12a
0090
(K12a
0090
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 9 12 4 11 6 1 7
Solving Sequence
5,10
6
3,11
2 1 4 9 7 8 12
c
5
c
10
c
2
c
1
c
4
c
9
c
6
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.89807 × 10
152
u
131
− 2.61475 × 10
152
u
130
+ ··· + 9.05319 × 10
152
b + 3.52721 × 10
153
,
6.80701 × 10
152
u
131
+ 3.00477 × 10
153
u
130
+ ··· + 1.53904 × 10
154
a − 7.27540 × 10
154
,
u
132
+ 2u
131
+ ··· − 19u − 17i
I
u
2
= hb + 1, 2u
8
+ u
7
− 5u
6
− 3u
5
+ 4u
4
+ 3u
3
+ 2u
2
+ a − 2, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
I
u
3
= h6u
3
a
2
− 2a
2
u
2
− 2u
3
a − 3a
2
u − 11u
2
a + 9u
3
+ 2a
2
− 4au + 13u
2
+ 23b + 26a − 19u − 4,
a
2
u
2
− 5u
3
a + a
3
− 3a
2
u − 2u
3
− 2a
2
+ au − u
2
+ a + 2u, u
4
− u
2
+ 1i
* 3 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
= h−1.90 × 10
152
u
131
− 2.61 × 10
152
u
130
+ · · · + 9.05 × 10
152
b + 3.53 ×
10
153
, 6.81 × 10
152
u
131
+ 3.00 × 10
153
u
130
+ · · · + 1.54 × 10
154
a − 7.28 ×
10
154
, u
132
+ 2u
131
+ · · · − 19u − 17i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
−0.0442288u
131
− 0.195236u
130
+ ··· − 4.35303u + 4.72722
0.209657u
131
+ 0.288821u
130
+ ··· − 0.869729u − 3.89610
a
11
=
−u
−u
3
+ u
a
2
=
0.165429u
131
+ 0.0935846u
130
+ ··· − 5.22276u + 0.831125
0.209657u
131
+ 0.288821u
130
+ ··· − 0.869729u − 3.89610
a
1
=
−0.0596357u
131
− 0.160770u
130
+ ··· + 2.00581u + 2.68170
0.0372237u
131
+ 0.0353922u
130
+ ··· − 2.49460u − 2.42937
a
4
=
−0.0650310u
131
− 0.298884u
130
+ ··· − 6.45305u − 3.27408
−0.238080u
131
− 0.407791u
130
+ ··· − 3.33764u + 0.873239
a
9
=
u
3
u
5
− u
3
+ u
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
8
=
0.245372u
131
+ 0.352709u
130
+ ··· − 0.795055u − 1.32177
−0.0921465u
131
− 0.0203027u
130
+ ··· + 1.54595u − 1.62641
a
12
=
−0.169720u
131
− 0.238241u
130
+ ··· + 2.75421u + 4.82837
0.0461740u
131
+ 0.0537793u
130
+ ··· − 1.73822u − 2.20458
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.807591u
131
+ 1.32474u
130
+ ··· + 3.73363u − 7.57808
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
132
+ 62u
131
+ ··· + 657u + 1
c
2
, c
4
u
132
− 14u
131
+ ··· + 57u − 1
c
3
, c
8
u
132
+ u
131
+ ··· − 1024u + 512
c
5
, c
10
u
132
+ 2u
131
+ ··· − 19u − 17
c
6
u
132
+ 6u
131
+ ··· − 19963915u − 1325201
c
7
, c
12
u
132
+ 2u
131
+ ··· − 273u − 49
c
9
u
132
+ 64u
131
+ ··· + 2163u + 289
c
11
u
132
− 66u
131
+ ··· + 6125u + 2401
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
132
+ 30y
131
+ ··· + 816247y + 1
c
2
, c
4
y
132
− 62y
131
+ ··· − 657y + 1
c
3
, c
8
y
132
− 69y
131
+ ··· − 21233664y + 262144
c
5
, c
10
y
132
− 64y
131
+ ··· − 2163y + 289
c
6
y
132
+ 32y
131
+ ··· − 307315706207635y + 1756157690401
c
7
, c
12
y
132
+ 66y
131
+ ··· − 6125y + 2401
c
9
y
132
+ 16y
131
+ ··· − 345303y + 83521
c
11
y
132
+ 14y
131
+ ··· − 531353305y + 5764801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.938713 + 0.353789I
a = −0.912868 + 0.245129I
b = 0.852741 − 0.845895I
3.55706 + 1.60482I 0
u = 0.938713 − 0.353789I
a = −0.912868 − 0.245129I
b = 0.852741 + 0.845895I
3.55706 − 1.60482I 0
u = 0.996053 + 0.218414I
a = 0.806619 + 0.651472I
b = 0.655788 + 0.568246I
2.67708 − 2.86490I 0
u = 0.996053 − 0.218414I
a = 0.806619 − 0.651472I
b = 0.655788 − 0.568246I
2.67708 + 2.86490I 0
u = −0.659438 + 0.782868I
a = −0.52968 + 1.82091I
b = 1.102780 − 0.631878I
4.31397 + 10.01200I 0
u = −0.659438 − 0.782868I
a = −0.52968 − 1.82091I
b = 1.102780 + 0.631878I
4.31397 − 10.01200I 0
u = 0.749682 + 0.698412I
a = −0.21443 − 1.76193I
b = 0.995579 + 0.602572I
2.40654 − 5.39653I 0
u = 0.749682 − 0.698412I
a = −0.21443 + 1.76193I
b = 0.995579 − 0.602572I
2.40654 + 5.39653I 0
u = −0.610161 + 0.753804I
a = −0.62566 − 1.42738I
b = 0.454578 + 0.827217I
6.25569 + 4.57061I 0
u = −0.610161 − 0.753804I
a = −0.62566 + 1.42738I
b = 0.454578 − 0.827217I
6.25569 − 4.57061I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.947583 + 0.406143I
a = 0.50762 − 1.84077I
b = 0.902846 + 0.825452I
3.41020 − 4.58419I 0
u = 0.947583 − 0.406143I
a = 0.50762 + 1.84077I
b = 0.902846 − 0.825452I
3.41020 + 4.58419I 0
u = −0.872602 + 0.556297I
a = 2.17519 − 4.29494I
b = −1.017190 + 0.072632I
−0.09566 + 2.10504I 0
u = −0.872602 − 0.556297I
a = 2.17519 + 4.29494I
b = −1.017190 − 0.072632I
−0.09566 − 2.10504I 0
u = −0.963172
a = 0.839614
b = 0.413715
−1.60890 0
u = −0.947959 + 0.466021I
a = −3.79700 − 1.54368I
b = −1.044910 − 0.117448I
−0.16618 + 1.93886I 0
u = −0.947959 − 0.466021I
a = −3.79700 + 1.54368I
b = −1.044910 + 0.117448I
−0.16618 − 1.93886I 0
u = 0.802222 + 0.492448I
a = 0.969752 + 0.187116I
b = 0.0300035 − 0.0194640I
1.74437 − 2.05841I 0
u = 0.802222 − 0.492448I
a = 0.969752 − 0.187116I
b = 0.0300035 + 0.0194640I
1.74437 + 2.05841I 0
u = 0.641510 + 0.685847I
a = 1.23681 + 2.06522I
b = −0.914484 − 0.466853I
1.59565 − 4.45381I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.641510 − 0.685847I
a = 1.23681 − 2.06522I
b = −0.914484 + 0.466853I
1.59565 + 4.45381I 0
u = −0.360440 + 0.851578I
a = −0.50460 − 1.61504I
b = 1.172380 + 0.647159I
2.56338 − 13.34790I 0
u = −0.360440 − 0.851578I
a = −0.50460 + 1.61504I
b = 1.172380 − 0.647159I
2.56338 + 13.34790I 0
u = 0.625840 + 0.664076I
a = −0.791932 + 1.017230I
b = 0.601541 − 0.717809I
3.57970 − 0.33630I 0
u = 0.625840 − 0.664076I
a = −0.791932 − 1.017230I
b = 0.601541 + 0.717809I
3.57970 + 0.33630I 0
u = 0.856038 + 0.688618I
a = −0.806317 + 0.319246I
b = 0.931389 − 0.556398I
2.11652 + 0.12357I 0
u = 0.856038 − 0.688618I
a = −0.806317 − 0.319246I
b = 0.931389 + 0.556398I
2.11652 − 0.12357I 0
u = −0.376878 + 0.812333I
a = −0.52210 + 1.47034I
b = 0.384441 − 0.938529I
4.96406 − 7.56007I 0
u = −0.376878 − 0.812333I
a = −0.52210 − 1.47034I
b = 0.384441 + 0.938529I
4.96406 + 7.56007I 0
u = 0.929102 + 0.614330I
a = 0.32412 − 1.61149I
b = 0.735604 + 0.656108I
2.70099 − 4.58722I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929102 − 0.614330I
a = 0.32412 + 1.61149I
b = 0.735604 − 0.656108I
2.70099 + 4.58722I 0
u = −0.647947 + 0.601783I
a = 0.491987 + 0.959083I
b = −1.184760 − 0.061496I
0.56167 + 2.39825I 0
u = −0.647947 − 0.601783I
a = 0.491987 − 0.959083I
b = −1.184760 + 0.061496I
0.56167 − 2.39825I 0
u = −1.096790 + 0.239039I
a = 0.579659 + 0.176633I
b = 0.181527 − 0.700915I
−2.19767 + 0.09783I 0
u = −1.096790 − 0.239039I
a = 0.579659 − 0.176633I
b = 0.181527 + 0.700915I
−2.19767 − 0.09783I 0
u = −1.085900 + 0.300273I
a = 0.095938 − 0.869917I
b = −0.404365 + 0.636334I
−2.72819 + 0.51907I 0
u = −1.085900 − 0.300273I
a = 0.095938 + 0.869917I
b = −0.404365 − 0.636334I
−2.72819 − 0.51907I 0
u = 0.945433 + 0.613886I
a = 1.64606 − 0.57975I
b = −0.887017 + 0.379364I
0.703011 − 0.552903I 0
u = 0.945433 − 0.613886I
a = 1.64606 + 0.57975I
b = −0.887017 − 0.379364I
0.703011 + 0.552903I 0
u = 0.295128 + 0.818177I
a = −0.28206 + 1.45199I
b = 1.136500 − 0.604191I
−0.03017 + 7.80820I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295128 − 0.818177I
a = −0.28206 − 1.45199I
b = 1.136500 + 0.604191I
−0.03017 − 7.80820I 0
u = 1.083660 + 0.331383I
a = 1.56052 − 0.49678I
b = 0.985997 − 0.543937I
1.63173 + 1.59811I 0
u = 1.083660 − 0.331383I
a = 1.56052 + 0.49678I
b = 0.985997 + 0.543937I
1.63173 − 1.59811I 0
u = 0.337218 + 0.784199I
a = 0.84119 − 1.93228I
b = −1.001370 + 0.579447I
0.02259 + 6.84914I −4.00000 − 5.53784I
u = 0.337218 − 0.784199I
a = 0.84119 + 1.93228I
b = −1.001370 − 0.579447I
0.02259 − 6.84914I −4.00000 + 5.53784I
u = 1.024480 + 0.520822I
a = −1.29521 + 3.21339I
b = −0.924258 − 0.397800I
0.53683 − 3.70519I 0
u = 1.024480 − 0.520822I
a = −1.29521 − 3.21339I
b = −0.924258 + 0.397800I
0.53683 + 3.70519I 0
u = 0.159327 + 0.831892I
a = −0.108112 − 0.299440I
b = 0.895825 + 0.313048I
−1.91184 + 1.48491I −1.39304 + 3.17304I
u = 0.159327 − 0.831892I
a = −0.108112 + 0.299440I
b = 0.895825 − 0.313048I
−1.91184 − 1.48491I −1.39304 − 3.17304I
u = −1.036320 + 0.520674I
a = −0.932067 − 0.350834I
b = 1.005970 + 0.821372I
4.37356 + 1.32673I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.036320 − 0.520674I
a = −0.932067 + 0.350834I
b = 1.005970 − 0.821372I
4.37356 − 1.32673I 0
u = 1.131370 + 0.259000I
a = −1.31602 + 0.87627I
b = −1.293990 − 0.230800I
−5.39528 + 1.34040I 0
u = 1.131370 − 0.259000I
a = −1.31602 − 0.87627I
b = −1.293990 + 0.230800I
−5.39528 − 1.34040I 0
u = 1.152310 + 0.164300I
a = 0.308713 − 0.257488I
b = 0.303735 + 0.886361I
−0.11437 + 4.94908I 0
u = 1.152310 − 0.164300I
a = 0.308713 + 0.257488I
b = 0.303735 − 0.886361I
−0.11437 − 4.94908I 0
u = −1.144660 + 0.220579I
a = −0.527007 + 0.739685I
b = −1.070060 − 0.530939I
−4.68472 − 4.05873I 0
u = −1.144660 − 0.220579I
a = −0.527007 − 0.739685I
b = −1.070060 + 0.530939I
−4.68472 + 4.05873I 0
u = 1.125110 + 0.318880I
a = −0.796915 − 0.375689I
b = −1.139860 + 0.425704I
−6.05694 − 1.08573I 0
u = 1.125110 − 0.318880I
a = −0.796915 + 0.375689I
b = −1.139860 − 0.425704I
−6.05694 + 1.08573I 0
u = 0.343158 + 0.749318I
a = −0.410013 − 1.181650I
b = 0.369198 + 0.821187I
2.25260 + 2.49043I −0.905133 − 0.809498I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.343158 − 0.749318I
a = −0.410013 + 1.181650I
b = 0.369198 − 0.821187I
2.25260 − 2.49043I −0.905133 + 0.809498I
u = −1.083540 + 0.462798I
a = 1.098280 + 0.386628I
b = −0.404462 − 0.613245I
−2.75739 + 2.11013I 0
u = −1.083540 − 0.462798I
a = 1.098280 − 0.386628I
b = −0.404462 + 0.613245I
−2.75739 − 2.11013I 0
u = −0.011622 + 0.818174I
a = −0.074123 + 0.544809I
b = 0.995714 − 0.406105I
−2.57787 + 4.21955I −4.17622 − 7.27467I
u = −0.011622 − 0.818174I
a = −0.074123 − 0.544809I
b = 0.995714 + 0.406105I
−2.57787 − 4.21955I −4.17622 + 7.27467I
u = −1.129070 + 0.361697I
a = −1.34802 − 1.42487I
b = −1.224270 + 0.331092I
−6.29679 + 3.76078I 0
u = −1.129070 − 0.361697I
a = −1.34802 + 1.42487I
b = −1.224270 − 0.331092I
−6.29679 − 3.76078I 0
u = 1.111690 + 0.415080I
a = −0.116457 + 0.565379I
b = −0.129765 − 0.688851I
−3.02776 − 5.24088I 0
u = 1.111690 − 0.415080I
a = −0.116457 − 0.565379I
b = −0.129765 + 0.688851I
−3.02776 + 5.24088I 0
u = −0.312510 + 0.749288I
a = 0.559212 − 0.401507I
b = −1.315870 + 0.147932I
−1.00364 − 4.19450I −1.63745 + 4.51933I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.312510 − 0.749288I
a = 0.559212 + 0.401507I
b = −1.315870 − 0.147932I
−1.00364 + 4.19450I −1.63745 − 4.51933I
u = −0.995453 + 0.653553I
a = 0.58402 + 1.61417I
b = 0.491466 − 0.765613I
5.11240 + 0.75650I 0
u = −0.995453 − 0.653553I
a = 0.58402 − 1.61417I
b = 0.491466 + 0.765613I
5.11240 − 0.75650I 0
u = −0.969402 + 0.693350I
a = −0.916161 − 0.259688I
b = 1.069190 + 0.616970I
3.39225 − 4.47700I 0
u = −0.969402 − 0.693350I
a = −0.916161 + 0.259688I
b = 1.069190 − 0.616970I
3.39225 + 4.47700I 0
u = −1.057870 + 0.551283I
a = 0.47108 + 1.74711I
b = 0.731815 − 0.928127I
5.19967 + 7.70446I 0
u = −1.057870 − 0.551283I
a = 0.47108 − 1.74711I
b = 0.731815 + 0.928127I
5.19967 − 7.70446I 0
u = −0.428230 + 0.678042I
a = −0.929528 + 0.869416I
b = 0.547873 − 0.796971I
6.80456 + 1.11989I 3.86206 − 1.92549I
u = −0.428230 − 0.678042I
a = −0.929528 − 0.869416I
b = 0.547873 + 0.796971I
6.80456 − 1.11989I 3.86206 + 1.92549I
u = −0.456083 + 0.647815I
a = −1.28709 − 1.39873I
b = 0.685091 + 0.880776I
6.96717 − 3.00924I 3.32571 + 3.86128I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.456083 − 0.647815I
a = −1.28709 + 1.39873I
b = 0.685091 − 0.880776I
6.96717 + 3.00924I 3.32571 − 3.86128I
u = −1.069980 + 0.563935I
a = −1.177620 + 0.292673I
b = 0.458506 + 0.776663I
4.93200 + 3.69354I 0
u = −1.069980 − 0.563935I
a = −1.177620 − 0.292673I
b = 0.458506 − 0.776663I
4.93200 − 3.69354I 0
u = 1.207800 + 0.171412I
a = 0.911181 + 0.392146I
b = 1.173710 − 0.603350I
−2.71725 + 10.40630I 0
u = 1.207800 − 0.171412I
a = 0.911181 − 0.392146I
b = 1.173710 + 0.603350I
−2.71725 − 10.40630I 0
u = −1.197460 + 0.242666I
a = 0.977541 − 0.101848I
b = 1.135970 + 0.538413I
−4.81427 − 4.59663I 0
u = −1.197460 − 0.242666I
a = 0.977541 + 0.101848I
b = 1.135970 − 0.538413I
−4.81427 + 4.59663I 0
u = 1.117630 + 0.498461I
a = −0.676563 + 0.843967I
b = −1.289970 + 0.221714I
−5.37815 − 3.93838I 0
u = 1.117630 − 0.498461I
a = −0.676563 − 0.843967I
b = −1.289970 − 0.221714I
−5.37815 + 3.93838I 0
u = −1.106580 + 0.533705I
a = 1.73174 + 2.09378I
b = 1.088060 − 0.612065I
3.05788 + 8.93644I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.106580 − 0.533705I
a = 1.73174 − 2.09378I
b = 1.088060 + 0.612065I
3.05788 − 8.93644I 0
u = 0.522112 + 0.567423I
a = 0.77915 − 2.60115I
b = −0.790674 + 0.435695I
2.02977 − 0.67823I −0.099465 − 0.605003I
u = 0.522112 − 0.567423I
a = 0.77915 + 2.60115I
b = −0.790674 − 0.435695I
2.02977 + 0.67823I −0.099465 + 0.605003I
u = 1.108190 + 0.543946I
a = 1.227840 − 0.550209I
b = −0.602852 + 0.701433I
−1.05039 − 6.85477I 0
u = 1.108190 − 0.543946I
a = 1.227840 + 0.550209I
b = −0.602852 − 0.701433I
−1.05039 + 6.85477I 0
u = −1.122840 + 0.527715I
a = −0.83912 − 2.37057I
b = −1.058380 + 0.532287I
−4.63903 + 6.62698I 0
u = −1.122840 − 0.527715I
a = −0.83912 + 2.37057I
b = −1.058380 − 0.532287I
−4.63903 − 6.62698I 0
u = 0.328399 + 0.681742I
a = 1.11325 + 1.84748I
b = −0.613102 − 0.608545I
1.20068 + 2.11842I −0.620669 − 1.025539I
u = 0.328399 − 0.681742I
a = 1.11325 − 1.84748I
b = −0.613102 + 0.608545I
1.20068 − 2.11842I −0.620669 + 1.025539I
u = 1.119650 + 0.565015I
a = −1.018000 + 0.273402I
b = 0.321102 − 0.890173I
−0.02760 − 7.46593I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.119650 − 0.565015I
a = −1.018000 − 0.273402I
b = 0.321102 + 0.890173I
−0.02760 + 7.46593I 0
u = −0.490425 + 0.555946I
a = −0.38404 + 2.53300I
b = 1.010330 − 0.762032I
5.98724 + 3.04019I 2.02455 − 0.66536I
u = −0.490425 − 0.555946I
a = −0.38404 − 2.53300I
b = 1.010330 + 0.762032I
5.98724 − 3.04019I 2.02455 + 0.66536I
u = −1.128360 + 0.558169I
a = −0.317718 − 1.111580I
b = −1.359020 − 0.159273I
−3.38814 + 9.13602I 0
u = −1.128360 − 0.558169I
a = −0.317718 + 1.111580I
b = −1.359020 + 0.159273I
−3.38814 − 9.13602I 0
u = −1.218150 + 0.345028I
a = 1.132930 + 0.520998I
b = 0.988137 − 0.326146I
−6.19060 + 2.43557I 0
u = −1.218150 − 0.345028I
a = 1.132930 − 0.520998I
b = 0.988137 + 0.326146I
−6.19060 − 2.43557I 0
u = 1.132190 + 0.575320I
a = −0.56953 + 2.43706I
b = −1.022680 − 0.616427I
−2.32672 − 11.95030I 0
u = 1.132190 − 0.575320I
a = −0.56953 − 2.43706I
b = −1.022680 + 0.616427I
−2.32672 + 11.95030I 0
u = −0.253345 + 0.682209I
a = 0.56522 + 1.88543I
b = −1.018930 − 0.461258I
−2.16964 − 1.98512I −6.10108 + 1.31187I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.253345 − 0.682209I
a = 0.56522 − 1.88543I
b = −1.018930 + 0.461258I
−2.16964 + 1.98512I −6.10108 − 1.31187I
u = −0.318883 + 0.652354I
a = 0.36035 − 1.78015I
b = 1.043930 + 0.648718I
5.31934 − 4.30409I 1.26144 + 3.66893I
u = −0.318883 − 0.652354I
a = 0.36035 + 1.78015I
b = 1.043930 − 0.648718I
5.31934 + 4.30409I 1.26144 − 3.66893I
u = −1.128960 + 0.597098I
a = −1.228480 − 0.443864I
b = 0.370224 + 0.977413I
2.72103 + 12.82500I 0
u = −1.128960 − 0.597098I
a = −1.228480 + 0.443864I
b = 0.370224 − 0.977413I
2.72103 − 12.82500I 0
u = 1.208150 + 0.425593I
a = 1.20203 − 0.92309I
b = 1.074360 + 0.404536I
−6.27164 − 8.60793I 0
u = 1.208150 − 0.425593I
a = 1.20203 + 0.92309I
b = 1.074360 − 0.404536I
−6.27164 + 8.60793I 0
u = −1.204540 + 0.443650I
a = 0.649828 + 0.613430I
b = 0.981597 + 0.323728I
−6.15922 + 0.24928I 0
u = −1.204540 − 0.443650I
a = 0.649828 − 0.613430I
b = 0.981597 − 0.323728I
−6.15922 − 0.24928I 0
u = 1.154830 + 0.571926I
a = 1.10233 − 2.07234I
b = 1.172180 + 0.610271I
−2.58180 − 12.96900I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.154830 − 0.571926I
a = 1.10233 + 2.07234I
b = 1.172180 − 0.610271I
−2.58180 + 12.96900I 0
u = −0.599739 + 0.377924I
a = 1.15835 − 1.88965I
b = −0.710203 + 0.336718I
−0.90824 + 1.35117I −6.39675 − 4.84265I
u = −0.599739 − 0.377924I
a = 1.15835 + 1.88965I
b = −0.710203 − 0.336718I
−0.90824 − 1.35117I −6.39675 + 4.84265I
u = −1.148170 + 0.605188I
a = 0.92041 + 2.29620I
b = 1.192770 − 0.653972I
0.1985 + 18.7424I 0
u = −1.148170 − 0.605188I
a = 0.92041 − 2.29620I
b = 1.192770 + 0.653972I
0.1985 − 18.7424I 0
u = 1.194740 + 0.518740I
a = 0.468319 − 0.708809I
b = 0.899742 − 0.240840I
−5.00169 − 6.42010I 0
u = 1.194740 − 0.518740I
a = 0.468319 + 0.708809I
b = 0.899742 + 0.240840I
−5.00169 + 6.42010I 0
u = 0.153844 + 0.624412I
a = 0.155142 + 0.840811I
b = −1.195540 − 0.217927I
−2.77912 − 0.38414I −5.60194 − 0.58668I
u = 0.153844 − 0.624412I
a = 0.155142 − 0.840811I
b = −1.195540 + 0.217927I
−2.77912 + 0.38414I −5.60194 + 0.58668I
u = 0.039096 + 0.550554I
a = 0.922121 − 1.064520I
b = −0.157515 + 0.448845I
−0.10731 + 1.54447I −1.37631 − 4.72080I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.039096 − 0.550554I
a = 0.922121 + 1.064520I
b = −0.157515 − 0.448845I
−0.10731 − 1.54447I −1.37631 + 4.72080I
u = 0.539309
a = −1.30564
b = −1.12306
−2.25551 −0.524520
18
II.
I
u
2
= hb +1, 2u
8
+u
7
+· · · + a −2, u
9
+u
8
−2u
7
−3u
6
+u
5
+3u
4
+2u
3
−u −1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
−2u
8
− u
7
+ 5u
6
+ 3u
5
− 4u
4
− 3u
3
− 2u
2
+ 2
−1
a
11
=
−u
−u
3
+ u
a
2
=
−2u
8
− u
7
+ 5u
6
+ 3u
5
− 4u
4
− 3u
3
− 2u
2
+ 1
−1
a
1
=
−1
0
a
4
=
−2u
8
− u
7
+ 5u
6
+ 3u
5
− 4u
4
− 3u
3
− 2u
2
+ 2
−1
a
9
=
u
3
u
5
− u
3
+ u
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
8
=
u
3
u
5
− u
3
+ u
a
12
=
−u
3
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
8
− 3u
7
+ 10u
6
+ 8u
5
− 2u
4
− 8u
3
− 12u
2
− 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
6
, c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
7
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
9
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
10
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
12
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
8
y
9
c
5
, c
10
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
, c
12
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
9
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 1.67861 + 2.31573I
b = −1.00000
0.13850 + 2.09337I −11.64247 + 5.88316I
u = −0.772920 − 0.510351I
a = 1.67861 − 2.31573I
b = −1.00000
0.13850 − 2.09337I −11.64247 − 5.88316I
u = 0.825933
a = −0.871015
b = −1.00000
−2.84338 −15.4610
u = 1.173910 + 0.391555I
a = −0.893484 + 0.630694I
b = −1.00000
−6.01628 − 1.33617I −7.94914 + 0.75351I
u = 1.173910 − 0.391555I
a = −0.893484 − 0.630694I
b = −1.00000
−6.01628 + 1.33617I −7.94914 − 0.75351I
u = −0.141484 + 0.739668I
a = 0.309843 + 0.043204I
b = −1.00000
−2.26187 − 2.45442I −4.75622 + 3.91612I
u = −0.141484 − 0.739668I
a = 0.309843 − 0.043204I
b = −1.00000
−2.26187 + 2.45442I −4.75622 − 3.91612I
u = −1.172470 + 0.500383I
a = −0.659464 − 0.874093I
b = −1.00000
−5.24306 + 7.08493I −7.92182 − 8.89461I
u = −1.172470 − 0.500383I
a = −0.659464 + 0.874093I
b = −1.00000
−5.24306 − 7.08493I −7.92182 + 8.89461I
22
III.
I
u
3
= h6u
3
a
2
− 2u
3
a + · · · + 26a − 4, −5u
3
a − 2u
3
+ · · · − 2a
2
+ a, u
4
− u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
a
−0.260870a
2
u
3
+ 0.0869565au
3
+ ··· − 1.13043a + 0.173913
a
11
=
−u
−u
3
+ u
a
2
=
−0.260870a
2
u
3
+ 0.0869565au
3
+ ··· − 0.130435a + 0.173913
−0.260870a
2
u
3
+ 0.0869565au
3
+ ··· − 1.13043a + 0.173913
a
1
=
0.0869565a
2
u
3
− 0.173913au
3
+ ··· − 0.347826a − 0.0434783
−0.173913a
2
u
3
− 0.608696au
3
+ ··· − 0.0869565a + 0.782609
a
4
=
0.130435a
2
u
3
− 0.478261au
3
+ ··· + 0.391304a + 0.956522
0.0869565a
2
u
3
− 0.695652au
3
+ ··· + 1.04348a − 0.391304
a
9
=
u
3
0
a
7
=
−u
2
+ 1
u
2
a
8
=
−0.391304a
2
u
3
− 0.0869565au
3
+ ··· − 0.782609a − 0.217391
0.434783au
3
− 0.739130u
3
+ ··· + 0.173913a + 0.956522
a
12
=
0.0869565a
2
u
3
− 0.173913au
3
+ ··· − 0.347826a − 0.0434783
−0.173913a
2
u
3
− 0.608696au
3
+ ··· − 0.0869565a + 0.782609
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
24
23
u
3
a
2
+
8
23
a
2
u
2
+
8
23
u
3
a+
12
23
a
2
u+
44
23
u
2
a−
36
23
u
3
−
8
23
a
2
+
16
23
au+
40
23
u
2
−
104
23
a+
76
23
u−
76
23
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
4
c
2
(u
3
+ u
2
− 1)
4
c
3
, c
8
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
4
(u
3
− u
2
+ 1)
4
c
5
, c
6
, c
10
(u
4
− u
2
+ 1)
3
c
7
, c
12
(u
2
+ 1)
6
c
9
(u
2
− u + 1)
6
c
11
(u + 1)
12
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
4
c
2
, c
4
(y
3
− y
2
+ 2y −1)
4
c
3
, c
8
(y
3
− 3y
2
+ 2y + 1)
4
c
5
, c
6
, c
10
(y
2
− y + 1)
6
c
7
, c
12
(y + 1)
12
c
9
(y
2
+ y + 1)
6
c
11
(y −1)
12
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.340177 − 1.221410I
b = 0.877439 + 0.744862I
4.66906 − 4.85801I 1.50976 + 6.44355I
u = 0.866025 + 0.500000I
a = −0.387682 + 0.039280I
b = 0.877439 − 0.744862I
4.66906 + 0.79824I 1.50976 + 0.48465I
u = 0.866025 + 0.500000I
a = 4.14558 + 1.81610I
b = −0.754878
0.53148 − 2.02988I −5.01951 + 3.46410I
u = 0.866025 − 0.500000I
a = 0.340177 + 1.221410I
b = 0.877439 − 0.744862I
4.66906 + 4.85801I 1.50976 − 6.44355I
u = 0.866025 − 0.500000I
a = −0.387682 − 0.039280I
b = 0.877439 + 0.744862I
4.66906 − 0.79824I 1.50976 − 0.48465I
u = 0.866025 − 0.500000I
a = 4.14558 − 1.81610I
b = −0.754878
0.53148 + 2.02988I −5.01951 − 3.46410I
u = −0.866025 + 0.500000I
a = 0.119052 + 0.508616I
b = −0.754878
0.53148 + 2.02988I −5.01951 − 3.46410I
u = −0.866025 + 0.500000I
a = −1.53477 − 0.67554I
b = 0.877439 + 0.744862I
4.66906 − 0.79824I 1.50976 − 0.48465I
u = −0.866025 + 0.500000I
a = 0.31765 + 2.53295I
b = 0.877439 − 0.744862I
4.66906 + 4.85801I 1.50976 − 6.44355I
u = −0.866025 − 0.500000I
a = 0.119052 − 0.508616I
b = −0.754878
0.53148 − 2.02988I −5.01951 + 3.46410I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866025 − 0.500000I
a = −1.53477 + 0.67554I
b = 0.877439 − 0.744862I
4.66906 + 0.79824I 1.50976 + 0.48465I
u = −0.866025 − 0.500000I
a = 0.31765 − 2.53295I
b = 0.877439 + 0.744862I
4.66906 − 4.85801I 1.50976 + 6.44355I
27
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
3
− u
2
+ 2u − 1)
4
(u
132
+ 62u
131
+ ··· + 657u + 1)
c
2
((u − 1)
9
)(u
3
+ u
2
− 1)
4
(u
132
− 14u
131
+ ··· + 57u − 1)
c
3
, c
8
u
9
(u
6
− 3u
4
+ 2u
2
+ 1)
2
(u
132
+ u
131
+ ··· − 1024u + 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)
4
(u
132
− 14u
131
+ ··· + 57u − 1)
c
5
(u
4
− u
2
+ 1)
3
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
132
+ 2u
131
+ ··· − 19u − 17)
c
6
(u
4
− u
2
+ 1)
3
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
132
+ 6u
131
+ ··· − 19963915u − 1325201)
c
7
(u
2
+ 1)
6
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
132
+ 2u
131
+ ··· − 273u − 49)
c
9
((u
2
− u + 1)
6
)(u
9
− 5u
8
+ ··· + u − 1)
· (u
132
+ 64u
131
+ ··· + 2163u + 289)
c
10
(u
4
− u
2
+ 1)
3
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
132
+ 2u
131
+ ··· − 19u − 17)
c
11
((u + 1)
12
)(u
9
+ 3u
8
+ ··· + u − 1)
· (u
132
− 66u
131
+ ··· + 6125u + 2401)
c
12
(u
2
+ 1)
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
132
+ 2u
131
+ ··· − 273u − 49)
28
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
3
+ 3y
2
+ 2y −1)
4
(y
132
+ 30y
131
+ ··· + 816247y + 1)
c
2
, c
4
((y −1)
9
)(y
3
− y
2
+ 2y −1)
4
(y
132
− 62y
131
+ ··· − 657y + 1)
c
3
, c
8
y
9
(y
3
− 3y
2
+ 2y + 1)
4
(y
132
− 69y
131
+ ··· − 2.12337 × 10
7
y + 262144)
c
5
, c
10
((y
2
− y + 1)
6
)(y
9
− 5y
8
+ ··· + y −1)
· (y
132
− 64y
131
+ ··· − 2163y + 289)
c
6
((y
2
− y + 1)
6
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
132
+ 32y
131
+ ··· − 307315706207635y + 1756157690401)
c
7
, c
12
((y + 1)
12
)(y
9
+ 3y
8
+ ··· + y −1)
· (y
132
+ 66y
131
+ ··· − 6125y + 2401)
c
9
(y
2
+ y + 1)
6
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
132
+ 16y
131
+ ··· − 345303y + 83521)
c
11
(y −1)
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
132
+ 14y
131
+ ··· − 531353305y + 5764801)
29
