12a
0059
(K12a
0059
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 9 4 11 1 12 8 6
Solving Sequence
8,11
9
4,12
7 3 6 1 10 5 2
c
8
c
11
c
7
c
3
c
6
c
12
c
10
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.71088 × 10
361
u
137
− 4.89757 × 10
362
u
136
+ ··· + 2.81012 × 10
363
b + 2.16214 × 10
363
,
3.37731 × 10
362
u
137
− 1.72512 × 10
363
u
136
+ ··· + 2.81012 × 10
363
a + 1.76728 × 10
364
,
u
138
+ 2u
137
+ ··· − 14u + 1i
I
u
2
= hb, u
8
+ 2u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ a + 1, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 147 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−4.71 × 10
361
u
137
− 4.90 × 10
362
u
136
+ · · · + 2.81 × 10
363
b + 2.16 ×
10
363
, 3.38 × 10
362
u
137
− 1.73 × 10
363
u
136
+ · · · + 2.81 × 10
363
a + 1.77 ×
10
364
, u
138
+ 2u
137
+ · · · − 14u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
4
=
−0.120184u
137
+ 0.613895u
136
+ ··· + 15.1732u − 6.28898
0.0167640u
137
+ 0.174283u
136
+ ··· + 12.4843u − 0.769412
a
12
=
−u
u
a
7
=
−0.560792u
137
− 0.490800u
136
+ ··· − 47.6605u + 3.40798
0.180158u
137
+ 0.477905u
136
+ ··· + 9.60968u − 1.21932
a
3
=
0.618598u
137
+ 1.87938u
136
+ ··· + 60.5458u − 12.1743
−0.0179355u
137
+ 0.0130907u
136
+ ··· + 5.49317u + 0.408548
a
6
=
−0.849545u
137
− 1.94068u
136
+ ··· − 47.8784u + 3.99652
0.333855u
137
+ 0.868326u
136
+ ··· − 2.31475u − 0.346952
a
1
=
−0.287569u
137
+ 0.783730u
136
+ ··· − 31.9924u + 4.35349
−1.43846u
137
− 2.79732u
136
+ ··· + 21.5369u − 1.72603
a
10
=
−u
3
u
3
+ u
a
5
=
−0.767107u
137
− 1.00356u
136
+ ··· − 57.8502u + 4.70515
0.200522u
137
+ 0.538058u
136
+ ··· + 10.8465u − 1.34799
a
2
=
−0.458501u
137
+ 0.239804u
136
+ ··· − 11.9475u − 5.01052
0.119330u
137
+ 0.460278u
136
+ ··· + 19.9372u − 1.43411
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.92502u
137
− 8.32211u
136
+ ··· − 15.6428u − 3.22352
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
138
+ 70u
137
+ ··· − 82u + 1
c
2
, c
4
u
138
− 10u
137
+ ··· + 14u − 1
c
3
, c
7
u
138
− u
137
+ ··· + 4096u + 512
c
5
u
138
+ 2u
137
+ ··· − 2626u − 97
c
6
u
138
+ 6u
137
+ ··· − 67104u − 2117
c
8
, c
11
u
138
− 2u
137
+ ··· + 14u + 1
c
9
u
138
− 14u
137
+ ··· − 2u + 1
c
10
u
138
− 54u
137
+ ··· + 14u + 1
c
12
u
138
− 10u
137
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
138
+ 6y
137
+ ··· − 5018y + 1
c
2
, c
4
y
138
− 70y
137
+ ··· + 82y + 1
c
3
, c
7
y
138
− 57y
137
+ ··· − 8912896y + 262144
c
5
y
138
− 166y
137
+ ··· + 9748742y + 9409
c
6
y
138
− 118y
137
+ ··· − 1356064422y + 4481689
c
8
, c
11
y
138
+ 54y
137
+ ··· − 14y + 1
c
9
y
138
− 10y
137
+ ··· − 14y + 1
c
10
y
138
+ 62y
137
+ ··· + 2378y + 1
c
12
y
138
− 14y
137
+ ··· − 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.340095 + 0.938631I
a = −2.65484 − 1.57222I
b = 1.084210 + 0.480895I
0.93099 + 3.37995I 0
u = 0.340095 − 0.938631I
a = −2.65484 + 1.57222I
b = 1.084210 − 0.480895I
0.93099 − 3.37995I 0
u = −0.565847 + 0.829711I
a = −1.89250 + 1.37711I
b = 1.243040 + 0.380663I
−3.90120 + 1.41992I 0
u = −0.565847 − 0.829711I
a = −1.89250 − 1.37711I
b = 1.243040 − 0.380663I
−3.90120 − 1.41992I 0
u = 0.523816 + 0.842586I
a = 0.49491 − 4.58806I
b = 0.513302 − 0.642122I
−2.14770 − 1.10222I 0
u = 0.523816 − 0.842586I
a = 0.49491 + 4.58806I
b = 0.513302 + 0.642122I
−2.14770 + 1.10222I 0
u = 0.555562 + 0.842147I
a = −5.63415 + 2.08299I
b = 0.371240 + 0.165548I
−2.14622 − 2.23521I 0
u = 0.555562 − 0.842147I
a = −5.63415 − 2.08299I
b = 0.371240 − 0.165548I
−2.14622 + 2.23521I 0
u = 0.586154 + 0.792966I
a = 1.72146 + 0.94919I
b = 1.028400 + 0.569460I
−0.64257 + 3.65096I 0
u = 0.586154 − 0.792966I
a = 1.72146 − 0.94919I
b = 1.028400 − 0.569460I
−0.64257 − 3.65096I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.420026 + 0.927286I
a = 2.99710 + 2.14722I
b = −1.042910 − 0.202388I
2.43266 − 1.40735I 0
u = 0.420026 − 0.927286I
a = 2.99710 − 2.14722I
b = −1.042910 + 0.202388I
2.43266 + 1.40735I 0
u = −0.867495 + 0.535351I
a = 0.858232 + 0.532125I
b = −0.974643 + 0.546694I
−5.66343 − 4.80751I 0
u = −0.867495 − 0.535351I
a = 0.858232 − 0.532125I
b = −0.974643 − 0.546694I
−5.66343 + 4.80751I 0
u = 0.527672 + 0.877110I
a = 3.63134 + 0.70902I
b = 0.475349 + 0.722868I
−2.03184 − 3.14136I 0
u = 0.527672 − 0.877110I
a = 3.63134 − 0.70902I
b = 0.475349 − 0.722868I
−2.03184 + 3.14136I 0
u = −0.570493 + 0.859311I
a = −0.816912 + 0.512172I
b = 1.193220 − 0.620973I
−3.80516 + 3.12708I 0
u = −0.570493 − 0.859311I
a = −0.816912 − 0.512172I
b = 1.193220 + 0.620973I
−3.80516 − 3.12708I 0
u = −0.805471 + 0.534825I
a = −0.459619 + 0.647350I
b = 0.399102 + 0.957238I
−2.80156 − 2.93042I 0
u = −0.805471 − 0.534825I
a = −0.459619 − 0.647350I
b = 0.399102 − 0.957238I
−2.80156 + 2.93042I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.897882 + 0.515328I
a = 0.312579 − 0.760968I
b = −0.607381 − 1.045900I
−5.02344 − 7.63080I 0
u = −0.897882 − 0.515328I
a = 0.312579 + 0.760968I
b = −0.607381 + 1.045900I
−5.02344 + 7.63080I 0
u = −0.544617 + 0.793755I
a = −1.27517 + 0.91926I
b = 0.791951 + 1.123120I
−3.20951 − 0.12052I 0
u = −0.544617 − 0.793755I
a = −1.27517 − 0.91926I
b = 0.791951 − 1.123120I
−3.20951 + 0.12052I 0
u = 0.939245 + 0.442594I
a = 0.741341 + 0.959246I
b = −0.643323 + 0.685004I
−5.01384 − 0.52036I 0
u = 0.939245 − 0.442594I
a = 0.741341 − 0.959246I
b = −0.643323 − 0.685004I
−5.01384 + 0.52036I 0
u = 0.921298 + 0.258898I
a = −0.612122 + 0.342593I
b = 0.775567 + 0.394484I
−1.60499 + 0.17048I 0
u = 0.921298 − 0.258898I
a = −0.612122 − 0.342593I
b = 0.775567 − 0.394484I
−1.60499 − 0.17048I 0
u = −0.926037 + 0.480444I
a = −0.494592 − 0.435788I
b = 1.155250 − 0.638410I
−0.45961 − 8.68715I 0
u = −0.926037 − 0.480444I
a = −0.494592 + 0.435788I
b = 1.155250 + 0.638410I
−0.45961 + 8.68715I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.443756 + 0.830350I
a = −2.01243 + 1.70574I
b = 0.261401 − 0.675701I
−1.47744 − 0.92019I 0
u = 0.443756 − 0.830350I
a = −2.01243 − 1.70574I
b = 0.261401 + 0.675701I
−1.47744 + 0.92019I 0
u = 0.526271 + 0.919440I
a = 2.00835 + 3.67470I
b = −1.007240 + 0.365828I
1.86133 − 3.37943I 0
u = 0.526271 − 0.919440I
a = 2.00835 − 3.67470I
b = −1.007240 − 0.365828I
1.86133 + 3.37943I 0
u = −0.567574 + 0.894548I
a = 0.764645 + 0.598660I
b = 0.621808 − 1.262870I
−2.87405 + 4.60153I 0
u = −0.567574 − 0.894548I
a = 0.764645 − 0.598660I
b = 0.621808 + 1.262870I
−2.87405 − 4.60153I 0
u = 0.515741 + 0.769892I
a = −1.25620 − 1.50356I
b = −0.901914 − 0.317542I
1.38659 − 0.85768I 0
u = 0.515741 − 0.769892I
a = −1.25620 + 1.50356I
b = −0.901914 + 0.317542I
1.38659 + 0.85768I 0
u = 0.566397 + 0.918644I
a = −1.35698 − 3.43726I
b = 1.077150 − 0.598666I
−0.24222 − 8.22199I 0
u = 0.566397 − 0.918644I
a = −1.35698 + 3.43726I
b = 1.077150 + 0.598666I
−0.24222 + 8.22199I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.949135 + 0.531029I
a = 0.523176 − 0.931856I
b = −0.607911 − 0.752609I
−4.92549 − 2.89963I 0
u = 0.949135 − 0.531029I
a = 0.523176 + 0.931856I
b = −0.607911 + 0.752609I
−4.92549 + 2.89963I 0
u = −0.966171 + 0.502589I
a = 0.379640 + 0.566707I
b = −1.152770 + 0.759561I
−3.2577 − 14.1817I 0
u = −0.966171 − 0.502589I
a = 0.379640 − 0.566707I
b = −1.152770 − 0.759561I
−3.2577 + 14.1817I 0
u = −0.568724 + 0.933541I
a = 1.070970 − 0.091178I
b = −0.332883 − 1.227780I
−0.88815 + 5.59474I 0
u = −0.568724 − 0.933541I
a = 1.070970 + 0.091178I
b = −0.332883 + 1.227780I
−0.88815 − 5.59474I 0
u = −0.640432 + 0.629019I
a = 0.124626 − 0.127664I
b = 1.106790 − 0.792448I
−2.00335 − 6.93606I 0
u = −0.640432 − 0.629019I
a = 0.124626 + 0.127664I
b = 1.106790 + 0.792448I
−2.00335 + 6.93606I 0
u = −0.880650 + 0.674813I
a = 0.120061 − 0.508459I
b = −0.669186 − 0.519624I
−6.65019 − 0.44704I 0
u = −0.880650 − 0.674813I
a = 0.120061 + 0.508459I
b = −0.669186 + 0.519624I
−6.65019 + 0.44704I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.503273 + 0.988805I
a = −0.645970 + 0.778771I
b = 0.012925 + 0.583466I
−0.84910 − 2.82406I 0
u = 0.503273 − 0.988805I
a = −0.645970 − 0.778771I
b = 0.012925 − 0.583466I
−0.84910 + 2.82406I 0
u = −0.506605 + 0.729659I
a = −1.176970 − 0.084622I
b = −0.037414 + 1.194540I
−1.56126 − 1.16042I 0
u = −0.506605 − 0.729659I
a = −1.176970 + 0.084622I
b = −0.037414 − 1.194540I
−1.56126 + 1.16042I 0
u = −0.556750 + 0.963875I
a = 1.81613 − 1.33143I
b = −1.26077 − 0.75154I
2.07530 + 6.01010I 0
u = −0.556750 − 0.963875I
a = 1.81613 + 1.33143I
b = −1.26077 + 0.75154I
2.07530 − 6.01010I 0
u = −0.041155 + 1.118680I
a = −0.578064 − 0.424438I
b = 0.049286 + 0.900920I
2.85912 − 1.44732I 0
u = −0.041155 − 1.118680I
a = −0.578064 + 0.424438I
b = 0.049286 − 0.900920I
2.85912 + 1.44732I 0
u = −0.089174 + 0.872710I
a = −1.91374 + 1.24914I
b = 1.226050 − 0.580758I
2.14280 − 6.67345I 0
u = −0.089174 − 0.872710I
a = −1.91374 − 1.24914I
b = 1.226050 + 0.580758I
2.14280 + 6.67345I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.791527 + 0.796986I
a = 0.290374 + 0.296175I
b = 0.565089 − 0.368280I
−6.08890 − 1.96052I 0
u = −0.791527 − 0.796986I
a = 0.290374 − 0.296175I
b = 0.565089 + 0.368280I
−6.08890 + 1.96052I 0
u = −0.248672 + 0.839981I
a = 1.78038 − 1.28114I
b = −1.315550 + 0.359668I
3.97771 − 0.99477I 0
u = −0.248672 − 0.839981I
a = 1.78038 + 1.28114I
b = −1.315550 − 0.359668I
3.97771 + 0.99477I 0
u = 0.640276 + 0.926105I
a = −0.316915 + 0.018862I
b = 0.219549 + 0.280103I
−0.60788 − 2.56876I 0
u = 0.640276 − 0.926105I
a = −0.316915 − 0.018862I
b = 0.219549 − 0.280103I
−0.60788 + 2.56876I 0
u = 1.090690 + 0.332375I
a = 0.327935 − 0.464455I
b = −0.995065 − 0.606465I
−3.92952 + 4.48424I 0
u = 1.090690 − 0.332375I
a = 0.327935 + 0.464455I
b = −0.995065 + 0.606465I
−3.92952 − 4.48424I 0
u = 0.960018 + 0.654883I
a = −0.542341 − 0.578508I
b = 0.891237 − 0.451061I
−1.21505 − 3.56819I 0
u = 0.960018 − 0.654883I
a = −0.542341 + 0.578508I
b = 0.891237 + 0.451061I
−1.21505 + 3.56819I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.614735 + 0.988958I
a = −1.73542 + 1.36678I
b = 1.20482 + 0.82034I
−0.93423 + 11.87520I 0
u = −0.614735 − 0.988958I
a = −1.73542 − 1.36678I
b = 1.20482 − 0.82034I
−0.93423 − 11.87520I 0
u = −0.519531 + 1.052460I
a = 1.73633 − 1.00520I
b = −1.45789 + 0.02040I
5.82999 + 4.34658I 0
u = −0.519531 − 1.052460I
a = 1.73633 + 1.00520I
b = −1.45789 − 0.02040I
5.82999 − 4.34658I 0
u = −0.254920 + 1.146160I
a = 2.05460 − 0.90445I
b = −1.288680 − 0.281651I
7.47653 + 2.85325I 0
u = −0.254920 − 1.146160I
a = 2.05460 + 0.90445I
b = −1.288680 + 0.281651I
7.47653 − 2.85325I 0
u = 0.052177 + 1.174100I
a = 2.44826 + 0.16287I
b = −0.821216 + 0.326395I
0.77318 − 3.15109I 0
u = 0.052177 − 1.174100I
a = 2.44826 − 0.16287I
b = −0.821216 − 0.326395I
0.77318 + 3.15109I 0
u = −0.735630 + 0.928061I
a = −0.329799 + 0.420148I
b = 0.577195 + 0.506526I
−5.67444 + 7.70604I 0
u = −0.735630 − 0.928061I
a = −0.329799 − 0.420148I
b = 0.577195 − 0.506526I
−5.67444 − 7.70604I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.466191 + 0.662679I
a = −0.256341 − 0.270104I
b = −1.008480 + 0.760858I
1.12610 − 1.66732I 0
u = −0.466191 − 0.662679I
a = −0.256341 + 0.270104I
b = −1.008480 − 0.760858I
1.12610 + 1.66732I 0
u = 0.204194 + 0.775884I
a = −0.107475 − 0.863173I
b = −0.614984 + 0.187284I
1.56307 − 1.66544I 0
u = 0.204194 − 0.775884I
a = −0.107475 + 0.863173I
b = −0.614984 − 0.187284I
1.56307 + 1.66544I 0
u = −0.743205 + 0.293413I
a = −0.414296 + 0.414264I
b = 1.273680 − 0.189034I
3.28436 − 5.64107I 0
u = −0.743205 − 0.293413I
a = −0.414296 − 0.414264I
b = 1.273680 + 0.189034I
3.28436 + 5.64107I 0
u = −0.170748 + 1.203340I
a = −2.09962 + 0.67220I
b = 1.276750 + 0.042565I
8.11672 − 2.73587I 0
u = −0.170748 − 1.203340I
a = −2.09962 − 0.67220I
b = 1.276750 − 0.042565I
8.11672 + 2.73587I 0
u = −0.569413 + 1.095080I
a = −1.81139 + 1.05047I
b = 1.42457 + 0.18628I
5.52769 + 10.52010I 0
u = −0.569413 − 1.095080I
a = −1.81139 − 1.05047I
b = 1.42457 − 0.18628I
5.52769 − 10.52010I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.072080 + 0.621660I
a = 0.423149 + 0.719322I
b = −1.030340 + 0.632780I
−3.62101 − 8.17819I 0
u = 1.072080 − 0.621660I
a = 0.423149 − 0.719322I
b = −1.030340 − 0.632780I
−3.62101 + 8.17819I 0
u = 0.840207 + 0.916366I
a = −0.268636 − 0.177104I
b = 0.807402 + 0.162485I
−0.41806 − 2.81299I 0
u = 0.840207 − 0.916366I
a = −0.268636 + 0.177104I
b = 0.807402 − 0.162485I
−0.41806 + 2.81299I 0
u = 0.043833 + 1.243540I
a = 0.731556 + 0.401121I
b = −0.447071 − 0.969480I
1.61097 − 5.54766I 0
u = 0.043833 − 1.243540I
a = 0.731556 − 0.401121I
b = −0.447071 + 0.969480I
1.61097 + 5.54766I 0
u = −0.655393 + 1.072350I
a = 0.629769 + 0.362432I
b = 0.356173 − 1.076340I
−1.18583 + 8.42374I 0
u = −0.655393 − 1.072350I
a = 0.629769 − 0.362432I
b = 0.356173 + 1.076340I
−1.18583 − 8.42374I 0
u = −0.743993 + 1.030390I
a = −0.257378 − 0.371069I
b = −0.580352 + 0.452643I
−5.55713 + 6.45135I 0
u = −0.743993 − 1.030390I
a = −0.257378 + 0.371069I
b = −0.580352 − 0.452643I
−5.55713 − 6.45135I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.678289 + 1.090390I
a = 1.96897 − 1.31967I
b = −1.052960 − 0.511029I
−3.97612 + 10.54010I 0
u = −0.678289 − 1.090390I
a = 1.96897 + 1.31967I
b = −1.052960 + 0.511029I
−3.97612 − 10.54010I 0
u = 0.722888 + 1.079420I
a = 1.71635 + 1.44442I
b = −0.660289 + 0.557121I
−3.27436 − 3.20135I 0
u = 0.722888 − 1.079420I
a = 1.71635 − 1.44442I
b = −0.660289 − 0.557121I
−3.27436 + 3.20135I 0
u = 0.005056 + 1.301740I
a = −1.93035 + 0.13195I
b = 1.161370 − 0.485891I
6.18648 − 6.09287I 0
u = 0.005056 − 1.301740I
a = −1.93035 − 0.13195I
b = 1.161370 + 0.485891I
6.18648 + 6.09287I 0
u = −0.682652 + 1.108700I
a = −0.577455 − 0.484277I
b = −0.595154 + 1.111130I
−3.21354 + 13.45620I 0
u = −0.682652 − 1.108700I
a = −0.577455 + 0.484277I
b = −0.595154 − 1.111130I
−3.21354 − 13.45620I 0
u = 0.697326
a = −0.709724
b = 0.484619
−1.42472 −7.17280
u = 0.475013 + 1.219590I
a = −1.43737 − 0.40185I
b = 1.002230 + 0.056995I
2.60318 − 4.38929I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.475013 − 1.219590I
a = −1.43737 + 0.40185I
b = 1.002230 − 0.056995I
2.60318 + 4.38929I 0
u = 0.332014 + 1.271120I
a = 1.117710 + 0.326993I
b = −0.983568 − 0.420621I
1.52583 − 0.05279I 0
u = 0.332014 − 1.271120I
a = 1.117710 − 0.326993I
b = −0.983568 + 0.420621I
1.52583 + 0.05279I 0
u = −0.679432 + 1.131560I
a = −1.80994 + 1.29141I
b = 1.215480 + 0.657197I
1.5306 + 14.5699I 0
u = −0.679432 − 1.131560I
a = −1.80994 − 1.29141I
b = 1.215480 − 0.657197I
1.5306 − 14.5699I 0
u = −0.701275 + 1.140790I
a = 1.75264 − 1.33487I
b = −1.18737 − 0.77838I
−1.2856 + 20.2575I 0
u = −0.701275 − 1.140790I
a = 1.75264 + 1.33487I
b = −1.18737 + 0.77838I
−1.2856 − 20.2575I 0
u = 0.708172 + 1.139180I
a = −0.0648661 − 0.0825119I
b = −0.535602 − 0.829305I
−2.92258 − 5.51420I 0
u = 0.708172 − 1.139180I
a = −0.0648661 + 0.0825119I
b = −0.535602 + 0.829305I
−2.92258 + 5.51420I 0
u = 0.047685 + 1.345810I
a = 1.76874 − 0.05657I
b = −1.164010 + 0.662985I
3.85974 − 11.48810I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047685 − 1.345810I
a = 1.76874 + 0.05657I
b = −1.164010 − 0.662985I
3.85974 + 11.48810I 0
u = 0.872691 + 1.063990I
a = 0.050170 + 0.183584I
b = −0.973914 − 0.548572I
−2.29363 + 1.26582I 0
u = 0.872691 − 1.063990I
a = 0.050170 − 0.183584I
b = −0.973914 + 0.548572I
−2.29363 − 1.26582I 0
u = 0.680256 + 1.204020I
a = −1.51515 − 0.95046I
b = 1.013460 − 0.467152I
1.14019 − 6.08874I 0
u = 0.680256 − 1.204020I
a = −1.51515 + 0.95046I
b = 1.013460 + 0.467152I
1.14019 + 6.08874I 0
u = −0.591841 + 0.148863I
a = 0.054230 − 0.880314I
b = −1.223500 − 0.025026I
3.62495 − 0.18798I −0.484423 + 0.189420I
u = −0.591841 − 0.148863I
a = 0.054230 + 0.880314I
b = −1.223500 + 0.025026I
3.62495 + 0.18798I −0.484423 − 0.189420I
u = 0.74149 + 1.22952I
a = 1.36782 + 1.02473I
b = −1.083240 + 0.646473I
−1.23497 − 11.03660I 0
u = 0.74149 − 1.22952I
a = 1.36782 − 1.02473I
b = −1.083240 − 0.646473I
−1.23497 + 11.03660I 0
u = 0.373876 + 0.232370I
a = −0.335474 + 0.827439I
b = 1.024840 − 0.606612I
−0.87217 − 6.18814I −0.85758 + 6.42606I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373876 − 0.232370I
a = −0.335474 − 0.827439I
b = 1.024840 + 0.606612I
−0.87217 + 6.18814I −0.85758 − 6.42606I
u = 0.118177 + 0.393125I
a = −0.495643 − 1.229900I
b = −0.856902 + 0.439878I
1.42734 − 1.67105I 2.08270 + 3.16763I
u = 0.118177 − 0.393125I
a = −0.495643 + 1.229900I
b = −0.856902 − 0.439878I
1.42734 + 1.67105I 2.08270 − 3.16763I
u = −0.030627 + 0.311856I
a = −3.28350 + 0.01360I
b = 0.142187 + 0.803358I
−1.18089 − 1.44155I −4.59977 + 5.03886I
u = −0.030627 − 0.311856I
a = −3.28350 − 0.01360I
b = 0.142187 − 0.803358I
−1.18089 + 1.44155I −4.59977 − 5.03886I
u = 0.208705
a = −7.07164
b = 0.535544
−2.39938 2.13270
u = 0.120903 + 0.077848I
a = −5.02322 + 0.08248I
b = 0.562307 + 0.712073I
−2.24121 − 1.11087I −4.19709 + 0.75951I
u = 0.120903 − 0.077848I
a = −5.02322 − 0.08248I
b = 0.562307 − 0.712073I
−2.24121 + 1.11087I −4.19709 − 0.75951I
18
II.
I
u
2
= hb, u
8
+ 2u
7
+ · · · + a + 1, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
4
=
−u
8
− 2u
7
− 3u
6
− 2u
5
− 3u
4
− 2u
3
− 2u
2
− 1
0
a
12
=
−u
u
a
7
=
1
0
a
3
=
−u
8
− 2u
7
− 3u
6
− 2u
5
− 3u
4
− 2u
3
− 2u
2
− 1
0
a
6
=
u
2
+ 1
u
4
a
1
=
−u
7
− 2u
5
− 2u
3
− 2u
u
8
+ u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ 2u − 1
a
10
=
−u
3
u
3
+ u
a
5
=
u
7
+ 2u
5
+ 2u
3
+ 2u
−u
8
− u
7
− u
6
− 2u
5
− u
4
− 2u
3
− 2u + 1
a
2
=
−u
8
− 3u
7
− 3u
6
− 4u
5
− 3u
4
− 4u
3
− 2u
2
− 2u − 1
u
8
+ u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
8
− 9u
7
− 12u
6
− 13u
5
− 15u
4
− 15u
3
− 8u
2
− 5u − 9
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
, c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
6
, c
10
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
8
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
11
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
12
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ 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
7
y
9
c
5
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
10
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
12
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 = 0.140343 + 0.966856I
a = 0.939568 + 0.981640I
b = 0
0.13850 − 2.09337I −3.38047 + 2.85927I
u = 0.140343 − 0.966856I
a = 0.939568 − 0.981640I
b = 0
0.13850 + 2.09337I −3.38047 − 2.85927I
u = 0.628449 + 0.875112I
a = −2.26219 + 2.13290I
b = 0
−2.26187 − 2.45442I −6.9022 + 12.4598I
u = 0.628449 − 0.875112I
a = −2.26219 − 2.13290I
b = 0
−2.26187 + 2.45442I −6.9022 − 12.4598I
u = −0.796005 + 0.733148I
a = −0.119081 + 0.409451I
b = 0
−6.01628 − 1.33617I −6.48878 − 2.15019I
u = −0.796005 − 0.733148I
a = −0.119081 − 0.409451I
b = 0
−6.01628 + 1.33617I −6.48878 + 2.15019I
u = −0.728966 + 0.986295I
a = 0.016164 − 0.378317I
b = 0
−5.24306 + 7.08493I −2.48514 − 6.49599I
u = −0.728966 − 0.986295I
a = 0.016164 + 0.378317I
b = 0
−5.24306 − 7.08493I −2.48514 + 6.49599I
u = 0.512358
a = −2.14893
b = 0
−2.84338 −17.4870
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
138
+ 70u
137
+ ··· − 82u + 1)
c
2
((u − 1)
9
)(u
138
− 10u
137
+ ··· + 14u − 1)
c
3
, c
7
u
9
(u
138
− u
137
+ ··· + 4096u + 512)
c
4
((u + 1)
9
)(u
138
− 10u
137
+ ··· + 14u − 1)
c
5
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
138
+ 2u
137
+ ··· − 2626u − 97)
c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
138
+ 6u
137
+ ··· − 67104u − 2117)
c
8
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
138
− 2u
137
+ ··· + 14u + 1)
c
9
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
138
− 14u
137
+ ··· − 2u + 1)
c
10
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
138
− 54u
137
+ ··· + 14u + 1)
c
11
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
138
− 2u
137
+ ··· + 14u + 1)
c
12
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
138
− 10u
137
+ ··· + 2u − 1)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
138
+ 6y
137
+ ··· − 5018y + 1)
c
2
, c
4
((y −1)
9
)(y
138
− 70y
137
+ ··· + 82y + 1)
c
3
, c
7
y
9
(y
138
− 57y
137
+ ··· − 8912896y + 262144)
c
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
138
− 166y
137
+ ··· + 9748742y + 9409)
c
6
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
138
− 118y
137
+ ··· − 1356064422y + 4481689)
c
8
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
138
+ 54y
137
+ ··· − 14y + 1)
c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
138
− 10y
137
+ ··· − 14y + 1)
c
10
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
138
+ 62y
137
+ ··· + 2378y + 1)
c
12
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
138
− 14y
137
+ ··· − 10y + 1)
24
