12a
0461
(K12a
0461
)
A knot diagram
1
Linearized knot diagam
3 6 10 1 8 2 12 5 11 4 7 9
Solving Sequence
3,10
4
6,11
2 7 1 5 9 8 12
c
3
c
10
c
2
c
6
c
1
c
4
c
9
c
8
c
12
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.78345 × 10
428
u
153
+ 4.11856 × 10
427
u
152
+ ··· + 4.56915 × 10
427
b − 9.76978 × 10
430
,
9.27335 × 10
430
u
153
− 7.70278 × 10
430
u
152
+ ··· + 1.64946 × 10
430
a + 5.63983 × 10
433
,
u
154
− u
153
+ ··· + 171u − 361i
I
u
2
= h63182u
37
+ 18834u
36
+ ··· + 9223b + 14567, −130140u
37
+ 149794u
36
+ ··· + 9223a − 397212,
u
38
− 12u
36
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 192 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−2.78 × 10
428
u
153
+ 4.12 × 10
427
u
152
+ · · · + 4.57 × 10
427
b − 9.77 ×
10
430
, 9.27 × 10
430
u
153
− 7.70 × 10
430
u
152
+ · · · + 1.65 × 10
430
a + 5.64 ×
10
433
, u
154
− u
153
+ · · · + 171u − 361i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−5.62204u
153
+ 4.66987u
152
+ ··· − 2354.78u − 3419.19
6.09184u
153
− 0.901385u
152
+ ··· + 568.938u + 2138.21
a
11
=
−u
−u
3
+ u
a
2
=
−5.24596u
153
+ 9.36123u
152
+ ··· − 4581.17u − 4917.49
6.95746u
153
− 3.20412u
152
+ ··· + 1434.58u + 3079.92
a
7
=
−5.07748u
153
+ 4.33395u
152
+ ··· − 2100.13u − 3095.74
2.24063u
153
− 1.35986u
152
+ ··· + 823.755u + 1352.76
a
1
=
1.71150u
153
+ 6.15711u
152
+ ··· − 3146.59u − 1837.57
6.95746u
153
− 3.20412u
152
+ ··· + 1434.58u + 3079.92
a
5
=
−1.38432u
153
+ 1.94270u
152
+ ··· − 904.514u − 960.807
−0.598030u
153
+ 0.453949u
152
+ ··· − 271.071u − 321.745
a
9
=
u
3
u
5
− u
3
+ u
a
8
=
2.43930u
153
+ 2.36182u
152
+ ··· − 1416.92u − 352.069
2.30804u
153
− 0.840085u
152
+ ··· + 467.621u + 1009.50
a
12
=
−5.77366u
153
+ 9.18108u
152
+ ··· − 4535.31u − 5011.51
6.24262u
153
− 3.12187u
152
+ ··· + 1465.57u + 2852.48
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.50475u
153
+ 1.30202u
152
+ ··· + 90.3994u − 1206.07
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
154
+ 64u
153
+ ··· + 54112666u + 1857769
c
2
, c
6
u
154
− 2u
153
+ ··· + 3074u + 1363
c
3
, c
10
u
154
− u
153
+ ··· + 171u − 361
c
4
u
154
− 6u
153
+ ··· + 28566941u + 26372777
c
5
, c
8
u
154
− 3u
153
+ ··· + 4572u + 4921
c
7
, c
11
u
154
+ 3u
153
+ ··· − 60545u − 9307
c
9
u
154
+ 71u
153
+ ··· + 2567071u + 130321
c
12
u
154
− 3u
153
+ ··· − 9312u − 521
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
154
+ 72y
153
+ ··· − 893114824048786y + 3451305657361
c
2
, c
6
y
154
+ 64y
153
+ ··· + 54112666y + 1857769
c
3
, c
10
y
154
− 71y
153
+ ··· − 2567071y + 130321
c
4
y
154
+ 46y
153
+ ··· + 19716884500334309y + 695523366691729
c
5
, c
8
y
154
+ 93y
153
+ ··· + 417233130y + 24216241
c
7
, c
11
y
154
− 89y
153
+ ··· − 3771070879y + 86620249
c
9
y
154
+ 45y
153
+ ··· − 127131132883y + 16983563041
c
12
y
154
+ 11y
153
+ ··· − 91631584y + 271441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822066 + 0.579429I
a = −0.444752 + 1.270860I
b = 1.167560 − 0.604263I
4.77078 − 1.29277I 0
u = −0.822066 − 0.579429I
a = −0.444752 − 1.270860I
b = 1.167560 + 0.604263I
4.77078 + 1.29277I 0
u = 0.894179 + 0.465461I
a = 2.58293 + 1.18423I
b = −0.544581 + 0.941019I
−2.03197 − 3.12428I 0
u = 0.894179 − 0.465461I
a = 2.58293 − 1.18423I
b = −0.544581 − 0.941019I
−2.03197 + 3.12428I 0
u = 0.574939 + 0.805385I
a = 1.265130 − 0.459295I
b = −0.826306 + 0.646658I
7.65595 + 1.31070I 0
u = 0.574939 − 0.805385I
a = 1.265130 + 0.459295I
b = −0.826306 − 0.646658I
7.65595 − 1.31070I 0
u = 0.947941 + 0.282051I
a = 0.30114 − 1.56279I
b = −0.479556 − 1.140250I
−3.60832 + 4.35982I 0
u = 0.947941 − 0.282051I
a = 0.30114 + 1.56279I
b = −0.479556 + 1.140250I
−3.60832 − 4.35982I 0
u = 0.987612 + 0.018641I
a = 0.00318 − 1.91294I
b = −0.217069 − 0.968326I
−3.71429 + 2.24347I 0
u = 0.987612 − 0.018641I
a = 0.00318 + 1.91294I
b = −0.217069 + 0.968326I
−3.71429 − 2.24347I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.668369 + 0.726264I
a = −0.718297 + 0.714281I
b = 0.551305 − 1.139770I
0.97716 − 2.43901I 0
u = −0.668369 − 0.726264I
a = −0.718297 − 0.714281I
b = 0.551305 + 1.139770I
0.97716 + 2.43901I 0
u = −0.579363 + 0.833528I
a = −1.173620 + 0.332681I
b = 0.591151 − 0.942502I
1.98078 − 2.74234I 0
u = −0.579363 − 0.833528I
a = −1.173620 − 0.332681I
b = 0.591151 + 0.942502I
1.98078 + 2.74234I 0
u = 0.871465 + 0.458008I
a = −1.35338 − 1.13202I
b = 0.682615 + 0.782945I
−1.94534 − 0.62809I 0
u = 0.871465 − 0.458008I
a = −1.35338 + 1.13202I
b = 0.682615 − 0.782945I
−1.94534 + 0.62809I 0
u = −0.918836 + 0.451681I
a = −0.605092 + 0.903934I
b = −0.175140 + 1.029180I
−1.93769 + 1.71433I 0
u = −0.918836 − 0.451681I
a = −0.605092 − 0.903934I
b = −0.175140 − 1.029180I
−1.93769 − 1.71433I 0
u = −0.729682 + 0.721684I
a = 0.486555 − 1.028990I
b = −0.79150 + 1.18399I
2.08567 − 3.75466I 0
u = −0.729682 − 0.721684I
a = 0.486555 + 1.028990I
b = −0.79150 − 1.18399I
2.08567 + 3.75466I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.520555 + 0.886692I
a = 1.54611 + 0.12124I
b = −0.953786 − 0.548158I
5.33324 − 7.64609I 0
u = −0.520555 − 0.886692I
a = 1.54611 − 0.12124I
b = −0.953786 + 0.548158I
5.33324 + 7.64609I 0
u = 0.917644 + 0.474316I
a = 1.07137 + 1.83095I
b = −0.568197 − 0.546614I
−0.18917 − 5.27709I 0
u = 0.917644 − 0.474316I
a = 1.07137 − 1.83095I
b = −0.568197 + 0.546614I
−0.18917 + 5.27709I 0
u = 0.850743 + 0.454824I
a = −3.54253 − 0.52996I
b = 0.433739 − 0.796809I
0.05968 + 1.50926I 0
u = 0.850743 − 0.454824I
a = −3.54253 + 0.52996I
b = 0.433739 + 0.796809I
0.05968 − 1.50926I 0
u = −0.497579 + 0.907977I
a = −1.54017 − 0.19865I
b = 0.775781 + 0.624816I
1.20572 − 1.73714I 0
u = −0.497579 − 0.907977I
a = −1.54017 + 0.19865I
b = 0.775781 − 0.624816I
1.20572 + 1.73714I 0
u = −0.876837 + 0.560697I
a = 1.66191 − 0.43835I
b = −1.21803 − 0.77054I
4.60760 + 5.83375I 0
u = −0.876837 − 0.560697I
a = 1.66191 + 0.43835I
b = −1.21803 + 0.77054I
4.60760 − 5.83375I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.878557 + 0.356936I
a = −0.899409 + 0.785346I
b = 0.511909 + 1.111000I
−3.76126 + 0.86569I 0
u = 0.878557 − 0.356936I
a = −0.899409 − 0.785346I
b = 0.511909 − 1.111000I
−3.76126 − 0.86569I 0
u = −0.892698 + 0.317318I
a = −0.142050 − 0.305134I
b = −0.651868 − 0.110332I
−0.748888 − 0.051632I 0
u = −0.892698 − 0.317318I
a = −0.142050 + 0.305134I
b = −0.651868 + 0.110332I
−0.748888 + 0.051632I 0
u = −0.923163 + 0.505766I
a = −0.780045 − 0.137098I
b = 0.759557 + 0.367110I
−1.46508 + 3.89283I 0
u = −0.923163 − 0.505766I
a = −0.780045 + 0.137098I
b = 0.759557 − 0.367110I
−1.46508 − 3.89283I 0
u = −0.906674 + 0.538347I
a = 0.95178 − 1.61428I
b = 0.083826 − 1.026110I
0.71731 + 5.70936I 0
u = −0.906674 − 0.538347I
a = 0.95178 + 1.61428I
b = 0.083826 + 1.026110I
0.71731 − 5.70936I 0
u = 0.820406 + 0.458403I
a = 0.647027 + 1.181240I
b = −1.05924 − 1.01980I
3.87296 + 2.04708I 0
u = 0.820406 − 0.458403I
a = 0.647027 − 1.181240I
b = −1.05924 + 1.01980I
3.87296 − 2.04708I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.491837 + 0.939919I
a = 1.149150 − 0.165391I
b = −0.665878 + 0.767357I
5.03680 + 3.07332I 0
u = −0.491837 − 0.939919I
a = 1.149150 + 0.165391I
b = −0.665878 − 0.767357I
5.03680 − 3.07332I 0
u = 0.945523 + 0.495565I
a = −1.99803 − 0.97327I
b = 0.882851 − 1.066330I
3.40570 − 5.90996I 0
u = 0.945523 − 0.495565I
a = −1.99803 + 0.97327I
b = 0.882851 + 1.066330I
3.40570 + 5.90996I 0
u = 0.770452 + 0.739156I
a = −1.248880 + 0.251459I
b = 0.594063 − 0.525342I
2.97747 − 1.79063I 0
u = 0.770452 − 0.739156I
a = −1.248880 − 0.251459I
b = 0.594063 + 0.525342I
2.97747 + 1.79063I 0
u = 0.462193 + 0.966845I
a = 1.176070 + 0.594409I
b = −0.713019 − 1.119190I
3.5607 + 13.7363I 0
u = 0.462193 − 0.966845I
a = 1.176070 − 0.594409I
b = −0.713019 + 1.119190I
3.5607 − 13.7363I 0
u = −0.470514 + 0.799319I
a = 1.355640 − 0.226669I
b = −0.701764 + 1.026230I
6.49583 − 7.02496I 0
u = −0.470514 − 0.799319I
a = 1.355640 + 0.226669I
b = −0.701764 − 1.026230I
6.49583 + 7.02496I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.815400 + 0.697882I
a = −1.089590 − 0.840715I
b = 1.078540 + 0.172318I
4.76065 − 2.44822I 0
u = 0.815400 − 0.697882I
a = −1.089590 + 0.840715I
b = 1.078540 − 0.172318I
4.76065 + 2.44822I 0
u = −0.754448 + 0.536803I
a = −0.392491 − 0.695246I
b = 0.146016 − 0.972184I
1.17020 − 1.35654I 0
u = −0.754448 − 0.536803I
a = −0.392491 + 0.695246I
b = 0.146016 + 0.972184I
1.17020 + 1.35654I 0
u = −1.083000 + 0.078736I
a = 0.174446 − 0.429268I
b = 0.610702 − 0.769764I
1.57089 + 0.38016I 0
u = −1.083000 − 0.078736I
a = 0.174446 + 0.429268I
b = 0.610702 + 0.769764I
1.57089 − 0.38016I 0
u = 1.022580 + 0.381336I
a = 0.89246 + 1.66749I
b = −0.375939 + 1.147050I
−4.26811 − 3.61828I 0
u = 1.022580 − 0.381336I
a = 0.89246 − 1.66749I
b = −0.375939 − 1.147050I
−4.26811 + 3.61828I 0
u = 0.423073 + 1.008590I
a = −1.198600 − 0.573364I
b = 0.673937 + 1.032060I
−0.02924 + 7.23734I 0
u = 0.423073 − 1.008590I
a = −1.198600 + 0.573364I
b = 0.673937 − 1.032060I
−0.02924 − 7.23734I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.691432 + 0.580549I
a = 0.46157 − 2.05865I
b = −0.496029 + 0.785846I
−1.45978 − 1.10196I 0
u = −0.691432 − 0.580549I
a = 0.46157 + 2.05865I
b = −0.496029 − 0.785846I
−1.45978 + 1.10196I 0
u = 1.093050 + 0.111168I
a = −0.06711 + 1.46631I
b = 0.591387 + 0.890936I
1.22073 + 5.13744I 0
u = 1.093050 − 0.111168I
a = −0.06711 − 1.46631I
b = 0.591387 − 0.890936I
1.22073 − 5.13744I 0
u = 0.333598 + 0.828789I
a = 1.32166 + 0.65256I
b = −0.786662 − 0.864514I
6.44245 + 1.96973I 0
u = 0.333598 − 0.828789I
a = 1.32166 − 0.65256I
b = −0.786662 + 0.864514I
6.44245 − 1.96973I 0
u = −0.957114 + 0.567759I
a = −2.30954 − 0.37752I
b = 0.624720 + 0.894756I
−2.28055 + 5.68893I 0
u = −0.957114 − 0.567759I
a = −2.30954 + 0.37752I
b = 0.624720 − 0.894756I
−2.28055 − 5.68893I 0
u = −0.415910 + 0.782812I
a = 1.68218 + 0.31117I
b = −0.803099 − 0.894750I
6.37596 + 3.98356I 0
u = −0.415910 − 0.782812I
a = 1.68218 − 0.31117I
b = −0.803099 + 0.894750I
6.37596 − 3.98356I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.880709 + 0.702773I
a = 1.34473 + 0.62320I
b = −1.070680 + 0.328745I
4.57020 − 2.91940I 0
u = 0.880709 − 0.702773I
a = 1.34473 − 0.62320I
b = −1.070680 − 0.328745I
4.57020 + 2.91940I 0
u = −0.639370 + 0.580078I
a = −1.55493 + 1.89990I
b = 0.478663 − 0.967647I
−0.59318 − 5.24593I 0
u = −0.639370 − 0.580078I
a = −1.55493 − 1.89990I
b = 0.478663 + 0.967647I
−0.59318 + 5.24593I 0
u = −0.991748 + 0.576448I
a = 2.80809 − 0.23504I
b = −0.565770 − 1.038220I
−1.68086 + 9.89233I 0
u = −0.991748 − 0.576448I
a = 2.80809 + 0.23504I
b = −0.565770 + 1.038220I
−1.68086 − 9.89233I 0
u = 1.15171
a = 0.872755
b = −0.557285
−5.43173 0
u = 1.116650 + 0.288251I
a = −0.551334 + 1.263380I
b = 0.009952 + 0.320767I
−1.03953 − 5.47135I 0
u = 1.116650 − 0.288251I
a = −0.551334 − 1.263380I
b = 0.009952 − 0.320767I
−1.03953 + 5.47135I 0
u = 0.842566 + 0.055109I
a = −0.43533 − 1.72832I
b = −0.341428 − 1.140430I
−3.91290 + 2.72338I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.842566 − 0.055109I
a = −0.43533 + 1.72832I
b = −0.341428 + 1.140430I
−3.91290 − 2.72338I 0
u = −1.137590 + 0.235343I
a = −1.22592 + 0.74369I
b = 0.167501 + 1.235820I
−6.05567 − 2.92910I 0
u = −1.137590 − 0.235343I
a = −1.22592 − 0.74369I
b = 0.167501 − 1.235820I
−6.05567 + 2.92910I 0
u = −0.948270 + 0.671042I
a = −2.00805 + 0.33990I
b = 0.75652 + 1.30385I
1.42242 + 9.08759I 0
u = −0.948270 − 0.671042I
a = −2.00805 − 0.33990I
b = 0.75652 − 1.30385I
1.42242 − 9.08759I 0
u = 0.948770 + 0.671579I
a = 0.447129 + 0.925716I
b = −0.676867 − 0.396420I
2.38838 − 3.60572I 0
u = 0.948770 − 0.671579I
a = 0.447129 − 0.925716I
b = −0.676867 + 0.396420I
2.38838 + 3.60572I 0
u = 1.121990 + 0.364900I
a = −0.27592 − 1.50625I
b = 0.447760 − 0.992496I
−4.54531 − 5.71755I 0
u = 1.121990 − 0.364900I
a = −0.27592 + 1.50625I
b = 0.447760 + 0.992496I
−4.54531 + 5.71755I 0
u = 0.639027 + 1.000420I
a = 1.242290 − 0.373765I
b = −0.632031 + 0.914157I
4.58793 − 8.11613I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.639027 − 1.000420I
a = 1.242290 + 0.373765I
b = −0.632031 − 0.914157I
4.58793 + 8.11613I 0
u = 1.055660 + 0.555609I
a = 0.986123 + 0.387552I
b = −0.05146 + 1.46074I
−4.01170 − 10.05950I 0
u = 1.055660 − 0.555609I
a = 0.986123 − 0.387552I
b = −0.05146 − 1.46074I
−4.01170 + 10.05950I 0
u = −0.993474 + 0.666991I
a = 2.02429 − 0.50756I
b = −0.533965 − 1.230380I
0.00033 + 7.78187I 0
u = −0.993474 − 0.666991I
a = 2.02429 + 0.50756I
b = −0.533965 + 1.230380I
0.00033 − 7.78187I 0
u = 0.807859 + 0.884061I
a = −1.293630 + 0.452149I
b = 0.498444 − 0.759435I
2.71484 − 1.73531I 0
u = 0.807859 − 0.884061I
a = −1.293630 − 0.452149I
b = 0.498444 + 0.759435I
2.71484 + 1.73531I 0
u = −0.706766 + 0.354686I
a = −0.282796 − 0.622551I
b = −0.524063 + 0.052177I
−0.798629 + 0.012049I 0
u = −0.706766 − 0.354686I
a = −0.282796 + 0.622551I
b = −0.524063 − 0.052177I
−0.798629 − 0.012049I 0
u = −1.110330 + 0.484386I
a = −1.112330 + 0.462518I
b = −0.294361 + 1.037930I
−3.47695 + 3.46248I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.110330 − 0.484386I
a = −1.112330 − 0.462518I
b = −0.294361 − 1.037930I
−3.47695 − 3.46248I 0
u = 1.211880 + 0.061782I
a = −0.476042 + 0.600916I
b = 0.671000 + 0.365578I
−1.23772 − 5.74341I 0
u = 1.211880 − 0.061782I
a = −0.476042 − 0.600916I
b = 0.671000 − 0.365578I
−1.23772 + 5.74341I 0
u = 0.106543 + 0.761246I
a = −0.792451 + 0.559262I
b = 0.013347 − 1.023550I
−4.27716 + 1.18904I 0
u = 0.106543 − 0.761246I
a = −0.792451 − 0.559262I
b = 0.013347 + 1.023550I
−4.27716 − 1.18904I 0
u = 0.913187 + 0.827058I
a = 0.333766 + 0.974109I
b = −0.321105 − 0.731793I
2.41371 − 4.51701I 0
u = 0.913187 − 0.827058I
a = 0.333766 − 0.974109I
b = −0.321105 + 0.731793I
2.41371 + 4.51701I 0
u = 1.122340 + 0.517563I
a = −0.585144 − 0.582633I
b = 0.005654 − 1.207420I
−7.07290 − 5.73501I 0
u = 1.122340 − 0.517563I
a = −0.585144 + 0.582633I
b = 0.005654 + 1.207420I
−7.07290 + 5.73501I 0
u = −1.142660 + 0.480684I
a = 0.991446 − 0.372542I
b = 0.407802 − 0.786236I
−3.76575 + 2.18592I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.142660 − 0.480684I
a = 0.991446 + 0.372542I
b = 0.407802 + 0.786236I
−3.76575 − 2.18592I 0
u = 1.048440 + 0.669478I
a = −0.157000 − 1.014550I
b = 0.820539 + 0.548469I
6.23300 − 6.84752I 0
u = 1.048440 − 0.669478I
a = −0.157000 + 1.014550I
b = 0.820539 − 0.548469I
6.23300 + 6.84752I 0
u = −1.057340 + 0.665573I
a = 1.97801 − 0.79727I
b = −0.562818 − 1.051300I
0.51473 + 8.33328I 0
u = −1.057340 − 0.665573I
a = 1.97801 + 0.79727I
b = −0.562818 + 1.051300I
0.51473 − 8.33328I 0
u = −1.095860 + 0.627858I
a = −1.97338 + 1.14086I
b = 0.658073 + 1.076560I
4.62438 + 12.39440I 0
u = −1.095860 − 0.627858I
a = −1.97338 − 1.14086I
b = 0.658073 − 1.076560I
4.62438 − 12.39440I 0
u = −0.140721 + 0.720089I
a = 0.182316 + 0.104872I
b = −0.558431 − 0.851273I
−0.87087 + 2.23864I 0
u = −0.140721 − 0.720089I
a = 0.182316 − 0.104872I
b = −0.558431 + 0.851273I
−0.87087 − 2.23864I 0
u = −1.102930 + 0.679166I
a = −0.562620 + 0.951998I
b = 1.035360 − 0.490369I
3.55762 + 13.43040I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.102930 − 0.679166I
a = −0.562620 − 0.951998I
b = 1.035360 + 0.490369I
3.55762 − 13.43040I 0
u = −1.112230 + 0.676396I
a = 0.589980 − 0.830670I
b = −0.876411 + 0.545244I
−0.66666 + 7.55235I 0
u = −1.112230 − 0.676396I
a = 0.589980 + 0.830670I
b = −0.876411 − 0.545244I
−0.66666 − 7.55235I 0
u = −1.151800 + 0.621427I
a = −0.354074 + 0.613260I
b = 0.822266 − 0.822898I
4.15465 + 1.33498I 0
u = −1.151800 − 0.621427I
a = −0.354074 − 0.613260I
b = 0.822266 + 0.822898I
4.15465 − 1.33498I 0
u = −1.275870 + 0.297568I
a = 1.008550 − 0.654374I
b = −0.245337 − 1.054360I
−8.61445 + 2.72790I 0
u = −1.275870 − 0.297568I
a = 1.008550 + 0.654374I
b = −0.245337 + 1.054360I
−8.61445 − 2.72790I 0
u = −0.228727 + 0.640057I
a = −0.314354 − 0.294683I
b = 0.371470 + 1.033300I
−0.966729 + 0.859390I −5.92499 + 0.I
u = −0.228727 − 0.640057I
a = −0.314354 + 0.294683I
b = 0.371470 − 1.033300I
−0.966729 − 0.859390I −5.92499 + 0.I
u = −1.134690 + 0.716778I
a = −1.57546 + 0.75755I
b = 0.568922 + 0.878250I
3.09471 + 2.98427I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.134690 − 0.716778I
a = −1.57546 − 0.75755I
b = 0.568922 − 0.878250I
3.09471 − 2.98427I 0
u = 1.155860 + 0.686217I
a = −1.91337 − 0.66981I
b = 0.718805 − 1.172310I
1.4255 − 19.7547I 0
u = 1.155860 − 0.686217I
a = −1.91337 + 0.66981I
b = 0.718805 + 1.172310I
1.4255 + 19.7547I 0
u = 1.207910 + 0.591732I
a = −1.61200 − 0.68765I
b = 0.769951 − 0.938293I
3.78528 − 7.29732I 0
u = 1.207910 − 0.591732I
a = −1.61200 + 0.68765I
b = 0.769951 + 0.938293I
3.78528 + 7.29732I 0
u = −1.352950 + 0.028199I
a = −0.380214 − 0.665078I
b = 0.598993 − 1.083700I
−3.19698 − 10.70540I 0
u = −1.352950 − 0.028199I
a = −0.380214 + 0.665078I
b = 0.598993 + 1.083700I
−3.19698 + 10.70540I 0
u = 1.177610 + 0.689514I
a = 1.84293 + 0.57964I
b = −0.689134 + 1.096760I
−2.34666 − 13.36180I 0
u = 1.177610 − 0.689514I
a = 1.84293 − 0.57964I
b = −0.689134 − 1.096760I
−2.34666 + 13.36180I 0
u = 1.085870 + 0.835827I
a = −0.274618 − 0.628927I
b = 0.554690 + 0.833924I
3.24985 + 1.50408I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.085870 − 0.835827I
a = −0.274618 + 0.628927I
b = 0.554690 − 0.833924I
3.24985 − 1.50408I 0
u = 0.267156 + 0.504152I
a = 1.28364 − 0.90605I
b = 0.163501 + 1.252410I
−2.12105 + 5.62580I −8.69169 − 6.13312I
u = 0.267156 − 0.504152I
a = 1.28364 + 0.90605I
b = 0.163501 − 1.252410I
−2.12105 − 5.62580I −8.69169 + 6.13312I
u = 0.522745 + 0.193253I
a = 1.71293 + 0.63012I
b = 0.326924 + 1.280390I
−2.07926 + 5.70484I −8.22383 − 7.39573I
u = 0.522745 − 0.193253I
a = 1.71293 − 0.63012I
b = 0.326924 − 1.280390I
−2.07926 − 5.70484I −8.22383 + 7.39573I
u = −0.534086
a = −0.703155
b = −0.362371
−0.932967 −10.1800
u = 1.47986 + 0.05680I
a = 0.858827 + 0.664018I
b = −0.533518 + 0.707425I
−5.87293 − 1.10773I 0
u = 1.47986 − 0.05680I
a = 0.858827 − 0.664018I
b = −0.533518 − 0.707425I
−5.87293 + 1.10773I 0
u = −1.48687 + 0.13620I
a = 0.476101 + 0.355357I
b = −0.562080 + 0.984677I
−6.81024 − 3.33209I 0
u = −1.48687 − 0.13620I
a = 0.476101 − 0.355357I
b = −0.562080 − 0.984677I
−6.81024 + 3.33209I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.055894 + 0.485909I
a = −0.270436 + 1.037490I
b = 0.612930 + 0.064066I
1.80576 + 2.53513I −2.13143 − 3.97247I
u = 0.055894 − 0.485909I
a = −0.270436 − 1.037490I
b = 0.612930 − 0.064066I
1.80576 − 2.53513I −2.13143 + 3.97247I
u = −0.176421 + 0.374536I
a = −1.151760 + 0.139094I
b = 0.288238 + 0.794600I
−0.452145 + 1.312550I −4.74769 − 4.89976I
u = −0.176421 − 0.374536I
a = −1.151760 − 0.139094I
b = 0.288238 − 0.794600I
−0.452145 − 1.312550I −4.74769 + 4.89976I
20
II. I
u
2
= h63182u
37
+ 18834u
36
+ · · · + 9223b + 14567, −1.30 × 10
5
u
37
+
1.50 × 10
5
u
36
+ · · · + 9223a − 3.97 × 10
5
, u
38
− 12u
36
+ · · · + 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
14.1104u
37
− 16.2414u
36
+ ··· + 92.0837u + 43.0675
−6.85048u
37
− 2.04207u
36
+ ··· + 20.1664u − 1.57942
a
11
=
−u
−u
3
+ u
a
2
=
−2.94123u
37
+ 0.382305u
36
+ ··· − 3.13618u − 0.270519
3.14876u
37
+ 0.790632u
36
+ ··· − 4.18974u + 2.62149
a
7
=
11.4728u
37
− 3.77263u
36
+ ··· + 30.8969u + 9.83259
−1.89602u
37
+ 4.91998u
36
+ ··· − 19.2041u − 12.5248
a
1
=
0.207525u
37
+ 1.17294u
36
+ ··· − 7.32592u + 2.35097
3.14876u
37
+ 0.790632u
36
+ ··· − 4.18974u + 2.62149
a
5
=
6.50038u
37
− 3.41635u
36
+ ··· + 60.6781u + 26.3995
−0.171311u
37
+ 0.523908u
36
+ ··· + 3.46341u − 3.79443
a
9
=
u
3
u
5
− u
3
+ u
a
8
=
27.6979u
37
− 5.58506u
36
+ ··· − 11.7576u + 16.9625
5.27366u
37
+ 0.894720u
36
+ ··· − 23.8593u − 9.72840
a
12
=
−0.792475u
37
+ 1.17294u
36
+ ··· − 7.32592u + 2.35097
3.14876u
37
+ 0.790632u
36
+ ··· − 3.18974u + 2.62149
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
125590
9223
u
37
+
9092
9223
u
36
+ ··· −
355732
9223
u −
476456
9223
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
38
− 19u
37
+ ··· − 24u + 1
c
2
u
38
− u
37
+ ··· + 12u
2
+ 1
c
3
u
38
− 12u
36
+ ··· + 3u + 1
c
4
u
38
+ u
37
+ ··· − 5u + 1
c
5
u
38
− 4u
37
+ ··· − 2u + 1
c
6
u
38
+ u
37
+ ··· + 12u
2
+ 1
c
7
u
38
+ 2u
37
+ ··· + u + 1
c
8
u
38
+ 4u
37
+ ··· + 2u + 1
c
9
u
38
− 24u
37
+ ··· − 21u + 1
c
10
u
38
− 12u
36
+ ··· − 3u + 1
c
11
u
38
− 2u
37
+ ··· − u + 1
c
12
u
38
+ 6u
37
+ ··· − 10u + 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 19y
37
+ ··· + 12y + 1
c
2
, c
6
y
38
+ 19y
37
+ ··· + 24y + 1
c
3
, c
10
y
38
− 24y
37
+ ··· − 21y + 1
c
4
y
38
+ 5y
37
+ ··· + 19y + 1
c
5
, c
8
y
38
+ 20y
37
+ ··· + 36y + 1
c
7
, c
11
y
38
− 30y
37
+ ··· − 33y + 1
c
9
y
38
− 28y
36
+ ··· − 21y + 1
c
12
y
38
− 6y
37
+ ··· − 42y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.991867 + 0.293008I
a = 0.088290 + 0.480131I
b = −0.341002 + 1.107610I
−3.11280 − 7.15236I −11.2847 + 9.0430I
u = 0.991867 − 0.293008I
a = 0.088290 − 0.480131I
b = −0.341002 − 1.107610I
−3.11280 + 7.15236I −11.2847 − 9.0430I
u = 0.732096 + 0.626334I
a = −1.67555 − 0.49709I
b = 1.036790 − 0.718459I
4.91223 − 4.80789I −3.00260 + 3.79185I
u = 0.732096 − 0.626334I
a = −1.67555 + 0.49709I
b = 1.036790 + 0.718459I
4.91223 + 4.80789I −3.00260 − 3.79185I
u = −0.748299 + 0.742347I
a = 0.711126 − 0.885387I
b = −0.582385 + 1.100190I
0.62663 − 3.36395I −9.20426 + 4.94587I
u = −0.748299 − 0.742347I
a = 0.711126 + 0.885387I
b = −0.582385 − 1.100190I
0.62663 + 3.36395I −9.20426 − 4.94587I
u = 0.839841 + 0.293635I
a = 1.06189 + 1.73136I
b = 0.358348 + 1.192970I
−2.56301 + 4.67338I −10.21931 − 3.08914I
u = 0.839841 − 0.293635I
a = 1.06189 − 1.73136I
b = 0.358348 − 1.192970I
−2.56301 − 4.67338I −10.21931 + 3.08914I
u = −1.075490 + 0.300288I
a = −0.14453 + 2.09621I
b = −0.205733 + 0.743835I
−1.56441 + 4.82049I −14.5664 − 2.6540I
u = −1.075490 − 0.300288I
a = −0.14453 − 2.09621I
b = −0.205733 − 0.743835I
−1.56441 − 4.82049I −14.5664 + 2.6540I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.854395 + 0.767581I
a = −0.682159 − 1.047860I
b = 0.281279 + 0.516482I
2.84860 − 4.96095I −2.01482 + 8.52252I
u = 0.854395 − 0.767581I
a = −0.682159 + 1.047860I
b = 0.281279 − 0.516482I
2.84860 + 4.96095I −2.01482 − 8.52252I
u = 1.075450 + 0.417540I
a = −0.16590 − 1.61326I
b = 0.290951 − 1.004320I
−5.01160 − 4.75346I −15.3943 + 3.4825I
u = 1.075450 − 0.417540I
a = −0.16590 + 1.61326I
b = 0.290951 + 1.004320I
−5.01160 + 4.75346I −15.3943 − 3.4825I
u = −0.943617 + 0.669429I
a = −2.23938 + 0.34377I
b = 0.552077 + 1.202540I
0.03099 + 8.74330I −8.91907 − 10.84509I
u = −0.943617 − 0.669429I
a = −2.23938 − 0.34377I
b = 0.552077 − 1.202540I
0.03099 − 8.74330I −8.91907 + 10.84509I
u = −0.686929 + 0.483998I
a = −0.62902 + 1.50618I
b = 1.027270 − 0.964833I
4.24690 − 2.58803I −2.22978 + 7.46639I
u = −0.686929 − 0.483998I
a = −0.62902 − 1.50618I
b = 1.027270 + 0.964833I
4.24690 + 2.58803I −2.22978 − 7.46639I
u = 0.895125 + 0.796856I
a = 1.375030 − 0.178060I
b = −0.393497 + 0.543408I
2.72633 − 0.91164I −6.33413 − 3.56727I
u = 0.895125 − 0.796856I
a = 1.375030 + 0.178060I
b = −0.393497 − 0.543408I
2.72633 + 0.91164I −6.33413 + 3.56727I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.068930 + 0.542210I
a = 1.82807 − 0.68045I
b = −0.868761 − 1.014880I
2.90354 + 6.79041I −10.77255 − 7.64968I
u = −1.068930 − 0.542210I
a = 1.82807 + 0.68045I
b = −0.868761 + 1.014880I
2.90354 − 6.79041I −10.77255 + 7.64968I
u = −1.104200 + 0.482481I
a = 1.41930 − 0.31782I
b = 0.256385 − 0.879117I
−4.49779 + 2.49920I −17.5876 − 2.3366I
u = −1.104200 − 0.482481I
a = 1.41930 + 0.31782I
b = 0.256385 + 0.879117I
−4.49779 − 2.49920I −17.5876 + 2.3366I
u = 1.008320 + 0.675509I
a = 0.585134 + 0.669247I
b = −0.868472 − 0.629081I
4.02350 − 0.28612I −5.68627 + 0.I
u = 1.008320 − 0.675509I
a = 0.585134 − 0.669247I
b = −0.868472 + 0.629081I
4.02350 + 0.28612I −5.68627 + 0.I
u = −0.750582 + 0.224491I
a = 2.48091 + 0.03823I
b = 0.130888 + 0.676207I
−0.27120 − 2.53382I −11.47078 + 5.16775I
u = −0.750582 − 0.224491I
a = 2.48091 − 0.03823I
b = 0.130888 − 0.676207I
−0.27120 + 2.53382I −11.47078 − 5.16775I
u = 0.697328 + 0.208539I
a = 0.39805 − 2.20775I
b = −0.387499 − 1.077190I
−3.23941 + 1.85645I −10.13432 − 0.54316I
u = 0.697328 − 0.208539I
a = 0.39805 + 2.20775I
b = −0.387499 + 1.077190I
−3.23941 − 1.85645I −10.13432 + 0.54316I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.188715 + 0.580646I
a = −0.315921 + 0.452263I
b = −0.386853 − 0.873194I
−2.02228 + 1.65299I −11.55346 − 2.70930I
u = −0.188715 − 0.580646I
a = −0.315921 − 0.452263I
b = −0.386853 + 0.873194I
−2.02228 − 1.65299I −11.55346 + 2.70930I
u = 1.400070 + 0.020540I
a = −0.511954 + 0.412824I
b = 0.492777 + 0.991292I
−6.99257 + 2.83923I 0
u = 1.400070 − 0.020540I
a = −0.511954 − 0.412824I
b = 0.492777 − 0.991292I
−6.99257 − 2.83923I 0
u = −1.43299 + 0.02985I
a = −0.910284 + 0.776573I
b = 0.494779 + 0.709703I
−6.02241 + 1.20982I 0
u = −1.43299 − 0.02985I
a = −0.910284 − 0.776573I
b = 0.494779 − 0.709703I
−6.02241 − 1.20982I 0
u = −0.494736 + 0.110162I
a = −1.17311 + 1.64447I
b = −0.387344 − 0.683093I
−1.82565 + 1.31247I −12.61929 − 3.30037I
u = −0.494736 − 0.110162I
a = −1.17311 − 1.64447I
b = −0.387344 + 0.683093I
−1.82565 − 1.31247I −12.61929 + 3.30037I
29
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
38
− 19u
37
+ ··· − 24u + 1)
· (u
154
+ 64u
153
+ ··· + 54112666u + 1857769)
c
2
(u
38
− u
37
+ ··· + 12u
2
+ 1)(u
154
− 2u
153
+ ··· + 3074u + 1363)
c
3
(u
38
− 12u
36
+ ··· + 3u + 1)(u
154
− u
153
+ ··· + 171u − 361)
c
4
(u
38
+ u
37
+ ··· − 5u + 1)
· (u
154
− 6u
153
+ ··· + 28566941u + 26372777)
c
5
(u
38
− 4u
37
+ ··· − 2u + 1)(u
154
− 3u
153
+ ··· + 4572u + 4921)
c
6
(u
38
+ u
37
+ ··· + 12u
2
+ 1)(u
154
− 2u
153
+ ··· + 3074u + 1363)
c
7
(u
38
+ 2u
37
+ ··· + u + 1)(u
154
+ 3u
153
+ ··· − 60545u − 9307)
c
8
(u
38
+ 4u
37
+ ··· + 2u + 1)(u
154
− 3u
153
+ ··· + 4572u + 4921)
c
9
(u
38
− 24u
37
+ ··· − 21u + 1)
· (u
154
+ 71u
153
+ ··· + 2567071u + 130321)
c
10
(u
38
− 12u
36
+ ··· − 3u + 1)(u
154
− u
153
+ ··· + 171u − 361)
c
11
(u
38
− 2u
37
+ ··· − u + 1)(u
154
+ 3u
153
+ ··· − 60545u − 9307)
c
12
(u
38
+ 6u
37
+ ··· − 10u + 1)(u
154
− 3u
153
+ ··· − 9312u − 521)
30
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
38
+ 19y
37
+ ··· + 12y + 1)
· (y
154
+ 72y
153
+ ··· − 893114824048786y + 3451305657361)
c
2
, c
6
(y
38
+ 19y
37
+ ··· + 24y + 1)
· (y
154
+ 64y
153
+ ··· + 54112666y + 1857769)
c
3
, c
10
(y
38
− 24y
37
+ ··· − 21y + 1)
· (y
154
− 71y
153
+ ··· − 2567071y + 130321)
c
4
(y
38
+ 5y
37
+ ··· + 19y + 1)
· (y
154
+ 46y
153
+ ··· + 19716884500334309y + 695523366691729)
c
5
, c
8
(y
38
+ 20y
37
+ ··· + 36y + 1)
· (y
154
+ 93y
153
+ ··· + 417233130y + 24216241)
c
7
, c
11
(y
38
− 30y
37
+ ··· − 33y + 1)
· (y
154
− 89y
153
+ ··· − 3771070879y + 86620249)
c
9
(y
38
− 28y
36
+ ··· − 21y + 1)
· (y
154
+ 45y
153
+ ··· − 127131132883y + 16983563041)
c
12
(y
38
− 6y
37
+ ··· − 42y + 1)
· (y
154
+ 11y
153
+ ··· − 91631584y + 271441)
31
