12a
0865
(K12a
0865
)
A knot diagram
1
Linearized knot diagam
4 5 11 9 10 3 12 1 2 6 8 7
Solving Sequence
7,12
8
1,4
2 9 5 11 3 6 10
c
7
c
12
c
1
c
8
c
4
c
11
c
3
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5.19820 × 10
201
u
139
+ 6.60058 × 10
201
u
138
+ ··· + 2.86650 × 10
201
b − 1.70750 × 10
201
,
6.84846 × 10
202
u
139
+ 1.27131 × 10
203
u
138
+ ··· + 2.86650 × 10
201
a − 4.52189 × 10
203
,
u
140
+ 2u
139
+ ··· − 29u − 1i
I
u
2
= h−17u
25
− 137u
24
+ ··· + 31b − 49, −127u
25
− 274u
24
+ ··· + 31a − 315, u
26
+ u
25
+ ··· + 6u + 1i
* 2 irreducible components of dim
C
= 0, with total 166 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
= h5.20 × 10
201
u
139
+ 6.60 × 10
201
u
138
+ · · · + 2.87 × 10
201
b − 1.71 ×
10
201
, 6.85 × 10
202
u
139
+ 1.27 × 10
203
u
138
+ · · · + 2.87 × 10
201
a − 4.52 ×
10
203
, u
140
+ 2u
139
+ · · · − 29u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
4
=
−23.8914u
139
− 44.3507u
138
+ ··· + 3396.80u + 157.750
−1.81343u
139
− 2.30267u
138
+ ··· + 38.5060u + 0.595675
a
2
=
−4.24614u
139
− 11.1656u
138
+ ··· + 511.349u + 4.19872
0.0697095u
139
− 1.99479u
138
+ ··· − 220.467u − 7.87942
a
9
=
−u
4
− u
2
+ 1
−u
4
− 2u
2
a
5
=
−27.0046u
139
− 46.2135u
138
+ ··· + 3518.44u + 162.574
−1.23012u
139
+ 2.21877u
138
+ ··· − 41.5813u − 2.31366
a
11
=
−u
u
3
+ u
a
3
=
−25.2211u
139
− 44.6624u
138
+ ··· + 3446.08u + 160.211
−0.652155u
139
+ 1.76471u
138
+ ··· − 77.5282u − 4.21315
a
6
=
13.6940u
139
+ 26.6243u
138
+ ··· − 1236.53u − 28.6211
2.72181u
139
+ 7.06780u
138
+ ··· − 331.465u − 15.6455
a
10
=
−0.00786984u
139
− 1.16765u
138
+ ··· − 309.091u − 43.0354
−1.98484u
139
− 8.29039u
138
+ ··· + 454.057u + 21.0848
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6.89858u
139
− 15.8047u
138
+ ··· + 1204.83u + 62.7229
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
140
+ 11u
139
+ ··· − 24651u − 2513
c
2
u
140
− 9u
139
+ ··· + 270u + 7
c
3
u
140
− 8u
138
+ ··· − 94043u + 17197
c
4
u
140
+ 3u
139
+ ··· + 8798u − 3781
c
5
, c
10
u
140
− 50u
138
+ ··· − 4u − 1
c
6
u
140
+ 2u
139
+ ··· − 20u − 1
c
7
, c
11
, c
12
u
140
− 2u
139
+ ··· + 29u − 1
c
8
u
140
+ 2u
139
+ ··· + 1113371u − 44197
c
9
u
140
− 2u
139
+ ··· + 71035u − 11231
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
140
+ y
139
+ ··· − 2719370831y + 6315169
c
2
y
140
+ 15y
139
+ ··· − 2382y + 49
c
3
y
140
− 16y
139
+ ··· − 26838854679y + 295736809
c
4
y
140
− 25y
139
+ ··· − 1468752308y + 14295961
c
5
, c
10
y
140
− 100y
139
+ ··· − 192y + 1
c
6
y
140
+ 8y
139
+ ··· + 32y + 1
c
7
, c
11
, c
12
y
140
+ 122y
139
+ ··· − 197y + 1
c
8
y
140
− 44y
139
+ ··· − 361041802395y + 1953374809
c
9
y
140
− 28y
139
+ ··· − 7929328317y + 126135361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699032 + 0.735483I
a = −0.002897 − 0.339529I
b = 0.213622 + 0.152636I
0.77056 − 2.64531I 0
u = −0.699032 − 0.735483I
a = −0.002897 + 0.339529I
b = 0.213622 − 0.152636I
0.77056 + 2.64531I 0
u = 0.544207 + 0.805924I
a = −0.489701 − 0.895906I
b = −0.438060 + 0.011080I
−4.10669 + 8.88255I 0
u = 0.544207 − 0.805924I
a = −0.489701 + 0.895906I
b = −0.438060 − 0.011080I
−4.10669 − 8.88255I 0
u = 0.394579 + 0.859613I
a = −1.131630 + 0.715654I
b = −0.079745 + 0.891189I
−0.29782 − 2.37813I 0
u = 0.394579 − 0.859613I
a = −1.131630 − 0.715654I
b = −0.079745 − 0.891189I
−0.29782 + 2.37813I 0
u = 0.472498 + 0.968616I
a = 0.829026 − 1.037290I
b = −0.219589 − 0.656120I
1.70342 − 4.58350I 0
u = 0.472498 − 0.968616I
a = 0.829026 + 1.037290I
b = −0.219589 + 0.656120I
1.70342 + 4.58350I 0
u = −0.460890 + 0.977356I
a = −0.88656 − 1.48895I
b = 0.362261 − 0.992992I
−3.34831 + 10.32660I 0
u = −0.460890 − 0.977356I
a = −0.88656 + 1.48895I
b = 0.362261 + 0.992992I
−3.34831 − 10.32660I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.286617 + 0.845325I
a = −1.022550 + 0.191229I
b = −0.283574 + 0.113795I
−0.20232 − 1.86529I 0
u = −0.286617 − 0.845325I
a = −1.022550 − 0.191229I
b = −0.283574 − 0.113795I
−0.20232 + 1.86529I 0
u = 0.798963 + 0.394167I
a = −0.0640261 + 0.0498232I
b = −0.630429 + 0.028242I
−2.77125 − 4.07901I 0
u = 0.798963 − 0.394167I
a = −0.0640261 − 0.0498232I
b = −0.630429 − 0.028242I
−2.77125 + 4.07901I 0
u = −0.853631 + 0.194477I
a = −0.1209890 + 0.0240797I
b = −0.471244 − 0.957436I
4.00764 − 2.40019I 0
u = −0.853631 − 0.194477I
a = −0.1209890 − 0.0240797I
b = −0.471244 + 0.957436I
4.00764 + 2.40019I 0
u = −0.806277 + 0.337217I
a = −0.323402 − 0.104556I
b = 0.326147 + 0.688530I
1.29205 − 2.18437I 0
u = −0.806277 − 0.337217I
a = −0.323402 + 0.104556I
b = 0.326147 − 0.688530I
1.29205 + 2.18437I 0
u = −0.234226 + 1.101490I
a = 1.30344 + 2.09572I
b = 0.30641 + 1.61658I
−4.83691 + 1.38716I 0
u = −0.234226 − 1.101490I
a = 1.30344 − 2.09572I
b = 0.30641 − 1.61658I
−4.83691 − 1.38716I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.835619 + 0.222340I
a = 0.1004540 − 0.0066237I
b = −0.82637 + 1.36466I
4.00903 + 9.23441I 0
u = 0.835619 − 0.222340I
a = 0.1004540 + 0.0066237I
b = −0.82637 − 1.36466I
4.00903 − 9.23441I 0
u = −0.836214 + 0.217940I
a = 0.0298363 − 0.0339143I
b = 1.10522 + 1.58007I
−1.0018 − 14.9566I 0
u = −0.836214 − 0.217940I
a = 0.0298363 + 0.0339143I
b = 1.10522 − 1.58007I
−1.0018 + 14.9566I 0
u = −0.512843 + 1.037880I
a = 0.448547 + 0.469658I
b = −0.060475 + 0.554886I
1.44816 − 2.40172I 0
u = −0.512843 − 1.037880I
a = 0.448547 − 0.469658I
b = −0.060475 − 0.554886I
1.44816 + 2.40172I 0
u = 0.793750 + 0.246725I
a = 0.293281 + 0.080782I
b = 0.43556 − 1.48959I
1.69280 + 6.70388I 0
u = 0.793750 − 0.246725I
a = 0.293281 − 0.080782I
b = 0.43556 + 1.48959I
1.69280 − 6.70388I 0
u = −0.824639
a = −0.567248
b = 1.18239
0.488916 0
u = 0.154361 + 1.181950I
a = −1.68351 + 1.36233I
b = −0.540055 + 1.146340I
−1.56656 − 1.31155I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.154361 − 1.181950I
a = −1.68351 − 1.36233I
b = −0.540055 − 1.146340I
−1.56656 + 1.31155I 0
u = 0.793092
a = −0.0806651
b = 1.53427
−2.58349 0
u = 0.791372
a = 0.799386
b = 0.861709
2.30047 0
u = −0.750566 + 0.146215I
a = −0.0957158 − 0.0484548I
b = −1.20575 − 1.93727I
−2.02859 − 5.11462I 0
u = −0.750566 − 0.146215I
a = −0.0957158 + 0.0484548I
b = −1.20575 + 1.93727I
−2.02859 + 5.11462I 0
u = 0.263724 + 1.213630I
a = −2.28924 + 1.40544I
b = −1.20765 + 1.17964I
−2.23381 − 2.33627I 0
u = 0.263724 − 1.213630I
a = −2.28924 − 1.40544I
b = −1.20765 − 1.17964I
−2.23381 + 2.33627I 0
u = 0.101179 + 1.246570I
a = 1.42493 − 1.52688I
b = 1.73158 − 1.63248I
−5.53848 − 4.43348I 0
u = 0.101179 − 1.246570I
a = 1.42493 + 1.52688I
b = 1.73158 + 1.63248I
−5.53848 + 4.43348I 0
u = −0.239253 + 1.231670I
a = −1.74160 + 0.07198I
b = −1.038660 − 0.033582I
−1.23220 − 2.64621I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.239253 − 1.231670I
a = −1.74160 − 0.07198I
b = −1.038660 + 0.033582I
−1.23220 + 2.64621I 0
u = −0.250859 + 1.242540I
a = 2.29923 + 1.40989I
b = 1.21683 + 2.45378I
−3.20135 + 1.99274I 0
u = −0.250859 − 1.242540I
a = 2.29923 − 1.40989I
b = 1.21683 − 2.45378I
−3.20135 − 1.99274I 0
u = −0.354369 + 1.218200I
a = 0.791897 − 0.893559I
b = 1.282500 + 0.117755I
−3.25883 − 4.26153I 0
u = −0.354369 − 1.218200I
a = 0.791897 + 0.893559I
b = 1.282500 − 0.117755I
−3.25883 + 4.26153I 0
u = 0.263563 + 1.244070I
a = −1.74414 + 0.50928I
b = −1.32904 + 1.54589I
0.89939 + 1.62384I 0
u = 0.263563 − 1.244070I
a = −1.74414 − 0.50928I
b = −1.32904 − 1.54589I
0.89939 − 1.62384I 0
u = 0.704979 + 0.164031I
a = −0.150435 + 0.275954I
b = 0.75076 − 1.65751I
1.17772 + 4.48967I 0. − 7.53783I
u = 0.704979 − 0.164031I
a = −0.150435 − 0.275954I
b = 0.75076 + 1.65751I
1.17772 − 4.48967I 0. + 7.53783I
u = −0.138523 + 1.273300I
a = 1.91958 + 1.67472I
b = 0.27945 + 1.45817I
−5.52155 + 3.54608I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.138523 − 1.273300I
a = 1.91958 − 1.67472I
b = 0.27945 − 1.45817I
−5.52155 − 3.54608I 0
u = 0.680138 + 0.223925I
a = −0.193380 + 0.683004I
b = −0.774622 + 1.149680I
−3.19836 + 6.87023I 0. − 7.99221I
u = 0.680138 − 0.223925I
a = −0.193380 − 0.683004I
b = −0.774622 − 1.149680I
−3.19836 − 6.87023I 0. + 7.99221I
u = 0.709719 + 0.068224I
a = −0.683746 − 0.317946I
b = 0.11986 − 1.99234I
1.24243 + 5.87125I 6.34904 − 7.19748I
u = 0.709719 − 0.068224I
a = −0.683746 + 0.317946I
b = 0.11986 + 1.99234I
1.24243 − 5.87125I 6.34904 + 7.19748I
u = −0.709889 + 0.062652I
a = −0.600356 + 0.023567I
b = −0.331801 + 0.869990I
2.27965 − 0.78103I 5.12667 + 2.33382I
u = −0.709889 − 0.062652I
a = −0.600356 − 0.023567I
b = −0.331801 − 0.869990I
2.27965 + 0.78103I 5.12667 − 2.33382I
u = 0.338264 + 1.242640I
a = 0.885981 + 0.992035I
b = 0.645640 + 0.882198I
−1.53639 + 4.07833I 0
u = 0.338264 − 1.242640I
a = 0.885981 − 0.992035I
b = 0.645640 − 0.882198I
−1.53639 − 4.07833I 0
u = −0.237859 + 1.267520I
a = 1.87506 + 0.52134I
b = 1.072570 + 0.110917I
−0.87635 − 1.45469I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.237859 − 1.267520I
a = 1.87506 − 0.52134I
b = 1.072570 − 0.110917I
−0.87635 + 1.45469I 0
u = −0.153130 + 1.286400I
a = −2.33191 − 0.81105I
b = −2.28428 − 1.09051I
−2.59239 − 0.40513I 0
u = −0.153130 − 1.286400I
a = −2.33191 + 0.81105I
b = −2.28428 + 1.09051I
−2.59239 + 0.40513I 0
u = 0.702759 + 0.035024I
a = 0.853019 + 0.137797I
b = −0.55503 − 1.35140I
4.60287 + 1.87168I 11.89122 − 4.10578I
u = 0.702759 − 0.035024I
a = 0.853019 − 0.137797I
b = −0.55503 + 1.35140I
4.60287 − 1.87168I 11.89122 + 4.10578I
u = 0.335754 + 0.602836I
a = 0.93091 − 1.29214I
b = 0.421732 − 0.159334I
−4.69130 − 3.41875I −4.42625 + 2.23362I
u = 0.335754 − 0.602836I
a = 0.93091 + 1.29214I
b = 0.421732 + 0.159334I
−4.69130 + 3.41875I −4.42625 − 2.23362I
u = −0.678583 + 0.049366I
a = −0.957749 + 0.458206I
b = 0.36880 − 2.25617I
0.45229 − 5.35060I 7.25971 + 5.20115I
u = −0.678583 − 0.049366I
a = −0.957749 − 0.458206I
b = 0.36880 + 2.25617I
0.45229 + 5.35060I 7.25971 − 5.20115I
u = 0.282654 + 1.290250I
a = 1.09719 − 1.34918I
b = −0.056532 − 0.990814I
0.47298 + 5.43679I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.282654 − 1.290250I
a = 1.09719 + 1.34918I
b = −0.056532 + 0.990814I
0.47298 − 5.43679I 0
u = 0.216260 + 1.312170I
a = 0.402189 + 0.478964I
b = 0.851919 − 0.831079I
−7.97931 + 2.80431I 0
u = 0.216260 − 1.312170I
a = 0.402189 − 0.478964I
b = 0.851919 + 0.831079I
−7.97931 − 2.80431I 0
u = −0.255683 + 1.305510I
a = −0.90800 − 1.66526I
b = −0.70433 − 2.40393I
−1.28242 − 4.99790I 0
u = −0.255683 − 1.305510I
a = −0.90800 + 1.66526I
b = −0.70433 + 2.40393I
−1.28242 + 4.99790I 0
u = −0.295633 + 1.297610I
a = 0.644611 + 1.000810I
b = 0.45480 + 1.38839I
−1.96637 − 4.43266I 0
u = −0.295633 − 1.297610I
a = 0.644611 − 1.000810I
b = 0.45480 − 1.38839I
−1.96637 + 4.43266I 0
u = −0.270539 + 1.306760I
a = −1.98197 − 2.10546I
b = −0.25403 − 1.98172I
−3.79851 − 8.78428I 0
u = −0.270539 − 1.306760I
a = −1.98197 + 2.10546I
b = −0.25403 + 1.98172I
−3.79851 + 8.78428I 0
u = −0.616335 + 0.237274I
a = −0.050993 + 1.088220I
b = −0.87278 − 1.49764I
−2.54122 − 5.60876I −1.84378 + 7.59056I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.616335 − 0.237274I
a = −0.050993 − 1.088220I
b = −0.87278 + 1.49764I
−2.54122 + 5.60876I −1.84378 − 7.59056I
u = 0.288865 + 1.311520I
a = 2.04975 − 1.85069I
b = 1.44642 − 2.60044I
−3.08162 + 9.48378I 0
u = 0.288865 − 1.311520I
a = 2.04975 + 1.85069I
b = 1.44642 + 2.60044I
−3.08162 − 9.48378I 0
u = 0.196363 + 1.336460I
a = 2.42702 + 0.15394I
b = 2.07468 − 0.64978I
−8.11323 + 3.27890I 0
u = 0.196363 − 1.336460I
a = 2.42702 − 0.15394I
b = 2.07468 + 0.64978I
−8.11323 − 3.27890I 0
u = −0.647650 + 0.036056I
a = 1.364760 − 0.168535I
b = 0.230064 − 1.253090I
2.93048 − 1.72674I 7.21258 + 2.95499I
u = −0.647650 − 0.036056I
a = 1.364760 + 0.168535I
b = 0.230064 + 1.253090I
2.93048 + 1.72674I 7.21258 − 2.95499I
u = −0.415644 + 0.496287I
a = 1.06763 + 1.02386I
b = −0.884039 + 0.741752I
−3.46790 + 2.34643I −3.04341 − 0.92950I
u = −0.415644 − 0.496287I
a = 1.06763 − 1.02386I
b = −0.884039 − 0.741752I
−3.46790 − 2.34643I −3.04341 + 0.92950I
u = 0.347685 + 1.307660I
a = 1.59582 + 1.05007I
b = 1.76428 + 0.05092I
−6.70121 + 4.11313I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.347685 − 1.307660I
a = 1.59582 − 1.05007I
b = 1.76428 − 0.05092I
−6.70121 − 4.11313I 0
u = 0.000861 + 1.383150I
a = 0.168138 + 0.031688I
b = −0.251627 − 1.128170I
−10.94410 + 2.03541I 0
u = 0.000861 − 1.383150I
a = 0.168138 − 0.031688I
b = −0.251627 + 1.128170I
−10.94410 − 2.03541I 0
u = −0.554619 + 0.267239I
a = −0.361565 + 0.484477I
b = 0.053646 + 0.830344I
0.77541 − 1.50731I −0.80674 + 3.53769I
u = −0.554619 − 0.267239I
a = −0.361565 − 0.484477I
b = 0.053646 − 0.830344I
0.77541 + 1.50731I −0.80674 − 3.53769I
u = −0.316855 + 1.352120I
a = −3.06791 − 0.70498I
b = −2.32383 − 1.85395I
−6.75326 − 8.98336I 0
u = −0.316855 − 1.352120I
a = −3.06791 + 0.70498I
b = −2.32383 + 1.85395I
−6.75326 + 8.98336I 0
u = 0.295740 + 1.358740I
a = 2.36365 − 0.87968I
b = 1.67826 − 1.90924I
−3.63387 + 8.13829I 0
u = 0.295740 − 1.358740I
a = 2.36365 + 0.87968I
b = 1.67826 + 1.90924I
−3.63387 − 8.13829I 0
u = 0.047339 + 1.403100I
a = 0.339250 + 0.232601I
b = 0.635018 − 0.562878I
−6.94612 − 0.75092I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047339 − 1.403100I
a = 0.339250 − 0.232601I
b = 0.635018 + 0.562878I
−6.94612 + 0.75092I 0
u = 0.129065 + 0.579302I
a = 0.85917 + 2.25285I
b = 0.419221 + 0.320317I
−5.00483 + 1.82985I −6.73370 − 4.41022I
u = 0.129065 − 0.579302I
a = 0.85917 − 2.25285I
b = 0.419221 − 0.320317I
−5.00483 − 1.82985I −6.73370 + 4.41022I
u = −0.260839 + 1.382420I
a = −2.31093 − 0.68137I
b = −1.50678 − 1.91307I
−7.66741 − 8.86666I 0
u = −0.260839 − 1.382420I
a = −2.31093 + 0.68137I
b = −1.50678 + 1.91307I
−7.66741 + 8.86666I 0
u = 0.281620 + 1.380760I
a = −2.28920 + 0.47079I
b = −2.06685 + 0.91123I
−8.27911 + 10.39120I 0
u = 0.281620 − 1.380760I
a = −2.28920 − 0.47079I
b = −2.06685 − 0.91123I
−8.27911 − 10.39120I 0
u = −0.252929 + 1.390350I
a = 1.56778 + 0.82379I
b = 1.39729 + 1.20425I
−4.47207 − 4.60035I 0
u = −0.252929 − 1.390350I
a = 1.56778 − 0.82379I
b = 1.39729 − 1.20425I
−4.47207 + 4.60035I 0
u = −0.35800 + 1.38540I
a = −1.49032 − 0.37570I
b = −1.06550 − 1.01527I
−0.98605 − 6.75226I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.35800 − 1.38540I
a = −1.49032 + 0.37570I
b = −1.06550 + 1.01527I
−0.98605 + 6.75226I 0
u = 0.139251 + 0.547050I
a = −1.28917 + 1.14830I
b = 0.197964 + 0.374273I
−0.93843 − 1.45328I −2.95166 + 1.50514I
u = 0.139251 − 0.547050I
a = −1.28917 − 1.14830I
b = 0.197964 − 0.374273I
−0.93843 + 1.45328I −2.95166 − 1.50514I
u = 0.06789 + 1.43640I
a = 0.756344 + 0.414480I
b = 0.614396 + 1.184790I
−11.16280 − 2.17630I 0
u = 0.06789 − 1.43640I
a = 0.756344 − 0.414480I
b = 0.614396 − 1.184790I
−11.16280 + 2.17630I 0
u = 0.560453
a = −2.29076
b = 0.803012
−3.80246 1.20200
u = −0.34940 + 1.39853I
a = 2.41537 + 0.60097I
b = 1.88452 + 1.73632I
−6.1257 − 19.2315I 0
u = −0.34940 − 1.39853I
a = 2.41537 − 0.60097I
b = 1.88452 − 1.73632I
−6.1257 + 19.2315I 0
u = 0.34817 + 1.39964I
a = −2.01913 + 0.65937I
b = −1.59183 + 1.64806I
−1.13256 + 13.50210I 0
u = 0.34817 − 1.39964I
a = −2.01913 − 0.65937I
b = −1.59183 − 1.64806I
−1.13256 − 13.50210I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11930 + 1.43951I
a = −0.741681 + 1.053440I
b = −1.187150 + 0.194659I
−9.65636 + 0.48989I 0
u = −0.11930 − 1.43951I
a = −0.741681 − 1.053440I
b = −1.187150 − 0.194659I
−9.65636 − 0.48989I 0
u = 0.32706 + 1.40776I
a = 1.80093 − 0.93488I
b = 1.04294 − 1.60093I
−3.56618 + 10.76380I 0
u = 0.32706 − 1.40776I
a = 1.80093 + 0.93488I
b = 1.04294 + 1.60093I
−3.56618 − 10.76380I 0
u = 0.521576 + 0.167755I
a = −0.096220 + 0.277378I
b = 1.270040 − 0.515394I
−3.42563 + 0.66649I −0.45885 − 2.75418I
u = 0.521576 − 0.167755I
a = −0.096220 − 0.277378I
b = 1.270040 + 0.515394I
−3.42563 − 0.66649I −0.45885 + 2.75418I
u = 0.25366 + 1.45092I
a = −1.054440 + 0.073125I
b = −0.995392 + 0.395885I
−8.80871 − 0.38474I 0
u = 0.25366 − 1.45092I
a = −1.054440 − 0.073125I
b = −0.995392 − 0.395885I
−8.80871 + 0.38474I 0
u = −0.35205 + 1.43479I
a = 1.185550 + 0.416143I
b = 1.08229 + 1.21643I
−4.32526 − 6.46466I 0
u = −0.35205 − 1.43479I
a = 1.185550 − 0.416143I
b = 1.08229 − 1.21643I
−4.32526 + 6.46466I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06057 + 1.48332I
a = −0.091101 + 0.234604I
b = −0.246697 + 0.908005I
−6.80931 − 4.55618I 0
u = −0.06057 − 1.48332I
a = −0.091101 − 0.234604I
b = −0.246697 − 0.908005I
−6.80931 + 4.55618I 0
u = 0.04907 + 1.48476I
a = 0.0491940 − 0.0865460I
b = 0.335989 + 0.737270I
−11.7320 + 10.3068I 0
u = 0.04907 − 1.48476I
a = 0.0491940 + 0.0865460I
b = 0.335989 − 0.737270I
−11.7320 − 10.3068I 0
u = 0.06103 + 1.49160I
a = −0.055806 + 0.650492I
b = 0.287980 + 0.259097I
−7.66364 − 1.37063I 0
u = 0.06103 − 1.49160I
a = −0.055806 − 0.650492I
b = 0.287980 − 0.259097I
−7.66364 + 1.37063I 0
u = −0.191515 + 0.006450I
a = −0.78891 + 3.15074I
b = −0.814477 + 0.455138I
1.22097 − 1.26060I 6.72230 − 0.52246I
u = −0.191515 − 0.006450I
a = −0.78891 − 3.15074I
b = −0.814477 − 0.455138I
1.22097 + 1.26060I 6.72230 + 0.52246I
u = −0.0880343 + 0.0402927I
a = −3.45905 + 11.49730I
b = 0.546837 − 0.884330I
−1.92018 − 4.82836I −0.56326 + 7.48494I
u = −0.0880343 − 0.0402927I
a = −3.45905 − 11.49730I
b = 0.546837 + 0.884330I
−1.92018 + 4.82836I −0.56326 − 7.48494I
18
II. I
u
2
= h−17u
25
− 137u
24
+ · · · + 31b − 49, −127u
25
− 274u
24
+ · · · + 31a −
315, u
26
+ u
25
+ · · · + 6u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
4
=
4.09677u
25
+ 8.83871u
24
+ ··· + 15.0323u + 10.1613
0.548387u
25
+ 4.41935u
24
+ ··· + 17.5161u + 1.58065
a
2
=
4.16129u
25
+ 3.06452u
24
+ ··· − 12.6129u + 8.93548
2.74194u
25
+ 2.09677u
24
+ ··· − 6.41935u − 3.09677
a
9
=
−u
4
− u
2
+ 1
−u
4
− 2u
2
a
5
=
3.61290u
25
+ 7.64516u
24
+ ··· + 14.8710u + 9.35484
−0.903226u
25
+ 1.83871u
24
+ ··· + 14.0323u + 1.16129
a
11
=
−u
u
3
+ u
a
3
=
4.09677u
25
+ 6.83871u
24
+ ··· + 8.03226u + 9.16129
0.548387u
25
+ 3.41935u
24
+ ··· + 12.5161u + 0.580645
a
6
=
−0.129032u
25
− 2.45161u
24
+ ··· − 1.70968u − 10.5484
0.870968u
25
− 2.45161u
24
+ ··· − 14.7097u − 0.548387
a
10
=
−1.06452u
25
− 3.22581u
24
+ ··· − 3.35484u − 13.7742
2u
25
+ 2u
24
+ ··· − u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
7
31
u
25
+
474
31
u
24
+ ··· +
2038
31
u +
53
31
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 12u
25
+ ··· + 6u − 1
c
2
u
26
+ 14u
25
+ ··· − 5u − 1
c
3
u
26
+ u
25
+ ··· − 4u − 1
c
4
u
26
− 3u
24
+ ··· + u + 1
c
5
u
26
− u
25
+ ··· − u + 1
c
6
u
26
+ 3u
25
+ ··· + 9u − 1
c
7
u
26
+ u
25
+ ··· + 6u + 1
c
8
u
26
− u
25
+ ··· + 6u + 1
c
9
u
26
− u
25
+ ··· − 3u
2
+ 1
c
10
u
26
+ u
25
+ ··· + u + 1
c
11
, c
12
u
26
− u
25
+ ··· − 6u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 12y
25
+ ··· − 12y + 1
c
2
y
26
+ 10y
25
+ ··· − 7y + 1
c
3
y
26
+ 3y
25
+ ··· + 8y + 1
c
4
y
26
− 6y
25
+ ··· − y + 1
c
5
, c
10
y
26
− 17y
25
+ ··· − 37y + 1
c
6
y
26
+ 7y
25
+ ··· − 9y + 1
c
7
, c
11
, c
12
y
26
+ 25y
25
+ ··· − 42y + 1
c
8
y
26
− y
25
+ ··· − 44y + 1
c
9
y
26
− y
25
+ ··· − 6y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570324 + 0.774756I
a = 0.062953 + 0.322877I
b = 0.056432 − 0.135013I
0.88149 − 2.48442I 4.82711 − 6.97053I
u = −0.570324 − 0.774756I
a = 0.062953 − 0.322877I
b = 0.056432 + 0.135013I
0.88149 + 2.48442I 4.82711 + 6.97053I
u = 0.194960 + 1.171460I
a = 0.116973 − 0.371816I
b = −0.876393 − 0.265512I
−4.09956 + 6.26420I −2.09614 − 7.20711I
u = 0.194960 − 1.171460I
a = 0.116973 + 0.371816I
b = −0.876393 + 0.265512I
−4.09956 − 6.26420I −2.09614 + 7.20711I
u = −0.153778 + 1.219990I
a = 2.37249 + 0.84166I
b = 1.61699 + 0.69044I
−1.55816 + 0.01449I 1.65823 − 1.09511I
u = −0.153778 − 1.219990I
a = 2.37249 − 0.84166I
b = 1.61699 − 0.69044I
−1.55816 − 0.01449I 1.65823 + 1.09511I
u = 0.218488 + 1.216950I
a = −2.50652 + 2.19733I
b = −1.08292 + 2.37475I
−3.91127 − 2.95711I −1.88290 + 5.00367I
u = 0.218488 − 1.216950I
a = −2.50652 − 2.19733I
b = −1.08292 − 2.37475I
−3.91127 + 2.95711I −1.88290 − 5.00367I
u = −0.654711 + 0.361426I
a = 0.395064 + 0.193261I
b = −0.060892 − 0.776077I
1.07061 − 2.37540I 1.32666 + 13.27884I
u = −0.654711 − 0.361426I
a = 0.395064 − 0.193261I
b = −0.060892 + 0.776077I
1.07061 + 2.37540I 1.32666 − 13.27884I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.743243
a = −0.836776
b = −0.457861
3.82899 11.0490
u = −0.294316 + 1.257160I
a = −0.562419 + 0.684762I
b = −0.240717 + 0.868005I
−0.03821 − 3.75384I 6.23391 + 3.06632I
u = −0.294316 − 1.257160I
a = −0.562419 − 0.684762I
b = −0.240717 − 0.868005I
−0.03821 + 3.75384I 6.23391 − 3.06632I
u = 0.672573 + 0.137645I
a = 0.182295 + 0.187445I
b = 0.37093 − 2.28388I
−0.69656 + 6.11279I 2.04958 − 8.84990I
u = 0.672573 − 0.137645I
a = 0.182295 − 0.187445I
b = 0.37093 + 2.28388I
−0.69656 − 6.11279I 2.04958 + 8.84990I
u = 0.514521 + 0.377424I
a = −1.108700 − 0.464445I
b = −0.016374 + 0.497312I
−1.75749 − 3.69110I 1.92676 + 2.35151I
u = 0.514521 − 0.377424I
a = −1.108700 + 0.464445I
b = −0.016374 − 0.497312I
−1.75749 + 3.69110I 1.92676 − 2.35151I
u = −0.049404 + 1.365310I
a = −1.155230 + 0.503664I
b = −1.148720 − 0.569898I
−9.35257 − 0.74122I −6.47141 + 0.74679I
u = −0.049404 − 1.365310I
a = −1.155230 − 0.503664I
b = −1.148720 + 0.569898I
−9.35257 + 0.74122I −6.47141 − 0.74679I
u = 0.286679 + 1.355700I
a = 2.57289 − 1.48433I
b = 1.52253 − 2.27511I
−5.43871 + 9.62915I −3.03359 − 9.44298I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.286679 − 1.355700I
a = 2.57289 + 1.48433I
b = 1.52253 + 2.27511I
−5.43871 − 9.62915I −3.03359 + 9.44298I
u = −0.32240 + 1.40604I
a = −1.41858 − 0.53533I
b = −1.22496 − 1.36260I
−4.44908 − 6.18514I −6.46604 − 0.51526I
u = −0.32240 − 1.40604I
a = −1.41858 + 0.53533I
b = −1.22496 + 1.36260I
−4.44908 + 6.18514I −6.46604 + 0.51526I
u = 0.10623 + 1.47024I
a = −0.036770 + 0.515141I
b = 0.412524 + 0.092105I
−8.02822 − 1.57552I −8.71426 + 9.37859I
u = 0.10623 − 1.47024I
a = −0.036770 − 0.515141I
b = 0.412524 − 0.092105I
−8.02822 + 1.57552I −8.71426 − 9.37859I
u = −0.153809
a = 8.00790
b = −1.19899
−4.74050 −8.76440
24
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 12u
25
+ ··· + 6u − 1)(u
140
+ 11u
139
+ ··· − 24651u − 2513)
c
2
(u
26
+ 14u
25
+ ··· − 5u − 1)(u
140
− 9u
139
+ ··· + 270u + 7)
c
3
(u
26
+ u
25
+ ··· − 4u − 1)(u
140
− 8u
138
+ ··· − 94043u + 17197)
c
4
(u
26
− 3u
24
+ ··· + u + 1)(u
140
+ 3u
139
+ ··· + 8798u − 3781)
c
5
(u
26
− u
25
+ ··· − u + 1)(u
140
− 50u
138
+ ··· − 4u − 1)
c
6
(u
26
+ 3u
25
+ ··· + 9u − 1)(u
140
+ 2u
139
+ ··· − 20u − 1)
c
7
(u
26
+ u
25
+ ··· + 6u + 1)(u
140
− 2u
139
+ ··· + 29u − 1)
c
8
(u
26
− u
25
+ ··· + 6u + 1)(u
140
+ 2u
139
+ ··· + 1113371u − 44197)
c
9
(u
26
− u
25
+ ··· − 3u
2
+ 1)(u
140
− 2u
139
+ ··· + 71035u − 11231)
c
10
(u
26
+ u
25
+ ··· + u + 1)(u
140
− 50u
138
+ ··· − 4u − 1)
c
11
, c
12
(u
26
− u
25
+ ··· − 6u + 1)(u
140
− 2u
139
+ ··· + 29u − 1)
25
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
+ 12y
25
+ ··· − 12y + 1)
· (y
140
+ y
139
+ ··· − 2719370831y + 6315169)
c
2
(y
26
+ 10y
25
+ ··· − 7y + 1)(y
140
+ 15y
139
+ ··· − 2382y + 49)
c
3
(y
26
+ 3y
25
+ ··· + 8y + 1)
· (y
140
− 16y
139
+ ··· − 26838854679y + 295736809)
c
4
(y
26
− 6y
25
+ ··· − y + 1)
· (y
140
− 25y
139
+ ··· − 1468752308y + 14295961)
c
5
, c
10
(y
26
− 17y
25
+ ··· − 37y + 1)(y
140
− 100y
139
+ ··· − 192y + 1)
c
6
(y
26
+ 7y
25
+ ··· − 9y + 1)(y
140
+ 8y
139
+ ··· + 32y + 1)
c
7
, c
11
, c
12
(y
26
+ 25y
25
+ ··· − 42y + 1)(y
140
+ 122y
139
+ ··· − 197y + 1)
c
8
(y
26
− y
25
+ ··· − 44y + 1)
· (y
140
− 44y
139
+ ··· − 361041802395y + 1953374809)
c
9
(y
26
− y
25
+ ··· − 6y + 1)
· (y
140
− 28y
139
+ ··· − 7929328317y + 126135361)
26
