0
u = −1.25219 + 0.71084I
a = 0.543757 + 0.865900I
b = 1.04106 − 2.08031I
0.1443 + 20.3788I 0
u = −1.25219 − 0.71084I
a = 0.543757 − 0.865900I
b = 1.04106 + 2.08031I
0.1443 − 20.3788I 0
u = 0.534851 + 0.132966I
a = 1.121550 − 0.197616I
b = 0.35022 + 3.10796I
−0.19642 + 6.85043I −1.84550 + 2.67603I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.534851 − 0.132966I
a = 1.121550 + 0.197616I
b = 0.35022 − 3.10796I
−0.19642 − 6.85043I −1.84550 − 2.67603I
u = −1.33846 + 0.58648I
a = −0.443468 − 0.617881I
b = −0.49859 + 1.62161I
−2.08247 + 3.93238I 0
u = −1.33846 − 0.58648I
a = −0.443468 + 0.617881I
b = −0.49859 − 1.62161I
−2.08247 − 3.93238I 0
u = 1.26749 + 0.74633I
a = 0.492857 − 0.802095I
b = 0.98971 + 2.07463I
4.1866 − 13.8875I 0
u = 1.26749 − 0.74633I
a = 0.492857 + 0.802095I
b = 0.98971 − 2.07463I
4.1866 + 13.8875I 0
u = 0.446362 + 0.272843I
a = 2.69827 − 1.07449I
b = 0.160409 + 0.341725I
3.88766 + 0.27154I 5.15604 + 5.66364I
u = 0.446362 − 0.272843I
a = 2.69827 + 1.07449I
b = 0.160409 − 0.341725I
3.88766 − 0.27154I 5.15604 − 5.66364I
u = −1.26094 + 0.77132I
a = 0.673439 − 0.161979I
b = 0.400369 − 0.223005I
−2.70929 + 1.16729I 0
u = −1.26094 − 0.77132I
a = 0.673439 + 0.161979I
b = 0.400369 + 0.223005I
−2.70929 − 1.16729I 0
u = −1.15098 + 1.00543I
a = 0.179396 + 0.754151I
b = 0.75282 − 2.03006I
−1.98794 + 6.58061I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.15098 − 1.00543I
a = 0.179396 − 0.754151I
b = 0.75282 + 2.03006I
−1.98794 − 6.58061I 0
u = 1.53401 + 0.01399I
a = −0.558959 − 0.287533I
b = −0.340586 + 0.213226I
−4.77758 + 9.26085I 0
u = 1.53401 − 0.01399I
a = −0.558959 + 0.287533I
b = −0.340586 − 0.213226I
−4.77758 − 9.26085I 0
u = 1.50727 + 0.33979I
a = 0.540012 + 0.063785I
b = 0.123494 + 0.461332I
−6.33708 + 2.52064I 0
u = 1.50727 − 0.33979I
a = 0.540012 − 0.063785I
b = 0.123494 − 0.461332I
−6.33708 − 2.52064I 0
u = −1.67875
a = 0.472938
b = 0.657377
−2.97193 0
u = −0.061501 + 0.315308I
a = 1.35388 − 0.54162I
b = −0.015852 − 0.379706I
−0.235966 + 0.960167I −4.61956 − 6.69387I
u = −0.061501 − 0.315308I
a = 1.35388 + 0.54162I
b = −0.015852 + 0.379706I
−0.235966 − 0.960167I −4.61956 + 6.69387I
u = 0.0646493 + 0.1162420I
a = 3.68249 + 3.57533I
b = 0.256926 + 1.011690I
−4.19477 − 3.63377I −8.37769 + 3.26370I
u = 0.0646493 − 0.1162420I
a = 3.68249 − 3.57533I
b = 0.256926 − 1.011690I
−4.19477 + 3.63377I −8.37769 − 3.26370I
21
II.
I
u
2
= h2.87 × 10
31
u
46
+ 1.05 × 10
32
u
45
+ · · · + 3.67 × 10
29
b − 6.08 × 10
31
, 1.01 ×
10
31
u
46
+3.83×10
31
u
45
+· · ·+3.67×10
29
a−1.99×10
31
, u
47
+3u
46
+· · ·−u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
3
=
−27.5820u
46
− 104.181u
45
+ ··· − 10.2611u + 54.2683
−78.2225u
46
− 284.743u
45
+ ··· + 69.3825u + 165.536
a
9
=
−u
−u
3
+ u
a
4
=
−61.0684u
46
− 225.594u
45
+ ··· + 16.0079u + 118.904
−57.7069u
46
− 209.213u
45
+ ··· + 55.6453u + 121.855
a
7
=
22.2310u
46
+ 105.841u
45
+ ··· + 82.2805u − 32.9718
−31.8947u
46
− 116.935u
45
+ ··· + 36.4035u + 61.6576
a
2
=
63.1278u
46
+ 191.176u
45
+ ··· − 181.832u − 83.3637
−72.8214u
46
− 256.230u
45
+ ··· + 83.9789u + 131.849
a
6
=
−9.66367u
46
− 11.0936u
45
+ ··· + 118.684u + 28.6858
−31.8947u
46
− 116.935u
45
+ ··· + 36.4035u + 61.6576
a
1
=
34.6423u
46
+ 73.7290u
45
+ ··· − 214.273u + 46.3463
13.3562u
46
+ 39.7678u
45
+ ··· − 49.9386u − 16.3906
a
5
=
−118.148u
46
− 397.924u
45
+ ··· + 145.219u + 33.4143
−4.96398u
46
− 13.6597u
45
+ ··· + 39.6336u + 18.8281
a
10
=
76.1492u
46
+ 228.217u
45
+ ··· − 231.378u + 35.4088
−54.2807u
46
− 200.494u
45
+ ··· + 20.5694u + 98.0489
(ii) Obstruction class = 1
(iii) Cusp Shapes = 517.085u
46
+ 1849.01u
45
+ ··· − 396.364u − 980.572
22
(iv) u-Polynomials at the component
23
Crossings u-Polynomials at each crossing
c
1
u
47
− 3u
46
+ ··· − 11u
2
+ 1
c
2
u
47
− 14u
45
+ ··· + 4u + 1
c
3
u
47
− 6u
45
+ ··· + 297u − 27
c
4
u
47
− 18u
45
+ ··· + 2u + 1
c
5
u
47
− u
46
+ ··· − 20u + 1
c
6
u
47
+ 15u
44
+ ··· + 178u − 13
c
7
u
47
− 14u
45
+ ··· + 4u − 1
c
8
u
47
− 3u
46
+ ··· − u − 1
c
9
u
47
+ 10u
45
+ ··· + 6u − 1
c
10
u
47
− 18u
45
+ ··· + 2u − 1
c
11
u
47
+ 3u
46
+ ··· − u + 1
c
12
u
47
+ u
46
+ ··· − 20u − 1
24
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
+ 7y
46
+ ··· + 22y −1
c
2
, c
7
y
47
− 28y
46
+ ··· + 36y −1
c
3
y
47
− 12y
46
+ ··· + 54837y −729
c
4
, c
10
y
47
− 36y
46
+ ··· + 4y −1
c
5
, c
12
y
47
+ 43y
46
+ ··· + 76y −1
c
6
y
47
+ 8y
45
+ ··· + 6490y −169
c
8
, c
11
y
47
− 27y
46
+ ··· + 35y −1
c
9
y
47
+ 20y
46
+ ··· − 16y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.889937 + 0.430073I
a = 0.405900 + 1.090710I
b = −0.249732 − 1.338120I
0.28405 + 4.81397I −4.00000 − 6.94228I
u = −0.889937 − 0.430073I
a = 0.405900 − 1.090710I
b = −0.249732 + 1.338120I
0.28405 − 4.81397I −4.00000 + 6.94228I
u = 0.902904 + 0.320536I
a = 1.14702 + 0.96787I
b = −0.593652 + 0.229428I
−5.10557 + 2.06707I −11.08081 − 8.65643I
u = 0.902904 − 0.320536I
a = 1.14702 − 0.96787I
b = −0.593652 − 0.229428I
−5.10557 − 2.06707I −11.08081 + 8.65643I
u = 0.906781 + 0.289471I
a = −0.106618 − 1.163250I
b = 0.492570 + 1.136090I
−5.05622 − 4.70892I −13.0918 + 9.2301I
u = 0.906781 − 0.289471I
a = −0.106618 + 1.163250I
b = 0.492570 − 1.136090I
−5.05622 + 4.70892I −13.0918 − 9.2301I
u = 0.811557 + 0.469734I
a = 0.358509 − 1.070080I
b = 1.06125 + 1.69320I
−4.71152 − 4.88182I −10.09232 + 5.63767I
u = 0.811557 − 0.469734I
a = 0.358509 + 1.070080I
b = 1.06125 − 1.69320I
−4.71152 + 4.88182I −10.09232 − 5.63767I
u = −0.935762 + 0.528889I
a = −0.665153 − 0.391796I
b = 0.48565 + 2.06102I
4.44804 + 2.04172I 0
u = −0.935762 − 0.528889I
a = −0.665153 + 0.391796I
b = 0.48565 − 2.06102I
4.44804 − 2.04172I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.450788 + 0.802899I
a = −0.462859 − 1.134600I
b = −0.885500 + 0.829356I
5.93746 + 2.73605I 4.39597 − 4.05385I
u = −0.450788 − 0.802899I
a = −0.462859 + 1.134600I
b = −0.885500 − 0.829356I
5.93746 − 2.73605I 4.39597 + 4.05385I
u = −1.083020 + 0.155939I
a = 0.725055 − 0.670192I
b = 0.185721 + 0.264913I
−1.88772 − 1.80438I 0
u = −1.083020 − 0.155939I
a = 0.725055 + 0.670192I
b = 0.185721 − 0.264913I
−1.88772 + 1.80438I 0
u = 0.065911 + 1.112560I
a = −0.272804 + 1.011100I
b = −0.04427 − 1.85749I
4.03902 + 5.09451I 0
u = 0.065911 − 1.112560I
a = −0.272804 − 1.011100I
b = −0.04427 + 1.85749I
4.03902 − 5.09451I 0
u = −0.501627 + 0.719259I
a = −0.580750 − 0.629272I
b = −0.27843 + 2.37718I
4.45750 + 1.72614I 4.41580 − 2.99878I
u = −0.501627 − 0.719259I
a = −0.580750 + 0.629272I
b = −0.27843 − 2.37718I
4.45750 − 1.72614I 4.41580 + 2.99878I
u = 1.094100 + 0.349905I
a = 0.740268 − 0.957578I
b = −0.091002 + 1.121130I
1.80658 − 4.57967I 0
u = 1.094100 − 0.349905I
a = 0.740268 + 0.957578I
b = −0.091002 − 1.121130I
1.80658 + 4.57967I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.225190 + 0.113002I
a = 0.314375 + 0.453265I
b = 0.225773 − 0.714056I
−2.10893 + 1.93292I 0
u = −1.225190 − 0.113002I
a = 0.314375 − 0.453265I
b = 0.225773 + 0.714056I
−2.10893 − 1.93292I 0
u = 0.712750 + 0.203668I
a = 2.14518 + 0.08588I
b = 0.839109 + 0.056598I
3.42656 + 2.09756I −10.94235 + 4.10081I
u = 0.712750 − 0.203668I
a = 2.14518 − 0.08588I
b = 0.839109 − 0.056598I
3.42656 − 2.09756I −10.94235 − 4.10081I
u = 1.156770 + 0.531285I
a = −0.845915 + 0.797237I
b = −1.03486 − 2.08640I
0.69570 − 10.11660I 0
u = 1.156770 − 0.531285I
a = −0.845915 − 0.797237I
b = −1.03486 + 2.08640I
0.69570 + 10.11660I 0
u = −1.174330 + 0.572544I
a = 0.525061 + 0.518322I
b = 0.77309 − 1.55639I
−1.24471 + 2.44194I 0
u = −1.174330 − 0.572544I
a = 0.525061 − 0.518322I
b = 0.77309 + 1.55639I
−1.24471 − 2.44194I 0
u = −0.303390 + 1.280700I
a = 0.261705 + 0.514561I
b = 0.57083 − 1.47279I
2.42673 + 3.32756I 0
u = −0.303390 − 1.280700I
a = 0.261705 − 0.514561I
b = 0.57083 + 1.47279I
2.42673 − 3.32756I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.328530 + 0.239810I
a = 0.341531 + 0.141402I
b = 0.259510 + 0.741575I
−6.74158 + 1.85994I 0
u = 1.328530 − 0.239810I
a = 0.341531 − 0.141402I
b = 0.259510 − 0.741575I
−6.74158 − 1.85994I 0
u = 1.361130 + 0.214761I
a = −0.297328 + 0.050725I
b = 0.060166 + 0.773436I
−4.25106 − 7.64066I 0
u = 1.361130 − 0.214761I
a = −0.297328 − 0.050725I
b = 0.060166 − 0.773436I
−4.25106 + 7.64066I 0
u = −0.600452 + 0.038623I
a = 2.41464 − 0.22924I
b = 0.977092 + 0.316977I
3.35221 − 0.49367I −9.49194 − 1.07798I
u = −0.600452 − 0.038623I
a = 2.41464 + 0.22924I
b = 0.977092 − 0.316977I
3.35221 + 0.49367I −9.49194 + 1.07798I
u = −1.066250 + 0.905397I
a = −0.205456 − 0.860858I
b = −0.84168 + 1.96246I
−1.71287 + 6.36824I 0
u = −1.066250 − 0.905397I
a = −0.205456 + 0.860858I
b = −0.84168 − 1.96246I
−1.71287 − 6.36824I 0
u = 0.570676 + 0.141826I
a = −0.854767 + 0.698128I
b = 0.11697 − 3.13616I
−0.33740 − 7.25565I −8.2236 + 14.6599I
u = 0.570676 − 0.141826I
a = −0.854767 − 0.698128I
b = 0.11697 + 3.13616I
−0.33740 + 7.25565I −8.2236 − 14.6599I
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.511816 + 0.218214I
a = −1.97577 − 1.00397I
b = −1.45878 − 0.53097I
6.22975 + 2.31382I 2.39074 − 3.00194I
u = −0.511816 − 0.218214I
a = −1.97577 + 1.00397I
b = −1.45878 + 0.53097I
6.22975 − 2.31382I 2.39074 + 3.00194I
u = −1.31030 + 0.63554I
a = −0.605765 + 0.229474I
b = −0.265858 − 0.061072I
−2.81336 + 0.83183I 0
u = −1.31030 − 0.63554I
a = −0.605765 − 0.229474I
b = −0.265858 + 0.061072I
−2.81336 − 0.83183I 0
u = 0.475870 + 0.171647I
a = −2.73580 + 0.77197I
b = −0.67721 − 1.52174I
3.70241 + 6.31816I −2.22797 − 7.95729I
u = 0.475870 − 0.171647I
a = −2.73580 − 0.77197I
b = −0.67721 + 1.52174I
3.70241 − 6.31816I −2.22797 + 7.95729I
u = −1.66828
a = 0.459483
b = 0.746478
−3.09044 0
31
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
47
− 3u
46
+ ··· − 11u
2
+ 1)(u
170
− 14u
169
+ ··· + 18u − 1)
c
2
(u
47
− 14u
45
+ ··· + 4u + 1)(u
170
+ u
169
+ ··· − 42944u + 1984)
c
3
(u
47
− 6u
45
+ ··· + 297u − 27)
· (u
170
− u
169
+ ··· − 276535005u − 23926117)
c
4
(u
47
− 18u
45
+ ··· + 2u + 1)(u
170
+ u
169
+ ··· + 60040u − 6379)
c
5
(u
47
− u
46
+ ··· − 20u + 1)(u
170
+ 2u
169
+ ··· + 6420u − 35591)
c
6
(u
47
+ 15u
44
+ ··· + 178u − 13)
· (u
170
− u
169
+ ··· + 9130974u + 5572759)
c
7
(u
47
− 14u
45
+ ··· + 4u − 1)(u
170
+ u
169
+ ··· − 42944u + 1984)
c
8
(u
47
− 3u
46
+ ··· − u − 1)(u
170
+ 8u
169
+ ··· − 715u + 221)
c
9
(u
47
+ 10u
45
+ ··· + 6u − 1)(u
170
+ 3u
169
+ ··· + 811454u + 271819)
c
10
(u
47
− 18u
45
+ ··· + 2u − 1)(u
170
+ u
169
+ ··· + 60040u − 6379)
c
11
(u
47
+ 3u
46
+ ··· − u + 1)(u
170
+ 8u
169
+ ··· − 715u + 221)
c
12
(u
47
+ u
46
+ ··· − 20u − 1)(u
170
+ 2u
169
+ ··· + 6420u − 35591)
32
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
47
+ 7y
46
+ ··· + 22y −1)(y
170
+ 6y
169
+ ··· − 760y + 1)
c
2
, c
7
(y
47
− 28y
46
+ ··· + 36y −1)
· (y
170
− 93y
169
+ ··· − 827236352y + 3936256)
c
3
(y
47
− 12y
46
+ ··· + 54837y −729)
· (y
170
− 41y
169
+ ··· − 46800698030178335y + 572459074697689)
c
4
, c
10
(y
47
− 36y
46
+ ··· + 4y −1)
· (y
170
− 113y
169
+ ··· − 1618495822y + 40691641)
c
5
, c
12
(y
47
+ 43y
46
+ ··· + 76y −1)
· (y
170
+ 118y
169
+ ··· + 25027873906y + 1266719281)
c
6
(y
47
+ 8y
45
+ ··· + 6490y −169)
· (y
170
− 9y
169
+ ··· + 1788240547802984y + 31055642872081)
c
8
, c
11
(y
47
− 27y
46
+ ··· + 35y −1)
· (y
170
− 88y
169
+ ··· + 1304511y + 48841)
c
9
(y
47
+ 20y
46
+ ··· − 16y −1)
· (y
170
+ 43y
169
+ ··· + 6707969409918y + 73885568761)
33
