12a
0492
(K12a
0492
)
A knot diagram
1
Linearized knot diagam
3 6 12 9 8 2 11 5 1 4 7 10
Solving Sequence
1,9 5,10
4 11 8 6 7 12 3 2
c
9
c
4
c
10
c
8
c
5
c
7
c
12
c
3
c
2
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.49532 × 10
457
u
131
+ 1.34440 × 10
459
u
130
+ ··· + 7.49258 × 10
458
b − 7.19414 × 10
459
,
1.32939 × 10
460
u
131
− 5.25151 × 10
460
u
130
+ ··· + 5.24480 × 10
459
a − 8.37691 × 10
461
,
u
132
− 3u
131
+ ··· − 163u + 7i
I
u
2
= h1904483u
33
+ 10211296u
32
+ ··· + 32131b − 1103768,
142988u
33
+ 2782382u
32
+ ··· + 32131a + 2978401, u
34
+ 6u
33
+ ··· + 6u + 1i
* 2 irreducible components of dim
C
= 0, with total 166 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
= h4.50 × 10
457
u
131
+ 1.34 × 10
459
u
130
+ · · · + 7.49 × 10
458
b − 7.19 ×
10
459
, 1.33 × 10
460
u
131
− 5.25 × 10
460
u
130
+ · · · + 5.24 × 10
459
a − 8.38 ×
10
461
, u
132
− 3u
131
+ · · · − 163u + 7i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−2.53469u
131
+ 10.0128u
130
+ ··· − 2944.38u + 159.718
−0.0599970u
131
− 1.79431u
130
+ ··· − 93.1612u + 9.60169
a
10
=
1
−u
2
a
4
=
−2.59468u
131
+ 8.21848u
130
+ ··· − 3037.54u + 169.320
−0.0599970u
131
− 1.79431u
130
+ ··· − 93.1612u + 9.60169
a
11
=
−2.43235u
131
+ 4.13228u
130
+ ··· − 933.324u + 44.4441
1.61308u
131
− 3.00750u
130
+ ··· + 74.0594u − 6.86179
a
8
=
4.08367u
131
− 9.26283u
130
+ ··· + 689.628u − 30.4569
−2.56390u
131
+ 5.88147u
130
+ ··· − 255.427u + 15.1075
a
6
=
−6.51879u
131
+ 19.3840u
130
+ ··· − 5603.96u + 307.796
−1.20351u
131
+ 6.16996u
130
+ ··· − 939.632u + 43.8102
a
7
=
8.38214u
131
− 20.0903u
130
+ ··· + 3504.62u − 174.236
−0.522846u
131
− 0.996017u
130
+ ··· + 146.734u − 3.59969
a
12
=
−u
u
3
+ u
a
3
=
−3.29886u
131
+ 11.0378u
130
+ ··· − 3275.81u + 180.206
0.395435u
131
− 3.87090u
130
+ ··· + 24.9734u + 3.66305
a
2
=
7.10298u
131
− 19.9316u
130
+ ··· + 3764.18u − 177.090
0.709157u
131
− 1.17970u
130
+ ··· − 83.6983u + 6.23531
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.14347u
131
− 7.73109u
130
+ ··· + 1768.78u − 99.4316
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
132
+ 58u
131
+ ··· + 174793220u + 8300161
c
2
, c
6
u
132
+ 29u
130
+ ··· − 9092u + 2881
c
3
u
132
− 3u
131
+ ··· + 11521u + 305
c
4
, c
5
, c
8
u
132
− 3u
131
+ ··· − 323u + 29
c
7
, c
11
u
132
− 3u
131
+ ··· − 1032u + 187
c
9
, c
12
u
132
+ 3u
131
+ ··· + 163u + 7
c
10
u
132
+ u
131
+ ··· + 27596u + 6781
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
132
+ 50y
131
+ ··· + 932283187604884y + 68892672625921
c
2
, c
6
y
132
+ 58y
131
+ ··· + 174793220y + 8300161
c
3
y
132
− 23y
131
+ ··· − 70481111y + 93025
c
4
, c
5
, c
8
y
132
+ 131y
131
+ ··· + 113925y + 841
c
7
, c
11
y
132
+ 71y
131
+ ··· + 1799442y + 34969
c
9
, c
12
y
132
+ 67y
131
+ ··· − 389y + 49
c
10
y
132
− 7y
131
+ ··· − 1094662622y + 45981961
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.370817 + 0.926367I
a = 1.50187 − 0.28588I
b = 0.38326 + 1.41227I
4.23216 − 3.87399I 0
u = −0.370817 − 0.926367I
a = 1.50187 + 0.28588I
b = 0.38326 − 1.41227I
4.23216 + 3.87399I 0
u = 0.344045 + 0.943861I
a = 2.48062 + 1.76373I
b = 0.10034 − 1.56062I
6.12040 + 5.20187I 0
u = 0.344045 − 0.943861I
a = 2.48062 − 1.76373I
b = 0.10034 + 1.56062I
6.12040 − 5.20187I 0
u = −0.962184 + 0.220164I
a = 0.289983 − 1.349370I
b = −0.150340 + 1.292800I
3.50596 − 0.99520I 0
u = −0.962184 − 0.220164I
a = 0.289983 + 1.349370I
b = −0.150340 − 1.292800I
3.50596 + 0.99520I 0
u = 0.416078 + 0.888263I
a = 1.75395 + 1.31569I
b = 0.22266 − 1.56369I
6.47571 + 5.11976I 0
u = 0.416078 − 0.888263I
a = 1.75395 − 1.31569I
b = 0.22266 + 1.56369I
6.47571 − 5.11976I 0
u = 0.970123 + 0.130982I
a = 0.555404 + 0.165465I
b = −0.743931 − 0.374897I
−1.65423 − 8.36082I 0
u = 0.970123 − 0.130982I
a = 0.555404 − 0.165465I
b = −0.743931 + 0.374897I
−1.65423 + 8.36082I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.974043 + 0.095068I
a = −0.32008 − 1.85271I
b = −0.15740 + 1.42347I
0.68924 + 3.85014I 0
u = 0.974043 − 0.095068I
a = −0.32008 + 1.85271I
b = −0.15740 − 1.42347I
0.68924 − 3.85014I 0
u = −0.504211 + 0.901497I
a = −1.67010 + 0.83876I
b = −0.44639 − 1.40217I
3.53056 − 9.07003I 0
u = −0.504211 − 0.901497I
a = −1.67010 − 0.83876I
b = −0.44639 + 1.40217I
3.53056 + 9.07003I 0
u = −0.959269 + 0.403263I
a = 0.068548 − 0.438689I
b = −0.192204 + 0.443065I
2.15875 − 1.72089I 0
u = −0.959269 − 0.403263I
a = 0.068548 + 0.438689I
b = −0.192204 − 0.443065I
2.15875 + 1.72089I 0
u = 0.379667 + 0.860808I
a = −1.89049 − 0.86787I
b = −0.11520 + 1.51310I
6.41423 − 1.14240I 0
u = 0.379667 − 0.860808I
a = −1.89049 + 0.86787I
b = −0.11520 − 1.51310I
6.41423 + 1.14240I 0
u = −0.311526 + 0.881637I
a = 3.16485 − 0.52901I
b = −0.051219 + 1.322640I
2.26858 + 4.93928I 0
u = −0.311526 − 0.881637I
a = 3.16485 + 0.52901I
b = −0.051219 − 1.322640I
2.26858 − 4.93928I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.017040 + 0.321411I
a = −0.07086 − 2.07323I
b = 0.24340 + 1.49413I
6.43011 − 6.51564I 0
u = 1.017040 − 0.321411I
a = −0.07086 + 2.07323I
b = 0.24340 − 1.49413I
6.43011 + 6.51564I 0
u = 0.046784 + 1.072330I
a = 0.600327 + 0.798981I
b = 0.457102 − 0.830634I
−2.14015 + 2.45626I 0
u = 0.046784 − 1.072330I
a = 0.600327 − 0.798981I
b = 0.457102 + 0.830634I
−2.14015 − 2.45626I 0
u = −0.466196 + 0.970697I
a = −0.174387 + 0.148307I
b = −0.956308 + 0.302071I
−2.06603 + 0.25233I 0
u = −0.466196 − 0.970697I
a = −0.174387 − 0.148307I
b = −0.956308 − 0.302071I
−2.06603 − 0.25233I 0
u = 0.210864 + 1.073280I
a = −0.737180 + 0.323161I
b = −0.492645 − 1.002100I
−7.09613 + 0.83999I 0
u = 0.210864 − 1.073280I
a = −0.737180 − 0.323161I
b = −0.492645 + 1.002100I
−7.09613 − 0.83999I 0
u = 0.532364 + 0.962045I
a = 1.18376 + 1.60298I
b = 0.330758 − 1.001060I
−1.53131 + 4.29764I 0
u = 0.532364 − 0.962045I
a = 1.18376 − 1.60298I
b = 0.330758 + 1.001060I
−1.53131 − 4.29764I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.266363 + 0.856894I
a = −0.73510 + 3.40492I
b = −0.11326 − 1.48966I
2.42468 − 7.53256I 0
u = −0.266363 − 0.856894I
a = −0.73510 − 3.40492I
b = −0.11326 + 1.48966I
2.42468 + 7.53256I 0
u = −0.533166 + 0.709917I
a = 0.241366 − 1.267940I
b = −0.30906 + 1.52943I
4.12541 + 4.86507I 0
u = −0.533166 − 0.709917I
a = 0.241366 + 1.267940I
b = −0.30906 − 1.52943I
4.12541 − 4.86507I 0
u = −0.420089 + 1.030940I
a = −2.34591 + 0.65057I
b = −0.004352 − 1.362610I
4.48174 − 1.59788I 0
u = −0.420089 − 1.030940I
a = −2.34591 − 0.65057I
b = −0.004352 + 1.362610I
4.48174 + 1.59788I 0
u = 0.439609 + 0.760044I
a = −1.15323 − 1.52672I
b = 0.08162 + 1.62896I
6.87032 − 1.52449I 0
u = 0.439609 − 0.760044I
a = −1.15323 + 1.52672I
b = 0.08162 − 1.62896I
6.87032 + 1.52449I 0
u = 0.314390 + 0.806526I
a = 0.77364 + 1.68635I
b = 0.01272 − 1.66822I
6.67591 + 4.24158I 0
u = 0.314390 − 0.806526I
a = 0.77364 − 1.68635I
b = 0.01272 + 1.66822I
6.67591 − 4.24158I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.399204 + 1.063130I
a = −0.0428257 + 0.0492380I
b = 0.899741 + 0.781640I
−2.27524 + 2.03511I 0
u = 0.399204 − 1.063130I
a = −0.0428257 − 0.0492380I
b = 0.899741 − 0.781640I
−2.27524 − 2.03511I 0
u = −0.245203 + 0.806401I
a = 0.048362 + 1.335930I
b = 0.23823 − 1.63168I
4.86393 + 1.11017I 0
u = −0.245203 − 0.806401I
a = 0.048362 − 1.335930I
b = 0.23823 + 1.63168I
4.86393 − 1.11017I 0
u = −0.268937 + 1.129230I
a = 0.146099 + 1.362100I
b = −0.230834 − 0.378040I
−3.85259 − 6.06823I 0
u = −0.268937 − 1.129230I
a = 0.146099 − 1.362100I
b = −0.230834 + 0.378040I
−3.85259 + 6.06823I 0
u = −0.339774 + 1.117450I
a = 0.187470 + 0.234928I
b = 0.875408 − 0.482875I
−2.41850 − 3.24410I 0
u = −0.339774 − 1.117450I
a = 0.187470 − 0.234928I
b = 0.875408 + 0.482875I
−2.41850 + 3.24410I 0
u = 0.811355 + 0.182204I
a = −0.497864 − 0.379251I
b = 0.677897 + 0.469186I
0.05251 − 3.13687I 0
u = 0.811355 − 0.182204I
a = −0.497864 + 0.379251I
b = 0.677897 − 0.469186I
0.05251 + 3.13687I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.344208 + 1.130570I
a = 0.233769 + 0.458826I
b = 0.700673 + 0.155840I
−4.06185 + 0.36405I 0
u = 0.344208 − 1.130570I
a = 0.233769 − 0.458826I
b = 0.700673 − 0.155840I
−4.06185 − 0.36405I 0
u = −0.236546 + 0.783085I
a = −0.843373 − 0.731008I
b = −0.040588 + 0.425144I
0.144723 − 1.347910I 0
u = −0.236546 − 0.783085I
a = −0.843373 + 0.731008I
b = −0.040588 − 0.425144I
0.144723 + 1.347910I 0
u = −1.165160 + 0.203134I
a = −0.307175 + 0.249764I
b = 0.379234 − 0.258204I
1.56141 + 2.33870I 0
u = −1.165160 − 0.203134I
a = −0.307175 − 0.249764I
b = 0.379234 + 0.258204I
1.56141 − 2.33870I 0
u = 0.411702 + 0.700934I
a = 0.423828 + 1.013190I
b = −0.027740 + 0.543911I
−5.25718 + 1.40383I 0
u = 0.411702 − 0.700934I
a = 0.423828 − 1.013190I
b = −0.027740 − 0.543911I
−5.25718 − 1.40383I 0
u = −0.254856 + 0.758387I
a = −1.71993 − 0.22808I
b = −0.0278006 + 0.1268810I
0.21514 − 1.51746I 0
u = −0.254856 − 0.758387I
a = −1.71993 + 0.22808I
b = −0.0278006 − 0.1268810I
0.21514 + 1.51746I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.412188 + 1.130090I
a = 0.096781 + 0.236929I
b = −0.894869 − 0.943707I
−3.72686 + 7.41483I 0
u = 0.412188 − 1.130090I
a = 0.096781 − 0.236929I
b = −0.894869 + 0.943707I
−3.72686 − 7.41483I 0
u = 1.175370 + 0.334323I
a = 0.13748 + 1.93967I
b = −0.28744 − 1.46407I
4.26312 − 12.13300I 0
u = 1.175370 − 0.334323I
a = 0.13748 − 1.93967I
b = −0.28744 + 1.46407I
4.26312 + 12.13300I 0
u = −0.527344 + 1.124350I
a = −0.646752 + 0.552732I
b = −0.483961 − 0.416641I
−0.16035 − 3.48082I 0
u = −0.527344 − 1.124350I
a = −0.646752 − 0.552732I
b = −0.483961 + 0.416641I
−0.16035 + 3.48082I 0
u = −1.128800 + 0.540127I
a = 0.13499 − 2.03439I
b = −0.09200 + 1.45514I
8.32483 − 0.51045I 0
u = −1.128800 − 0.540127I
a = 0.13499 + 2.03439I
b = −0.09200 − 1.45514I
8.32483 + 0.51045I 0
u = −0.244743 + 1.239620I
a = 0.370949 − 0.130965I
b = 0.760360 + 0.165226I
−4.29259 − 1.70900I 0
u = −0.244743 − 1.239620I
a = 0.370949 + 0.130965I
b = 0.760360 − 0.165226I
−4.29259 + 1.70900I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.348117 + 1.217520I
a = −0.827413 − 0.316744I
b = −0.724190 + 0.288497I
−9.15517 + 5.15283I 0
u = 0.348117 − 1.217520I
a = −0.827413 + 0.316744I
b = −0.724190 − 0.288497I
−9.15517 − 5.15283I 0
u = 0.868367 + 0.938437I
a = 0.97693 + 2.16001I
b = 0.008279 − 1.301660I
−2.19114 + 1.39042I 0
u = 0.868367 − 0.938437I
a = 0.97693 − 2.16001I
b = 0.008279 + 1.301660I
−2.19114 − 1.39042I 0
u = 0.602090 + 1.138050I
a = −0.81084 − 1.71587I
b = −0.338944 + 1.258290I
−2.58776 + 0.25553I 0
u = 0.602090 − 1.138050I
a = −0.81084 + 1.71587I
b = −0.338944 − 1.258290I
−2.58776 − 0.25553I 0
u = 0.509896 + 1.183450I
a = 0.560844 + 0.802147I
b = 0.895128 − 0.497014I
−2.94885 + 7.98550I 0
u = 0.509896 − 1.183450I
a = 0.560844 − 0.802147I
b = 0.895128 + 0.497014I
−2.94885 − 7.98550I 0
u = 0.242473 + 0.667232I
a = 2.51695 + 1.65154I
b = −0.065445 − 0.501593I
−1.09286 + 4.24065I 0
u = 0.242473 − 0.667232I
a = 2.51695 − 1.65154I
b = −0.065445 + 0.501593I
−1.09286 − 4.24065I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.287477 + 0.639928I
a = −1.13401 − 3.23222I
b = 0.06227 + 1.56276I
7.07292 − 2.20872I 0
u = 0.287477 − 0.639928I
a = −1.13401 + 3.23222I
b = 0.06227 − 1.56276I
7.07292 + 2.20872I 0
u = 0.134761 + 1.295480I
a = −0.112400 − 0.468219I
b = 0.191497 + 1.293050I
0.37223 − 2.81175I 0
u = 0.134761 − 1.295480I
a = −0.112400 + 0.468219I
b = 0.191497 − 1.293050I
0.37223 + 2.81175I 0
u = 0.647030 + 0.225620I
a = −0.285309 + 0.090142I
b = −0.455136 + 0.390042I
−5.02742 + 1.60710I 0
u = 0.647030 − 0.225620I
a = −0.285309 − 0.090142I
b = −0.455136 − 0.390042I
−5.02742 − 1.60710I 0
u = −0.635641 + 1.156710I
a = −0.914412 + 1.021010I
b = −0.416547 − 1.207240I
0.78836 − 4.71066I 0
u = −0.635641 − 1.156710I
a = −0.914412 − 1.021010I
b = −0.416547 + 1.207240I
0.78836 + 4.71066I 0
u = 0.631785 + 1.188410I
a = −0.200530 − 0.588653I
b = −0.375356 + 0.039068I
−7.26458 + 3.54385I 0
u = 0.631785 − 1.188410I
a = −0.200530 + 0.588653I
b = −0.375356 − 0.039068I
−7.26458 − 3.54385I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.446500 + 1.272000I
a = −1.49797 − 0.86717I
b = −0.25571 + 1.44710I
−3.52954 + 8.66075I 0
u = 0.446500 − 1.272000I
a = −1.49797 + 0.86717I
b = −0.25571 − 1.44710I
−3.52954 − 8.66075I 0
u = 0.546002 + 1.245620I
a = −0.361163 − 0.733779I
b = −0.989649 + 0.441015I
−5.0627 + 13.7509I 0
u = 0.546002 − 1.245620I
a = −0.361163 + 0.733779I
b = −0.989649 − 0.441015I
−5.0627 − 13.7509I 0
u = 0.853423 + 1.072990I
a = −0.83962 − 2.07885I
b = −0.121449 + 1.374000I
−2.59393 + 5.26648I 0
u = 0.853423 − 1.072990I
a = −0.83962 + 2.07885I
b = −0.121449 − 1.374000I
−2.59393 − 5.26648I 0
u = 0.622262 + 1.225570I
a = 1.38647 + 1.41342I
b = 0.32453 − 1.52896I
3.59048 + 12.41450I 0
u = 0.622262 − 1.225570I
a = 1.38647 − 1.41342I
b = 0.32453 + 1.52896I
3.59048 − 12.41450I 0
u = −0.556172 + 1.269430I
a = 0.397371 − 0.636257I
b = 0.684632 + 0.523584I
−2.00142 − 8.18530I 0
u = −0.556172 − 1.269430I
a = 0.397371 + 0.636257I
b = 0.684632 − 0.523584I
−2.00142 + 8.18530I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.310484 + 1.355700I
a = −0.115157 − 0.413051I
b = −0.746091 + 0.046900I
−6.63575 − 3.68967I 0
u = 0.310484 − 1.355700I
a = −0.115157 + 0.413051I
b = −0.746091 − 0.046900I
−6.63575 + 3.68967I 0
u = −0.350052 + 0.494480I
a = −1.07883 + 1.17867I
b = −0.846587 + 0.117901I
−0.70132 − 4.02934I 0
u = −0.350052 − 0.494480I
a = −1.07883 − 1.17867I
b = −0.846587 − 0.117901I
−0.70132 + 4.02934I 0
u = −0.705908 + 1.210450I
a = −1.24528 + 1.48390I
b = −0.19299 − 1.47343I
6.02818 − 6.06205I 0
u = −0.705908 − 1.210450I
a = −1.24528 − 1.48390I
b = −0.19299 + 1.47343I
6.02818 + 6.06205I 0
u = −0.453833 + 1.330620I
a = 1.085290 − 0.410245I
b = 0.061545 + 1.251680I
−1.24372 − 5.89195I 0
u = −0.453833 − 1.330620I
a = 1.085290 + 0.410245I
b = 0.061545 − 1.251680I
−1.24372 + 5.89195I 0
u = −1.286520 + 0.568163I
a = −0.25298 + 1.94885I
b = 0.16209 − 1.42109I
7.05256 + 4.45083I 0
u = −1.286520 − 0.568163I
a = −0.25298 − 1.94885I
b = 0.16209 + 1.42109I
7.05256 − 4.45083I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.002695 + 0.586507I
a = 1.70094 + 0.40332I
b = 0.893310 − 0.191618I
−0.101307 + 0.882084I 0
u = 0.002695 − 0.586507I
a = 1.70094 − 0.40332I
b = 0.893310 + 0.191618I
−0.101307 − 0.882084I 0
u = −0.466730 + 0.327581I
a = −0.83263 − 2.51334I
b = 0.07787 + 1.48106I
6.40321 − 2.07101I 7.59070 + 4.24172I
u = −0.466730 − 0.327581I
a = −0.83263 + 2.51334I
b = 0.07787 − 1.48106I
6.40321 + 2.07101I 7.59070 − 4.24172I
u = 0.45072 + 1.36256I
a = 0.310364 + 0.741127I
b = −0.122916 − 1.257050I
−3.38920 + 1.62851I 0
u = 0.45072 − 1.36256I
a = 0.310364 − 0.741127I
b = −0.122916 + 1.257050I
−3.38920 − 1.62851I 0
u = −0.53433 + 1.33818I
a = 0.730601 − 1.048370I
b = 0.337975 + 1.329780I
0.34351 − 5.68135I 0
u = −0.53433 − 1.33818I
a = 0.730601 + 1.048370I
b = 0.337975 − 1.329780I
0.34351 + 5.68135I 0
u = 0.67579 + 1.27518I
a = −1.20108 − 1.47064I
b = −0.37030 + 1.52551I
1.2518 + 18.6552I 0
u = 0.67579 − 1.27518I
a = −1.20108 + 1.47064I
b = −0.37030 − 1.52551I
1.2518 − 18.6552I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.75136 + 1.27192I
a = 1.04383 − 1.58428I
b = 0.25222 + 1.50413I
4.54428 − 11.64450I 0
u = −0.75136 − 1.27192I
a = 1.04383 + 1.58428I
b = 0.25222 − 1.50413I
4.54428 + 11.64450I 0
u = −1.52281 + 0.21917I
a = −0.09966 + 1.67154I
b = 0.060516 − 1.270250I
4.72695 − 1.13928I 0
u = −1.52281 − 0.21917I
a = −0.09966 − 1.67154I
b = 0.060516 + 1.270250I
4.72695 + 1.13928I 0
u = −0.00203 + 1.56629I
a = −0.043704 + 0.732008I
b = −0.235183 − 1.216960I
−3.13224 − 7.24941I 0
u = −0.00203 − 1.56629I
a = −0.043704 − 0.732008I
b = −0.235183 + 1.216960I
−3.13224 + 7.24941I 0
u = 0.147871 + 0.246599I
a = −1.67452 − 0.95756I
b = 0.296245 + 0.445939I
−0.004818 − 1.052880I 0.23128 + 5.60614I
u = 0.147871 − 0.246599I
a = −1.67452 + 0.95756I
b = 0.296245 − 0.445939I
−0.004818 + 1.052880I 0.23128 − 5.60614I
u = 0.224593 + 0.080422I
a = −3.34387 − 4.39417I
b = −0.595058 + 0.464601I
−0.92749 − 4.04590I 1.93954 + 2.79306I
u = 0.224593 − 0.080422I
a = −3.34387 + 4.39417I
b = −0.595058 − 0.464601I
−0.92749 + 4.04590I 1.93954 − 2.79306I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.219187 + 0.050600I
a = −1.43415 − 3.66365I
b = 0.497576 + 0.381384I
0.084207 − 1.025790I 0.33492 + 2.06199I
u = 0.219187 − 0.050600I
a = −1.43415 + 3.66365I
b = 0.497576 − 0.381384I
0.084207 + 1.025790I 0.33492 − 2.06199I
18
II. I
u
2
= h1.90 × 10
6
u
33
+ 1.02 × 10
7
u
32
+ · · · + 3.21 × 10
4
b − 1.10 × 10
6
, 1.43 ×
10
5
u
33
+2.78×10
6
u
32
+· · · +3.21×10
4
a+2.98×10
6
, u
34
+6u
33
+· · · +6u +1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−4.45016u
33
− 86.5949u
32
+ ··· − 408.274u − 92.6956
−59.2724u
33
− 317.802u
32
+ ··· + 76.0232u + 34.3521
a
10
=
1
−u
2
a
4
=
−63.7226u
33
− 404.397u
32
+ ··· − 332.250u − 58.3434
−59.2724u
33
− 317.802u
32
+ ··· + 76.0232u + 34.3521
a
11
=
−178.405u
33
− 1011.99u
32
+ ··· − 601.234u − 55.9930
106.867u
33
+ 668.485u
32
+ ··· + 816.439u + 116.428
a
8
=
130.490u
33
+ 820.328u
32
+ ··· + 1022.76u + 153.992
−85.0449u
33
− 598.534u
32
+ ··· − 1076.26u − 167.305
a
6
=
−17.3658u
33
− 62.2334u
32
+ ··· + 288.340u + 67.6224
41.4639u
33
+ 141.885u
32
+ ··· − 699.710u − 144.941
a
7
=
136.592u
33
+ 840.946u
32
+ ··· + 810.642u + 122.982
−15.8130u
33
− 254.092u
32
+ ··· − 1398.11u − 251.276
a
12
=
−u
u
3
+ u
a
3
=
−23.6342u
33
− 172.767u
32
+ ··· − 283.340u − 58.6224
−74.3360u
33
− 409.846u
32
+ ··· + 13.8024u + 25.7312
a
2
=
46.9395u
33
+ 349.553u
32
+ ··· + 974.208u + 170.196
−25.8721u
33
− 225.961u
32
+ ··· − 607.908u − 110.209
(ii) Obstruction class = 1
(iii) Cusp Shapes =
6008925
32131
u
33
+
27961822
32131
u
32
+ ··· −
49690749
32131
u −
9989565
32131
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
− 17u
33
+ ··· − 19u + 1
c
2
u
34
− 3u
33
+ ··· − u + 1
c
3
u
34
+ 6u
33
+ ··· + 6u + 1
c
4
, c
5
u
34
− 2u
33
+ ··· − 4u + 1
c
6
u
34
+ 3u
33
+ ··· + u + 1
c
7
u
34
− 2u
33
+ ··· − u + 1
c
8
u
34
+ 2u
33
+ ··· + 4u + 1
c
9
u
34
+ 6u
33
+ ··· + 6u + 1
c
10
u
34
− 8u
31
+ ··· − 9u + 1
c
11
u
34
+ 2u
33
+ ··· + u + 1
c
12
u
34
− 6u
33
+ ··· − 6u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
+ 17y
33
+ ··· + 11y + 1
c
2
, c
6
y
34
+ 17y
33
+ ··· + 19y + 1
c
3
y
34
− 4y
33
+ ··· + 12y + 1
c
4
, c
5
, c
8
y
34
+ 38y
33
+ ··· + 24y + 1
c
7
, c
11
y
34
+ 22y
33
+ ··· + 21y + 1
c
9
, c
12
y
34
+ 14y
33
+ ··· + 22y + 1
c
10
y
34
− 52y
31
+ ··· + 65y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.305113 + 0.948801I
a = −2.13285 + 1.48214I
b = −0.15018 − 1.60015I
5.81660 − 4.91386I −7.61106 − 1.27838I
u = −0.305113 − 0.948801I
a = −2.13285 − 1.48214I
b = −0.15018 + 1.60015I
5.81660 + 4.91386I −7.61106 + 1.27838I
u = −0.338986 + 0.975548I
a = −0.171310 − 0.076935I
b = −0.815884 + 0.411911I
−1.41372 − 0.80336I −0.34450 + 1.58550I
u = −0.338986 − 0.975548I
a = −0.171310 + 0.076935I
b = −0.815884 − 0.411911I
−1.41372 + 0.80336I −0.34450 − 1.58550I
u = −1.032140 + 0.062759I
a = 0.281610 + 0.565689I
b = −0.133826 − 0.226933I
1.58148 − 1.91347I −3.86448 − 2.86106I
u = −1.032140 − 0.062759I
a = 0.281610 − 0.565689I
b = −0.133826 + 0.226933I
1.58148 + 1.91347I −3.86448 + 2.86106I
u = 0.456014 + 0.806044I
a = 0.133868 + 0.813453I
b = 0.301341 + 0.661804I
−5.11226 + 0.71628I −2.57750 + 4.24171I
u = 0.456014 − 0.806044I
a = 0.133868 − 0.813453I
b = 0.301341 − 0.661804I
−5.11226 − 0.71628I −2.57750 − 4.24171I
u = −0.199117 + 0.816736I
a = −1.52929 + 0.09902I
b = −0.715288 − 0.052872I
−0.60958 − 1.63182I −4.87414 + 4.20691I
u = −0.199117 − 0.816736I
a = −1.52929 − 0.09902I
b = −0.715288 + 0.052872I
−0.60958 + 1.63182I −4.87414 − 4.20691I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.458382 + 1.102250I
a = −0.322166 + 0.063076I
b = −0.142231 − 0.652634I
−6.25539 + 3.20448I −3.06950 − 3.95856I
u = 0.458382 − 1.102250I
a = −0.322166 − 0.063076I
b = −0.142231 + 0.652634I
−6.25539 − 3.20448I −3.06950 + 3.95856I
u = −0.244087 + 0.758464I
a = 1.34246 − 2.02313I
b = −0.06167 + 1.62778I
6.55190 + 2.30412I −4.70346 − 4.62528I
u = −0.244087 − 0.758464I
a = 1.34246 + 2.02313I
b = −0.06167 − 1.62778I
6.55190 − 2.30412I −4.70346 + 4.62528I
u = −0.771498 + 0.134185I
a = 0.51013 − 2.63421I
b = −0.05480 + 1.49953I
7.63061 + 2.64374I 5.24927 − 2.78778I
u = −0.771498 − 0.134185I
a = 0.51013 + 2.63421I
b = −0.05480 − 1.49953I
7.63061 − 2.64374I 5.24927 + 2.78778I
u = 0.841191 + 0.879565I
a = 0.72369 + 2.13001I
b = 0.143152 − 1.192720I
−3.11346 + 2.35095I −4.07368 − 3.72454I
u = 0.841191 − 0.879565I
a = 0.72369 − 2.13001I
b = 0.143152 + 1.192720I
−3.11346 − 2.35095I −4.07368 + 3.72454I
u = −0.248605 + 1.206960I
a = −0.130990 + 0.769520I
b = 0.406791 − 0.573632I
−3.95291 − 4.99961I −5.58621 + 0.I
u = −0.248605 − 1.206960I
a = −0.130990 − 0.769520I
b = 0.406791 + 0.573632I
−3.95291 + 4.99961I −5.58621 + 0.I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.004352 + 0.746837I
a = 2.39136 + 0.71354I
b = 0.542656 + 0.300152I
−1.70557 + 3.93746I −9.02486 − 1.52225I
u = −0.004352 − 0.746837I
a = 2.39136 − 0.71354I
b = 0.542656 − 0.300152I
−1.70557 − 3.93746I −9.02486 + 1.52225I
u = 0.134530 + 0.644552I
a = 2.49152 + 3.01641I
b = 0.18421 − 1.44263I
2.71179 + 6.62421I 0.42958 − 3.80297I
u = 0.134530 − 0.644552I
a = 2.49152 − 3.01641I
b = 0.18421 + 1.44263I
2.71179 − 6.62421I 0.42958 + 3.80297I
u = −0.605513 + 1.197300I
a = −0.777958 + 0.995958I
b = −0.385151 − 1.232150I
1.39357 − 5.24505I 0
u = −0.605513 − 1.197300I
a = −0.777958 − 0.995958I
b = −0.385151 + 1.232150I
1.39357 + 5.24505I 0
u = 0.741390 + 1.195020I
a = −0.96542 − 1.49515I
b = −0.081217 + 1.201990I
−4.17683 + 4.05681I 0
u = 0.741390 − 1.195020I
a = −0.96542 + 1.49515I
b = −0.081217 − 1.201990I
−4.17683 − 4.05681I 0
u = −0.35335 + 1.39959I
a = 0.619491 − 0.319711I
b = 0.199313 + 1.259680I
−1.35608 − 7.23948I 0
u = −0.35335 − 1.39959I
a = 0.619491 + 0.319711I
b = 0.199313 − 1.259680I
−1.35608 + 7.23948I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.072376 + 0.543867I
a = −1.099020 − 0.753940I
b = −0.19145 + 1.56025I
5.14892 + 1.81053I 1.75848 − 3.89471I
u = −0.072376 − 0.543867I
a = −1.099020 + 0.753940I
b = −0.19145 − 1.56025I
5.14892 − 1.81053I 1.75848 + 3.89471I
u = −1.45638 + 0.20016I
a = 0.13486 − 1.55868I
b = −0.045750 + 1.276600I
5.08562 − 1.27399I 0
u = −1.45638 − 0.20016I
a = 0.13486 + 1.55868I
b = −0.045750 − 1.276600I
5.08562 + 1.27399I 0
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
34
− 17u
33
+ ··· − 19u + 1)
· (u
132
+ 58u
131
+ ··· + 174793220u + 8300161)
c
2
(u
34
− 3u
33
+ ··· − u + 1)(u
132
+ 29u
130
+ ··· − 9092u + 2881)
c
3
(u
34
+ 6u
33
+ ··· + 6u + 1)(u
132
− 3u
131
+ ··· + 11521u + 305)
c
4
, c
5
(u
34
− 2u
33
+ ··· − 4u + 1)(u
132
− 3u
131
+ ··· − 323u + 29)
c
6
(u
34
+ 3u
33
+ ··· + u + 1)(u
132
+ 29u
130
+ ··· − 9092u + 2881)
c
7
(u
34
− 2u
33
+ ··· − u + 1)(u
132
− 3u
131
+ ··· − 1032u + 187)
c
8
(u
34
+ 2u
33
+ ··· + 4u + 1)(u
132
− 3u
131
+ ··· − 323u + 29)
c
9
(u
34
+ 6u
33
+ ··· + 6u + 1)(u
132
+ 3u
131
+ ··· + 163u + 7)
c
10
(u
34
− 8u
31
+ ··· − 9u + 1)(u
132
+ u
131
+ ··· + 27596u + 6781)
c
11
(u
34
+ 2u
33
+ ··· + u + 1)(u
132
− 3u
131
+ ··· − 1032u + 187)
c
12
(u
34
− 6u
33
+ ··· − 6u + 1)(u
132
+ 3u
131
+ ··· + 163u + 7)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
34
+ 17y
33
+ ··· + 11y + 1)
· (y
132
+ 50y
131
+ ··· + 932283187604884y + 68892672625921)
c
2
, c
6
(y
34
+ 17y
33
+ ··· + 19y + 1)
· (y
132
+ 58y
131
+ ··· + 174793220y + 8300161)
c
3
(y
34
− 4y
33
+ ··· + 12y + 1)
· (y
132
− 23y
131
+ ··· − 70481111y + 93025)
c
4
, c
5
, c
8
(y
34
+ 38y
33
+ ··· + 24y + 1)(y
132
+ 131y
131
+ ··· + 113925y + 841)
c
7
, c
11
(y
34
+ 22y
33
+ ··· + 21y + 1)
· (y
132
+ 71y
131
+ ··· + 1799442y + 34969)
c
9
, c
12
(y
34
+ 14y
33
+ ··· + 22y + 1)(y
132
+ 67y
131
+ ··· − 389y + 49)
c
10
(y
34
− 52y
31
+ ··· + 65y + 1)
· (y
132
− 7y
131
+ ··· − 1094662622y + 45981961)
27
