12a
1201
(K12a
1201
)
A knot diagram
1
Linearized knot diagam
4 10 12 9 1 3 11 2 5 7 8 6
Solving Sequence
7,11
8
3,12
4 6 1 5 10 2 9
c
7
c
11
c
3
c
6
c
12
c
5
c
10
c
2
c
8
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.70258 × 10
345
u
139
+ 1.45980 × 10
346
u
138
+ ··· + 2.18893 × 10
345
b + 3.04112 × 10
346
,
3.74652 × 10
346
u
139
− 1.17909 × 10
347
u
138
+ ··· + 2.18893 × 10
345
a − 1.90043 × 10
347
,
u
140
− 3u
139
+ ··· − 27u − 1i
I
u
2
= h−286723u
34
+ 444928u
33
+ ··· + 69517b + 453427,
8945075u
34
− 15497918u
33
+ ··· + 69517a − 7160101, u
35
− 3u
34
+ ··· − 3u + 1i
I
u
3
= hb − 1, a, u − 1i
* 3 irreducible components of dim
C
= 0, with total 176 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−4.70 × 10
345
u
139
+ 1.46 × 10
346
u
138
+ · · · + 2.19 × 10
345
b + 3.04 ×
10
346
, 3.75 × 10
346
u
139
− 1.18 × 10
347
u
138
+ · · · + 2.19 × 10
345
a − 1.90 ×
10
347
, u
140
− 3u
139
+ · · · − 27u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
−17.1157u
139
+ 53.8661u
138
+ ··· + 1840.02u + 86.8198
2.14834u
139
− 6.66899u
138
+ ··· − 278.821u − 13.8932
a
12
=
u
−u
3
+ u
a
4
=
−17.4779u
139
+ 55.4038u
138
+ ··· + 1913.85u + 90.1905
1.24479u
139
− 4.12684u
138
+ ··· − 216.821u − 10.9738
a
6
=
−2.34681u
139
+ 4.30372u
138
+ ··· + 657.341u + 40.8192
2.78708u
139
− 6.59659u
138
+ ··· − 259.251u − 13.1983
a
1
=
−15.4483u
139
+ 49.0551u
138
+ ··· + 2205.24u + 104.962
1.59584u
139
− 6.60896u
138
+ ··· − 250.220u − 12.3168
a
5
=
−13.4458u
139
+ 41.6387u
138
+ ··· + 1644.46u + 82.0808
2.89425u
139
− 7.86046u
138
+ ··· − 350.112u − 16.8488
a
10
=
−u
u
a
2
=
−15.8887u
139
+ 50.8414u
138
+ ··· + 1793.03u + 84.5248
0.921328u
139
− 3.64428u
138
+ ··· − 231.824u − 11.5982
a
9
=
−4.06898u
139
+ 13.2143u
138
+ ··· + 1095.07u + 58.9998
1.75915u
139
− 6.31156u
138
+ ··· − 361.334u − 16.8026
(ii) Obstruction class = −1
(iii) Cusp Shapes = 28.6964u
139
− 93.7293u
138
+ ··· − 3097.74u − 147.900
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
140
+ u
139
+ ··· + 405u + 119
c
2
u
140
+ 4u
139
+ ··· + 44695798u − 3369031
c
3
u
140
− 4u
139
+ ··· − 29465412u + 1871711
c
4
, c
9
u
140
− 2u
139
+ ··· − 8527u + 2089
c
5
, c
12
u
140
+ 3u
139
+ ··· + 63834u − 5809
c
6
u
140
+ 7u
139
+ ··· + 208242066u − 166275911
c
7
, c
10
, c
11
u
140
− 3u
139
+ ··· − 27u − 1
c
8
u
140
+ 15u
138
+ ··· + 315207u − 35883
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
140
− 5y
139
+ ··· + 6830319y + 14161
c
2
y
140
− 34y
139
+ ··· − 510524756422924y + 11350369878961
c
3
y
140
+ 56y
139
+ ··· + 52970751482880y + 3503302067521
c
4
, c
9
y
140
− 74y
139
+ ··· − 86881505y + 4363921
c
5
, c
12
y
140
+ 105y
139
+ ··· + 2341783754y + 33744481
c
6
y
140
+ 57y
139
+ ··· + 1894560234749566132y + 27647678578879921
c
7
, c
10
, c
11
y
140
− 139y
139
+ ··· − 63y + 1
c
8
y
140
+ 30y
139
+ ··· + 67712278617y + 1287589689
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.462379 + 0.872851I
a = 0.457037 − 0.280992I
b = 0.668404 + 0.884753I
−3.71972 − 8.53606I 0
u = −0.462379 − 0.872851I
a = 0.457037 + 0.280992I
b = 0.668404 − 0.884753I
−3.71972 + 8.53606I 0
u = −0.704341 + 0.737453I
a = 0.776491 − 0.006136I
b = −0.504752 + 1.084340I
1.77897 + 9.64332I 0
u = −0.704341 − 0.737453I
a = 0.776491 + 0.006136I
b = −0.504752 − 1.084340I
1.77897 − 9.64332I 0
u = 0.686254 + 0.756748I
a = −0.715275 − 0.188941I
b = 0.395128 + 0.982604I
4.72890 − 3.27964I 0
u = 0.686254 − 0.756748I
a = −0.715275 + 0.188941I
b = 0.395128 − 0.982604I
4.72890 + 3.27964I 0
u = 0.377083 + 0.883614I
a = 0.539975 − 0.407438I
b = −0.046896 − 0.826372I
2.01560 − 1.61773I 0
u = 0.377083 − 0.883614I
a = 0.539975 + 0.407438I
b = −0.046896 + 0.826372I
2.01560 + 1.61773I 0
u = 0.478507 + 0.828531I
a = 0.577416 + 0.614164I
b = 0.667428 − 1.197920I
4.12877 + 8.61622I 0
u = 0.478507 − 0.828531I
a = 0.577416 − 0.614164I
b = 0.667428 + 1.197920I
4.12877 − 8.61622I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.456133 + 0.833311I
a = −0.674185 + 0.539381I
b = −0.80454 − 1.28700I
1.0425 − 14.9384I 0
u = −0.456133 − 0.833311I
a = −0.674185 − 0.539381I
b = −0.80454 + 1.28700I
1.0425 + 14.9384I 0
u = 0.964246 + 0.434277I
a = 0.562867 + 0.368503I
b = −0.137014 − 0.528866I
1.46755 + 0.80554I 0
u = 0.964246 − 0.434277I
a = 0.562867 − 0.368503I
b = −0.137014 + 0.528866I
1.46755 − 0.80554I 0
u = −0.328180 + 0.878078I
a = 0.354828 − 0.320483I
b = 0.309412 + 0.571510I
−3.62334 + 1.06275I 0
u = −0.328180 − 0.878078I
a = 0.354828 + 0.320483I
b = 0.309412 − 0.571510I
−3.62334 − 1.06275I 0
u = 0.403616 + 0.815553I
a = −0.425989 − 0.236906I
b = −0.456070 + 0.937118I
0.10647 + 3.89798I 0
u = 0.403616 − 0.815553I
a = −0.425989 + 0.236906I
b = −0.456070 − 0.937118I
0.10647 − 3.89798I 0
u = −0.170842 + 0.884336I
a = −0.458227 − 0.527772I
b = 0.006089 − 0.657947I
1.93663 − 0.61257I 0
u = −0.170842 − 0.884336I
a = −0.458227 + 0.527772I
b = 0.006089 + 0.657947I
1.93663 + 0.61257I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.818840 + 0.775513I
a = −0.418165 − 0.019733I
b = 0.167714 − 0.698294I
−2.76939 + 2.90326I 0
u = −0.818840 − 0.775513I
a = −0.418165 + 0.019733I
b = 0.167714 + 0.698294I
−2.76939 − 2.90326I 0
u = 0.623465 + 0.592662I
a = −0.355432 − 0.388206I
b = −0.666980 + 1.179240I
3.08454 + 6.40753I 0
u = 0.623465 − 0.592662I
a = −0.355432 + 0.388206I
b = −0.666980 − 1.179240I
3.08454 − 6.40753I 0
u = −1.136100 + 0.122033I
a = −0.434683 + 0.268499I
b = 0.804708 + 0.523340I
4.56061 − 3.17341I 0
u = −1.136100 − 0.122033I
a = −0.434683 − 0.268499I
b = 0.804708 − 0.523340I
4.56061 + 3.17341I 0
u = 1.16073
a = 0.0578993
b = 1.04319
−1.61847 0
u = −0.465931 + 0.682708I
a = −0.715701 + 0.938995I
b = −0.735843 − 0.794635I
−2.80541 − 4.22675I 0
u = −0.465931 − 0.682708I
a = −0.715701 − 0.938995I
b = −0.735843 + 0.794635I
−2.80541 + 4.22675I 0
u = 0.805832 + 0.171888I
a = −0.72972 + 1.84695I
b = 0.542835 − 0.558432I
3.36428 + 0.17780I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805832 − 0.171888I
a = −0.72972 − 1.84695I
b = 0.542835 + 0.558432I
3.36428 − 0.17780I 0
u = −0.631596 + 0.501522I
a = 0.293717 + 0.046531I
b = −0.684176 + 0.529370I
−2.30853 + 0.01280I 0
u = −0.631596 − 0.501522I
a = 0.293717 − 0.046531I
b = −0.684176 − 0.529370I
−2.30853 − 0.01280I 0
u = −1.217270 + 0.004425I
a = 1.30064 − 2.33815I
b = −1.07297 + 1.32920I
1.04242 − 5.47669I 0
u = −1.217270 − 0.004425I
a = 1.30064 + 2.33815I
b = −1.07297 − 1.32920I
1.04242 + 5.47669I 0
u = 0.601253 + 0.469515I
a = 0.759163 + 0.277979I
b = 0.183519 − 0.606937I
1.29364 + 0.77209I 0
u = 0.601253 − 0.469515I
a = 0.759163 − 0.277979I
b = 0.183519 + 0.606937I
1.29364 − 0.77209I 0
u = −1.070230 + 0.636332I
a = −0.092737 + 0.241677I
b = 0.134547 − 0.437874I
−1.48417 − 6.45366I 0
u = −1.070230 − 0.636332I
a = −0.092737 − 0.241677I
b = 0.134547 + 0.437874I
−1.48417 + 6.45366I 0
u = 0.398072 + 0.626175I
a = −0.946969 − 0.318541I
b = −0.79762 + 1.43794I
2.96797 + 2.33819I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.398072 − 0.626175I
a = −0.946969 + 0.318541I
b = −0.79762 − 1.43794I
2.96797 − 2.33819I 0
u = 1.241780 + 0.220632I
a = −0.90441 − 1.62834I
b = 0.609759 + 1.255110I
2.80271 + 0.23073I 0
u = 1.241780 − 0.220632I
a = −0.90441 + 1.62834I
b = 0.609759 − 1.255110I
2.80271 − 0.23073I 0
u = 1.260930 + 0.082460I
a = 0.086207 − 0.530918I
b = −1.184450 − 0.384164I
2.27831 − 4.47551I 0
u = 1.260930 − 0.082460I
a = 0.086207 + 0.530918I
b = −1.184450 + 0.384164I
2.27831 + 4.47551I 0
u = −1.315690 + 0.009991I
a = −0.36004 − 2.74746I
b = 0.05423 + 1.82083I
0.10570 + 2.10964I 0
u = −1.315690 − 0.009991I
a = −0.36004 + 2.74746I
b = 0.05423 − 1.82083I
0.10570 − 2.10964I 0
u = −1.313990 + 0.111074I
a = −0.23144 − 1.79391I
b = 0.031189 + 0.365803I
−0.70589 − 4.44648I 0
u = −1.313990 − 0.111074I
a = −0.23144 + 1.79391I
b = 0.031189 − 0.365803I
−0.70589 + 4.44648I 0
u = 0.423118 + 0.522894I
a = 1.237050 − 0.528772I
b = −0.158698 − 1.136510I
3.23668 + 1.44238I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.423118 − 0.522894I
a = 1.237050 + 0.528772I
b = −0.158698 + 1.136510I
3.23668 − 1.44238I 0
u = −0.129908 + 0.651480I
a = 0.133831 + 0.582906I
b = 0.060763 − 1.345760I
−1.41806 + 3.01802I 0
u = −0.129908 − 0.651480I
a = 0.133831 − 0.582906I
b = 0.060763 + 1.345760I
−1.41806 − 3.01802I 0
u = −0.565129 + 0.345483I
a = −0.086280 − 0.838713I
b = 0.699439 + 1.051320I
4.07356 − 3.29083I 0
u = −0.565129 − 0.345483I
a = −0.086280 + 0.838713I
b = 0.699439 − 1.051320I
4.07356 + 3.29083I 0
u = 1.329060 + 0.180992I
a = 1.162230 + 0.506902I
b = −1.107950 − 0.567617I
2.37634 + 1.48237I 0
u = 1.329060 − 0.180992I
a = 1.162230 − 0.506902I
b = −1.107950 + 0.567617I
2.37634 − 1.48237I 0
u = 1.343570 + 0.059602I
a = 0.17148 − 1.95113I
b = −0.017383 + 1.108000I
3.06942 + 1.61488I 0
u = 1.343570 − 0.059602I
a = 0.17148 + 1.95113I
b = −0.017383 − 1.108000I
3.06942 − 1.61488I 0
u = −0.320764 + 0.569441I
a = 1.31405 − 0.73024I
b = 1.08104 + 1.24019I
3.26804 − 5.06148I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.320764 − 0.569441I
a = 1.31405 + 0.73024I
b = 1.08104 − 1.24019I
3.26804 + 5.06148I 0
u = −0.425132 + 0.490297I
a = −1.53497 + 0.84982I
b = −0.674783 − 0.719553I
−1.89546 − 4.32229I 0
u = −0.425132 − 0.490297I
a = −1.53497 − 0.84982I
b = −0.674783 + 0.719553I
−1.89546 + 4.32229I 0
u = −0.560763 + 0.315780I
a = 2.53851 − 1.29915I
b = −0.154600 + 0.718380I
0.39792 − 6.14230I 0. + 8.00126I
u = −0.560763 − 0.315780I
a = 2.53851 + 1.29915I
b = −0.154600 − 0.718380I
0.39792 + 6.14230I 0. − 8.00126I
u = −1.359650 + 0.117728I
a = −1.105820 − 0.418584I
b = 1.69043 + 0.21809I
5.88239 − 4.59774I 0
u = −1.359650 − 0.117728I
a = −1.105820 + 0.418584I
b = 1.69043 − 0.21809I
5.88239 + 4.59774I 0
u = −1.362510 + 0.085272I
a = 0.43387 + 2.68486I
b = −0.568408 − 0.582435I
2.91886 − 7.73986I 0
u = −1.362510 − 0.085272I
a = 0.43387 − 2.68486I
b = −0.568408 + 0.582435I
2.91886 + 7.73986I 0
u = −1.372620 + 0.041492I
a = 0.910453 − 0.463763I
b = −1.62467 + 0.42421I
2.97120 − 0.46899I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.372620 − 0.041492I
a = 0.910453 + 0.463763I
b = −1.62467 − 0.42421I
2.97120 + 0.46899I 0
u = 1.381760 + 0.136726I
a = 1.72384 − 0.47772I
b = −2.23547 − 0.03375I
3.20477 + 9.15153I 0
u = 1.381760 − 0.136726I
a = 1.72384 + 0.47772I
b = −2.23547 + 0.03375I
3.20477 − 9.15153I 0
u = 1.376280 + 0.254400I
a = −1.28784 − 1.04043I
b = 0.209891 + 1.329590I
8.43189 + 0.58347I 0
u = 1.376280 − 0.254400I
a = −1.28784 + 1.04043I
b = 0.209891 − 1.329590I
8.43189 − 0.58347I 0
u = 1.400760 + 0.095179I
a = −1.14022 − 1.06949I
b = 1.62050 + 1.13483I
1.58883 + 4.27435I 0
u = 1.400760 − 0.095179I
a = −1.14022 + 1.06949I
b = 1.62050 − 1.13483I
1.58883 − 4.27435I 0
u = −1.406880 + 0.006416I
a = 0.464909 − 1.094690I
b = 0.772828 + 0.884649I
7.98154 − 2.83433I 0
u = −1.406880 − 0.006416I
a = 0.464909 + 1.094690I
b = 0.772828 − 0.884649I
7.98154 + 2.83433I 0
u = −0.235792 + 0.542392I
a = −0.141507 + 0.081514I
b = −0.674308 + 0.917975I
−2.46402 + 1.20422I −4.02039 + 3.48565I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.235792 − 0.542392I
a = −0.141507 − 0.081514I
b = −0.674308 − 0.917975I
−2.46402 − 1.20422I −4.02039 − 3.48565I
u = 1.42433 + 0.04690I
a = −0.84533 + 2.00807I
b = −0.056543 − 0.949934I
8.82467 + 3.19321I 0
u = 1.42433 − 0.04690I
a = −0.84533 − 2.00807I
b = −0.056543 + 0.949934I
8.82467 − 3.19321I 0
u = 1.42947 + 0.21457I
a = 0.00176 + 2.48122I
b = 1.23337 − 1.60979I
8.90630 + 7.94848I 0
u = 1.42947 − 0.21457I
a = 0.00176 − 2.48122I
b = 1.23337 + 1.60979I
8.90630 − 7.94848I 0
u = −1.43761 + 0.22669I
a = 0.76019 − 1.50877I
b = 0.40645 + 1.55265I
9.06008 − 4.26529I 0
u = −1.43761 − 0.22669I
a = 0.76019 + 1.50877I
b = 0.40645 − 1.55265I
9.06008 + 4.26529I 0
u = 0.140123 + 0.513834I
a = 0.435608 − 0.512064I
b = 1.100810 + 0.143302I
1.21463 + 2.45922I −2.53647 − 5.18448I
u = 0.140123 − 0.513834I
a = 0.435608 + 0.512064I
b = 1.100810 − 0.143302I
1.21463 − 2.45922I −2.53647 + 5.18448I
u = −1.45639 + 0.23069I
a = −0.23608 + 2.35336I
b = −1.00629 − 1.91711I
8.94598 − 5.47573I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45639 − 0.23069I
a = −0.23608 − 2.35336I
b = −1.00629 + 1.91711I
8.94598 + 5.47573I 0
u = 1.46338 + 0.18353I
a = −0.15300 − 1.61650I
b = −0.951185 + 0.925574I
4.22217 + 6.83856I 0
u = 1.46338 − 0.18353I
a = −0.15300 + 1.61650I
b = −0.951185 − 0.925574I
4.22217 − 6.83856I 0
u = 0.037476 + 0.513388I
a = 1.27392 + 1.70079I
b = 0.643809 − 0.085613I
−4.82975 + 2.31062I −12.87978 − 2.96394I
u = 0.037476 − 0.513388I
a = 1.27392 − 1.70079I
b = 0.643809 + 0.085613I
−4.82975 − 2.31062I −12.87978 + 2.96394I
u = 1.46922 + 0.31257I
a = 0.332409 + 1.305150I
b = 0.390051 − 0.964932I
2.19099 + 3.17343I 0
u = 1.46922 − 0.31257I
a = 0.332409 − 1.305150I
b = 0.390051 + 0.964932I
2.19099 − 3.17343I 0
u = 1.49507 + 0.15095I
a = −0.18905 + 2.12309I
b = 0.65123 − 1.66952I
10.73410 + 5.31948I 0
u = 1.49507 − 0.15095I
a = −0.18905 − 2.12309I
b = 0.65123 + 1.66952I
10.73410 − 5.31948I 0
u = 1.50099 + 0.12695I
a = 1.20794 + 1.23655I
b = 0.310004 − 0.618174I
7.09391 + 7.88138I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50099 − 0.12695I
a = 1.20794 − 1.23655I
b = 0.310004 + 0.618174I
7.09391 − 7.88138I 0
u = −1.50561 + 0.18920I
a = 0.122833 − 1.396170I
b = 0.706279 + 1.137180I
8.03732 − 3.36556I 0
u = −1.50561 − 0.18920I
a = 0.122833 + 1.396170I
b = 0.706279 − 1.137180I
8.03732 + 3.36556I 0
u = −0.166408 + 0.447749I
a = −0.942548 − 0.314060I
b = −1.64904 + 0.38973I
−1.75661 − 7.07071I −8.13787 + 10.46929I
u = −0.166408 − 0.447749I
a = −0.942548 + 0.314060I
b = −1.64904 − 0.38973I
−1.75661 + 7.07071I −8.13787 − 10.46929I
u = −1.49430 + 0.29806I
a = −0.22812 + 1.56211I
b = −0.68396 − 1.30037I
6.26553 − 7.93967I 0
u = −1.49430 − 0.29806I
a = −0.22812 − 1.56211I
b = −0.68396 + 1.30037I
6.26553 + 7.93967I 0
u = −0.174597 + 0.431979I
a = −0.93253 − 1.48595I
b = 0.527948 − 1.043380I
3.54406 + 2.27639I 2.72382 − 3.59475I
u = −0.174597 − 0.431979I
a = −0.93253 + 1.48595I
b = 0.527948 + 1.043380I
3.54406 − 2.27639I 2.72382 + 3.59475I
u = −1.52156 + 0.19604I
a = 0.07461 + 2.01691I
b = −0.81738 − 1.78384I
10.04850 − 9.28275I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52156 − 0.19604I
a = 0.07461 − 2.01691I
b = −0.81738 + 1.78384I
10.04850 + 9.28275I 0
u = 1.51551 + 0.23988I
a = −0.14461 − 1.82163I
b = −0.713646 + 1.051090I
3.69617 + 7.60542I 0
u = 1.51551 − 0.23988I
a = −0.14461 + 1.82163I
b = −0.713646 − 1.051090I
3.69617 − 7.60542I 0
u = 1.49132 + 0.38149I
a = −0.402125 − 0.713805I
b = −0.482485 + 0.782696I
7.35578 + 5.43628I 0
u = 1.49132 − 0.38149I
a = −0.402125 + 0.713805I
b = −0.482485 − 0.782696I
7.35578 − 5.43628I 0
u = 1.50988 + 0.30607I
a = −0.23946 − 1.98071I
b = −0.93962 + 1.54380I
7.4013 + 19.0874I 0
u = 1.50988 − 0.30607I
a = −0.23946 + 1.98071I
b = −0.93962 − 1.54380I
7.4013 − 19.0874I 0
u = −1.51849 + 0.29906I
a = 0.25687 − 1.91430I
b = 0.76941 + 1.46778I
10.6023 − 12.7252I 0
u = −1.51849 − 0.29906I
a = 0.25687 + 1.91430I
b = 0.76941 − 1.46778I
10.6023 + 12.7252I 0
u = 1.51561 + 0.31438I
a = 0.07138 + 1.52212I
b = 0.92434 − 1.20152I
2.67796 + 12.83410I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51561 − 0.31438I
a = 0.07138 − 1.52212I
b = 0.92434 + 1.20152I
2.67796 − 12.83410I 0
u = 1.55157 + 0.11010I
a = 0.164884 − 1.312400I
b = −0.595253 + 1.162150I
5.63135 − 0.31745I 0
u = 1.55157 − 0.11010I
a = 0.164884 + 1.312400I
b = −0.595253 − 1.162150I
5.63135 + 0.31745I 0
u = −1.54716 + 0.28316I
a = 0.240136 − 1.013790I
b = 0.634566 + 1.046300I
8.53481 − 2.77939I 0
u = −1.54716 − 0.28316I
a = 0.240136 + 1.013790I
b = 0.634566 − 1.046300I
8.53481 + 2.77939I 0
u = −1.58782 + 0.17188I
a = −0.588633 + 1.249210I
b = −0.053271 − 1.001920I
12.48620 − 0.04830I 0
u = −1.58782 − 0.17188I
a = −0.588633 − 1.249210I
b = −0.053271 + 1.001920I
12.48620 + 0.04830I 0
u = 1.59024 + 0.15756I
a = 0.569657 + 1.184930I
b = 0.024023 − 1.161970I
9.63114 − 6.45309I 0
u = 1.59024 − 0.15756I
a = 0.569657 − 1.184930I
b = 0.024023 + 1.161970I
9.63114 + 6.45309I 0
u = 0.017699 + 0.384118I
a = −3.89080 − 1.70197I
b = −1.001280 + 0.347221I
−1.52056 + 6.23501I −10.80190 − 5.48008I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.017699 − 0.384118I
a = −3.89080 + 1.70197I
b = −1.001280 − 0.347221I
−1.52056 − 6.23501I −10.80190 + 5.48008I
u = −1.63491 + 0.01230I
a = −0.37883 + 1.73983I
b = 0.113022 − 0.779294I
11.76030 + 0.35175I 0
u = −1.63491 − 0.01230I
a = −0.37883 − 1.73983I
b = 0.113022 + 0.779294I
11.76030 − 0.35175I 0
u = −0.152233 + 0.282285I
a = 1.61654 + 1.16705I
b = 0.831591 − 1.127100I
−3.51286 − 2.88025I −9.55579 + 9.24687I
u = −0.152233 − 0.282285I
a = 1.61654 − 1.16705I
b = 0.831591 + 1.127100I
−3.51286 + 2.88025I −9.55579 − 9.24687I
u = −0.061907 + 0.296312I
a = −0.56077 + 2.06142I
b = −0.697467 − 0.464867I
−1.325650 − 0.356775I −7.64122 + 0.81952I
u = −0.061907 − 0.296312I
a = −0.56077 − 2.06142I
b = −0.697467 + 0.464867I
−1.325650 + 0.356775I −7.64122 − 0.81952I
u = −0.177777 + 0.060265I
a = −4.92355 − 5.09239I
b = 0.432886 + 0.824106I
3.46607 − 2.61249I 2.41623 + 8.11633I
u = −0.177777 − 0.060265I
a = −4.92355 + 5.09239I
b = 0.432886 − 0.824106I
3.46607 + 2.61249I 2.41623 − 8.11633I
u = −0.120784
a = 3.91761
b = −0.952491
−1.20266 −11.0970
18
II.
I
u
2
= h−2.87 × 10
5
u
34
+ 4.45 × 10
5
u
33
+ · · · + 6.95 × 10
4
b + 4.53 × 10
5
, 8.95 ×
10
6
u
34
−1.55×10
7
u
33
+· · · +6.95×10
4
a−7.16×10
6
, u
35
−3u
34
+· · · − 3u +1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
−128.675u
34
+ 222.937u
33
+ ··· − 226.268u + 102.998
4.12450u
34
− 6.40028u
33
+ ··· + 12.3272u − 6.52253
a
12
=
u
−u
3
+ u
a
4
=
6.03280u
34
− 7.95293u
33
+ ··· − 2.50307u + 2.63185
−90.5807u
34
+ 154.735u
33
+ ··· − 148.898u + 66.3438
a
6
=
−226.478u
34
+ 392.489u
33
+ ··· − 392.861u + 178.616
71.4202u
34
− 127.836u
33
+ ··· + 117.537u − 55.4666
a
1
=
−138.839u
34
+ 241.855u
33
+ ··· − 209.572u + 102.371
138.715u
34
− 238.136u
33
+ ··· + 229.656u − 101.872
a
5
=
52.0321u
34
− 89.7995u
33
+ ··· + 76.6775u − 40.8356
−17.3997u
34
+ 30.9632u
33
+ ··· − 18.3790u + 8.66213
a
10
=
−u
u
a
2
=
76.8678u
34
− 130.421u
33
+ ··· + 120.523u − 54.1158
−201.418u
34
+ 346.958u
33
+ ··· − 334.463u + 150.591
a
9
=
75.3933u
34
− 127.969u
33
+ ··· + 131.334u − 52.9898
−6.86766u
34
+ 15.2250u
33
+ ··· − 10.4685u + 6.51446
(ii) Obstruction class = 1
(iii) Cusp Shapes =
36916538
69517
u
34
−
62488291
69517
u
33
+ ··· +
8907764
9931
u −
27480848
69517
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
− 15u
34
+ ··· + 33u − 1
c
2
u
35
+ 4u
33
+ ··· + 2u − 1
c
3
u
35
− 2u
34
+ ··· + 4u + 1
c
4
u
35
− 8u
33
+ ··· + u − 1
c
5
u
35
− u
34
+ ··· + 2u + 1
c
6
u
35
+ u
34
+ ··· + 6u + 1
c
7
u
35
− 3u
34
+ ··· − 3u + 1
c
8
u
35
+ 6u
33
+ ··· + u + 1
c
9
u
35
− 8u
33
+ ··· + u + 1
c
10
, c
11
u
35
+ 3u
34
+ ··· − 3u − 1
c
12
u
35
+ u
34
+ ··· + 2u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 5y
34
+ ··· + 403y −1
c
2
y
35
+ 8y
34
+ ··· − 46y −1
c
3
y
35
+ 30y
34
+ ··· + 10y −1
c
4
, c
9
y
35
− 16y
34
+ ··· + 27y −1
c
5
, c
12
y
35
+ 31y
34
+ ··· + 4y −1
c
6
y
35
+ 7y
34
+ ··· − 10y −1
c
7
, c
10
, c
11
y
35
− 37y
34
+ ··· + 21y −1
c
8
y
35
+ 12y
34
+ ··· − 27y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.182027 + 0.869874I
a = −0.265202 − 0.612893I
b = 0.097048 − 0.828256I
2.24178 + 1.25666I 6.57050 + 0.34190I
u = −0.182027 − 0.869874I
a = −0.265202 + 0.612893I
b = 0.097048 + 0.828256I
2.24178 − 1.25666I 6.57050 − 0.34190I
u = 0.964804 + 0.569873I
a = −0.192692 − 0.641958I
b = −0.324644 + 0.264937I
−1.80184 + 6.85242I 0. − 11.06449I
u = 0.964804 − 0.569873I
a = −0.192692 + 0.641958I
b = −0.324644 − 0.264937I
−1.80184 − 6.85242I 0. + 11.06449I
u = −1.081130 + 0.358298I
a = 0.534291 − 0.627651I
b = −0.346617 + 0.425172I
0.976536 − 0.883404I −7.82210 + 0.I
u = −1.081130 − 0.358298I
a = 0.534291 + 0.627651I
b = −0.346617 − 0.425172I
0.976536 + 0.883404I −7.82210 + 0.I
u = −1.193960 + 0.021929I
a = −0.915369 + 0.173290I
b = 1.137950 + 0.481293I
5.33868 − 2.88602I 0
u = −1.193960 − 0.021929I
a = −0.915369 − 0.173290I
b = 1.137950 − 0.481293I
5.33868 + 2.88602I 0
u = −1.275640 + 0.144725I
a = 0.874481 − 1.012320I
b = −0.905324 + 0.799645I
1.26217 − 0.71404I 0
u = −1.275640 − 0.144725I
a = 0.874481 + 1.012320I
b = −0.905324 − 0.799645I
1.26217 + 0.71404I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.294680 + 0.008256I
a = 1.00955 − 1.82451I
b = −1.223060 + 0.311366I
2.51918 − 6.12462I 0
u = 1.294680 − 0.008256I
a = 1.00955 + 1.82451I
b = −1.223060 − 0.311366I
2.51918 + 6.12462I 0
u = 1.314160 + 0.068087I
a = −0.70685 − 2.25164I
b = 0.77303 + 1.34967I
0.17439 + 3.36654I 0
u = 1.314160 − 0.068087I
a = −0.70685 + 2.25164I
b = 0.77303 − 1.34967I
0.17439 − 3.36654I 0
u = 0.499645 + 0.422968I
a = −0.449921 − 0.365854I
b = 0.208413 − 0.619429I
−3.24269 − 2.15204I −5.41903 + 0.14772I
u = 0.499645 − 0.422968I
a = −0.449921 + 0.365854I
b = 0.208413 + 0.619429I
−3.24269 + 2.15204I −5.41903 − 0.14772I
u = 0.330711 + 0.550139I
a = −0.493823 + 0.056777I
b = 0.016658 − 0.730193I
−3.25264 − 2.13348I −6.23780 + 1.01138I
u = 0.330711 − 0.550139I
a = −0.493823 − 0.056777I
b = 0.016658 + 0.730193I
−3.25264 + 2.13348I −6.23780 − 1.01138I
u = −0.543392 + 0.313210I
a = −1.90486 + 0.89582I
b = 0.426421 − 0.681486I
3.69092 + 1.79872I 3.64028 − 0.38372I
u = −0.543392 − 0.313210I
a = −1.90486 − 0.89582I
b = 0.426421 + 0.681486I
3.69092 − 1.79872I 3.64028 + 0.38372I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.352598 + 0.502215I
a = 0.911125 − 0.726593I
b = 0.92760 + 1.28545I
3.44033 − 4.18639I −0.79336 + 5.06589I
u = −0.352598 − 0.502215I
a = 0.911125 + 0.726593I
b = 0.92760 − 1.28545I
3.44033 + 4.18639I −0.79336 − 5.06589I
u = −1.40315 + 0.25434I
a = 0.456337 − 0.755163I
b = 0.671332 + 0.746854I
6.42691 − 5.17350I 0
u = −1.40315 − 0.25434I
a = 0.456337 + 0.755163I
b = 0.671332 − 0.746854I
6.42691 + 5.17350I 0
u = −0.571961
a = −0.124725
b = −1.02027
−0.646384 6.65490
u = 1.44398 + 0.20199I
a = 0.02646 + 2.46256I
b = 1.03497 − 1.84981I
9.26260 + 6.85096I 0
u = 1.44398 − 0.20199I
a = 0.02646 − 2.46256I
b = 1.03497 + 1.84981I
9.26260 − 6.85096I 0
u = −1.48312 + 0.14024I
a = 0.12900 + 1.69004I
b = −1.030030 − 0.732629I
5.41730 − 7.98416I 0
u = −1.48312 − 0.14024I
a = 0.12900 − 1.69004I
b = −1.030030 + 0.732629I
5.41730 + 7.98416I 0
u = 1.48610 + 0.28274I
a = −0.404587 − 1.153440I
b = −0.593221 + 1.243270I
8.00621 + 2.96663I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48610 − 0.28274I
a = −0.404587 + 1.153440I
b = −0.593221 − 1.243270I
8.00621 − 2.96663I 0
u = 0.323585 + 0.153891I
a = −1.66337 − 3.68000I
b = −0.978139 + 0.144666I
−0.84120 + 6.48790I 0.37015 − 8.47950I
u = 0.323585 − 0.153891I
a = −1.66337 + 3.68000I
b = −0.978139 − 0.144666I
−0.84120 − 6.48790I 0.37015 + 8.47950I
u = 1.64331 + 0.04001I
a = −0.38220 − 1.66220I
b = 0.117745 + 0.781991I
11.69750 − 0.56989I 0
u = 1.64331 − 0.04001I
a = −0.38220 + 1.66220I
b = 0.117745 − 0.781991I
11.69750 + 0.56989I 0
25
III. I
u
3
= hb − 1, a, u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
1
a
8
=
1
−1
a
3
=
0
1
a
12
=
1
0
a
4
=
−1
1
a
6
=
1
−1
a
1
=
0
1
a
5
=
1
−2
a
10
=
−1
1
a
2
=
−1
2
a
9
=
2
−3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
9
u + 1
c
2
, c
5
, c
6
c
7
, c
8
, c
10
c
11
, c
12
u − 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
29
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
35
− 15u
34
+ ··· + 33u − 1)(u
140
+ u
139
+ ··· + 405u + 119)
c
2
(u − 1)(u
35
+ 4u
33
+ ··· + 2u − 1)
· (u
140
+ 4u
139
+ ··· + 44695798u − 3369031)
c
3
(u + 1)(u
35
− 2u
34
+ ··· + 4u + 1)
· (u
140
− 4u
139
+ ··· − 29465412u + 1871711)
c
4
(u + 1)(u
35
− 8u
33
+ ··· + u − 1)(u
140
− 2u
139
+ ··· − 8527u + 2089)
c
5
(u − 1)(u
35
− u
34
+ ··· + 2u + 1)(u
140
+ 3u
139
+ ··· + 63834u − 5809)
c
6
(u − 1)(u
35
+ u
34
+ ··· + 6u + 1)
· (u
140
+ 7u
139
+ ··· + 208242066u − 166275911)
c
7
(u − 1)(u
35
− 3u
34
+ ··· − 3u + 1)(u
140
− 3u
139
+ ··· − 27u − 1)
c
8
(u − 1)(u
35
+ 6u
33
+ ··· + u + 1)
· (u
140
+ 15u
138
+ ··· + 315207u − 35883)
c
9
(u + 1)(u
35
− 8u
33
+ ··· + u + 1)(u
140
− 2u
139
+ ··· − 8527u + 2089)
c
10
, c
11
(u − 1)(u
35
+ 3u
34
+ ··· − 3u − 1)(u
140
− 3u
139
+ ··· − 27u − 1)
c
12
(u − 1)(u
35
+ u
34
+ ··· + 2u − 1)(u
140
+ 3u
139
+ ··· + 63834u − 5809)
30
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
35
+ 5y
34
+ ··· + 403y −1)
· (y
140
− 5y
139
+ ··· + 6830319y + 14161)
c
2
(y −1)(y
35
+ 8y
34
+ ··· − 46y −1)
· (y
140
− 34y
139
+ ··· − 510524756422924y + 11350369878961)
c
3
(y −1)(y
35
+ 30y
34
+ ··· + 10y −1)
· (y
140
+ 56y
139
+ ··· + 52970751482880y + 3503302067521)
c
4
, c
9
(y −1)(y
35
− 16y
34
+ ··· + 27y −1)
· (y
140
− 74y
139
+ ··· − 86881505y + 4363921)
c
5
, c
12
(y −1)(y
35
+ 31y
34
+ ··· + 4y −1)
· (y
140
+ 105y
139
+ ··· + 2341783754y + 33744481)
c
6
(y −1)(y
35
+ 7y
34
+ ··· − 10y −1)
· (y
140
+ 57y
139
+ ··· + 1894560234749566132y + 27647678578879921)
c
7
, c
10
, c
11
(y −1)(y
35
− 37y
34
+ ··· + 21y −1)(y
140
− 139y
139
+ ··· − 63y + 1)
c
8
(y −1)(y
35
+ 12y
34
+ ··· − 27y −1)
· (y
140
+ 30y
139
+ ··· + 67712278617y + 1287589689)
31
