12n
0030
(K12n
0030
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 11 12 5 7 1 9 10
Solving Sequence
5,8
9
4,12
7 10 1 11 6 3 2
c
8
c
4
c
7
c
9
c
12
c
11
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.62545 × 10
313
u
83
+ 6.15170 × 10
313
u
82
+ ··· + 6.32484 × 10
315
b + 7.92185 × 10
316
,
− 3.59853 × 10
313
u
83
− 1.80819 × 10
314
u
82
+ ··· + 2.52993 × 10
316
a − 6.87140 × 10
317
,
u
84
+ 2u
83
+ ··· + 3072u + 1024i
I
u
2
= h2u
3
+ u
2
+ b + 5u + 1, −3u
3
− 4u
2
+ a − 8u − 8, u
4
+ u
3
+ 3u
2
+ 2u + 1i
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
* 3 irreducible components of dim
C
= 0, with total 98 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
= h3.63 × 10
313
u
83
+ 6.15 × 10
313
u
82
+ · · · + 6.32 × 10
315
b + 7.92 ×
10
316
, −3.60 × 10
313
u
83
− 1.81 × 10
314
u
82
+ · · · + 2.53 × 10
316
a − 6.87 ×
10
317
, u
84
+ 2u
83
+ · · · + 3072u + 1024i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
12
=
0.00142238u
83
+ 0.00714717u
82
+ ··· + 4.37921u + 27.1604
−0.00573208u
83
− 0.00972627u
82
+ ··· − 21.7493u − 12.5250
a
7
=
−0.00440220u
83
− 0.0155721u
82
+ ··· − 21.1672u − 21.6501
0.00850686u
83
+ 0.0117475u
82
+ ··· + 21.9408u + 4.77851
a
10
=
−0.00557181u
83
− 0.00516502u
82
+ ··· − 14.6483u + 9.47061
0.000335853u
83
+ 0.000887942u
82
+ ··· − 1.07766u + 3.84523
a
1
=
0.00764905u
83
+ 0.0136726u
82
+ ··· + 20.6805u + 20.3223
0.00313239u
83
+ 0.00646405u
82
+ ··· + 8.74407u + 11.6319
a
11
=
−0.000790893u
83
+ 0.00283051u
82
+ ··· − 2.69654u + 19.0410
−0.00542175u
83
− 0.00957199u
82
+ ··· − 19.8204u − 12.6375
a
6
=
0.00451666u
83
+ 0.00720851u
82
+ ··· + 11.9364u + 8.69044
−0.00262839u
83
− 0.00551221u
82
+ ··· − 7.76333u − 9.76326
a
3
=
−0.0106686u
83
− 0.0158171u
82
+ ··· − 36.1449u − 16.7400
−0.00641780u
83
− 0.0100395u
82
+ ··· − 20.3360u − 13.7909
a
2
=
−0.0106686u
83
− 0.0158171u
82
+ ··· − 36.1449u − 16.7400
−0.00837526u
83
− 0.0135852u
82
+ ··· − 26.3690u − 19.4434
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0168619u
83
− 0.00458246u
82
+ ··· + 15.0455u + 47.7451
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
84
+ 43u
83
+ ··· − 18u + 1
c
2
, c
5
u
84
+ 7u
83
+ ··· + 8u + 1
c
3
u
84
− 7u
83
+ ··· + 18564u + 47236
c
4
, c
8
u
84
+ 2u
83
+ ··· + 3072u + 1024
c
6
u
84
− 5u
83
+ ··· + 78942u + 33589
c
7
u
84
+ u
83
+ ··· − 1664u + 101
c
9
u
84
+ 4u
83
+ ··· + 3u + 1
c
10
, c
12
u
84
+ 7u
83
+ ··· + 19u + 1
c
11
u
84
− 13u
83
+ ··· + 104u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
84
+ 3y
83
+ ··· − 590y + 1
c
2
, c
5
y
84
+ 43y
83
+ ··· − 18y + 1
c
3
y
84
− 37y
83
+ ··· − 5800852456y + 2231239696
c
4
, c
8
y
84
− 50y
83
+ ··· − 22020096y + 1048576
c
6
y
84
+ 85y
83
+ ··· − 18778069822y + 1128220921
c
7
y
84
+ 69y
83
+ ··· − 1278338y + 10201
c
9
y
84
− 24y
83
+ ··· + 11y + 1
c
10
, c
12
y
84
− 49y
83
+ ··· − 211y + 1
c
11
y
84
− 21y
83
+ ··· − 19776y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.841987 + 0.437455I
a = −0.264125 − 1.135590I
b = −0.274994 − 0.228453I
−0.303408 + 1.335140I 0
u = −0.841987 − 0.437455I
a = −0.264125 + 1.135590I
b = −0.274994 + 0.228453I
−0.303408 − 1.335140I 0
u = 0.886655 + 0.055494I
a = −1.59300 + 1.49212I
b = −0.527659 + 0.467864I
−0.72347 + 3.79694I −4.78687 − 5.26590I
u = 0.886655 − 0.055494I
a = −1.59300 − 1.49212I
b = −0.527659 − 0.467864I
−0.72347 − 3.79694I −4.78687 + 5.26590I
u = 1.072820 + 0.309098I
a = 0.342724 − 0.766994I
b = 0.220027 + 1.047230I
0.99043 − 3.63889I 0
u = 1.072820 − 0.309098I
a = 0.342724 + 0.766994I
b = 0.220027 − 1.047230I
0.99043 + 3.63889I 0
u = −1.141120 + 0.127904I
a = −0.75584 + 1.46099I
b = −0.19924 + 2.65235I
−0.637274 + 0.732588I 0
u = −1.141120 − 0.127904I
a = −0.75584 − 1.46099I
b = −0.19924 − 2.65235I
−0.637274 − 0.732588I 0
u = −0.046941 + 1.155630I
a = 0.338929 + 0.087109I
b = 0.748631 + 0.426172I
−3.15026 − 4.66896I 0
u = −0.046941 − 1.155630I
a = 0.338929 − 0.087109I
b = 0.748631 − 0.426172I
−3.15026 + 4.66896I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.186540 + 0.223808I
a = 1.61465 + 0.24749I
b = 0.276148 − 0.192975I
−0.33247 + 3.91395I 0
u = −1.186540 − 0.223808I
a = 1.61465 − 0.24749I
b = 0.276148 + 0.192975I
−0.33247 − 3.91395I 0
u = 0.790274
a = 2.22730
b = −0.0927414
2.51357 6.43370
u = 0.471133 + 1.126030I
a = 0.225686 + 0.214193I
b = 0.489548 + 0.020552I
−2.28832 + 2.96266I 0
u = 0.471133 − 1.126030I
a = 0.225686 − 0.214193I
b = 0.489548 − 0.020552I
−2.28832 − 2.96266I 0
u = −1.229850 + 0.012969I
a = 0.363787 + 0.498046I
b = 0.341018 − 1.175440I
−2.69617 + 0.11948I 0
u = −1.229850 − 0.012969I
a = 0.363787 − 0.498046I
b = 0.341018 + 1.175440I
−2.69617 − 0.11948I 0
u = −0.231724 + 0.709721I
a = 1.98561 + 2.84121I
b = −0.396332 − 0.930995I
1.55672 − 3.93406I 5.95351 + 6.01840I
u = −0.231724 − 0.709721I
a = 1.98561 − 2.84121I
b = −0.396332 + 0.930995I
1.55672 + 3.93406I 5.95351 − 6.01840I
u = 0.443646 + 0.570101I
a = 2.38081 − 1.64856I
b = −0.357450 + 0.659687I
2.97676 + 0.06912I 8.15601 − 0.00886I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.443646 − 0.570101I
a = 2.38081 + 1.64856I
b = −0.357450 − 0.659687I
2.97676 − 0.06912I 8.15601 + 0.00886I
u = 0.535311 + 0.479375I
a = 0.553170 + 0.091063I
b = 0.530724 − 0.879230I
−0.20954 + 2.08673I −1.51899 − 3.33594I
u = 0.535311 − 0.479375I
a = 0.553170 − 0.091063I
b = 0.530724 + 0.879230I
−0.20954 − 2.08673I −1.51899 + 3.33594I
u = −0.446102 + 0.557829I
a = 0.651382 − 0.372945I
b = −0.221050 − 0.694468I
−0.194651 + 1.319340I −1.46532 − 4.00362I
u = −0.446102 − 0.557829I
a = 0.651382 + 0.372945I
b = −0.221050 + 0.694468I
−0.194651 − 1.319340I −1.46532 + 4.00362I
u = 0.597250 + 0.382933I
a = 0.86560 − 2.16525I
b = 0.402385 + 0.725463I
2.92160 − 2.77404I 6.32422 + 8.38902I
u = 0.597250 − 0.382933I
a = 0.86560 + 2.16525I
b = 0.402385 − 0.725463I
2.92160 + 2.77404I 6.32422 − 8.38902I
u = −0.100108 + 0.676504I
a = 2.46560 + 3.99891I
b = −0.62925 − 1.63616I
0.83780 + 1.60534I 11.55428 − 5.80054I
u = −0.100108 − 0.676504I
a = 2.46560 − 3.99891I
b = −0.62925 + 1.63616I
0.83780 − 1.60534I 11.55428 + 5.80054I
u = −0.210845 + 0.645700I
a = 0.524500 − 0.248408I
b = 0.297103 − 0.522586I
−0.081645 + 1.388350I −0.20547 − 3.77437I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.210845 − 0.645700I
a = 0.524500 + 0.248408I
b = 0.297103 + 0.522586I
−0.081645 − 1.388350I −0.20547 + 3.77437I
u = −0.449648 + 0.505965I
a = 0.733323 − 0.546576I
b = 0.002097 − 0.373578I
−0.176677 + 1.378470I −2.64856 − 4.43072I
u = −0.449648 − 0.505965I
a = 0.733323 + 0.546576I
b = 0.002097 + 0.373578I
−0.176677 − 1.378470I −2.64856 + 4.43072I
u = 0.232207 + 1.303470I
a = 0.0976042 − 0.0966176I
b = −1.032530 + 0.870360I
2.64295 + 5.32501I 0
u = 0.232207 − 1.303470I
a = 0.0976042 + 0.0966176I
b = −1.032530 − 0.870360I
2.64295 − 5.32501I 0
u = −1.263120 + 0.405364I
a = 0.179173 + 0.675618I
b = 0.126913 − 1.133430I
−1.81006 + 8.25159I 0
u = −1.263120 − 0.405364I
a = 0.179173 − 0.675618I
b = 0.126913 + 1.133430I
−1.81006 − 8.25159I 0
u = 1.339460 + 0.104413I
a = −0.361683 + 1.004890I
b = −0.61375 + 2.46446I
−4.18720 − 3.29608I 0
u = 1.339460 − 0.104413I
a = −0.361683 − 1.004890I
b = −0.61375 − 2.46446I
−4.18720 + 3.29608I 0
u = 1.328400 + 0.308712I
a = 1.40163 + 0.29106I
b = 1.08954 + 0.93988I
2.03077 − 8.41785I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.328400 − 0.308712I
a = 1.40163 − 0.29106I
b = 1.08954 − 0.93988I
2.03077 + 8.41785I 0
u = −1.359410 + 0.160067I
a = 1.185480 − 0.430459I
b = 1.059200 − 0.760145I
1.64539 + 2.41566I 0
u = −1.359410 − 0.160067I
a = 1.185480 + 0.430459I
b = 1.059200 + 0.760145I
1.64539 − 2.41566I 0
u = 1.337020 + 0.298292I
a = −0.982452 − 0.930609I
b = −0.38347 − 2.94198I
−3.79074 − 5.18593I 0
u = 1.337020 − 0.298292I
a = −0.982452 + 0.930609I
b = −0.38347 + 2.94198I
−3.79074 + 5.18593I 0
u = −0.353810 + 0.514641I
a = −8.96206 − 5.53073I
b = −0.61059 + 3.96105I
1.40295 + 1.45862I −89.698 − 115.931I
u = −0.353810 − 0.514641I
a = −8.96206 + 5.53073I
b = −0.61059 − 3.96105I
1.40295 − 1.45862I −89.698 + 115.931I
u = 1.341220 + 0.421284I
a = −1.49100 + 0.04191I
b = −0.975466 − 0.634144I
−4.54665 − 5.72043I 0
u = 1.341220 − 0.421284I
a = −1.49100 − 0.04191I
b = −0.975466 + 0.634144I
−4.54665 + 5.72043I 0
u = 0.465396 + 0.288139I
a = 0.0853726 − 0.0912661I
b = −0.509528 + 1.280680I
5.71423 + 6.06522I −1.77330 + 4.32385I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.465396 − 0.288139I
a = 0.0853726 + 0.0912661I
b = −0.509528 − 1.280680I
5.71423 − 6.06522I −1.77330 − 4.32385I
u = −0.490366 + 0.227601I
a = 0.0855734 − 0.0910038I
b = −0.361826 + 1.222090I
5.61123 + 2.65441I −4.29638 − 9.51286I
u = −0.490366 − 0.227601I
a = 0.0855734 + 0.0910038I
b = −0.361826 − 1.222090I
5.61123 − 2.65441I −4.29638 + 9.51286I
u = −0.40463 + 1.41385I
a = 0.0930273 + 0.1036470I
b = −1.20423 − 1.01593I
−0.55121 − 10.15270I 0
u = −0.40463 − 1.41385I
a = 0.0930273 − 0.1036470I
b = −1.20423 + 1.01593I
−0.55121 + 10.15270I 0
u = −1.27769 + 0.73843I
a = −0.689832 − 0.368710I
b = −0.510369 + 0.405135I
−2.21135 + 4.59052I 0
u = −1.27769 − 0.73843I
a = −0.689832 + 0.368710I
b = −0.510369 − 0.405135I
−2.21135 − 4.59052I 0
u = −0.08024 + 1.47776I
a = 0.114890 + 0.102038I
b = −1.193040 − 0.588194I
−1.47667 − 1.22264I 0
u = −0.08024 − 1.47776I
a = 0.114890 − 0.102038I
b = −1.193040 + 0.588194I
−1.47667 + 1.22264I 0
u = −0.431983 + 0.240711I
a = 3.56103 + 4.41691I
b = 0.741583 − 0.575469I
2.34989 − 1.68894I −3.22664 − 4.70152I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.431983 − 0.240711I
a = 3.56103 − 4.41691I
b = 0.741583 + 0.575469I
2.34989 + 1.68894I −3.22664 + 4.70152I
u = −1.48932 + 0.27924I
a = 0.952437 + 0.255511I
b = 1.385620 − 0.031678I
−3.91699 + 0.49402I 0
u = −1.48932 − 0.27924I
a = 0.952437 − 0.255511I
b = 1.385620 + 0.031678I
−3.91699 − 0.49402I 0
u = 1.39972 + 0.58890I
a = −0.771211 + 0.440695I
b = −0.730765 − 0.241151I
−7.54628 − 1.28985I 0
u = 1.39972 − 0.58890I
a = −0.771211 − 0.440695I
b = −0.730765 + 0.241151I
−7.54628 + 1.28985I 0
u = −1.50848 + 0.24962I
a = −1.270500 + 0.118685I
b = −1.058770 + 0.479119I
−9.11776 + 1.81197I 0
u = −1.50848 − 0.24962I
a = −1.270500 − 0.118685I
b = −1.058770 − 0.479119I
−9.11776 − 1.81197I 0
u = −1.42256 + 0.56215I
a = −1.374560 − 0.199389I
b = −1.055600 + 0.714255I
−7.54281 + 10.87570I 0
u = −1.42256 − 0.56215I
a = −1.374560 + 0.199389I
b = −1.055600 − 0.714255I
−7.54281 − 10.87570I 0
u = 0.460345
a = 2.98021
b = −0.432563
2.55442 4.59390
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31857 + 0.81362I
a = −0.742286 + 0.349720I
b = −0.568332 − 0.538548I
−4.74130 − 10.12840I 0
u = 1.31857 − 0.81362I
a = −0.742286 − 0.349720I
b = −0.568332 + 0.538548I
−4.74130 + 10.12840I 0
u = 1.39322 + 0.68481I
a = 1.380420 − 0.253552I
b = 1.22232 + 1.28720I
−1.06531 − 12.31450I 0
u = 1.39322 − 0.68481I
a = 1.380420 + 0.253552I
b = 1.22232 − 1.28720I
−1.06531 + 12.31450I 0
u = 1.53635 + 0.47412I
a = 0.932224 − 0.321024I
b = 1.56257 + 0.23956I
−7.27588 − 5.64053I 0
u = 1.53635 − 0.47412I
a = 0.932224 + 0.321024I
b = 1.56257 − 0.23956I
−7.27588 + 5.64053I 0
u = −1.40379 + 0.79175I
a = 1.320760 + 0.367634I
b = 1.23754 − 1.38161I
−3.7955 + 17.8954I 0
u = −1.40379 − 0.79175I
a = 1.320760 − 0.367634I
b = 1.23754 + 1.38161I
−3.7955 − 17.8954I 0
u = −0.07827 + 1.61239I
a = 0.0768134 − 0.0133793I
b = −0.502088 + 0.081114I
8.34326 + 3.21240I 0
u = −0.07827 − 1.61239I
a = 0.0768134 + 0.0133793I
b = −0.502088 − 0.081114I
8.34326 − 3.21240I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55633 + 0.59261I
a = 1.222390 + 0.124537I
b = 1.37056 − 1.18960I
−6.44809 + 8.61020I 0
u = −1.55633 − 0.59261I
a = 1.222390 − 0.124537I
b = 1.37056 + 1.18960I
−6.44809 − 8.61020I 0
u = 1.68119 + 0.16001I
a = 0.920196 − 0.227277I
b = 1.57545 − 0.24084I
−8.44334 + 3.92581I 0
u = 1.68119 − 0.16001I
a = 0.920196 + 0.227277I
b = 1.57545 + 0.24084I
−8.44334 − 3.92581I 0
13
II.
I
u
2
= h2u
3
+ u
2
+ b + 5u + 1 , −3u
3
− 4u
2
+ a − 8u − 8, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
12
=
3u
3
+ 4u
2
+ 8u + 8
−2u
3
− u
2
− 5u − 1
a
7
=
8u
3
+ 19u − 3
3u
3
+ 4u
2
+ 8u + 8
a
10
=
3u
3
+ 5u
2
+ 8u + 9
−2u
3
− 5u − 1
a
1
=
−u
2
− 1
−u
2
a
11
=
3u
3
+ 4u
2
+ 8u + 8
−2u
3
− u
2
− 5u − 1
a
6
=
1
0
a
3
=
u
3
+ 2u
u
3
+ u
a
2
=
u
3
+ 2u
u
3
+ u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 15u
3
+ 3u
2
+ 46u + 36
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
u
4
+ u
3
+ 5u
2
− u + 2
c
5
u
4
+ u
3
+ u
2
+ 1
c
6
, c
7
u
4
− 2u
3
+ 7u
2
− 5u + 1
c
8
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
9
u
4
− 5u
3
+ 7u
2
− 2u + 1
c
10
(u + 1)
4
c
11
u
4
c
12
(u − 1)
4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
6
, c
7
y
4
+ 10y
3
+ 31y
2
− 11y + 1
c
9
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
10
, c
12
(y −1)
4
c
11
y
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 5.16441 + 2.77418I
b = 0.59074 − 2.34806I
1.43393 + 1.41510I 21.1644 + 23.7210I
u = −0.395123 − 0.506844I
a = 5.16441 − 2.77418I
b = 0.59074 + 2.34806I
1.43393 − 1.41510I 21.1644 − 23.7210I
u = −0.10488 + 1.55249I
a = −0.164409 + 0.045467I
b = 0.409261 − 0.055548I
8.43568 + 3.16396I 35.3356 + 15.0782I
u = −0.10488 − 1.55249I
a = −0.164409 − 0.045467I
b = 0.409261 + 0.055548I
8.43568 − 3.16396I 35.3356 − 15.0782I
17
III. I
v
1
= ha, 1728v
9
− 4936v
8
+ · · · + 3335b − 613, v
10
− 3v
9
+ · · · − v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
4
=
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
3
=
0.0737631v
9
− 0.147526v
8
+ ··· + 5.22189v − 0.331634
0.147826v
9
− 0.295652v
8
+ ··· + 7v − 0.756522
a
2
=
−0.0740630v
9
+ 0.278561v
8
+ ··· + 5.22189v − 0.183808
0.147826v
9
− 0.295652v
8
+ ··· + 7v − 0.756522
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
75
667
v
9
−
30
29
v
8
+
2395
667
v
7
−
6267
667
v
6
−
4697
667
v
5
+
16833
667
v
4
+
537
29
v
3
−
55309
667
v
2
+
263
23
v +
8994
667
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, 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
3
c
5
(y
2
+ y + 1)
5
c
4
, 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
0.329100 + 0.499304I 2.01870 + 2.82203I
v = 1.38814 − 0.78973I
a = 0
b = 0.339110 − 0.822375I
0.329100 − 0.499304I 2.01870 − 2.82203I
v = −1.37799 + 0.80730I
a = 0
b = 0.339110 + 0.822375I
0.32910 − 3.56046I 1.95395 + 6.01185I
v = −1.37799 − 0.80730I
a = 0
b = 0.339110 − 0.822375I
0.32910 + 3.56046I 1.95395 − 6.01185I
v = −0.294694 + 0.220725I
a = 0
b = −0.455697 − 1.200150I
5.87256 − 6.43072I 6.8570 + 13.9114I
v = −0.294694 − 0.220725I
a = 0
b = −0.455697 + 1.200150I
5.87256 + 6.43072I 6.8570 − 13.9114I
v = 0.338500 + 0.144851I
a = 0
b = −0.455697 − 1.200150I
5.87256 − 2.37095I 9.93110 − 5.20350I
v = 0.338500 − 0.144851I
a = 0
b = −0.455697 + 1.200150I
5.87256 + 2.37095I 9.93110 + 5.20350I
v = 1.44605 + 2.50463I
a = 0
b = −0.766826
2.40108 − 2.02988I −2.76075 + 10.60420I
v = 1.44605 − 2.50463I
a = 0
b = −0.766826
2.40108 + 2.02988I −2.76075 − 10.60420I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
84
+ 43u
83
+ ··· − 18u + 1)
c
2
((u
2
+ u + 1)
5
)(u
4
− u
3
+ u
2
+ 1)(u
84
+ 7u
83
+ ··· + 8u + 1)
c
3
(u
2
− u + 1)
5
(u
4
+ u
3
+ 5u
2
− u + 2)
· (u
84
− 7u
83
+ ··· + 18564u + 47236)
c
4
u
10
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
84
+ 2u
83
+ ··· + 3072u + 1024)
c
5
((u
2
− u + 1)
5
)(u
4
+ u
3
+ u
2
+ 1)(u
84
+ 7u
83
+ ··· + 8u + 1)
c
6
(u
4
− 2u
3
+ 7u
2
− 5u + 1)(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
· (u
84
− 5u
83
+ ··· + 78942u + 33589)
c
7
(u
4
− 2u
3
+ 7u
2
− 5u + 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
· (u
84
+ u
83
+ ··· − 1664u + 101)
c
8
u
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
84
+ 2u
83
+ ··· + 3072u + 1024)
c
9
(u
4
− 5u
3
+ 7u
2
− 2u + 1)(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· (u
84
+ 4u
83
+ ··· + 3u + 1)
c
10
((u + 1)
4
)(u
5
− u
4
+ ··· + u + 1)
2
(u
84
+ 7u
83
+ ··· + 19u + 1)
c
11
u
4
(u
5
− u
4
+ ··· + u − 1)
2
(u
84
− 13u
83
+ ··· + 104u + 16)
c
12
((u − 1)
4
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
84
+ 7u
83
+ ··· + 19u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
84
+ 3y
83
+ ··· − 590y + 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
84
+ 43y
83
+ ··· − 18y + 1)
c
3
(y
2
+ y + 1)
5
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
· (y
84
− 37y
83
+ ··· − 5800852456y + 2231239696)
c
4
, c
8
y
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
84
− 50y
83
+ ··· − 22020096y + 1048576)
c
6
(y
4
+ 10y
3
+ 31y
2
− 11y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
84
+ 85y
83
+ ··· − 18778069822y + 1128220921)
c
7
(y
4
+ 10y
3
+ 31y
2
− 11y + 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
· (y
84
+ 69y
83
+ ··· − 1278338y + 10201)
c
9
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
84
− 24y
83
+ ··· + 11y + 1)
c
10
, c
12
(y − 1)
4
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
84
− 49y
83
+ ··· − 211y + 1)
c
11
y
4
(y
5
+ 3y
4
+ ··· − y − 1)
2
(y
84
− 21y
83
+ ··· − 19776y + 256)
23
