12a
0132
(K12a
0132
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 11 12 4 7 1 9 10
Solving Sequence
4,9
8
3,12
7 10 1 11 6 5 2
c
8
c
3
c
7
c
9
c
12
c
11
c
6
c
4
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.62500 × 10
507
u
123
+ 6.31929 × 10
507
u
122
+ ··· + 2.55470 × 10
510
b − 2.21789 × 10
511
,
− 6.08901 × 10
508
u
123
− 1.58391 × 10
509
u
122
+ ··· + 1.02188 × 10
511
a − 1.29482 × 10
512
,
u
124
+ u
123
+ ··· − 5120u + 1024i
I
v
1
= ha, 1728v
9
+ 4936v
8
+ 9872v
7
− 12908v
6
− 24680v
5
+ 34552v
4
+ 91527v
3
− 4936v
2
+ 3335b + 613,
v
10
+ 3v
9
+ 6v
8
− 7v
7
− 16v
6
+ 19v
5
+ 58v
4
+ 2v
3
− 7v
2
+ v + 1i
* 2 irreducible components of dim
C
= 0, with total 134 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
= h5.63 × 10
507
u
123
+ 6.32 × 10
507
u
122
+ · · · + 2.55 × 10
510
b − 2.22 ×
10
511
, −6.09 × 10
508
u
123
− 1.58 × 10
509
u
122
+ · · · + 1.02 × 10
511
a − 1.29 ×
10
512
, u
124
+ u
123
+ · · · − 5120u + 1024i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
12
=
0.00595864u
123
+ 0.0155000u
122
+ ··· + 16.8620u + 12.6709
−0.00220183u
123
− 0.00247360u
122
+ ··· − 26.2981u + 8.68161
a
7
=
−0.0324749u
123
− 0.0607838u
122
+ ··· − 230.963u + 46.6844
0.00378830u
123
+ 0.00499386u
122
+ ··· + 8.89055u − 5.72918
a
10
=
0.0182618u
123
+ 0.0309327u
122
+ ··· + 105.201u − 21.3586
−0.00140036u
123
− 0.00248372u
122
+ ··· + 12.7388u − 3.20499
a
1
=
−0.00690886u
123
− 0.00829307u
122
+ ··· − 79.1920u + 29.3712
−0.00140036u
123
− 0.00248372u
122
+ ··· + 12.7388u − 3.20499
a
11
=
0.00816047u
123
+ 0.0179736u
122
+ ··· + 43.1601u + 3.98933
−0.00220183u
123
− 0.00247360u
122
+ ··· − 26.2981u + 8.68161
a
6
=
−0.0106337u
123
− 0.0146047u
122
+ ··· − 66.4407u + 24.7488
0.00372489u
123
+ 0.00631165u
122
+ ··· − 12.7513u + 4.62242
a
5
=
0.00761734u
123
+ 0.00955153u
122
+ ··· + 44.0856u − 14.0585
0.0119599u
123
+ 0.0204629u
122
+ ··· + 101.335u − 28.7078
a
2
=
−0.00597755u
123
− 0.00670190u
122
+ ··· − 69.7496u + 25.3049
−0.00252974u
123
− 0.00392118u
122
+ ··· + 5.72123u + 0.185587
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0208807u
123
− 0.0235904u
122
+ ··· − 165.877u + 74.8282
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
124
+ 42u
123
+ ··· + 2u + 1
c
2
, c
5
u
124
+ 6u
123
+ ··· + 2u + 1
c
3
, c
8
u
124
− u
123
+ ··· + 5120u + 1024
c
6
u
124
+ 3u
123
+ ··· − 376993u − 48793
c
7
u
124
− 3u
123
+ ··· + 1975u + 1031
c
9
u
124
− 9u
123
+ ··· − 3u + 1
c
10
, c
12
u
124
− 3u
123
+ ··· − 17u + 1
c
11
u
124
+ 21u
123
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
124
+ 86y
123
+ ··· − 1250y + 1
c
2
, c
5
y
124
+ 42y
123
+ ··· + 2y + 1
c
3
, c
8
y
124
− 55y
123
+ ··· − 26214400y + 1048576
c
6
y
124
+ 83y
123
+ ··· − 318551403169y + 2380756849
c
7
y
124
+ 131y
123
+ ··· + 138554707y + 1062961
c
9
y
124
− 21y
123
+ ··· − 9y + 1
c
10
, c
12
y
124
− 85y
123
+ ··· − 17y + 1
c
11
y
124
+ 3y
123
+ ··· − 17y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.522189 + 0.849715I
a = 0.0863169 + 0.0937477I
b = 0.822352 + 1.127080I
−7.69575 + 7.07073I 0
u = −0.522189 − 0.849715I
a = 0.0863169 − 0.0937477I
b = 0.822352 − 1.127080I
−7.69575 − 7.07073I 0
u = −0.761135 + 0.655567I
a = 1.73888 + 1.08981I
b = 1.38408 − 0.94824I
−6.14991 − 0.54757I 0
u = −0.761135 − 0.655567I
a = 1.73888 − 1.08981I
b = 1.38408 + 0.94824I
−6.14991 + 0.54757I 0
u = 0.890683 + 0.466793I
a = 1.38896 − 0.33416I
b = 0.294252 + 0.387769I
−1.73197 + 2.72965I 0
u = 0.890683 − 0.466793I
a = 1.38896 + 0.33416I
b = 0.294252 − 0.387769I
−1.73197 − 2.72965I 0
u = 0.797869 + 0.557988I
a = −3.22687 − 0.82452I
b = −0.405742 + 0.130680I
−3.73679 + 2.23882I 0
u = 0.797869 − 0.557988I
a = −3.22687 + 0.82452I
b = −0.405742 − 0.130680I
−3.73679 − 2.23882I 0
u = −1.03358
a = 1.17878
b = 0.419420
1.67471 0
u = 0.152273 + 0.950799I
a = 0.439586 + 0.095214I
b = 0.352639 − 0.121692I
0.94696 − 2.64839I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.152273 − 0.950799I
a = 0.439586 − 0.095214I
b = 0.352639 + 0.121692I
0.94696 + 2.64839I 0
u = 0.111280 + 0.950958I
a = 0.0891030 − 0.0899186I
b = 0.632776 − 0.873813I
−4.19980 − 4.72472I 0
u = 0.111280 − 0.950958I
a = 0.0891030 + 0.0899186I
b = 0.632776 + 0.873813I
−4.19980 + 4.72472I 0
u = 0.402887 + 0.866992I
a = 0.0821980 + 0.0901132I
b = 0.214260 + 0.899169I
−7.15417 + 1.85942I 0
u = 0.402887 − 0.866992I
a = 0.0821980 − 0.0901132I
b = 0.214260 − 0.899169I
−7.15417 − 1.85942I 0
u = 0.280900 + 1.008390I
a = 0.391230 − 0.030549I
b = −1.077510 + 0.875402I
2.42925 − 1.41500I 0
u = 0.280900 − 1.008390I
a = 0.391230 + 0.030549I
b = −1.077510 − 0.875402I
2.42925 + 1.41500I 0
u = 1.031570 + 0.216136I
a = 0.478722 + 0.364587I
b = −0.13582 + 1.68474I
2.05301 − 3.14695I 0
u = 1.031570 − 0.216136I
a = 0.478722 − 0.364587I
b = −0.13582 − 1.68474I
2.05301 + 3.14695I 0
u = −0.473625 + 0.808076I
a = 1.61929 + 1.80920I
b = 0.90344 − 1.17489I
−2.69231 + 4.85276I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.473625 − 0.808076I
a = 1.61929 − 1.80920I
b = 0.90344 + 1.17489I
−2.69231 − 4.85276I 0
u = −0.869219 + 0.624266I
a = −0.026699 + 1.149100I
b = 1.15222 + 1.28001I
−5.81970 − 4.41330I 0
u = −0.869219 − 0.624266I
a = −0.026699 − 1.149100I
b = 1.15222 − 1.28001I
−5.81970 + 4.41330I 0
u = 1.011480 + 0.407367I
a = 1.72293 − 0.53877I
b = 1.78222 + 0.59259I
−0.730807 + 0.398436I 0
u = 1.011480 − 0.407367I
a = 1.72293 + 0.53877I
b = 1.78222 − 0.59259I
−0.730807 − 0.398436I 0
u = −1.030000 + 0.366353I
a = 0.450444 − 0.294246I
b = −0.33214 − 1.71255I
1.53090 − 2.31840I 0
u = −1.030000 − 0.366353I
a = 0.450444 + 0.294246I
b = −0.33214 + 1.71255I
1.53090 + 2.31840I 0
u = −0.623007 + 0.656376I
a = 0.475591 − 0.097288I
b = −0.72278 − 1.27191I
−2.52436 + 2.17800I 0
u = −0.623007 − 0.656376I
a = 0.475591 + 0.097288I
b = −0.72278 + 1.27191I
−2.52436 − 2.17800I 0
u = 1.053460 + 0.334053I
a = −2.01750 − 0.15227I
b = −1.13686 − 0.92726I
2.86743 + 4.32090I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.053460 − 0.334053I
a = −2.01750 + 0.15227I
b = −1.13686 + 0.92726I
2.86743 − 4.32090I 0
u = −0.414510 + 1.030550I
a = 0.383786 − 0.005613I
b = −1.12283 − 1.02161I
1.80176 + 6.87033I 0
u = −0.414510 − 1.030550I
a = 0.383786 + 0.005613I
b = −1.12283 + 1.02161I
1.80176 − 6.87033I 0
u = −0.572881 + 0.659676I
a = 0.344044 − 0.599325I
b = −0.544766 + 0.047925I
1.20860 − 1.42458I 0
u = −0.572881 − 0.659676I
a = 0.344044 + 0.599325I
b = −0.544766 − 0.047925I
1.20860 + 1.42458I 0
u = 0.665383 + 0.564962I
a = 0.570587 + 0.554244I
b = 0.060268 − 0.573061I
−2.39931 + 1.48408I 0
u = 0.665383 − 0.564962I
a = 0.570587 − 0.554244I
b = 0.060268 + 0.573061I
−2.39931 − 1.48408I 0
u = −0.989470 + 0.558874I
a = −2.06439 − 0.45163I
b = −1.09167 + 1.19055I
−1.39443 − 6.91886I 0
u = −0.989470 − 0.558874I
a = −2.06439 + 0.45163I
b = −1.09167 − 1.19055I
−1.39443 + 6.91886I 0
u = 0.772728 + 0.361889I
a = 0.63020 − 1.27375I
b = 0.705390 − 1.112000I
−1.69027 + 2.64124I 0. − 7.32213I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772728 − 0.361889I
a = 0.63020 + 1.27375I
b = 0.705390 + 1.112000I
−1.69027 − 2.64124I 0. + 7.32213I
u = −0.818440 + 0.227503I
a = −2.82221 + 0.73628I
b = −0.865751 + 0.851616I
0.462211 − 0.187148I 0. + 3.23998I
u = −0.818440 − 0.227503I
a = −2.82221 − 0.73628I
b = −0.865751 − 0.851616I
0.462211 + 0.187148I 0. − 3.23998I
u = −1.125240 + 0.301866I
a = 0.057941 − 1.051830I
b = −0.118948 + 0.739585I
3.08312 − 0.32521I 0
u = −1.125240 − 0.301866I
a = 0.057941 + 1.051830I
b = −0.118948 − 0.739585I
3.08312 + 0.32521I 0
u = −1.042560 + 0.521582I
a = 1.60410 + 0.63813I
b = 1.82232 − 0.76467I
−1.57172 − 5.89073I 0
u = −1.042560 − 0.521582I
a = 1.60410 − 0.63813I
b = 1.82232 + 0.76467I
−1.57172 + 5.89073I 0
u = −1.104320 + 0.436031I
a = 1.96749 − 0.16728I
b = 0.932441 − 0.941120I
−3.47353 − 5.02118I 0
u = −1.104320 − 0.436031I
a = 1.96749 + 0.16728I
b = 0.932441 + 0.941120I
−3.47353 + 5.02118I 0
u = −0.800951 + 0.123276I
a = −0.50824 + 3.34040I
b = −0.154570 − 0.369898I
−0.377994 − 0.348299I −6.5840 − 17.4589I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.800951 − 0.123276I
a = −0.50824 − 3.34040I
b = −0.154570 + 0.369898I
−0.377994 + 0.348299I −6.5840 + 17.4589I
u = 1.122900 + 0.422857I
a = 0.122336 + 0.898226I
b = −0.056448 − 0.778332I
2.44745 + 5.97053I 0
u = 1.122900 − 0.422857I
a = 0.122336 − 0.898226I
b = −0.056448 + 0.778332I
2.44745 − 5.97053I 0
u = −1.128670 + 0.439324I
a = −1.55399 + 1.04306I
b = −0.515617 − 0.382823I
2.30512 − 1.82489I 0
u = −1.128670 − 0.439324I
a = −1.55399 − 1.04306I
b = −0.515617 + 0.382823I
2.30512 + 1.82489I 0
u = 0.263079 + 0.743277I
a = −2.35828 + 4.83736I
b = −0.206461 − 0.254708I
−1.07695 − 2.69734I −3.0103 − 34.5307I
u = 0.263079 − 0.743277I
a = −2.35828 − 4.83736I
b = −0.206461 + 0.254708I
−1.07695 + 2.69734I −3.0103 + 34.5307I
u = 1.091400 + 0.526029I
a = 0.124055 − 0.849262I
b = 0.99817 − 1.63936I
0.26862 + 4.52922I 0
u = 1.091400 − 0.526029I
a = 0.124055 + 0.849262I
b = 0.99817 + 1.63936I
0.26862 − 4.52922I 0
u = 0.358024 + 0.691040I
a = 2.07004 − 2.16220I
b = 0.700858 + 0.957251I
−1.89822 + 0.09517I −4.80349 + 0.55423I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.358024 − 0.691040I
a = 2.07004 + 2.16220I
b = 0.700858 − 0.957251I
−1.89822 − 0.09517I −4.80349 − 0.55423I
u = −0.548214 + 0.539086I
a = −0.21849 + 2.23693I
b = 1.049530 + 0.745594I
−3.12646 + 1.54964I −7.31060 + 2.48742I
u = −0.548214 − 0.539086I
a = −0.21849 − 2.23693I
b = 1.049530 − 0.745594I
−3.12646 − 1.54964I −7.31060 − 2.48742I
u = 1.134040 + 0.538784I
a = −1.66723 − 0.77821I
b = −0.575903 + 0.332609I
1.44662 + 7.51048I 0
u = 1.134040 − 0.538784I
a = −1.66723 + 0.77821I
b = −0.575903 − 0.332609I
1.44662 − 7.51048I 0
u = −1.107310 + 0.608690I
a = 0.039119 + 0.838470I
b = 1.12965 + 1.66104I
−0.73749 − 10.18020I 0
u = −1.107310 − 0.608690I
a = 0.039119 − 0.838470I
b = 1.12965 − 1.66104I
−0.73749 + 10.18020I 0
u = 0.487128 + 1.185850I
a = 0.0890273 − 0.0979403I
b = 1.019830 − 0.928370I
−1.27305 − 6.74434I 0
u = 0.487128 − 1.185850I
a = 0.0890273 + 0.0979403I
b = 1.019830 + 0.928370I
−1.27305 + 6.74434I 0
u = −0.037445 + 0.711656I
a = 1.07301 − 5.25738I
b = −0.041771 + 0.373326I
−0.80831 − 2.19531I −22.6702 + 11.0897I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.037445 − 0.711656I
a = 1.07301 + 5.25738I
b = −0.041771 − 0.373326I
−0.80831 + 2.19531I −22.6702 − 11.0897I
u = −1.122670 + 0.656209I
a = 1.82218 + 0.36853I
b = 1.06382 − 1.08588I
−5.82157 − 12.73140I 0
u = −1.122670 − 0.656209I
a = 1.82218 − 0.36853I
b = 1.06382 + 1.08588I
−5.82157 + 12.73140I 0
u = −0.577754 + 1.177690I
a = 0.0872278 + 0.0983051I
b = 1.06457 + 0.99987I
−2.19410 + 12.52910I 0
u = −0.577754 − 1.177690I
a = 0.0872278 − 0.0983051I
b = 1.06457 − 0.99987I
−2.19410 − 12.52910I 0
u = 1.202970 + 0.528332I
a = 1.72596 − 0.05863I
b = 1.05629 + 0.94904I
−0.88277 + 9.86930I 0
u = 1.202970 − 0.528332I
a = 1.72596 + 0.05863I
b = 1.05629 − 0.94904I
−0.88277 − 9.86930I 0
u = 1.338550 + 0.060961I
a = −1.200800 + 0.491892I
b = −1.37664 + 0.39891I
8.48525 − 3.48002I 0
u = 1.338550 − 0.060961I
a = −1.200800 − 0.491892I
b = −1.37664 − 0.39891I
8.48525 + 3.48002I 0
u = −1.334290 + 0.165279I
a = −1.090250 − 0.544164I
b = −1.337840 − 0.272471I
8.29858 − 2.50158I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.334290 − 0.165279I
a = −1.090250 + 0.544164I
b = −1.337840 + 0.272471I
8.29858 + 2.50158I 0
u = −0.622883 + 0.196411I
a = 0.0851403 + 0.0910220I
b = 0.52188 + 1.34588I
−5.55367 + 1.98303I 3.60934 + 5.15894I
u = −0.622883 − 0.196411I
a = 0.0851403 − 0.0910220I
b = 0.52188 − 1.34588I
−5.55367 − 1.98303I 3.60934 − 5.15894I
u = −1.012920 + 0.889662I
a = −0.185216 − 0.296205I
b = −0.519688 + 0.071470I
1.05796 − 1.60667I 0
u = −1.012920 − 0.889662I
a = −0.185216 + 0.296205I
b = −0.519688 − 0.071470I
1.05796 + 1.60667I 0
u = 0.543833 + 0.354658I
a = 1.57825 + 1.71039I
b = −0.317225 + 0.358191I
0.00137 − 2.90749I 3.98420 + 0.02765I
u = 0.543833 − 0.354658I
a = 1.57825 − 1.71039I
b = −0.317225 − 0.358191I
0.00137 + 2.90749I 3.98420 − 0.02765I
u = 1.340500 + 0.172751I
a = 0.427491 − 0.594295I
b = 0.420976 − 0.390169I
−2.35592 − 4.60181I 0
u = 1.340500 − 0.172751I
a = 0.427491 + 0.594295I
b = 0.420976 + 0.390169I
−2.35592 + 4.60181I 0
u = 1.216000 + 0.593726I
a = −1.62065 + 0.32100I
b = −1.36191 − 1.20877I
5.38445 + 7.13126I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.216000 − 0.593726I
a = −1.62065 − 0.32100I
b = −1.36191 + 1.20877I
5.38445 − 7.13126I 0
u = −1.261230 + 0.502325I
a = 1.062930 + 0.358933I
b = 0.620231 − 0.433308I
5.08524 − 2.34478I 0
u = −1.261230 − 0.502325I
a = 1.062930 − 0.358933I
b = 0.620231 + 0.433308I
5.08524 + 2.34478I 0
u = 1.237370 + 0.593454I
a = 1.064950 − 0.419824I
b = 0.590970 + 0.515301I
4.15621 + 8.24899I 0
u = 1.237370 − 0.593454I
a = 1.064950 + 0.419824I
b = 0.590970 − 0.515301I
4.15621 − 8.24899I 0
u = −1.203630 + 0.665473I
a = −1.58877 − 0.42920I
b = −1.35457 + 1.29679I
4.30507 − 12.99410I 0
u = −1.203630 − 0.665473I
a = −1.58877 + 0.42920I
b = −1.35457 − 1.29679I
4.30507 + 12.99410I 0
u = 0.605995 + 0.116615I
a = 0.0855743 + 0.0908465I
b = 0.380380 + 1.325520I
−5.48389 + 6.66654I 5.37950 − 9.94095I
u = 0.605995 − 0.116615I
a = 0.0855743 − 0.0908465I
b = 0.380380 − 1.325520I
−5.48389 − 6.66654I 5.37950 + 9.94095I
u = 1.181600 + 0.767106I
a = −0.578829 − 0.010468I
b = −0.364094 − 0.535351I
−4.64464 + 4.28743I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.181600 − 0.767106I
a = −0.578829 + 0.010468I
b = −0.364094 + 0.535351I
−4.64464 − 4.28743I 0
u = 0.84560 + 1.16938I
a = 0.021562 + 0.167398I
b = −0.432638 + 0.258240I
−0.61080 − 4.13411I 0
u = 0.84560 − 1.16938I
a = 0.021562 − 0.167398I
b = −0.432638 − 0.258240I
−0.61080 + 4.13411I 0
u = −1.20560 + 0.80402I
a = −0.691714 − 0.240354I
b = −0.687438 + 0.614652I
2.31904 − 5.54243I 0
u = −1.20560 − 0.80402I
a = −0.691714 + 0.240354I
b = −0.687438 − 0.614652I
2.31904 + 5.54243I 0
u = 1.25024 + 0.73843I
a = 1.53837 − 0.40008I
b = 1.20147 + 1.08806I
1.23211 + 13.59160I 0
u = 1.25024 − 0.73843I
a = 1.53837 + 0.40008I
b = 1.20147 − 1.08806I
1.23211 − 13.59160I 0
u = −1.22576 + 0.78665I
a = 1.53180 + 0.48591I
b = 1.20414 − 1.13799I
−0.0610 − 19.5513I 0
u = −1.22576 − 0.78665I
a = 1.53180 − 0.48591I
b = 1.20414 + 1.13799I
−0.0610 + 19.5513I 0
u = 1.19592 + 0.83461I
a = −0.754460 + 0.225245I
b = −0.665998 − 0.723271I
0.91583 + 11.46570I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.19592 − 0.83461I
a = −0.754460 − 0.225245I
b = −0.665998 + 0.723271I
0.91583 − 11.46570I 0
u = −1.46133
a = 0.591265
b = 0.500107
1.32843 0
u = −0.07430 + 1.46227I
a = 0.1088840 − 0.0314711I
b = 0.470050 − 0.134106I
0.47580 − 3.10935I 0
u = −0.07430 − 1.46227I
a = 0.1088840 + 0.0314711I
b = 0.470050 + 0.134106I
0.47580 + 3.10935I 0
u = 0.467577 + 0.174362I
a = 5.08174 − 2.70674I
b = 0.498582 − 0.379667I
−2.27737 + 2.37996I 6.22895 − 4.88387I
u = 0.467577 − 0.174362I
a = 5.08174 + 2.70674I
b = 0.498582 + 0.379667I
−2.27737 − 2.37996I 6.22895 + 4.88387I
u = 1.49416 + 0.19380I
a = 1.127830 + 0.253505I
b = 1.080230 + 0.458190I
6.82559 + 8.92441I 0
u = 1.49416 − 0.19380I
a = 1.127830 − 0.253505I
b = 1.080230 − 0.458190I
6.82559 − 8.92441I 0
u = −1.50310 + 0.10971I
a = 1.049690 − 0.283454I
b = 1.024120 − 0.354423I
7.06445 − 2.67846I 0
u = −1.50310 − 0.10971I
a = 1.049690 + 0.283454I
b = 1.024120 + 0.354423I
7.06445 + 2.67846I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.042812 + 0.461983I
a = 0.607968 − 0.141210I
b = −0.483667 + 0.704865I
−0.05266 − 1.50098I −0.02197 + 4.29764I
u = −0.042812 − 0.461983I
a = 0.607968 + 0.141210I
b = −0.483667 − 0.704865I
−0.05266 + 1.50098I −0.02197 − 4.29764I
u = 0.356191 + 0.267829I
a = 3.24304 − 0.81630I
b = 0.893142 + 0.274911I
−2.56232 − 0.10384I −4.50255 − 2.19281I
u = 0.356191 − 0.267829I
a = 3.24304 + 0.81630I
b = 0.893142 − 0.274911I
−2.56232 + 0.10384I −4.50255 + 2.19281I
17
II. I
v
1
= ha, 1728v
9
+ 4936v
8
+ · · · + 3335b + 613, v
10
+ 3v
9
+ · · · + v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
8
=
1
0
a
3
=
v
0
a
12
=
0
−0.518141v
9
− 1.48006v
8
+ ··· + 1.48006v
2
− 0.183808
a
7
=
1
−0.462969v
9
− 1.33373v
8
+ ··· + 1.33373v
2
− 1.81379
a
10
=
−0.462969v
9
− 1.33373v
8
+ ··· + 1.33373v
2
− 0.813793
1.14783v
9
+ 3.29565v
8
+ ··· − 3.29565v
2
+ 1.75652
a
1
=
−0.684858v
9
− 1.96192v
8
+ ··· + 1.96192v
2
− 0.942729
1.14783v
9
+ 3.29565v
8
+ ··· − 3.29565v
2
+ 1.75652
a
11
=
0.518141v
9
+ 1.48006v
8
+ ··· − 1.48006v
2
+ 0.183808
−0.518141v
9
− 1.48006v
8
+ ··· + 1.48006v
2
− 0.183808
a
6
=
0.684858v
9
+ 1.96192v
8
+ ··· − 1.96192v
2
+ 0.942729
−1.14783v
9
− 3.29565v
8
+ ··· + 3.29565v
2
− 1.75652
a
5
=
0.0737631v
9
+ 0.147526v
8
+ ··· + 5.22189v + 0.331634
−0.147826v
9
− 0.295652v
8
+ ··· − 7v − 0.756522
a
2
=
−0.832684v
9
− 2.38801v
8
+ ··· + v − 1.09055
1.14783v
9
+ 3.29565v
8
+ ··· − 3.29565v
2
+ 1.75652
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
3569
3335
v
9
+
11338
3335
v
8
+
24271
3335
v
7
−
19009
3335
v
6
−
11425
667
v
5
+
47611
3335
v
4
+
210931
3335
v
3
+
62177
3335
v
2
+
151
23
v−
27686
3335
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
8
u
10
c
6
, c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
7
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
9
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
5
c
3
, c
8
y
10
c
6
, c
10
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
c
7
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
c
9
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.38814 + 0.78973I
a = 0
b = −0.339110 + 0.822375I
−0.32910 − 3.56046I −2.01870 + 9.75023I
v = −1.38814 − 0.78973I
a = 0
b = −0.339110 − 0.822375I
−0.32910 + 3.56046I −2.01870 − 9.75023I
v = 1.37799 + 0.80730I
a = 0
b = −0.339110 + 0.822375I
−0.329100 + 0.499304I −1.95395 − 0.91636I
v = 1.37799 − 0.80730I
a = 0
b = −0.339110 − 0.822375I
−0.329100 − 0.499304I −1.95395 + 0.91636I
v = 0.294694 + 0.220725I
a = 0
b = 0.455697 − 1.200150I
−5.87256 − 2.37095I −6.85700 + 6.98324I
v = 0.294694 − 0.220725I
a = 0
b = 0.455697 + 1.200150I
−5.87256 + 2.37095I −6.85700 − 6.98324I
v = −0.338500 + 0.144851I
a = 0
b = 0.455697 − 1.200150I
−5.87256 − 6.43072I −9.93110 + 1.72471I
v = −0.338500 − 0.144851I
a = 0
b = 0.455697 + 1.200150I
−5.87256 + 6.43072I −9.93110 − 1.72471I
v = −1.44605 + 2.50463I
a = 0
b = 0.766826
−2.40108 + 2.02988I 2.76075 + 3.67600I
v = −1.44605 − 2.50463I
a = 0
b = 0.766826
−2.40108 − 2.02988I 2.76075 − 3.67600I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
5
)(u
124
+ 42u
123
+ ··· + 2u + 1)
c
2
((u
2
+ u + 1)
5
)(u
124
+ 6u
123
+ ··· + 2u + 1)
c
3
, c
8
u
10
(u
124
− u
123
+ ··· + 5120u + 1024)
c
5
((u
2
− u + 1)
5
)(u
124
+ 6u
123
+ ··· + 2u + 1)
c
6
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
124
+ 3u
123
+ ··· − 376993u − 48793)
c
7
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
124
− 3u
123
+ ··· + 1975u + 1031)
c
9
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
)(u
124
− 9u
123
+ ··· − 3u + 1)
c
10
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
124
− 3u
123
+ ··· − 17u + 1)
c
11
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
124
+ 21u
123
+ ··· + 3u + 1)
c
12
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
124
− 3u
123
+ ··· − 17u + 1)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
5
)(y
124
+ 86y
123
+ ··· − 1250y + 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
124
+ 42y
123
+ ··· + 2y + 1)
c
3
, c
8
y
10
(y
124
− 55y
123
+ ··· − 2.62144 × 10
7
y + 1048576)
c
6
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
124
+ 83y
123
+ ··· − 318551403169y + 2380756849)
c
7
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
· (y
124
+ 131y
123
+ ··· + 138554707y + 1062961)
c
9
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
)(y
124
− 21y
123
+ ··· − 9y + 1)
c
10
, c
12
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
)(y
124
− 85y
123
+ ··· − 17y + 1)
c
11
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
)(y
124
+ 3y
123
+ ··· − 17y + 1)
23
