12a
1239
(K12a
1239
)
A knot diagram
1
Linearized knot diagam
5 6 9 1 10 11 12 3 4 2 8 7
Solving Sequence
3,8
9 4
10,12
7 1 11 6 2 5
c
8
c
3
c
9
c
7
c
12
c
11
c
6
c
2
c
5
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.16293 × 10
238
u
108
+ 4.57466 × 10
237
u
107
+ ··· + 6.35674 × 10
238
b + 6.92303 × 10
239
,
7.38011 × 10
240
u
108
+ 2.03785 × 10
240
u
107
+ ··· + 9.09013 × 10
240
a − 5.28559 × 10
242
,
u
109
− u
108
+ ··· − 702u + 77i
I
u
2
= h−2u
20
− u
19
+ ··· + b + 1, 2u
20
+ u
19
+ ··· + a − 2, u
21
− 12u
19
+ ··· − 6u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 130 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−2.16 × 10
238
u
108
+ 4.57 × 10
237
u
107
+ · · · + 6.36 × 10
238
b + 6.92 ×
10
239
, 7.38 × 10
240
u
108
+ 2.04 × 10
240
u
107
+ · · · + 9.09 × 10
240
a − 5.29 ×
10
242
, u
109
− u
108
+ · · · − 702u + 77i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
12
=
−0.811882u
108
− 0.224183u
107
+ ··· − 454.989u + 58.1464
0.340258u
108
− 0.0719655u
107
+ ··· + 91.1539u − 10.8909
a
7
=
0.269423u
108
+ 0.00887088u
107
+ ··· + 230.443u − 22.9965
0.146266u
108
− 0.00239065u
107
+ ··· + 70.3322u − 6.96378
a
1
=
0.461750u
108
+ 0.259214u
107
+ ··· + 364.820u − 44.4482
−0.0841838u
108
− 0.307556u
107
+ ··· − 178.076u + 19.9457
a
11
=
−0.471623u
108
− 0.296148u
107
+ ··· − 363.835u + 47.2556
0.340258u
108
− 0.0719655u
107
+ ··· + 91.1539u − 10.8909
a
6
=
0.203576u
108
+ 0.00498689u
107
+ ··· + 159.911u − 17.2909
−0.235376u
108
− 0.228601u
107
+ ··· − 161.577u + 19.6613
a
2
=
−0.438650u
108
− 0.253632u
107
+ ··· − 318.988u + 43.9323
0.160932u
108
− 0.103965u
107
+ ··· + 3.80476u − 0.189305
a
5
=
0.391839u
108
+ 0.143609u
107
+ ··· + 269.772u − 30.1477
−0.109641u
108
− 0.134993u
107
+ ··· − 92.6369u + 11.6066
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.377168u
108
− 0.939926u
107
+ ··· − 782.643u + 90.1335
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
109
− 2u
108
+ ··· + 1917u + 82
c
2
u
109
− 7u
108
+ ··· − 18586u + 1549
c
3
, c
8
, c
9
u
109
− u
108
+ ··· − 702u + 77
c
5
u
109
+ 3u
108
+ ··· − 4u − 1
c
6
u
109
− 11u
107
+ ··· + 485349u + 49014
c
7
, c
11
, c
12
u
109
+ 49u
107
+ ··· + 86u + 7
c
10
u
109
+ 2u
108
+ ··· − 33482u − 3797
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
109
− 68y
108
+ ··· + 688121y −6724
c
2
y
109
− 7y
108
+ ··· + 266973252y −2399401
c
3
, c
8
, c
9
y
109
− 107y
108
+ ··· − 49892y −5929
c
5
y
109
+ y
108
+ ··· + 276y −1
c
6
y
109
− 22y
108
+ ··· + 45167886549y −2402372196
c
7
, c
11
, c
12
y
109
+ 98y
108
+ ··· + 1866y −49
c
10
y
109
− 28y
108
+ ··· + 893011692y −14417209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.402166 + 0.903386I
a = −0.645464 − 0.395709I
b = −0.779161 + 0.223079I
−4.97037 + 8.83338I 0
u = 0.402166 − 0.903386I
a = −0.645464 + 0.395709I
b = −0.779161 − 0.223079I
−4.97037 − 8.83338I 0
u = 0.409660 + 0.939407I
a = 1.37430 + 0.42777I
b = 0.141105 − 1.335290I
2.90773 + 0.15092I 0
u = 0.409660 − 0.939407I
a = 1.37430 − 0.42777I
b = 0.141105 + 1.335290I
2.90773 − 0.15092I 0
u = −0.479093 + 0.959436I
a = −1.27070 + 0.95386I
b = −0.31750 − 1.39255I
0.15694 − 12.79750I 0
u = −0.479093 − 0.959436I
a = −1.27070 − 0.95386I
b = −0.31750 + 1.39255I
0.15694 + 12.79750I 0
u = 0.888136 + 0.221520I
a = −0.434492 + 0.515899I
b = 0.076175 − 1.337740I
4.61771 + 4.78282I 0
u = 0.888136 − 0.221520I
a = −0.434492 − 0.515899I
b = 0.076175 + 1.337740I
4.61771 − 4.78282I 0
u = −0.012761 + 0.871508I
a = 1.055820 − 0.620238I
b = 0.205778 + 1.378580I
4.06152 − 3.86430I 0
u = −0.012761 − 0.871508I
a = 1.055820 + 0.620238I
b = 0.205778 − 1.378580I
4.06152 + 3.86430I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.723802 + 0.420986I
a = 0.58615 − 1.57520I
b = −0.094032 + 1.368090I
6.35292 − 0.00652I 0
u = −0.723802 − 0.420986I
a = 0.58615 + 1.57520I
b = −0.094032 − 1.368090I
6.35292 + 0.00652I 0
u = −0.302564 + 0.777666I
a = −0.439464 − 0.257334I
b = −0.376279 + 0.918943I
−2.78988 − 4.61220I 0
u = −0.302564 − 0.777666I
a = −0.439464 + 0.257334I
b = −0.376279 − 0.918943I
−2.78988 + 4.61220I 0
u = −1.004910 + 0.610298I
a = 1.24202 − 1.50121I
b = 0.206815 + 1.140270I
−0.757207 − 0.159867I 0
u = −1.004910 − 0.610298I
a = 1.24202 + 1.50121I
b = 0.206815 − 1.140270I
−0.757207 + 0.159867I 0
u = 0.876916 + 0.797051I
a = 0.239792 + 0.275895I
b = 0.675277 + 0.146480I
−3.65883 − 3.10618I 0
u = 0.876916 − 0.797051I
a = 0.239792 − 0.275895I
b = 0.675277 − 0.146480I
−3.65883 + 3.10618I 0
u = −0.065013 + 0.785502I
a = 0.813491 + 0.209447I
b = 0.461186 − 0.247431I
−1.06660 + 1.28575I 0. − 4.36944I
u = −0.065013 − 0.785502I
a = 0.813491 − 0.209447I
b = 0.461186 + 0.247431I
−1.06660 − 1.28575I 0. + 4.36944I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.706186 + 0.310193I
a = −0.458785 + 0.915601I
b = 0.057777 − 1.389560I
4.60557 + 4.78957I 3.27657 − 7.06300I
u = 0.706186 − 0.310193I
a = −0.458785 − 0.915601I
b = 0.057777 + 1.389560I
4.60557 − 4.78957I 3.27657 + 7.06300I
u = 1.229600 + 0.042886I
a = 0.868263 + 0.659453I
b = 0.373419 − 1.260200I
1.35403 + 4.32888I 0
u = 1.229600 − 0.042886I
a = 0.868263 − 0.659453I
b = 0.373419 + 1.260200I
1.35403 − 4.32888I 0
u = −1.23501
a = 0.566495
b = 0.830761
−2.55153 0
u = −1.237070 + 0.045221I
a = 0.349532 + 1.329470I
b = 0.475480 − 0.101342I
0.84742 − 2.96547I 0
u = −1.237070 − 0.045221I
a = 0.349532 − 1.329470I
b = 0.475480 + 0.101342I
0.84742 + 2.96547I 0
u = −0.845077 + 0.926171I
a = 0.038004 + 1.007000I
b = 0.269827 − 1.355260I
1.09925 + 6.53748I 0
u = −0.845077 − 0.926171I
a = 0.038004 − 1.007000I
b = 0.269827 + 1.355260I
1.09925 − 6.53748I 0
u = 0.387936 + 0.629916I
a = −2.16003 − 0.35618I
b = −0.271893 + 1.371710I
4.02135 + 7.40202I 1.48621 − 8.34449I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387936 − 0.629916I
a = −2.16003 + 0.35618I
b = −0.271893 − 1.371710I
4.02135 − 7.40202I 1.48621 + 8.34449I
u = −1.271310 + 0.063914I
a = 0.312411 − 1.082760I
b = −0.725766 + 0.514272I
0.83894 + 1.77988I 0
u = −1.271310 − 0.063914I
a = 0.312411 + 1.082760I
b = −0.725766 − 0.514272I
0.83894 − 1.77988I 0
u = −1.28616
a = 0.447895
b = −1.09734
−1.88852 0
u = 0.199830 + 0.671170I
a = 0.568605 − 0.410665I
b = −0.264456 − 1.270140I
−1.01524 − 1.96553I −6.38016 + 0.12406I
u = 0.199830 − 0.671170I
a = 0.568605 + 0.410665I
b = −0.264456 + 1.270140I
−1.01524 + 1.96553I −6.38016 − 0.12406I
u = 0.215861 + 0.660226I
a = 0.696973 − 0.315430I
b = 0.222402 + 1.384000I
3.94108 − 3.85885I 3.50122 − 0.26371I
u = 0.215861 − 0.660226I
a = 0.696973 + 0.315430I
b = 0.222402 − 1.384000I
3.94108 + 3.85885I 3.50122 + 0.26371I
u = 1.312440 + 0.058338I
a = −1.03261 − 2.67872I
b = −0.27777 + 1.48571I
7.22104 + 5.46339I 0
u = 1.312440 − 0.058338I
a = −1.03261 + 2.67872I
b = −0.27777 − 1.48571I
7.22104 − 5.46339I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.314640 + 0.115295I
a = −0.039631 − 1.372770I
b = −0.622814 + 1.146730I
1.57876 + 5.92457I 0
u = 1.314640 − 0.115295I
a = −0.039631 + 1.372770I
b = −0.622814 − 1.146730I
1.57876 − 5.92457I 0
u = 0.498353 + 0.438479I
a = 1.22480 + 1.23190I
b = 0.358009 − 1.365210I
0.24196 + 5.33437I −2.60697 − 8.66869I
u = 0.498353 − 0.438479I
a = 1.22480 − 1.23190I
b = 0.358009 + 1.365210I
0.24196 − 5.33437I −2.60697 + 8.66869I
u = 1.341430 + 0.039329I
a = 1.99786 + 3.00047I
b = 0.193376 − 1.347340I
5.48826 − 0.46976I 0
u = 1.341430 − 0.039329I
a = 1.99786 − 3.00047I
b = 0.193376 + 1.347340I
5.48826 + 0.46976I 0
u = −0.366704 + 0.534973I
a = 1.48531 + 0.45009I
b = 0.140708 + 0.096859I
−1.56031 + 1.32922I −2.76084 + 3.85029I
u = −0.366704 − 0.534973I
a = 1.48531 − 0.45009I
b = 0.140708 − 0.096859I
−1.56031 − 1.32922I −2.76084 − 3.85029I
u = −1.340090 + 0.290087I
a = −0.97196 + 1.07562I
b = 0.171881 − 1.249210I
3.81193 − 1.57029I 0
u = −1.340090 − 0.290087I
a = −0.97196 − 1.07562I
b = 0.171881 + 1.249210I
3.81193 + 1.57029I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351555 + 0.519947I
a = −1.39467 + 0.74443I
b = −0.668954 − 0.194817I
−0.94509 − 3.96567I −3.76250 + 8.34585I
u = −0.351555 − 0.519947I
a = −1.39467 − 0.74443I
b = −0.668954 + 0.194817I
−0.94509 + 3.96567I −3.76250 − 8.34585I
u = 0.526085 + 0.316443I
a = 2.28973 − 0.10814I
b = 0.050084 − 1.190630I
1.43570 + 1.35410I −2.21511 − 4.75341I
u = 0.526085 − 0.316443I
a = 2.28973 + 0.10814I
b = 0.050084 + 1.190630I
1.43570 − 1.35410I −2.21511 + 4.75341I
u = 1.386830 + 0.165924I
a = 0.359079 − 0.885169I
b = −0.832950 + 0.454638I
0.54555 + 3.28560I 0
u = 1.386830 − 0.165924I
a = 0.359079 + 0.885169I
b = −0.832950 − 0.454638I
0.54555 − 3.28560I 0
u = 1.395460 + 0.201113I
a = −0.230205 + 1.033450I
b = 0.579701 − 0.107176I
0.34831 + 4.21288I 0
u = 1.395460 − 0.201113I
a = −0.230205 − 1.033450I
b = 0.579701 + 0.107176I
0.34831 − 4.21288I 0
u = −1.412100 + 0.005572I
a = −0.368823 + 0.723200I
b = −0.216358 − 0.896293I
6.75578 − 2.21309I 0
u = −1.412100 − 0.005572I
a = −0.368823 − 0.723200I
b = −0.216358 + 0.896293I
6.75578 + 2.21309I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.255083 + 0.522829I
a = −0.56447 + 1.37469I
b = −0.706122 − 0.003147I
−4.92917 − 1.53125I −11.49746 + 4.59325I
u = −0.255083 − 0.522829I
a = −0.56447 − 1.37469I
b = −0.706122 + 0.003147I
−4.92917 + 1.53125I −11.49746 − 4.59325I
u = 1.40333 + 0.26342I
a = 0.072123 + 0.454527I
b = −0.477583 − 0.476051I
3.94288 + 2.18839I 0
u = 1.40333 − 0.26342I
a = 0.072123 − 0.454527I
b = −0.477583 + 0.476051I
3.94288 − 2.18839I 0
u = −1.42510 + 0.11645I
a = −0.276315 + 0.568667I
b = 0.337968 − 0.861510I
6.84573 − 2.50887I 0
u = −1.42510 − 0.11645I
a = −0.276315 − 0.568667I
b = 0.337968 + 0.861510I
6.84573 + 2.50887I 0
u = 0.468042 + 0.324213I
a = 0.424108 − 0.048597I
b = −0.150328 − 0.479453I
0.815027 + 1.022850I 3.02919 − 3.25441I
u = 0.468042 − 0.324213I
a = 0.424108 + 0.048597I
b = −0.150328 + 0.479453I
0.815027 − 1.022850I 3.02919 + 3.25441I
u = −0.268724 + 0.498523I
a = 0.902578 − 0.112241I
b = 0.570966 − 0.198366I
−1.12964 + 0.95097I −4.40235 − 0.17666I
u = −0.268724 − 0.498523I
a = 0.902578 + 0.112241I
b = 0.570966 + 0.198366I
−1.12964 − 0.95097I −4.40235 + 0.17666I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39044 + 0.38463I
a = −0.359755 + 0.855120I
b = −0.624840 − 0.325101I
3.32026 − 5.78123I 0
u = −1.39044 − 0.38463I
a = −0.359755 − 0.855120I
b = −0.624840 + 0.325101I
3.32026 + 5.78123I 0
u = 1.43421 + 0.20052I
a = 0.286900 + 0.880032I
b = 0.775807 − 0.235290I
4.79964 + 6.65469I 0
u = 1.43421 − 0.20052I
a = 0.286900 − 0.880032I
b = 0.775807 + 0.235290I
4.79964 − 6.65469I 0
u = 1.45126 + 0.17482I
a = −0.350683 − 0.497655I
b = −0.660874 + 0.191423I
4.56693 + 1.18183I 0
u = 1.45126 − 0.17482I
a = −0.350683 + 0.497655I
b = −0.660874 − 0.191423I
4.56693 − 1.18183I 0
u = −1.46485 + 0.15689I
a = 1.16123 − 3.16291I
b = 0.231074 + 1.346100I
4.97716 − 7.18249I 0
u = −1.46485 − 0.15689I
a = 1.16123 + 3.16291I
b = 0.231074 − 1.346100I
4.97716 + 7.18249I 0
u = −0.057313 + 0.522945I
a = −0.151813 − 0.255917I
b = 0.465107 + 0.874491I
−2.55513 − 3.73158I −8.70339 + 7.84333I
u = −0.057313 − 0.522945I
a = −0.151813 + 0.255917I
b = 0.465107 − 0.874491I
−2.55513 + 3.73158I −8.70339 − 7.84333I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44683 + 0.28962I
a = −0.297664 − 0.751662I
b = 0.561893 + 0.861763I
2.86009 + 8.45184I 0
u = 1.44683 − 0.28962I
a = −0.297664 + 0.751662I
b = 0.561893 − 0.861763I
2.86009 − 8.45184I 0
u = −1.46109 + 0.24052I
a = 1.58791 − 1.91112I
b = 0.31802 + 1.40080I
9.9995 − 10.6187I 0
u = −1.46109 − 0.24052I
a = 1.58791 + 1.91112I
b = 0.31802 − 1.40080I
9.9995 + 10.6187I 0
u = −0.257351 + 0.449604I
a = 0.352827 − 0.610460I
b = 0.855234 + 0.210318I
−4.68867 − 0.97102I −13.3723 + 6.4240I
u = −0.257351 − 0.449604I
a = 0.352827 + 0.610460I
b = 0.855234 − 0.210318I
−4.68867 + 0.97102I −13.3723 − 6.4240I
u = −1.48988 + 0.17115I
a = −0.18079 + 2.56300I
b = 0.01048 − 1.55879I
11.34460 − 6.97363I 0
u = −1.48988 − 0.17115I
a = −0.18079 − 2.56300I
b = 0.01048 + 1.55879I
11.34460 + 6.97363I 0
u = −1.49162 + 0.16869I
a = −0.69571 + 2.37449I
b = −0.34801 − 1.48421I
6.72009 − 7.65156I 0
u = −1.49162 − 0.16869I
a = −0.69571 − 2.37449I
b = −0.34801 + 1.48421I
6.72009 + 7.65156I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.335283 + 0.366575I
a = −2.76096 − 2.87597I
b = −0.292158 + 1.267780I
−0.99137 + 5.14839I −5.97316 − 9.02612I
u = 0.335283 − 0.366575I
a = −2.76096 + 2.87597I
b = −0.292158 − 1.267780I
−0.99137 − 5.14839I −5.97316 + 9.02612I
u = 1.45480 + 0.43655I
a = −1.44926 − 2.00390I
b = −0.24491 + 1.41953I
8.88562 + 8.97574I 0
u = 1.45480 − 0.43655I
a = −1.44926 + 2.00390I
b = −0.24491 − 1.41953I
8.88562 − 8.97574I 0
u = −1.48994 + 0.33995I
a = 0.079255 − 0.848166I
b = 0.837072 + 0.296873I
1.10152 − 13.31460I 0
u = −1.48994 − 0.33995I
a = 0.079255 + 0.848166I
b = 0.837072 − 0.296873I
1.10152 + 13.31460I 0
u = −1.51254 + 0.23164I
a = −0.12120 − 2.24691I
b = −0.16243 + 1.44020I
10.05140 + 0.10640I 0
u = −1.51254 − 0.23164I
a = −0.12120 + 2.24691I
b = −0.16243 − 1.44020I
10.05140 − 0.10640I 0
u = −1.52922 + 0.27611I
a = −1.29031 + 1.71734I
b = −0.252493 − 1.365950I
9.49480 − 4.48007I 0
u = −1.52922 − 0.27611I
a = −1.29031 − 1.71734I
b = −0.252493 + 1.365950I
9.49480 + 4.48007I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55785 + 0.09503I
a = −0.33657 − 2.57920I
b = 0.03854 + 1.45816I
13.95690 + 1.81696I 0
u = 1.55785 − 0.09503I
a = −0.33657 + 2.57920I
b = 0.03854 − 1.45816I
13.95690 − 1.81696I 0
u = 1.53265 + 0.35483I
a = 1.27460 + 2.05127I
b = 0.33695 − 1.43594I
6.6262 + 17.5573I 0
u = 1.53265 − 0.35483I
a = 1.27460 − 2.05127I
b = 0.33695 + 1.43594I
6.6262 − 17.5573I 0
u = 0.183641 + 0.225251I
a = 1.03198 − 4.98737I
b = −0.095671 − 1.198460I
1.51818 + 1.16554I −1.88500 − 5.55795I
u = 0.183641 − 0.225251I
a = 1.03198 + 4.98737I
b = −0.095671 + 1.198460I
1.51818 − 1.16554I −1.88500 + 5.55795I
u = −1.72887
a = 0.0331435
b = −0.449454
6.32375 0
u = 1.77079 + 0.10526I
a = −0.22227 + 2.10518I
b = −0.176744 − 1.335810I
10.68110 − 2.27846I 0
u = 1.77079 − 0.10526I
a = −0.22227 − 2.10518I
b = −0.176744 + 1.335810I
10.68110 + 2.27846I 0
15
II.
I
u
2
= h−2u
20
−u
19
+· · ·+b+1, 2u
20
+u
19
+· · ·+a−2, u
21
−12u
19
+· · ·−6u
2
+1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
12
=
−2u
20
− u
19
+ ··· + 4u + 2
2u
20
+ u
19
+ ··· − 3u − 1
a
7
=
u
20
− 12u
18
+ ··· − 5u − 1
2u
18
− 20u
16
+ ··· + 3u + 1
a
1
=
−u
20
+ 11u
18
+ ··· − 10u
3
+ 5u
u
20
− u
19
+ ··· − 3u + 1
a
11
=
u
18
− 10u
16
+ ··· + u + 1
2u
20
+ u
19
+ ··· − 3u − 1
a
6
=
−u
19
+ 11u
17
+ ··· − 2u + 1
−u
19
+ u
18
+ ··· − u
2
+ 3u
a
2
=
u
19
− 10u
17
+ ··· − 4u
3
+ u
2
u
20
+ 3u
19
+ ··· + u − 3
a
5
=
−u
19
− u
18
+ ··· − 4u + 1
−u
19
+ u
18
+ ··· − u
2
+ 4u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −6u
20
+ 65u
18
+ 4u
17
− 285u
16
− 34u
15
+ 644u
14
+ 114u
13
− 788u
12
− 195u
11
+
509u
10
+ 186u
9
− 187u
8
− 108u
7
+ 77u
6
+ 42u
5
− 28u
4
− 12u
3
+ 15u
2
+ 7u − 10
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 3u
20
+ ··· − 3u − 1
c
2
u
21
+ 2u
19
+ ··· − 4u
3
+ 1
c
3
u
21
− 12u
19
+ ··· + 6u
2
− 1
c
4
u
21
− 3u
20
+ ··· − 3u + 1
c
5
u
21
+ 4u
18
+ ··· + 2u
2
+ 1
c
6
u
21
− u
20
+ ··· + 5u
2
− 1
c
7
u
21
+ u
20
+ ··· − 2u − 1
c
8
, c
9
u
21
− 12u
19
+ ··· − 6u
2
+ 1
c
10
u
21
+ 3u
20
+ ··· + 6u
2
− 1
c
11
, c
12
u
21
− u
20
+ ··· − 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
21
− 17y
20
+ ··· + 21y −1
c
2
y
21
+ 4y
20
+ ··· + 4y
2
− 1
c
3
, c
8
, c
9
y
21
− 24y
20
+ ··· + 12y −1
c
5
y
21
− 8y
19
+ ··· − 4y −1
c
6
y
21
− 7y
20
+ ··· + 10y −1
c
7
, c
11
, c
12
y
21
+ 21y
20
+ ··· + 14y −1
c
10
y
21
− 9y
20
+ ··· + 12y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.566384 + 0.496972I
a = 3.02528 − 0.66447I
b = 0.118068 + 1.275040I
1.63926 + 0.08626I −1.301348 + 0.318760I
u = −0.566384 − 0.496972I
a = 3.02528 + 0.66447I
b = 0.118068 − 1.275040I
1.63926 − 0.08626I −1.301348 − 0.318760I
u = −1.243910 + 0.203080I
a = 1.303970 − 0.410642I
b = −0.094643 + 1.210930I
4.17287 − 2.59275I 0.87542 + 5.07430I
u = −1.243910 − 0.203080I
a = 1.303970 + 0.410642I
b = −0.094643 − 1.210930I
4.17287 + 2.59275I 0.87542 − 5.07430I
u = 1.265450 + 0.078216I
a = −0.082073 − 0.771166I
b = −0.400308 + 1.163200I
1.97955 + 5.01003I 1.80881 − 5.40503I
u = 1.265450 − 0.078216I
a = −0.082073 + 0.771166I
b = −0.400308 − 1.163200I
1.97955 − 5.01003I 1.80881 + 5.40503I
u = −1.29372
a = 0.0962644
b = −0.984366
−1.46311 4.12380
u = −0.273763 + 0.622169I
a = 1.141210 + 0.256775I
b = 0.197775 − 1.398750I
3.36706 + 4.31329I −5.11414 − 5.72301I
u = −0.273763 − 0.622169I
a = 1.141210 − 0.256775I
b = 0.197775 + 1.398750I
3.36706 − 4.31329I −5.11414 + 5.72301I
u = 1.326810 + 0.169805I
a = 0.271075 − 1.190820I
b = −0.470586 + 0.411070I
1.64802 + 4.21985I −0.03014 − 6.34461I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.326810 − 0.169805I
a = 0.271075 + 1.190820I
b = −0.470586 − 0.411070I
1.64802 − 4.21985I −0.03014 + 6.34461I
u = 0.397507 + 0.494888I
a = 1.63977 + 0.04899I
b = 0.426638 + 0.185914I
−1.84535 − 1.88456I −9.29763 + 6.87121I
u = 0.397507 − 0.494888I
a = 1.63977 − 0.04899I
b = 0.426638 − 0.185914I
−1.84535 + 1.88456I −9.29763 − 6.87121I
u = 0.555572 + 0.152875I
a = 0.04568 − 2.41036I
b = 0.334075 + 1.250500I
−0.72441 − 4.14061I −4.08467 + 2.20420I
u = 0.555572 − 0.152875I
a = 0.04568 + 2.41036I
b = 0.334075 − 1.250500I
−0.72441 + 4.14061I −4.08467 − 2.20420I
u = −1.42772 + 0.20404I
a = −1.02867 + 2.61430I
b = −0.26074 − 1.46036I
7.76493 − 7.28682I 4.21292 + 5.62890I
u = −1.42772 − 0.20404I
a = −1.02867 − 2.61430I
b = −0.26074 + 1.46036I
7.76493 + 7.28682I 4.21292 − 5.62890I
u = −0.483520
a = −0.562123
b = 0.815366
−4.54133 −10.0310
u = −1.67287
a = −0.276615
b = −0.289165
6.65866 12.4220
u = 1.69150 + 0.06247I
a = −0.44500 + 2.13250I
b = −0.121197 − 1.370090I
11.27980 − 1.51430I 6.67341 − 0.66697I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.69150 − 0.06247I
a = −0.44500 − 2.13250I
b = −0.121197 + 1.370090I
11.27980 + 1.51430I 6.67341 + 0.66697I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
+ 3u
20
+ ··· − 3u − 1)(u
109
− 2u
108
+ ··· + 1917u + 82)
c
2
(u
21
+ 2u
19
+ ··· − 4u
3
+ 1)(u
109
− 7u
108
+ ··· − 18586u + 1549)
c
3
(u
21
− 12u
19
+ ··· + 6u
2
− 1)(u
109
− u
108
+ ··· − 702u + 77)
c
4
(u
21
− 3u
20
+ ··· − 3u + 1)(u
109
− 2u
108
+ ··· + 1917u + 82)
c
5
(u
21
+ 4u
18
+ ··· + 2u
2
+ 1)(u
109
+ 3u
108
+ ··· − 4u − 1)
c
6
(u
21
− u
20
+ ··· + 5u
2
− 1)(u
109
− 11u
107
+ ··· + 485349u + 49014)
c
7
(u
21
+ u
20
+ ··· − 2u − 1)(u
109
+ 49u
107
+ ··· + 86u + 7)
c
8
, c
9
(u
21
− 12u
19
+ ··· − 6u
2
+ 1)(u
109
− u
108
+ ··· − 702u + 77)
c
10
(u
21
+ 3u
20
+ ··· + 6u
2
− 1)(u
109
+ 2u
108
+ ··· − 33482u − 3797)
c
11
, c
12
(u
21
− u
20
+ ··· − 2u + 1)(u
109
+ 49u
107
+ ··· + 86u + 7)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
21
− 17y
20
+ ··· + 21y −1)(y
109
− 68y
108
+ ··· + 688121y −6724)
c
2
(y
21
+ 4y
20
+ ··· + 4y
2
− 1)
· (y
109
− 7y
108
+ ··· + 266973252y −2399401)
c
3
, c
8
, c
9
(y
21
− 24y
20
+ ··· + 12y −1)(y
109
− 107y
108
+ ··· − 49892y −5929)
c
5
(y
21
− 8y
19
+ ··· − 4y −1)(y
109
+ y
108
+ ··· + 276y −1)
c
6
(y
21
− 7y
20
+ ··· + 10y −1)
· (y
109
− 22y
108
+ ··· + 45167886549y −2402372196)
c
7
, c
11
, c
12
(y
21
+ 21y
20
+ ··· + 14y −1)(y
109
+ 98y
108
+ ··· + 1866y −49)
c
10
(y
21
− 9y
20
+ ··· + 12y −1)
· (y
109
− 28y
108
+ ··· + 893011692y −14417209)
23
