12a
0334
(K12a
0334
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 10 2 4 7 12 1 9 5
Solving Sequence
3,6
2 7
1,10
11 5 4 8 12 9
c
2
c
6
c
1
c
10
c
5
c
4
c
7
c
12
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.06298 × 10
20
u
52
+ 1.60476 × 10
20
u
51
+ ··· + 4.29074 × 10
20
b − 4.12339 × 10
20
,
1.99532 × 10
20
u
52
+ 2.05042 × 10
20
u
51
+ ··· + 2.14537 × 10
20
a − 6.01161 × 10
20
, u
53
+ u
52
+ ··· − u + 1i
I
u
2
= h8.20708 × 10
90
u
81
+ 1.10415 × 10
91
u
80
+ ··· + 2.42746 × 10
91
b + 4.21770 × 10
91
,
− 1.38634 × 10
91
u
81
+ 4.31343 × 10
91
u
80
+ ··· + 4.12668 × 10
92
a + 3.38112 × 10
93
,
u
82
+ u
81
+ ··· + 80u + 17i
I
u
3
= ha
4
− a
3
u + 2a
2
− au + b − a + u + 2, a
5
+ a
4
+ 2a
3
+ a
2
+ a + 1, u
2
+ 1i
I
u
4
= h4b − 1, 2a − 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 146 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
= h2.06 × 10
20
u
52
+ 1.60 × 10
20
u
51
+ · · · + 4.29 × 10
20
b − 4.12 × 10
20
, 2.00 ×
10
20
u
52
+2.05×10
20
u
51
+· · ·+2.15×10
20
a−6.01×10
20
, u
53
+u
52
+· · ·−u+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
−0.930057u
52
− 0.955742u
51
+ ··· − 6.21940u + 2.80213
−0.480798u
52
− 0.374006u
51
+ ··· − 2.83945u + 0.960996
a
11
=
−1.04871u
52
− 0.780472u
51
+ ··· − 8.33773u + 3.26868
0.0764895u
52
+ 0.115237u
51
+ ··· − 1.80155u + 0.599031
a
5
=
0.000620096u
52
+ 0.181918u
51
+ ··· − 5.81545u + 4.31836
−0.579013u
52
− 0.551580u
51
+ ··· − 2.53269u + 0.624293
a
4
=
−0.0312500u
51
− 0.0312500u
50
+ ··· + 0.0312500u + 0.968750
−u
2
a
8
=
−0.0312500u
52
− 0.0312500u
51
+ ··· + 0.0312500u
2
+ 1.96875u
u
a
12
=
−0.295508u
52
− 0.746196u
51
+ ··· − 5.12386u + 1.87778
0.0786937u
52
− 0.0771515u
51
+ ··· − 0.889392u + 0.294843
a
9
=
0.0312500u
52
+ 0.0312500u
51
+ ··· − 0.0312500u
2
− 1.96875u
−u
5
− u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2512848915749488921699
1716297684974631141376
u
52
+
46238999124133173149
13408575663864305792
u
51
+ ··· +
6617581644865299112413
858148842487315570688
u −
2419364251029364180253
1716297684974631141376
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
53
+ 23u
52
+ ··· − 11u − 1
c
2
, c
3
, c
6
c
7
u
53
− u
52
+ ··· − u − 1
c
4
2(2u
53
+ 7u
52
+ ··· − 449u − 106)
c
5
2(2u
53
+ 19u
52
+ ··· − 27u − 22)
c
9
, c
11
u
53
− 2u
52
+ ··· + 145u − 16
c
10
u
53
+ 9u
52
+ ··· + 44u − 32
c
12
u
53
− 11u
52
+ ··· + 12u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
53
+ 19y
52
+ ··· + 17y −1
c
2
, c
3
, c
6
c
7
y
53
+ 23y
52
+ ··· − 11y −1
c
4
4(4y
53
− 109y
52
+ ··· + 600797y −11236)
c
5
4(4y
53
− 253y
52
+ ··· − 47627y −484)
c
9
, c
11
y
53
− 40y
52
+ ··· + 9057y −256
c
10
y
53
+ 9y
52
+ ··· − 3504y −1024
c
12
y
53
+ 5y
52
+ ··· − 40y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.668388 + 0.804816I
a = −0.286952 − 0.841129I
b = 1.30427 − 1.07663I
3.52267 + 5.89067I 5.80325 − 7.99379I
u = 0.668388 − 0.804816I
a = −0.286952 + 0.841129I
b = 1.30427 + 1.07663I
3.52267 − 5.89067I 5.80325 + 7.99379I
u = 0.885875 + 0.312846I
a = 1.58012 + 0.57776I
b = 0.249661 + 1.267570I
−1.48025 − 8.82229I 2.86158 + 4.69458I
u = 0.885875 − 0.312846I
a = 1.58012 − 0.57776I
b = 0.249661 − 1.267570I
−1.48025 + 8.82229I 2.86158 − 4.69458I
u = 0.488135 + 0.771928I
a = −0.297346 + 1.142240I
b = −0.098380 + 1.389640I
−1.79557 + 4.79512I −1.34672 − 10.51121I
u = 0.488135 − 0.771928I
a = −0.297346 − 1.142240I
b = −0.098380 − 1.389640I
−1.79557 − 4.79512I −1.34672 + 10.51121I
u = −1.082370 + 0.233203I
a = −0.313022 − 0.099491I
b = −0.116005 + 0.128996I
0.067068 + 0.198707I −6.3019 − 29.2641I
u = −1.082370 − 0.233203I
a = −0.313022 + 0.099491I
b = −0.116005 − 0.128996I
0.067068 − 0.198707I −6.3019 + 29.2641I
u = −0.686446 + 0.549470I
a = 0.797892 − 0.702983I
b = −0.185476 − 0.857683I
1.60260 − 1.16734I 6.57040 + 3.72731I
u = −0.686446 − 0.549470I
a = 0.797892 + 0.702983I
b = −0.185476 + 0.857683I
1.60260 + 1.16734I 6.57040 − 3.72731I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328034 + 1.084130I
a = 0.133474 − 1.011380I
b = −0.127047 − 0.619492I
−10.08720 + 6.08959I −7.49622 − 8.58423I
u = 0.328034 − 1.084130I
a = 0.133474 + 1.011380I
b = −0.127047 + 0.619492I
−10.08720 − 6.08959I −7.49622 + 8.58423I
u = −0.639214 + 0.938411I
a = −0.498896 + 0.213519I
b = 0.042019 + 1.288230I
2.69803 − 4.29240I 5.39369 + 5.58339I
u = −0.639214 − 0.938411I
a = −0.498896 − 0.213519I
b = 0.042019 − 1.288230I
2.69803 + 4.29240I 5.39369 − 5.58339I
u = −0.833257 + 0.778192I
a = 0.816570 − 0.328287I
b = 0.235105 − 0.990515I
1.75225 − 0.51446I 5.84851 − 3.70601I
u = −0.833257 − 0.778192I
a = 0.816570 + 0.328287I
b = 0.235105 + 0.990515I
1.75225 + 0.51446I 5.84851 + 3.70601I
u = −0.526363 + 0.667694I
a = 1.77266 + 2.14536I
b = 1.63014 + 0.06741I
−0.55286 − 1.95233I −0.23618 − 5.29610I
u = −0.526363 − 0.667694I
a = 1.77266 − 2.14536I
b = 1.63014 − 0.06741I
−0.55286 + 1.95233I −0.23618 + 5.29610I
u = −0.355899 + 1.098010I
a = −0.914127 − 0.977251I
b = −0.473545 − 0.727776I
−10.41080 + 2.52581I −5.67621 + 2.33570I
u = −0.355899 − 1.098010I
a = −0.914127 + 0.977251I
b = −0.473545 + 0.727776I
−10.41080 − 2.52581I −5.67621 − 2.33570I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734405 + 0.375376I
a = −1.167300 − 0.462515I
b = 0.125668 − 1.354120I
2.50533 − 3.21218I 6.47711 + 3.14636I
u = 0.734405 − 0.375376I
a = −1.167300 + 0.462515I
b = 0.125668 + 1.354120I
2.50533 + 3.21218I 6.47711 − 3.14636I
u = −0.476735 + 1.090590I
a = 0.837733 + 0.594251I
b = −0.168261 + 0.426397I
−4.11384 − 2.65488I 0
u = −0.476735 − 1.090590I
a = 0.837733 − 0.594251I
b = −0.168261 − 0.426397I
−4.11384 + 2.65488I 0
u = 0.745113 + 0.940742I
a = 0.227342 + 1.177620I
b = −1.20324 + 1.37822I
0.77711 + 11.19170I 0. − 10.51592I
u = 0.745113 − 0.940742I
a = 0.227342 − 1.177620I
b = −1.20324 − 1.37822I
0.77711 − 11.19170I 0. + 10.51592I
u = 0.012932 + 0.796961I
a = −0.54661 + 1.60348I
b = −0.302926 + 0.786949I
−8.28369 − 4.33865I 3.59300 + 2.46883I
u = 0.012932 − 0.796961I
a = −0.54661 − 1.60348I
b = −0.302926 − 0.786949I
−8.28369 + 4.33865I 3.59300 − 2.46883I
u = 0.518764 + 1.094270I
a = −1.11519 + 0.88338I
b = −1.165260 − 0.045151I
−3.47528 + 6.51067I 0. − 9.23313I
u = 0.518764 − 1.094270I
a = −1.11519 − 0.88338I
b = −1.165260 + 0.045151I
−3.47528 − 6.51067I 0. + 9.23313I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.360598 + 0.663100I
a = −0.1286910 − 0.0067991I
b = −1.49656 + 0.86506I
−3.51640 + 1.45258I −4.16595 − 4.82658I
u = 0.360598 − 0.663100I
a = −0.1286910 + 0.0067991I
b = −1.49656 − 0.86506I
−3.51640 − 1.45258I −4.16595 + 4.82658I
u = −0.502393 + 1.140790I
a = −0.078413 − 0.487074I
b = −1.30590 − 1.98115I
−7.66286 − 6.07116I 0
u = −0.502393 − 1.140790I
a = −0.078413 + 0.487074I
b = −1.30590 + 1.98115I
−7.66286 + 6.07116I 0
u = 0.535551 + 1.136960I
a = 1.04842 − 2.35451I
b = 2.80983 − 1.99427I
−4.81372 + 7.90988I 0
u = 0.535551 − 1.136960I
a = 1.04842 + 2.35451I
b = 2.80983 + 1.99427I
−4.81372 − 7.90988I 0
u = −0.532362 + 1.165170I
a = −0.316339 − 0.652315I
b = 0.45485 − 1.39382I
−7.14528 − 10.40640I 0
u = −0.532362 − 1.165170I
a = −0.316339 + 0.652315I
b = 0.45485 + 1.39382I
−7.14528 + 10.40640I 0
u = −0.507169 + 0.506059I
a = −2.30852 − 2.83554I
b = −1.296690 + 0.107271I
−0.684418 − 0.948826I −0.1446 + 19.9877I
u = −0.507169 − 0.506059I
a = −2.30852 + 2.83554I
b = −1.296690 − 0.107271I
−0.684418 + 0.948826I −0.1446 − 19.9877I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.575449 + 1.149730I
a = 0.566641 + 0.921275I
b = −0.57415 + 1.69849I
−2.39951 + 8.82556I 0
u = 0.575449 − 1.149730I
a = 0.566641 − 0.921275I
b = −0.57415 − 1.69849I
−2.39951 − 8.82556I 0
u = −0.570687 + 1.179090I
a = −0.317122 + 0.893231I
b = 1.31695 + 2.13247I
−2.39245 − 13.37930I 0
u = −0.570687 − 1.179090I
a = −0.317122 − 0.893231I
b = 1.31695 − 2.13247I
−2.39245 + 13.37930I 0
u = −0.585845 + 1.224270I
a = 0.230425 − 1.261910I
b = −1.35761 − 2.39508I
−7.1037 − 19.7990I 0
u = −0.585845 − 1.224270I
a = 0.230425 + 1.261910I
b = −1.35761 + 2.39508I
−7.1037 + 19.7990I 0
u = 0.582720 + 1.244220I
a = 0.054678 − 0.544611I
b = 0.929131 − 0.998070I
−6.21709 + 11.57740I 0
u = 0.582720 − 1.244220I
a = 0.054678 + 0.544611I
b = 0.929131 + 0.998070I
−6.21709 − 11.57740I 0
u = 0.518365 + 0.233763I
a = 1.56899 − 0.12441I
b = −0.413003 − 0.501825I
−2.00575 − 1.39990I 0.13252 + 2.66596I
u = 0.518365 − 0.233763I
a = 1.56899 + 0.12441I
b = −0.413003 + 0.501825I
−2.00575 + 1.39990I 0.13252 − 2.66596I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.094948 + 0.500791I
a = 1.09549 − 1.74373I
b = −0.184132 − 0.666756I
−1.65145 − 1.39860I −0.71853 + 3.02391I
u = 0.094948 − 0.500791I
a = 1.09549 + 1.74373I
b = −0.184132 + 0.666756I
−1.65145 + 1.39860I −0.71853 − 3.02391I
u = −0.501079
a = 0.616206
b = 0.491104
0.979888 11.0840
10
II. I
u
2
= h8.21 × 10
90
u
81
+ 1.10 × 10
91
u
80
+ · · · + 2.43 × 10
91
b + 4.22 ×
10
91
, −1.39 × 10
91
u
81
+ 4.31 × 10
91
u
80
+ · · · + 4.13 × 10
92
a + 3.38 ×
10
93
, u
82
+ u
81
+ · · · + 80u + 17i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
0.0335946u
81
− 0.104526u
80
+ ··· − 30.8539u − 8.19333
−0.338094u
81
− 0.454858u
80
+ ··· − 18.9801u − 1.73750
a
11
=
−0.115101u
81
− 0.232328u
80
+ ··· − 37.2193u − 9.00600
−0.372443u
81
− 0.392556u
80
+ ··· − 10.9756u − 0.449622
a
5
=
−0.312769u
81
− 0.318140u
80
+ ··· − 9.62030u − 2.11610
0.0743269u
81
+ 0.840095u
80
+ ··· + 69.4199u + 14.0460
a
4
=
−0.146314u
81
− 0.133467u
80
+ ··· + 2.18765u + 1.24972
0.0959173u
81
+ 0.176156u
80
+ ··· + 1.45965u + 0.781618
a
8
=
0.0588235u
81
+ 0.0588235u
80
+ ··· + 14.1176u + 4.70588
0.0128460u
81
+ 0.108763u
80
+ ··· + 11.9548u + 2.48733
a
12
=
−0.0580723u
81
− 0.149404u
80
+ ··· − 25.1399u − 5.85705
−0.235936u
81
− 0.0863109u
80
+ ··· + 11.0930u + 3.00489
a
9
=
0.0214155u
81
− 0.0371577u
80
+ ··· − 21.0094u − 6.33648
−0.0261267u
81
− 0.204159u
80
+ ··· − 15.5248u − 3.12218
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.241656u
81
− 0.239165u
80
+ ··· − 13.5265u + 0.445704
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
82
+ 47u
81
+ ··· + 1760u + 289
c
2
, c
3
, c
6
c
7
u
82
− u
81
+ ··· − 80u + 17
c
4
(u
41
− u
40
+ ··· + 289u + 77)
2
c
5
(u
41
− 3u
40
+ ··· − 129u + 31)
2
c
9
, c
11
(u
41
− u
40
+ ··· + 7u + 1)
2
c
10
(u
41
+ 7u
40
+ ··· − u − 1)
2
c
12
(u
41
+ 3u
40
+ ··· + u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
82
− 25y
81
+ ··· + 237460y + 83521
c
2
, c
3
, c
6
c
7
y
82
+ 47y
81
+ ··· + 1760y + 289
c
4
(y
41
− 25y
40
+ ··· − 76331y −5929)
2
c
5
(y
41
− 45y
40
+ ··· + 24081y −961)
2
c
9
, c
11
(y
41
− 29y
40
+ ··· − 7y −1)
2
c
10
(y
41
+ 3y
40
+ ··· − 7y −1)
2
c
12
(y
41
+ 7y
40
+ ··· − 3y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.985492 + 0.187431I
a = −0.601056 − 0.061606I
b = −0.123823 − 0.448139I
−2.99088 − 5.96215I −2.24062 + 8.95093I
u = 0.985492 − 0.187431I
a = −0.601056 + 0.061606I
b = −0.123823 + 0.448139I
−2.99088 + 5.96215I −2.24062 − 8.95093I
u = 0.653301 + 0.771321I
a = −0.722807 − 0.195367I
b = 0.054351 − 1.396580I
3.61608 − 0.82118I 7.22724 + 0.I
u = 0.653301 − 0.771321I
a = −0.722807 + 0.195367I
b = 0.054351 + 1.396580I
3.61608 + 0.82118I 7.22724 + 0.I
u = −0.945615 + 0.225342I
a = 1.57967 − 0.70411I
b = 0.241504 − 1.236450I
−4.0673 + 14.2581I 0. − 8.23400I
u = −0.945615 − 0.225342I
a = 1.57967 + 0.70411I
b = 0.241504 + 1.236450I
−4.0673 − 14.2581I 0. + 8.23400I
u = −0.439234 + 0.938019I
a = −0.92316 − 1.30144I
b = −1.227420 − 0.040586I
−1.28254 − 2.04071I 0
u = −0.439234 − 0.938019I
a = −0.92316 + 1.30144I
b = −1.227420 + 0.040586I
−1.28254 + 2.04071I 0
u = 0.276393 + 0.921871I
a = 0.764527 − 0.804946I
b = −0.295593 − 0.452709I
−1.82452 − 1.30012I 0. + 4.02639I
u = 0.276393 − 0.921871I
a = 0.764527 + 0.804946I
b = −0.295593 + 0.452709I
−1.82452 + 1.30012I 0. − 4.02639I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.701838 + 0.621645I
a = −0.227828 + 0.774426I
b = 1.052510 + 0.712403I
3.61608 − 0.82118I 7.22724 + 1.08764I
u = −0.701838 − 0.621645I
a = −0.227828 − 0.774426I
b = 1.052510 − 0.712403I
3.61608 + 0.82118I 7.22724 − 1.08764I
u = 0.845750 + 0.662432I
a = 1.117590 + 0.331221I
b = 0.314324 + 1.186560I
1.60464 − 5.37316I 0
u = 0.845750 − 0.662432I
a = 1.117590 − 0.331221I
b = 0.314324 − 1.186560I
1.60464 + 5.37316I 0
u = 0.125396 + 0.890425I
a = 0.839410 + 1.046050I
b = −3.40553 + 2.53563I
−5.21373 + 0.70569I −0.73633 + 1.49377I
u = 0.125396 − 0.890425I
a = 0.839410 − 1.046050I
b = −3.40553 − 2.53563I
−5.21373 − 0.70569I −0.73633 − 1.49377I
u = 0.064515 + 1.103490I
a = −0.837111 + 0.699746I
b = −4.56897 + 3.50244I
−5.21373 − 0.70569I 0
u = 0.064515 − 1.103490I
a = −0.837111 − 0.699746I
b = −4.56897 − 3.50244I
−5.21373 + 0.70569I 0
u = −0.855068 + 0.256917I
a = −1.132500 + 0.650238I
b = 0.092057 + 1.325760I
0.36044 + 8.13712I 2.61173 − 7.81814I
u = −0.855068 − 0.256917I
a = −1.132500 − 0.650238I
b = 0.092057 − 1.325760I
0.36044 − 8.13712I 2.61173 + 7.81814I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.350317 + 1.060040I
a = 0.294171 + 0.799722I
b = −1.38699 + 1.41892I
−4.64726 + 0.57043I 0
u = 0.350317 − 1.060040I
a = 0.294171 − 0.799722I
b = −1.38699 − 1.41892I
−4.64726 − 0.57043I 0
u = 0.808095 + 0.314434I
a = 1.017030 + 0.892959I
b = 0.074269 + 0.903046I
0.08231 − 3.66290I 3.58979 + 1.40051I
u = 0.808095 − 0.314434I
a = 1.017030 − 0.892959I
b = 0.074269 − 0.903046I
0.08231 + 3.66290I 3.58979 − 1.40051I
u = −0.785972 + 0.826020I
a = 0.209581 − 1.078080I
b = −0.99508 − 1.03869I
1.60464 − 5.37316I 0
u = −0.785972 − 0.826020I
a = 0.209581 + 1.078080I
b = −0.99508 + 1.03869I
1.60464 + 5.37316I 0
u = 0.410177 + 1.065600I
a = −0.159381 + 0.423837I
b = −1.60715 + 1.91064I
−4.93281 + 1.58754I 0
u = 0.410177 − 1.065600I
a = −0.159381 − 0.423837I
b = −1.60715 − 1.91064I
−4.93281 − 1.58754I 0
u = −0.483561 + 1.036610I
a = 1.18463 + 2.48322I
b = 3.24923 + 1.43098I
−2.27217 − 3.12959I 0
u = −0.483561 − 1.036610I
a = 1.18463 − 2.48322I
b = 3.24923 − 1.43098I
−2.27217 + 3.12959I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.003226 + 1.159550I
a = 0.360311 − 0.536547I
b = −0.418853 − 0.128520I
−2.29574 − 1.43665I 0
u = −0.003226 − 1.159550I
a = 0.360311 + 0.536547I
b = −0.418853 + 0.128520I
−2.29574 + 1.43665I 0
u = 0.690646 + 0.474659I
a = −0.432606 + 0.962142I
b = −0.916049 − 0.123060I
−6.24124 + 3.82132I −6.20968 − 8.07346I
u = 0.690646 − 0.474659I
a = −0.432606 − 0.962142I
b = −0.916049 + 0.123060I
−6.24124 − 3.82132I −6.20968 + 8.07346I
u = −0.428801 + 1.080980I
a = −0.312278 + 0.887837I
b = 1.98200 + 2.21193I
−4.46894 − 4.49890I 0
u = −0.428801 − 1.080980I
a = −0.312278 − 0.887837I
b = 1.98200 − 2.21193I
−4.46894 + 4.49890I 0
u = 0.312579 + 1.137150I
a = 0.75573 − 2.74932I
b = 4.48388 − 3.25580I
−6.34069 0
u = 0.312579 − 1.137150I
a = 0.75573 + 2.74932I
b = 4.48388 + 3.25580I
−6.34069 0
u = −0.562810 + 1.043120I
a = 0.556473 − 0.818950I
b = −0.62933 − 1.44802I
0.08231 − 3.66290I 0
u = −0.562810 − 1.043120I
a = 0.556473 + 0.818950I
b = −0.62933 + 1.44802I
0.08231 + 3.66290I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.776911 + 0.203083I
a = 1.109940 + 0.191140I
b = −0.409102 + 0.674856I
−4.33918 + 5.53805I −3.90913 − 6.85663I
u = −0.776911 − 0.203083I
a = 1.109940 − 0.191140I
b = −0.409102 − 0.674856I
−4.33918 − 5.53805I −3.90913 + 6.85663I
u = 0.487357 + 1.094930I
a = −0.247123 + 0.713016I
b = 0.39100 + 1.54528I
−4.33918 + 5.53805I 0
u = 0.487357 − 1.094930I
a = −0.247123 − 0.713016I
b = 0.39100 − 1.54528I
−4.33918 − 5.53805I 0
u = −0.376610 + 1.148160I
a = −0.138160 − 0.597899I
b = 0.70047 − 1.72101I
−8.54703 − 1.92366I 0
u = −0.376610 − 1.148160I
a = −0.138160 + 0.597899I
b = 0.70047 + 1.72101I
−8.54703 + 1.92366I 0
u = 0.249681 + 1.185590I
a = −0.604777 + 0.500748I
b = −0.992600 − 0.018721I
−4.64726 − 0.57043I 0
u = 0.249681 − 1.185590I
a = −0.604777 − 0.500748I
b = −0.992600 + 0.018721I
−4.64726 + 0.57043I 0
u = 0.725676 + 0.258615I
a = −3.83605 + 1.40458I
b = −1.267900 − 0.049606I
−2.27217 − 3.12959I 15.2117 − 9.6931I
u = 0.725676 − 0.258615I
a = −3.83605 − 1.40458I
b = −1.267900 + 0.049606I
−2.27217 + 3.12959I 15.2117 + 9.6931I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.526926 + 1.115530I
a = 0.224956 − 1.260480I
b = −1.82173 − 2.23021I
−9.17741 − 9.99849I 0
u = −0.526926 − 1.115530I
a = 0.224956 + 1.260480I
b = −1.82173 + 2.23021I
−9.17741 + 9.99849I 0
u = 0.561316 + 1.103110I
a = −0.316268 − 0.887342I
b = 1.48519 − 1.97154I
0.36044 + 8.13712I 0
u = 0.561316 − 1.103110I
a = −0.316268 + 0.887342I
b = 1.48519 + 1.97154I
0.36044 − 8.13712I 0
u = −0.332047 + 1.197330I
a = −0.210447 − 0.558443I
b = −1.56775 − 2.42710I
−8.54703 + 1.92366I 0
u = −0.332047 − 1.197330I
a = −0.210447 + 0.558443I
b = −1.56775 + 2.42710I
−8.54703 − 1.92366I 0
u = 0.592012 + 1.131900I
a = 0.293407 − 0.411857I
b = 1.078880 − 0.241257I
−8.20023 + 1.30258I 0
u = 0.592012 − 1.131900I
a = 0.293407 + 0.411857I
b = 1.078880 + 0.241257I
−8.20023 − 1.30258I 0
u = −0.276176 + 1.249140I
a = 0.687575 + 0.509103I
b = −0.180816 + 0.280837I
−4.46894 + 4.49890I 0
u = −0.276176 − 1.249140I
a = 0.687575 − 0.509103I
b = −0.180816 − 0.280837I
−4.46894 − 4.49890I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.651322 + 0.305211I
a = 1.92823 − 0.30964I
b = 0.194539 − 1.371550I
−6.83660 + 5.39109I −2.16171 − 3.24475I
u = −0.651322 − 0.305211I
a = 1.92823 + 0.30964I
b = 0.194539 + 1.371550I
−6.83660 − 5.39109I −2.16171 + 3.24475I
u = 0.193146 + 1.277710I
a = −0.738960 + 0.797259I
b = −0.481291 + 0.613476I
−6.83660 − 5.39109I 0
u = 0.193146 − 1.277710I
a = −0.738960 − 0.797259I
b = −0.481291 − 0.613476I
−6.83660 + 5.39109I 0
u = −0.672119 + 0.169109I
a = 0.724846 + 0.176406I
b = −0.697933 − 0.732080I
−4.93281 + 1.58754I −5.30506 − 0.71829I
u = −0.672119 − 0.169109I
a = 0.724846 − 0.176406I
b = −0.697933 + 0.732080I
−4.93281 − 1.58754I −5.30506 + 0.71829I
u = 0.607355 + 0.327938I
a = 1.87061 − 1.49459I
b = 0.727822 − 0.468850I
−1.28254 − 2.04071I 0.19519 + 5.50278I
u = 0.607355 − 0.327938I
a = 1.87061 + 1.49459I
b = 0.727822 + 0.468850I
−1.28254 + 2.04071I 0.19519 − 5.50278I
u = 0.597296 + 1.171100I
a = 0.230966 + 1.257840I
b = −1.45496 + 2.23693I
−4.0673 + 14.2581I 0
u = 0.597296 − 1.171100I
a = 0.230966 − 1.257840I
b = −1.45496 − 2.23693I
−4.0673 − 14.2581I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598585 + 1.215200I
a = 0.074645 + 0.441170I
b = 0.786868 + 0.767933I
−2.99088 − 5.96215I 0
u = −0.598585 − 1.215200I
a = 0.074645 − 0.441170I
b = 0.786868 − 0.767933I
−2.99088 + 5.96215I 0
u = −0.124316 + 1.349810I
a = −0.286192 + 0.586042I
b = −0.299789 + 0.434089I
−6.24124 − 3.82132I 0
u = −0.124316 − 1.349810I
a = −0.286192 − 0.586042I
b = −0.299789 − 0.434089I
−6.24124 + 3.82132I 0
u = −0.306030 + 1.331880I
a = −0.863629 − 0.768297I
b = −0.541990 − 0.646446I
−9.17741 + 9.99849I 0
u = −0.306030 − 1.331880I
a = −0.863629 + 0.768297I
b = −0.541990 + 0.646446I
−9.17741 − 9.99849I 0
u = −0.094582 + 0.608934I
a = −0.827391 − 0.891283I
b = 0.95905 + 1.87981I
−2.29574 + 1.43665I 4.46376 − 2.78521I
u = −0.094582 − 0.608934I
a = −0.827391 + 0.891283I
b = 0.95905 − 1.87981I
−2.29574 − 1.43665I 4.46376 + 2.78521I
u = 0.31537 + 1.38799I
a = 0.039125 − 0.452126I
b = −0.127553 − 0.386108I
−8.20023 − 1.30258I 0
u = 0.31537 − 1.38799I
a = 0.039125 + 0.452126I
b = −0.127553 + 0.386108I
−8.20023 + 1.30258I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.410127 + 0.241813I
a = −1.21040 − 1.88967I
b = 0.050254 − 1.101790I
−1.82452 − 1.30012I 0.27514 + 4.02639I
u = −0.410127 − 0.241813I
a = −1.21040 + 1.88967I
b = 0.050254 + 1.101790I
−1.82452 + 1.30012I 0.27514 − 4.02639I
22
III.
I
u
3
= ha
4
− a
3
u + 2a
2
− au + b − a + u + 2, a
5
+ a
4
+ 2a
3
+ a
2
+ a + 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−1
a
7
=
u
0
a
1
=
0
−1
a
10
=
a
−a
4
+ a
3
u − 2a
2
+ au + a − u − 2
a
11
=
a
−a
4
+ a
3
u − 2a
2
+ au − u − 2
a
5
=
a
2
u
a
4
u − a
4
+ 2a
2
u − a
2
− au + a + 2u
a
4
=
−a
4
u
1
a
8
=
−a
4
+ u
−u
a
12
=
−a
4
−a
4
− 2a
2
− u − 2
a
9
=
−a
4
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
3
− 4a
2
− 4a − 8
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
c
2
, c
3
, c
6
c
7
(u
2
+ 1)
5
c
4
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
5
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
8
(u + 1)
10
c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
10
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
12
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y −1)
10
c
2
, c
3
, c
6
c
7
(y + 1)
10
c
4
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
5
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
9
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
12
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.339110 + 0.822375I
b = −1.09217 − 0.97690I
−3.61897 + 1.53058I −4.51511 − 4.43065I
u = 1.000000I
a = 0.339110 − 0.822375I
b = 0.00765 − 1.64293I
−3.61897 − 1.53058I −4.51511 + 4.43065I
u = 1.000000I
a = −0.766826
b = −4.28864 − 2.21774I
−5.69095 −5.48110
u = 1.000000I
a = −0.455697 + 1.200150I
b = −0.532590 + 1.109860I
−9.16243 − 4.40083I −8.74431 + 3.49859I
u = 1.000000I
a = −0.455697 − 1.200150I
b = −0.094259 − 0.272297I
−9.16243 + 4.40083I −8.74431 − 3.49859I
u = − 1.000000I
a = 0.339110 + 0.822375I
b = 0.00765 + 1.64293I
−3.61897 + 1.53058I −4.51511 − 4.43065I
u = − 1.000000I
a = 0.339110 − 0.822375I
b = −1.09217 + 0.97690I
−3.61897 − 1.53058I −4.51511 + 4.43065I
u = − 1.000000I
a = −0.766826
b = −4.28864 + 2.21774I
−5.69095 −5.48110
u = − 1.000000I
a = −0.455697 + 1.200150I
b = −0.094259 + 0.272297I
−9.16243 − 4.40083I −8.74431 + 3.49859I
u = − 1.000000I
a = −0.455697 − 1.200150I
b = −0.532590 − 1.109860I
−9.16243 + 4.40083I −8.74431 − 3.49859I
26
IV. I
u
4
= h4b − 1, 2a − 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
−1
a
2
=
1
1
a
7
=
−1
−2
a
1
=
2
1
a
10
=
0.5
0.25
a
11
=
0.5
0.25
a
5
=
−0.25
−1.125
a
4
=
0
−1
a
8
=
−1
−1
a
12
=
2.5
3.25
a
9
=
−2
−3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14.0625
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
11
u + 1
c
4
, c
5
2(2u − 1)
c
6
, c
7
, c
8
c
9
u − 1
c
10
u
c
12
u + 2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
9
, c
11
y −1
c
4
, c
5
4(4y −1)
c
10
y
c
12
y −4
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.500000
b = 0.250000
0 −14.0620
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u + 1)(u
53
+ 23u
52
+ ··· − 11u − 1)
· (u
82
+ 47u
81
+ ··· + 1760u + 289)
c
2
, c
3
(u + 1)(u
2
+ 1)
5
(u
53
− u
52
+ ··· − u − 1)(u
82
− u
81
+ ··· − 80u + 17)
c
4
4(2u − 1)(u
10
+ 5u
8
+ ··· − u
2
+ 1)(u
41
− u
40
+ ··· + 289u + 77)
2
· (2u
53
+ 7u
52
+ ··· − 449u − 106)
c
5
4(2u − 1)(u
10
− 3u
8
+ ··· − u
2
+ 1)(u
41
− 3u
40
+ ··· − 129u + 31)
2
· (2u
53
+ 19u
52
+ ··· − 27u − 22)
c
6
, c
7
(u − 1)(u
2
+ 1)
5
(u
53
− u
52
+ ··· − u − 1)(u
82
− u
81
+ ··· − 80u + 17)
c
8
(u − 1)(u + 1)
10
(u
53
+ 23u
52
+ ··· − 11u − 1)
· (u
82
+ 47u
81
+ ··· + 1760u + 289)
c
9
(u − 1)(u
5
+ u
4
+ ··· + u − 1)
2
(u
41
− u
40
+ ··· + 7u + 1)
2
· (u
53
− 2u
52
+ ··· + 145u − 16)
c
10
u(u
5
− u
4
+ ··· + u − 1)
2
(u
41
+ 7u
40
+ ··· − u − 1)
2
· (u
53
+ 9u
52
+ ··· + 44u − 32)
c
11
(u + 1)(u
5
− u
4
+ ··· + u + 1)
2
(u
41
− u
40
+ ··· + 7u + 1)
2
· (u
53
− 2u
52
+ ··· + 145u − 16)
c
12
(u + 2)(u
10
+ u
8
+ ··· + 3u
2
+ 1)(u
41
+ 3u
40
+ ··· + u + 1)
2
· (u
53
− 11u
52
+ ··· + 12u − 4)
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
((y −1)
11
)(y
53
+ 19y
52
+ ··· + 17y −1)
· (y
82
− 25y
81
+ ··· + 237460y + 83521)
c
2
, c
3
, c
6
c
7
(y −1)(y + 1)
10
(y
53
+ 23y
52
+ ··· − 11y −1)
· (y
82
+ 47y
81
+ ··· + 1760y + 289)
c
4
16(4y −1)(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
· (y
41
− 25y
40
+ ··· − 76331y −5929)
2
· (4y
53
− 109y
52
+ ··· + 600797y −11236)
c
5
16(4y −1)(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
· (y
41
− 45y
40
+ ··· + 24081y −961)
2
· (4y
53
− 253y
52
+ ··· − 47627y −484)
c
9
, c
11
(y −1)(y
5
− 5y
4
+ ··· − y −1)
2
(y
41
− 29y
40
+ ··· − 7y −1)
2
· (y
53
− 40y
52
+ ··· + 9057y −256)
c
10
y(y
5
+ 3y
4
+ ··· − y −1)
2
(y
41
+ 3y
40
+ ··· − 7y −1)
2
· (y
53
+ 9y
52
+ ··· − 3504y −1024)
c
12
(y −4)(y
5
+ y
4
+ ··· + 3y + 1)
2
(y
41
+ 7y
40
+ ··· − 3y −1)
2
· (y
53
+ 5y
52
+ ··· − 40y −16)
32
