12a
0776
(K12a
0776
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 1 9 2 11 4 7 6 5
Solving Sequence
4,12 5,9
10 1 6 7 3 11 8 2
c
4
c
9
c
12
c
5
c
6
c
3
c
11
c
8
c
2
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h6.98170 × 10
214
u
129
+ 4.61169 × 10
214
u
128
+ ··· + 5.45825 × 10
214
b − 8.94276 × 10
215
,
6.48861 × 10
215
u
129
+ 6.31891 × 10
215
u
128
+ ··· + 1.03707 × 10
216
a + 1.53636 × 10
215
,
u
130
+ 2u
129
+ ··· + 107u − 19i
I
u
2
= h−u
22
+ 11u
20
+ ··· + b + 1, 4u
22
+ u
21
+ ··· + a − 6, u
23
− u
22
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 153 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
= h6.98 × 10
214
u
129
+ 4.61 × 10
214
u
128
+ · · · + 5.46 × 10
214
b − 8.94 ×
10
215
, 6.49 × 10
215
u
129
+ 6.32 × 10
215
u
128
+ · · · + 1.04 × 10
216
a + 1.54 ×
10
215
, u
130
+ 2u
129
+ · · · + 107u − 19i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
−0.625668u
129
− 0.609305u
128
+ ··· − 27.4160u − 0.148144
−1.27911u
129
− 0.844901u
128
+ ··· − 95.2397u + 16.3839
a
10
=
−1.90478u
129
− 1.45421u
128
+ ··· − 122.656u + 16.2358
−1.27911u
129
− 0.844901u
128
+ ··· − 95.2397u + 16.3839
a
1
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
2.56893u
129
+ 2.78359u
128
+ ··· + 230.909u − 39.9412
0.412250u
129
+ 0.950242u
128
+ ··· + 44.8273u − 6.37800
a
3
=
3.56700u
129
+ 2.55922u
128
+ ··· + 345.494u − 54.3475
4.11991u
129
+ 3.15276u
128
+ ··· + 415.557u − 63.9594
a
11
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
−1.64224u
129
− 0.895692u
128
+ ··· − 84.3781u + 10.1577
−1.83002u
129
− 1.24918u
128
+ ··· − 126.166u + 21.6069
a
2
=
−3.81368u
129
− 1.73033u
128
+ ··· − 160.211u + 30.0156
−2.52627u
129
− 1.03451u
128
+ ··· − 186.927u + 28.6906
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.84806u
129
+ 2.00475u
128
+ ··· + 371.144u − 52.0264
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
130
+ 57u
129
+ ··· + 113740u + 5776
c
2
, c
7
u
130
+ u
129
+ ··· + 90u + 76
c
3
, c
9
u
130
+ u
129
+ ··· + 7u − 1
c
4
, c
5
, c
12
u
130
+ 2u
129
+ ··· + 107u − 19
c
6
u
130
+ 12u
129
+ ··· − 270u − 19
c
8
u
130
+ 18u
129
+ ··· − 2103u + 1217
c
10
u
130
+ u
129
+ ··· − 49u − 1
c
11
u
130
− 6u
129
+ ··· + 1396235u − 512411
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
130
+ 43y
129
+ ··· − 401377392y + 33362176
c
2
, c
7
y
130
− 57y
129
+ ··· − 113740y + 5776
c
3
, c
9
y
130
+ 87y
129
+ ··· + 41y + 1
c
4
, c
5
, c
12
y
130
− 116y
129
+ ··· + 4815y + 361
c
6
y
130
+ 4y
129
+ ··· + 53792y + 361
c
8
y
130
− 28y
129
+ ··· − 151952217y + 1481089
c
10
y
130
+ y
129
+ ··· − 73y + 1
c
11
y
130
+ 28y
129
+ ··· − 9070292069281y + 262565032921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.858387 + 0.531211I
a = −0.000790 + 0.509860I
b = −0.582173 − 1.234630I
−1.99971 + 9.85947I 0
u = 0.858387 − 0.531211I
a = −0.000790 − 0.509860I
b = −0.582173 + 1.234630I
−1.99971 − 9.85947I 0
u = −0.898768 + 0.468623I
a = −0.081360 + 0.538066I
b = 0.521121 − 1.115890I
−0.11864 − 4.16240I 0
u = −0.898768 − 0.468623I
a = −0.081360 − 0.538066I
b = 0.521121 + 1.115890I
−0.11864 + 4.16240I 0
u = −0.083322 + 0.963348I
a = −0.084625 − 0.382231I
b = 0.037380 + 0.621768I
2.83683 + 2.67689I 0
u = −0.083322 − 0.963348I
a = −0.084625 + 0.382231I
b = 0.037380 − 0.621768I
2.83683 − 2.67689I 0
u = −1.004880 + 0.290209I
a = 0.865674 − 0.893082I
b = −1.030620 − 0.343395I
0.91394 − 4.12561I 0
u = −1.004880 − 0.290209I
a = 0.865674 + 0.893082I
b = −1.030620 + 0.343395I
0.91394 + 4.12561I 0
u = 0.420538 + 0.836988I
a = 0.873483 − 0.065030I
b = −0.284296 + 1.068210I
0.87806 − 4.73563I 0
u = 0.420538 − 0.836988I
a = 0.873483 + 0.065030I
b = −0.284296 − 1.068210I
0.87806 + 4.73563I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335113 + 0.836804I
a = −0.931730 − 0.080138I
b = 0.441840 + 0.934661I
1.33578 + 0.56403I 0
u = −0.335113 − 0.836804I
a = −0.931730 + 0.080138I
b = 0.441840 − 0.934661I
1.33578 − 0.56403I 0
u = −1.10302
a = 0.775817
b = −0.789416
−1.76903 0
u = 0.285462 + 0.825901I
a = −1.81147 + 0.60588I
b = 0.64553 − 1.32946I
−0.1981 − 14.6031I 0
u = 0.285462 − 0.825901I
a = −1.81147 − 0.60588I
b = 0.64553 + 1.32946I
−0.1981 + 14.6031I 0
u = −0.987953 + 0.541065I
a = −0.571922 − 0.059134I
b = 0.266608 + 0.830546I
0.09367 + 2.56827I 0
u = −0.987953 − 0.541065I
a = −0.571922 + 0.059134I
b = 0.266608 − 0.830546I
0.09367 − 2.56827I 0
u = 0.541925 + 0.684342I
a = 0.652657 + 0.110887I
b = 0.166422 + 0.851085I
0.333452 − 0.252683I 0
u = 0.541925 − 0.684342I
a = 0.652657 − 0.110887I
b = 0.166422 − 0.851085I
0.333452 + 0.252683I 0
u = 1.102160 + 0.253758I
a = −1.066500 − 0.898377I
b = 0.851738 − 0.518125I
1.86982 − 0.83103I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.102160 − 0.253758I
a = −1.066500 + 0.898377I
b = 0.851738 + 0.518125I
1.86982 + 0.83103I 0
u = 1.136000 + 0.030176I
a = 0.981440 − 0.667637I
b = −0.042634 + 1.045810I
−6.23069 − 2.66080I 0
u = 1.136000 − 0.030176I
a = 0.981440 + 0.667637I
b = −0.042634 − 1.045810I
−6.23069 + 2.66080I 0
u = −0.251176 + 0.814299I
a = 1.79456 + 0.70713I
b = −0.610782 − 1.215540I
1.91441 + 8.72257I 0
u = −0.251176 − 0.814299I
a = 1.79456 − 0.70713I
b = −0.610782 + 1.215540I
1.91441 − 8.72257I 0
u = −0.037572 + 0.806192I
a = −0.399881 + 0.366390I
b = 0.291035 + 0.079569I
2.95991 + 2.80966I 0
u = −0.037572 − 0.806192I
a = −0.399881 − 0.366390I
b = 0.291035 − 0.079569I
2.95991 − 2.80966I 0
u = −0.647077 + 0.466955I
a = −0.221642 + 0.331704I
b = −0.496804 + 0.477870I
0.13637 + 4.01955I 0
u = −0.647077 − 0.466955I
a = −0.221642 − 0.331704I
b = −0.496804 − 0.477870I
0.13637 − 4.01955I 0
u = −0.183392 + 0.749630I
a = −1.87602 + 0.53667I
b = 1.255920 − 0.197610I
3.40227 + 8.02397I 0. − 8.23743I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.183392 − 0.749630I
a = −1.87602 − 0.53667I
b = 1.255920 + 0.197610I
3.40227 − 8.02397I 0. + 8.23743I
u = −1.191740 + 0.311840I
a = 0.024118 + 1.067890I
b = 0.161195 − 0.679089I
−0.171796 + 0.563010I 0
u = −1.191740 − 0.311840I
a = 0.024118 − 1.067890I
b = 0.161195 + 0.679089I
−0.171796 − 0.563010I 0
u = −0.070853 + 0.764239I
a = 1.06562 + 1.55913I
b = −0.280012 − 0.707308I
3.24360 + 3.35091I 6.53466 − 8.76240I
u = −0.070853 − 0.764239I
a = 1.06562 − 1.55913I
b = −0.280012 + 0.707308I
3.24360 − 3.35091I 6.53466 + 8.76240I
u = 0.246615 + 0.720604I
a = −2.13436 + 0.83952I
b = 0.337598 − 1.206740I
−4.66475 − 5.87886I −6.12270 + 7.07846I
u = 0.246615 − 0.720604I
a = −2.13436 − 0.83952I
b = 0.337598 + 1.206740I
−4.66475 + 5.87886I −6.12270 − 7.07846I
u = 1.23931
a = −1.85412
b = 0.145370
−1.16737 0
u = 1.134870 + 0.535688I
a = 0.626428 + 0.107886I
b = −0.394333 + 0.864051I
−0.82512 − 7.90541I 0
u = 1.134870 − 0.535688I
a = 0.626428 − 0.107886I
b = −0.394333 − 0.864051I
−0.82512 + 7.90541I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.245080 + 0.173938I
a = 1.021120 − 0.397967I
b = −0.492548 − 1.109200I
−3.46073 + 3.05016I 0
u = 1.245080 − 0.173938I
a = 1.021120 + 0.397967I
b = −0.492548 + 1.109200I
−3.46073 − 3.05016I 0
u = 0.143744 + 0.721391I
a = 1.87656 + 0.52922I
b = −1.061160 − 0.341838I
4.71433 − 2.79991I 3.67971 + 2.47559I
u = 0.143744 − 0.721391I
a = 1.87656 − 0.52922I
b = −1.061160 + 0.341838I
4.71433 + 2.79991I 3.67971 − 2.47559I
u = 0.649728 + 0.327883I
a = 0.253720 + 0.133156I
b = −0.204354 − 1.251600I
−6.29212 + 2.13876I −10.09902 − 1.16229I
u = 0.649728 − 0.327883I
a = 0.253720 − 0.133156I
b = −0.204354 + 1.251600I
−6.29212 − 2.13876I −10.09902 + 1.16229I
u = −1.251240 + 0.302585I
a = 0.536351 + 0.071547I
b = −0.613211 − 0.091360I
−0.796656 + 1.165520I 0
u = −1.251240 − 0.302585I
a = 0.536351 − 0.071547I
b = −0.613211 + 0.091360I
−0.796656 − 1.165520I 0
u = −0.265715 + 0.657057I
a = −1.77184 + 0.24968I
b = 0.790079 + 0.494585I
−0.07306 + 2.71892I −4.07089 − 6.67892I
u = −0.265715 − 0.657057I
a = −1.77184 − 0.24968I
b = 0.790079 − 0.494585I
−0.07306 − 2.71892I −4.07089 + 6.67892I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.289740 + 0.091959I
a = 0.487671 − 0.497441I
b = −0.919604 + 0.424918I
−2.79729 − 0.29925I 0
u = −1.289740 − 0.091959I
a = 0.487671 + 0.497441I
b = −0.919604 − 0.424918I
−2.79729 + 0.29925I 0
u = −1.286060 + 0.217213I
a = −0.942728 + 0.296382I
b = 0.602910 − 0.732975I
−1.14693 + 3.01047I 0
u = −1.286060 − 0.217213I
a = −0.942728 − 0.296382I
b = 0.602910 + 0.732975I
−1.14693 − 3.01047I 0
u = 1.297020 + 0.168197I
a = 0.803997 + 0.674909I
b = 0.06844 + 1.75600I
−7.43887 − 0.64726I 0
u = 1.297020 − 0.168197I
a = 0.803997 − 0.674909I
b = 0.06844 − 1.75600I
−7.43887 + 0.64726I 0
u = 1.314830 + 0.065784I
a = −0.432923 − 0.952214I
b = 1.027710 + 0.621020I
−4.97328 + 5.01201I 0
u = 1.314830 − 0.065784I
a = −0.432923 + 0.952214I
b = 1.027710 − 0.621020I
−4.97328 − 5.01201I 0
u = 1.309110 + 0.220391I
a = −1.69121 − 1.55482I
b = 0.272681 − 0.998474I
−1.34053 − 2.82972I 0
u = 1.309110 − 0.220391I
a = −1.69121 + 1.55482I
b = 0.272681 + 0.998474I
−1.34053 + 2.82972I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.226503 + 0.629720I
a = −1.82895 − 0.59609I
b = 0.595575 + 0.950772I
−0.17888 + 2.24153I −2.03920 − 4.83013I
u = −0.226503 − 0.629720I
a = −1.82895 + 0.59609I
b = 0.595575 − 0.950772I
−0.17888 − 2.24153I −2.03920 + 4.83013I
u = 1.309960 + 0.318270I
a = −1.308210 + 0.373986I
b = 0.402858 − 0.719122I
−1.07582 − 7.25709I 0
u = 1.309960 − 0.318270I
a = −1.308210 − 0.373986I
b = 0.402858 + 0.719122I
−1.07582 + 7.25709I 0
u = −1.338960 + 0.174442I
a = 2.24878 − 1.21891I
b = −0.024251 − 0.916418I
−5.56464 − 2.29092I 0
u = −1.338960 − 0.174442I
a = 2.24878 + 1.21891I
b = −0.024251 + 0.916418I
−5.56464 + 2.29092I 0
u = −1.340680 + 0.210493I
a = −0.877607 + 0.528762I
b = −0.30500 + 1.81718I
−8.12771 + 4.44289I 0
u = −1.340680 − 0.210493I
a = −0.877607 − 0.528762I
b = −0.30500 − 1.81718I
−8.12771 − 4.44289I 0
u = 1.318240 + 0.347178I
a = −0.302737 + 0.449145I
b = 0.0350078 − 0.1026420I
−1.33416 − 6.99228I 0
u = 1.318240 − 0.347178I
a = −0.302737 − 0.449145I
b = 0.0350078 + 0.1026420I
−1.33416 + 6.99228I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.342730 + 0.240858I
a = 1.20491 − 1.89788I
b = −0.256076 − 1.209960I
−4.66530 + 8.85846I 0
u = −1.342730 − 0.240858I
a = 1.20491 + 1.89788I
b = −0.256076 + 1.209960I
−4.66530 − 8.85846I 0
u = −1.349190 + 0.211300I
a = −1.83931 + 0.52479I
b = 0.57970 + 1.46511I
−8.08214 + 2.22669I 0
u = −1.349190 − 0.211300I
a = −1.83931 − 0.52479I
b = 0.57970 − 1.46511I
−8.08214 − 2.22669I 0
u = 0.277760 + 0.559975I
a = 2.75484 − 0.37789I
b = −0.83736 + 1.18337I
−2.26658 − 6.27963I −6.34357 + 11.22337I
u = 0.277760 − 0.559975I
a = 2.75484 + 0.37789I
b = −0.83736 − 1.18337I
−2.26658 + 6.27963I −6.34357 − 11.22337I
u = 1.371230 + 0.136561I
a = 0.096261 − 0.232470I
b = 0.629399 + 0.641989I
−6.90132 − 2.06770I 0
u = 1.371230 − 0.136561I
a = 0.096261 + 0.232470I
b = 0.629399 − 0.641989I
−6.90132 + 2.06770I 0
u = −1.350410 + 0.292276I
a = −0.574263 + 0.744951I
b = 1.203480 − 0.246195I
−0.00337 + 6.46781I 0
u = −1.350410 − 0.292276I
a = −0.574263 − 0.744951I
b = 1.203480 + 0.246195I
−0.00337 − 6.46781I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.109627 + 0.601306I
a = −2.02450 − 0.50174I
b = 0.351609 − 1.133120I
−0.05515 − 5.77718I 2.75164 + 8.40546I
u = 0.109627 − 0.601306I
a = −2.02450 + 0.50174I
b = 0.351609 + 1.133120I
−0.05515 + 5.77718I 2.75164 − 8.40546I
u = 1.374500 + 0.260783I
a = 1.36759 + 0.71622I
b = −0.653101 + 1.173240I
−5.24269 − 5.52378I 0
u = 1.374500 − 0.260783I
a = 1.36759 − 0.71622I
b = −0.653101 − 1.173240I
−5.24269 + 5.52378I 0
u = −0.479566 + 0.355001I
a = −0.436840 − 0.693374I
b = −0.215840 + 0.910078I
−1.29796 + 0.90199I −5.18087 − 4.06045I
u = −0.479566 − 0.355001I
a = −0.436840 + 0.693374I
b = −0.215840 − 0.910078I
−1.29796 − 0.90199I −5.18087 + 4.06045I
u = 1.370910 + 0.305032I
a = 0.533182 + 0.876918I
b = −1.382640 − 0.102108I
−1.51815 − 11.83770I 0
u = 1.370910 − 0.305032I
a = 0.533182 − 0.876918I
b = −1.382640 + 0.102108I
−1.51815 + 11.83770I 0
u = −0.013333 + 0.592223I
a = 2.42975 + 0.29872I
b = −0.392539 − 0.807900I
2.82904 − 0.08807I 5.60147 + 0.37026I
u = −0.013333 − 0.592223I
a = 2.42975 − 0.29872I
b = −0.392539 + 0.807900I
2.82904 + 0.08807I 5.60147 − 0.37026I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.397730 + 0.189525I
a = 0.958506 + 0.724031I
b = −0.177783 + 0.029116I
−5.89100 − 6.15905I 0
u = 1.397730 − 0.189525I
a = 0.958506 − 0.724031I
b = −0.177783 − 0.029116I
−5.89100 + 6.15905I 0
u = 0.362563 + 0.457638I
a = 0.208409 − 1.271840I
b = 0.569372 + 1.258850I
−2.66428 + 3.24443I −6.17705 − 2.02777I
u = 0.362563 − 0.457638I
a = 0.208409 + 1.271840I
b = 0.569372 − 1.258850I
−2.66428 − 3.24443I −6.17705 + 2.02777I
u = −1.39806 + 0.22871I
a = −1.58146 + 1.09204I
b = 0.94345 + 1.32751I
−7.59586 + 9.21921I 0
u = −1.39806 − 0.22871I
a = −1.58146 − 1.09204I
b = 0.94345 − 1.32751I
−7.59586 − 9.21921I 0
u = −1.40906 + 0.18020I
a = −0.736086 + 0.285567I
b = −0.55498 + 1.46645I
−8.27139 − 0.86389I 0
u = −1.40906 − 0.18020I
a = −0.736086 − 0.285567I
b = −0.55498 − 1.46645I
−8.27139 + 0.86389I 0
u = 1.41549 + 0.13332I
a = 0.418946 + 0.403074I
b = 0.214404 + 1.204350I
−7.22098 − 2.65469I 0
u = 1.41549 − 0.13332I
a = 0.418946 − 0.403074I
b = 0.214404 − 1.204350I
−7.22098 + 2.65469I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39810 + 0.29350I
a = 1.93006 − 0.63919I
b = −0.405049 − 1.248080I
−9.89266 + 9.57242I 0
u = −1.39810 − 0.29350I
a = 1.93006 + 0.63919I
b = −0.405049 + 1.248080I
−9.89266 − 9.57242I 0
u = 1.40689 + 0.25940I
a = 1.025100 + 0.918783I
b = −0.815266 + 0.674857I
−5.41669 − 6.06942I 0
u = 1.40689 − 0.25940I
a = 1.025100 − 0.918783I
b = −0.815266 − 0.674857I
−5.41669 + 6.06942I 0
u = −0.486120 + 0.286145I
a = 0.185350 − 0.667609I
b = −0.568095 + 0.418020I
−1.31003 + 0.54175I −6.81683 − 1.31516I
u = −0.486120 − 0.286145I
a = 0.185350 + 0.667609I
b = −0.568095 − 0.418020I
−1.31003 − 0.54175I −6.81683 + 1.31516I
u = 0.133677 + 0.536129I
a = 2.10326 − 2.26270I
b = −0.392636 + 1.317170I
−3.37384 + 0.52133I −4.26987 + 2.66669I
u = 0.133677 − 0.536129I
a = 2.10326 + 2.26270I
b = −0.392636 − 1.317170I
−3.37384 − 0.52133I −4.26987 − 2.66669I
u = 1.41088 + 0.33302I
a = −1.59820 − 0.69108I
b = 0.63561 − 1.29752I
−3.36834 − 12.86740I 0
u = 1.41088 − 0.33302I
a = −1.59820 + 0.69108I
b = 0.63561 + 1.29752I
−3.36834 + 12.86740I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45618 + 0.07653I
a = −0.039806 − 1.092760I
b = 0.212168 − 1.380370I
−12.94690 − 0.82105I 0
u = −1.45618 − 0.07653I
a = −0.039806 + 1.092760I
b = 0.212168 + 1.380370I
−12.94690 + 0.82105I 0
u = 1.42202 + 0.35852I
a = 0.998334 + 0.626365I
b = −0.413990 + 1.173780I
−4.21413 − 4.94470I 0
u = 1.42202 − 0.35852I
a = 0.998334 − 0.626365I
b = −0.413990 − 1.173780I
−4.21413 + 4.94470I 0
u = −1.42895 + 0.33404I
a = 1.58291 − 0.81065I
b = −0.65275 − 1.40414I
−5.6600 + 18.7966I 0
u = −1.42895 − 0.33404I
a = 1.58291 + 0.81065I
b = −0.65275 + 1.40414I
−5.6600 − 18.7966I 0
u = 0.076022 + 0.521366I
a = 0.08077 − 1.73568I
b = 0.15097 + 1.72552I
−3.58802 − 1.74131I −1.39572 + 5.92415I
u = 0.076022 − 0.521366I
a = 0.08077 + 1.73568I
b = 0.15097 − 1.72552I
−3.58802 + 1.74131I −1.39572 − 5.92415I
u = 1.49460 + 0.01515I
a = 0.054877 + 0.764810I
b = −0.241243 + 1.238930I
−8.21426 − 3.52836I 0
u = 1.49460 − 0.01515I
a = 0.054877 − 0.764810I
b = −0.241243 − 1.238930I
−8.21426 + 3.52836I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48241 + 0.26739I
a = −1.011520 + 0.728457I
b = 0.054138 + 0.901494I
−6.09411 + 3.76031I 0
u = −1.48241 − 0.26739I
a = −1.011520 − 0.728457I
b = 0.054138 − 0.901494I
−6.09411 − 3.76031I 0
u = −1.47562 + 0.34827I
a = −0.982200 + 0.694474I
b = 0.264731 + 1.228100I
−5.16016 + 9.09654I 0
u = −1.47562 − 0.34827I
a = −0.982200 − 0.694474I
b = 0.264731 − 1.228100I
−5.16016 − 9.09654I 0
u = −1.54342 + 0.01292I
a = 0.097509 − 0.778763I
b = 0.356165 − 1.265910I
−10.29580 − 8.53203I 0
u = −1.54342 − 0.01292I
a = 0.097509 + 0.778763I
b = 0.356165 + 1.265910I
−10.29580 + 8.53203I 0
u = 0.076394 + 0.385183I
a = −3.85398 + 1.50660I
b = −0.219834 − 0.730621I
−1.02291 + 4.47699I −1.50211 − 1.73310I
u = 0.076394 − 0.385183I
a = −3.85398 − 1.50660I
b = −0.219834 + 0.730621I
−1.02291 − 4.47699I −1.50211 + 1.73310I
u = 0.221791 + 0.154271I
a = −1.16786 + 2.68312I
b = 0.406142 − 0.079977I
1.50967 − 0.46289I 6.10398 − 0.66773I
u = 0.221791 − 0.154271I
a = −1.16786 − 2.68312I
b = 0.406142 + 0.079977I
1.50967 + 0.46289I 6.10398 + 0.66773I
17
II.
I
u
2
= h−u
22
+11u
20
+· · ·+b+1, 4u
22
+u
21
+· · ·+a−6, u
23
−u
22
+· · ·−u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
−4u
22
− u
21
+ ··· − 11u + 6
u
22
− 11u
20
+ ··· + 5u − 1
a
10
=
−3u
22
− u
21
+ ··· − 6u + 5
u
22
− 11u
20
+ ··· + 5u − 1
a
1
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
2u
22
− 19u
20
+ ··· − 4u − 3
−u
22
+ 11u
20
+ ··· + 7u
2
+ 2
a
3
=
u
22
− u
21
+ ··· + 10u + 3
3u
22
− 30u
20
+ ··· − 2u − 4
a
11
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
−6u
22
− 3u
21
+ ··· − 10u + 8
−u
22
− 2u
21
+ ··· + 5u + 1
a
2
=
u
19
+ 2u
18
+ ··· + 2u + 4
6u
22
+ u
21
+ ··· + 4u − 7
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
22
−5u
21
+3u
20
+46u
19
−73u
18
−181u
17
+312u
16
+403u
15
−562u
14
−569u
13
+326u
12
+
517u
11
+ 332u
10
−226u
9
−544u
8
−79u
7
+ 201u
6
+ 115u
5
−45u
4
−10u
3
+ 67u
2
−6u −3
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 12u
22
+ ··· + 15u − 1
c
2
u
23
− 6u
21
+ ··· + u + 1
c
3
u
23
+ 12u
21
+ ··· + u + 1
c
4
, c
5
u
23
− u
22
+ ··· − u + 1
c
6
u
23
− u
22
+ ··· + 2u + 1
c
7
u
23
− 6u
21
+ ··· + u − 1
c
8
u
23
− u
22
+ ··· + 11u + 1
c
9
u
23
+ 12u
21
+ ··· + u − 1
c
10
u
23
− 2u
22
+ ··· − u − 1
c
11
u
23
− 3u
22
+ ··· + u + 1
c
12
u
23
+ u
22
+ ··· − u − 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 8y
22
+ ··· + 15y −1
c
2
, c
7
y
23
− 12y
22
+ ··· + 15y −1
c
3
, c
9
y
23
+ 24y
22
+ ··· − 19y −1
c
4
, c
5
, c
12
y
23
− 23y
22
+ ··· − 17y −1
c
6
y
23
− 3y
22
+ ··· + 2y −1
c
8
y
23
− 11y
22
+ ··· + 11y −1
c
10
y
23
− 2y
22
+ ··· + 3y −1
c
11
y
23
+ 5y
22
+ ··· − 13y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.136765 + 0.886584I
a = −0.464886 − 0.768538I
b = 0.074383 + 0.711970I
2.48459 + 2.92368I −5.95131 − 7.29773I
u = −0.136765 − 0.886584I
a = −0.464886 + 0.768538I
b = 0.074383 − 0.711970I
2.48459 − 2.92368I −5.95131 + 7.29773I
u = −1.137400 + 0.237603I
a = 0.598332 − 0.648516I
b = −0.001655 + 0.543381I
−0.135533 + 1.181210I −0.14945 − 3.84915I
u = −1.137400 − 0.237603I
a = 0.598332 + 0.648516I
b = −0.001655 − 0.543381I
−0.135533 − 1.181210I −0.14945 + 3.84915I
u = −1.18937
a = 1.57849
b = −0.595455
−0.649623 4.33110
u = −0.464086 + 0.619189I
a = −0.780759 + 0.520096I
b = 0.322899 + 0.676984I
0.86827 + 1.45338I 0.49234 − 5.72010I
u = −0.464086 − 0.619189I
a = −0.780759 − 0.520096I
b = 0.322899 − 0.676984I
0.86827 − 1.45338I 0.49234 + 5.72010I
u = 1.260330 + 0.119748I
a = −1.46115 − 0.66855I
b = 0.525408 + 0.828935I
−4.41882 + 3.57519I −5.80927 − 5.34802I
u = 1.260330 − 0.119748I
a = −1.46115 + 0.66855I
b = 0.525408 − 0.828935I
−4.41882 − 3.57519I −5.80927 + 5.34802I
u = 1.280310 + 0.369130I
a = 0.577225 − 0.404945I
b = −0.234517 + 0.714938I
−1.81288 − 7.46568I −10.12623 + 9.56548I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.280310 − 0.369130I
a = 0.577225 + 0.404945I
b = −0.234517 − 0.714938I
−1.81288 + 7.46568I −10.12623 − 9.56548I
u = 1.353890 + 0.130129I
a = 0.751565 + 0.094140I
b = 0.27703 + 1.62075I
−8.53828 − 2.94002I −13.49393 + 2.30648I
u = 1.353890 − 0.130129I
a = 0.751565 − 0.094140I
b = 0.27703 − 1.62075I
−8.53828 + 2.94002I −13.49393 − 2.30648I
u = −1.369740 + 0.143102I
a = −1.139000 + 0.741405I
b = −0.04448 + 1.63544I
−8.77933 + 0.50052I −12.97044 + 0.14608I
u = −1.369740 − 0.143102I
a = −1.139000 − 0.741405I
b = −0.04448 − 1.63544I
−8.77933 − 0.50052I −12.97044 − 0.14608I
u = −1.41992 + 0.22958I
a = −1.22821 + 1.25746I
b = 0.457852 + 1.150840I
−6.70083 + 8.08144I −8.35369 − 6.88540I
u = −1.41992 − 0.22958I
a = −1.22821 − 1.25746I
b = 0.457852 − 1.150840I
−6.70083 − 8.08144I −8.35369 + 6.88540I
u = 1.44924 + 0.28311I
a = 0.875266 + 0.848679I
b = −0.526388 + 0.943193I
−5.19446 − 4.96649I −7.36181 + 3.19745I
u = 1.44924 − 0.28311I
a = 0.875266 − 0.848679I
b = −0.526388 − 0.943193I
−5.19446 + 4.96649I −7.36181 − 3.19745I
u = 0.252157 + 0.442817I
a = 2.36364 + 1.41634I
b = −0.437807 + 0.961477I
−1.18000 − 5.38216I −3.42253 + 8.35444I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.252157 − 0.442817I
a = 2.36364 − 1.41634I
b = −0.437807 − 0.961477I
−1.18000 + 5.38216I −3.42253 − 8.35444I
u = 0.026666 + 0.331345I
a = 1.61873 − 3.31404I
b = −0.11499 + 1.57789I
−4.10141 + 1.27066I −11.01927 + 0.35294I
u = 0.026666 − 0.331345I
a = 1.61873 + 3.31404I
b = −0.11499 − 1.57789I
−4.10141 − 1.27066I −11.01927 − 0.35294I
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 12u
22
+ ··· + 15u − 1)(u
130
+ 57u
129
+ ··· + 113740u + 5776)
c
2
(u
23
− 6u
21
+ ··· + u + 1)(u
130
+ u
129
+ ··· + 90u + 76)
c
3
(u
23
+ 12u
21
+ ··· + u + 1)(u
130
+ u
129
+ ··· + 7u − 1)
c
4
, c
5
(u
23
− u
22
+ ··· − u + 1)(u
130
+ 2u
129
+ ··· + 107u − 19)
c
6
(u
23
− u
22
+ ··· + 2u + 1)(u
130
+ 12u
129
+ ··· − 270u − 19)
c
7
(u
23
− 6u
21
+ ··· + u − 1)(u
130
+ u
129
+ ··· + 90u + 76)
c
8
(u
23
− u
22
+ ··· + 11u + 1)(u
130
+ 18u
129
+ ··· − 2103u + 1217)
c
9
(u
23
+ 12u
21
+ ··· + u − 1)(u
130
+ u
129
+ ··· + 7u − 1)
c
10
(u
23
− 2u
22
+ ··· − u − 1)(u
130
+ u
129
+ ··· − 49u − 1)
c
11
(u
23
− 3u
22
+ ··· + u + 1)(u
130
− 6u
129
+ ··· + 1396235u − 512411)
c
12
(u
23
+ u
22
+ ··· − u − 1)(u
130
+ 2u
129
+ ··· + 107u − 19)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 8y
22
+ ··· + 15y −1)
· (y
130
+ 43y
129
+ ··· − 401377392y + 33362176)
c
2
, c
7
(y
23
− 12y
22
+ ··· + 15y −1)(y
130
− 57y
129
+ ··· − 113740y + 5776)
c
3
, c
9
(y
23
+ 24y
22
+ ··· − 19y −1)(y
130
+ 87y
129
+ ··· + 41y + 1)
c
4
, c
5
, c
12
(y
23
− 23y
22
+ ··· − 17y −1)(y
130
− 116y
129
+ ··· + 4815y + 361)
c
6
(y
23
− 3y
22
+ ··· + 2y −1)(y
130
+ 4y
129
+ ··· + 53792y + 361)
c
8
(y
23
− 11y
22
+ ··· + 11y −1)
· (y
130
− 28y
129
+ ··· − 151952217y + 1481089)
c
10
(y
23
− 2y
22
+ ··· + 3y −1)(y
130
+ y
129
+ ··· − 73y + 1)
c
11
(y
23
+ 5y
22
+ ··· − 13y −1)
· (y
130
+ 28y
129
+ ··· − 9070292069281y + 262565032921)
25
