12n
0022
(K12n
0022
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 10 11 5 12 1 9 7
Solving Sequence
9,11
12
5,10
4 8 7 1 6 3 2
c
11
c
9
c
4
c
8
c
7
c
12
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.22558 × 10
224
u
83
+ 1.62605 × 10
225
u
82
+ ··· + 2.32318 × 10
225
b + 2.05431 × 10
225
,
1.34240 × 10
225
u
83
+ 9.14747 × 10
225
u
82
+ ··· + 2.32318 × 10
225
a + 1.22489 × 10
225
, u
84
+ 7u
83
+ ··· + 19u + 1i
I
u
2
= h−u
4
b − u
3
b + 2u
4
+ u
2
b + 4u
3
+ b
2
− b − u + 2, a, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
I
u
3
= h−2a
3
+ b − 5a − 1, a
4
− a
3
+ 3a
2
− 2a + 1, u − 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
= h2.23 × 10
224
u
83
+ 1.63 × 10
225
u
82
+ · · · + 2.32 × 10
225
b + 2.05 ×
10
225
, 1.34 × 10
225
u
83
+ 9.15 × 10
225
u
82
+ · · · + 2.32 × 10
225
a + 1.22 ×
10
225
, u
84
+ 7u
83
+ · · · + 19u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
5
=
−0.577827u
83
− 3.93748u
82
+ ··· − 101.647u − 0.527248
−0.0957989u
83
− 0.699925u
82
+ ··· − 13.0229u − 0.884264
a
10
=
u
−u
3
+ u
a
4
=
−0.577827u
83
− 3.93748u
82
+ ··· − 101.647u − 0.527248
−0.0821773u
83
− 0.611145u
82
+ ··· − 11.5617u − 0.776950
a
8
=
0.982090u
83
+ 6.78620u
82
+ ··· + 125.606u + 9.18920
0.0715056u
83
+ 0.535672u
82
+ ··· + 11.4628u + 1.15633
a
7
=
0.910584u
83
+ 6.25053u
82
+ ··· + 114.143u + 8.03287
0.0715056u
83
+ 0.535672u
82
+ ··· + 11.4628u + 1.15633
a
1
=
0.222432u
83
+ 1.54054u
82
+ ··· + 4.65720u + 4.57953
0.0211304u
83
+ 0.0895277u
82
+ ··· − 0.444083u + 0.205948
a
6
=
0.860405u
83
+ 5.98086u
82
+ ··· + 112.669u + 7.91304
0.116676u
83
+ 0.831091u
82
+ ··· + 11.4882u + 1.11809
a
3
=
−0.337224u
83
− 2.15359u
82
+ ··· − 80.3989u + 4.87290
−0.0485546u
83
− 0.398974u
82
+ ··· − 10.5681u − 0.387718
a
2
=
−1.01424u
83
− 6.93488u
82
+ ··· − 144.713u − 6.43592
−0.171241u
83
− 1.16510u
82
+ ··· − 12.7424u − 1.08398
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.661245u
83
− 4.69918u
82
+ ··· − 96.1927u − 11.9327
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
+ u
83
+ ··· − 1664u + 101
c
7
u
84
− 5u
83
+ ··· + 78942u + 33589
c
9
, c
11
u
84
+ 7u
83
+ ··· + 19u + 1
c
10
u
84
− 13u
83
+ ··· + 104u + 16
c
12
u
84
+ 4u
83
+ ··· + 3u + 1
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
+ 69y
83
+ ··· − 1278338y + 10201
c
7
y
84
+ 85y
83
+ ··· − 18778069822y + 1128220921
c
9
, c
11
y
84
− 49y
83
+ ··· − 211y + 1
c
10
y
84
− 21y
83
+ ··· − 19776y + 256
c
12
y
84
− 24y
83
+ ··· + 11y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972442 + 0.213795I
a = −1.091770 + 0.371559I
b = 0.06522 + 2.55411I
−0.637274 + 0.732588I 0
u = 0.972442 − 0.213795I
a = −1.091770 − 0.371559I
b = 0.06522 − 2.55411I
−0.637274 − 0.732588I 0
u = 1.008760 + 0.011115I
a = −0.356315 − 0.506244I
b = −4.87249 − 4.18408I
1.40295 − 1.45862I 0
u = 1.008760 − 0.011115I
a = −0.356315 + 0.506244I
b = −4.87249 + 4.18408I
1.40295 + 1.45862I 0
u = 0.910290 + 0.355435I
a = 1.315660 − 0.399016I
b = 0.02342 − 2.05906I
−4.18720 − 3.29608I 0
u = 0.910290 − 0.355435I
a = 1.315660 + 0.399016I
b = 0.02342 + 2.05906I
−4.18720 + 3.29608I 0
u = −0.320871 + 0.909040I
a = −1.114210 + 0.444929I
b = −0.125891 + 0.751460I
−3.15026 + 4.66896I 0
u = −0.320871 − 0.909040I
a = −1.114210 − 0.444929I
b = −0.125891 − 0.751460I
−3.15026 − 4.66896I 0
u = −0.955077 + 0.022703I
a = 0.04180 + 1.68922I
b = −0.014974 + 0.435556I
8.34326 − 3.21240I 0
u = −0.955077 − 0.022703I
a = 0.04180 − 1.68922I
b = −0.014974 − 0.435556I
8.34326 + 3.21240I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.924612 + 0.497424I
a = 0.734134 − 1.203290I
b = 0.236759 − 0.476931I
−1.47667 − 1.22264I 0
u = −0.924612 − 0.497424I
a = 0.734134 + 1.203290I
b = 0.236759 + 0.476931I
−1.47667 + 1.22264I 0
u = 0.331216 + 0.881361I
a = 0.676599 − 0.353102I
b = −0.240051 − 0.675771I
−0.20954 + 2.08673I 0
u = 0.331216 − 0.881361I
a = 0.676599 + 0.353102I
b = −0.240051 + 0.675771I
−0.20954 − 2.08673I 0
u = −0.617703 + 0.685861I
a = −1.34773 − 1.23740I
b = 0.162497 − 1.031290I
−8.44334 − 3.92581I 0
u = −0.617703 − 0.685861I
a = −1.34773 + 1.23740I
b = 0.162497 + 1.031290I
−8.44334 + 3.92581I 0
u = 1.079180 + 0.258468I
a = 1.109110 − 0.542042I
b = 0.36270 − 2.45765I
−3.79074 + 5.18593I 0
u = 1.079180 − 0.258468I
a = 1.109110 + 0.542042I
b = 0.36270 + 2.45765I
−3.79074 − 5.18593I 0
u = 0.993301 + 0.517113I
a = −0.476198 − 0.466599I
b = 1.093620 − 0.529398I
1.55672 + 3.93406I 0
u = 0.993301 − 0.517113I
a = −0.476198 + 0.466599I
b = 1.093620 + 0.529398I
1.55672 − 3.93406I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.030100 + 0.473272I
a = 0.752223 + 1.062450I
b = −0.26649 + 1.44063I
−2.21135 − 4.59052I 0
u = −1.030100 − 0.473272I
a = 0.752223 − 1.062450I
b = −0.26649 − 1.44063I
−2.21135 + 4.59052I 0
u = 0.858393 + 0.054295I
a = −0.165809 − 0.777617I
b = 2.21383 − 0.21187I
0.83780 − 1.60534I 11.55428 + 0.I
u = 0.858393 − 0.054295I
a = −0.165809 + 0.777617I
b = 2.21383 + 0.21187I
0.83780 + 1.60534I 11.55428 + 0.I
u = −1.058300 + 0.459470I
a = 1.025540 + 0.596498I
b = −1.05338 + 1.07754I
1.64539 − 2.41566I 0
u = −1.058300 − 0.459470I
a = 1.025540 − 0.596498I
b = −1.05338 − 1.07754I
1.64539 + 2.41566I 0
u = 1.142540 + 0.177564I
a = −0.337203 + 0.263085I
b = 3.94715 + 2.02247I
2.34989 − 1.68894I 0
u = 1.142540 − 0.177564I
a = −0.337203 − 0.263085I
b = 3.94715 − 2.02247I
2.34989 + 1.68894I 0
u = −0.935581 + 0.684978I
a = −0.673974 − 1.122900I
b = 0.10781 − 1.52966I
−7.54628 − 1.28985I 0
u = −0.935581 − 0.684978I
a = −0.673974 + 1.122900I
b = 0.10781 + 1.52966I
−7.54628 + 1.28985I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.646868 + 0.523459I
a = −1.29135 + 0.69575I
b = −0.171529 + 0.706893I
−2.28832 − 2.96266I 0
u = −0.646868 − 0.523459I
a = −1.29135 − 0.69575I
b = −0.171529 − 0.706893I
−2.28832 + 2.96266I 0
u = −1.126650 + 0.469056I
a = −0.586175 + 0.912908I
b = −0.242673 + 0.366478I
2.64295 − 5.32501I 0
u = −1.126650 − 0.469056I
a = −0.586175 − 0.912908I
b = −0.242673 − 0.366478I
2.64295 + 5.32501I 0
u = −1.142420 + 0.498662I
a = −0.708361 − 1.021390I
b = 0.32261 − 1.53994I
−4.74130 − 10.12840I 0
u = −1.142420 − 0.498662I
a = −0.708361 + 1.021390I
b = 0.32261 + 1.53994I
−4.74130 + 10.12840I 0
u = 1.194600 + 0.385549I
a = 0.359098 − 0.436451I
b = −2.04003 − 1.89368I
2.92160 + 2.77404I 0
u = 1.194600 − 0.385549I
a = 0.359098 + 0.436451I
b = −2.04003 + 1.89368I
2.92160 − 2.77404I 0
u = −0.226720 + 1.234900I
a = −0.522923 − 0.990090I
b = −0.02217 − 1.67883I
−4.54665 + 5.72043I 0
u = −0.226720 − 1.234900I
a = −0.522923 + 0.990090I
b = −0.02217 + 1.67883I
−4.54665 − 5.72043I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.153780 + 0.515980I
a = −0.859747 − 0.652054I
b = 1.11954 − 1.39330I
2.03077 − 8.41785I 0
u = −1.153780 − 0.515980I
a = −0.859747 + 0.652054I
b = 1.11954 + 1.39330I
2.03077 + 8.41785I 0
u = −0.190457 + 0.689630I
a = −0.255146 − 1.215230I
b = −0.34868 − 1.70071I
−0.72347 + 3.79694I −4.78687 − 5.26590I
u = −0.190457 − 0.689630I
a = −0.255146 + 1.215230I
b = −0.34868 + 1.70071I
−0.72347 − 3.79694I −4.78687 + 5.26590I
u = −0.280053 + 0.652017I
a = −1.46834 − 1.72562I
b = −0.225602 − 0.904495I
−7.27588 + 5.64053I −4.23717 − 1.44618I
u = −0.280053 − 0.652017I
a = −1.46834 + 1.72562I
b = −0.225602 + 0.904495I
−7.27588 − 5.64053I −4.23717 + 1.44618I
u = −0.413220 + 1.230540I
a = 0.552234 + 1.040430I
b = 0.04555 + 1.65819I
−9.11776 + 1.81197I 0
u = −0.413220 − 1.230540I
a = 0.552234 − 1.040430I
b = 0.04555 − 1.65819I
−9.11776 − 1.81197I 0
u = 1.258140 + 0.371030I
a = 0.447345 + 0.321206I
b = −0.744087 + 0.186455I
2.97676 + 0.06912I 0
u = 1.258140 − 0.371030I
a = 0.447345 − 0.321206I
b = −0.744087 − 0.186455I
2.97676 − 0.06912I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.173850 + 0.596639I
a = 0.760441 − 0.817940I
b = 0.321304 − 0.359548I
−0.55121 − 10.15270I 0
u = −1.173850 − 0.596639I
a = 0.760441 + 0.817940I
b = 0.321304 + 0.359548I
−0.55121 + 10.15270I 0
u = −0.432278 + 0.520555I
a = 1.72365 + 1.42967I
b = 0.019219 + 0.763148I
−3.91699 + 0.49402I −1.75716 + 2.00639I
u = −0.432278 − 0.520555I
a = 1.72365 − 1.42967I
b = 0.019219 − 0.763148I
−3.91699 − 0.49402I −1.75716 − 2.00639I
u = 1.35490
a = 0.339763
b = −0.449694
2.55442 0
u = −0.198732 + 1.355280I
a = 0.556728 + 0.968007I
b = 0.00784 + 1.65359I
−7.54281 + 10.87570I 0
u = −0.198732 − 1.355280I
a = 0.556728 − 0.968007I
b = 0.00784 − 1.65359I
−7.54281 − 10.87570I 0
u = −1.24156 + 0.72441I
a = 0.727402 + 0.901724I
b = −0.73376 + 1.74424I
−6.44809 − 8.61020I 0
u = −1.24156 − 0.72441I
a = 0.727402 − 0.901724I
b = −0.73376 − 1.74424I
−6.44809 + 8.61020I 0
u = −1.44705 + 0.17137I
a = 0.315816 + 0.194686I
b = 0.118682 + 0.118584I
5.61123 − 2.65441I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44705 − 0.17137I
a = 0.315816 − 0.194686I
b = 0.118682 − 0.118584I
5.61123 + 2.65441I 0
u = 1.18182 + 0.87280I
a = 0.462410 − 0.603044I
b = −0.84076 − 1.49220I
0.99043 + 3.63889I 0
u = 1.18182 − 0.87280I
a = 0.462410 + 0.603044I
b = −0.84076 + 1.49220I
0.99043 − 3.63889I 0
u = −1.45343 + 0.26296I
a = −0.344788 + 0.135869I
b = −0.165511 + 0.031545I
5.71423 − 6.06522I 0
u = −1.45343 − 0.26296I
a = −0.344788 − 0.135869I
b = −0.165511 − 0.031545I
5.71423 + 6.06522I 0
u = −1.32402 + 0.65852I
a = −0.637359 − 0.834221I
b = 0.86308 − 1.90054I
−1.06531 − 12.31450I 0
u = −1.32402 − 0.65852I
a = −0.637359 + 0.834221I
b = 0.86308 + 1.90054I
−1.06531 + 12.31450I 0
u = 0.99893 + 1.09943I
a = −0.550292 + 0.618639I
b = 0.56906 + 1.29599I
−2.69617 + 0.11948I 0
u = 0.99893 − 1.09943I
a = −0.550292 − 0.618639I
b = 0.56906 − 1.29599I
−2.69617 − 0.11948I 0
u = −0.383297 + 0.340658I
a = 0.66058 + 1.72839I
b = 0.333450 + 1.212380I
−0.303408 − 1.335140I −3.78742 + 3.57340I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.383297 − 0.340658I
a = 0.66058 − 1.72839I
b = 0.333450 − 1.212380I
−0.303408 + 1.335140I −3.78742 − 3.57340I
u = −1.37417 + 0.68442I
a = 0.588585 + 0.869316I
b = −0.79291 + 1.99045I
−3.7955 − 17.8954I 0
u = −1.37417 − 0.68442I
a = 0.588585 − 0.869316I
b = −0.79291 − 1.99045I
−3.7955 + 17.8954I 0
u = −0.056966 + 0.445178I
a = 1.48669 + 0.28338I
b = 0.203441 − 0.603272I
−0.081645 + 1.388350I −0.20547 − 3.77437I
u = −0.056966 − 0.445178I
a = 1.48669 − 0.28338I
b = 0.203441 + 0.603272I
−0.081645 − 1.388350I −0.20547 + 3.77437I
u = 1.55444
a = 0.508397
b = −0.418678
2.51357 0
u = 1.30994 + 1.00098I
a = −0.459489 + 0.660570I
b = 0.66060 + 1.60930I
−1.81006 + 8.25159I 0
u = 1.30994 − 1.00098I
a = −0.459489 − 0.660570I
b = 0.66060 − 1.60930I
−1.81006 − 8.25159I 0
u = 0.172995 + 0.034028I
a = −1.87202 + 3.59277I
b = 0.345343 − 0.709443I
−0.194651 + 1.319340I −1.46532 − 4.00362I
u = 0.172995 − 0.034028I
a = −1.87202 − 3.59277I
b = 0.345343 + 0.709443I
−0.194651 − 1.319340I −1.46532 + 4.00362I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.82009 + 0.15092I
a = −0.657590 − 0.068438I
b = 0.287435 − 0.079406I
−0.33247 − 3.91395I 0
u = 1.82009 − 0.15092I
a = −0.657590 + 0.068438I
b = 0.287435 + 0.079406I
−0.33247 + 3.91395I 0
u = −0.0795493 + 0.0409515I
a = 7.05665 − 2.72768I
b = 0.405023 − 0.635618I
−0.176677 + 1.378470I −2.64856 − 4.43072I
u = −0.0795493 − 0.0409515I
a = 7.05665 + 2.72768I
b = 0.405023 + 0.635618I
−0.176677 − 1.378470I −2.64856 + 4.43072I
13
II. I
u
2
= h−u
4
b + 2u
4
+ · · · − b + 2, a, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
5
=
0
b
a
10
=
u
−u
3
+ u
a
4
=
0
b
a
8
=
0
u
a
7
=
−u
u
a
1
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
6
=
u
4
− u
2
− 1
−u
4
+ 2u
2
a
3
=
u
4
b − u
3
b − 2u
2
b + 3bu − b
−bu + 2b
a
2
=
u
4
b − u
3
b − 2u
2
b + 3bu − b
−u
4
− u
3
− bu + u
2
+ 2b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
4
b + 5u
3
b − u
4
+ 9u
2
b + u
3
− 6bu − 2u
2
+ 6b − 7u + 3
14
(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
, c
9
(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
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
15
(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
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
7
, c
9
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 0
b = 1.76091 + 3.04998I
2.40108 − 2.02988I −2.76075 + 10.60420I
u = 1.21774
a = 0
b = 1.76091 − 3.04998I
2.40108 + 2.02988I −2.76075 − 10.60420I
u = 0.309916 + 0.549911I
a = 0
b = 0.864485 + 0.518603I
0.329100 − 0.499304I 2.01870 − 2.82203I
u = 0.309916 + 0.549911I
a = 0
b = 0.016881 − 1.007970I
0.32910 + 3.56046I 1.95395 − 6.01185I
u = 0.309916 − 0.549911I
a = 0
b = 0.864485 − 0.518603I
0.329100 + 0.499304I 2.01870 + 2.82203I
u = 0.309916 − 0.549911I
a = 0
b = 0.016881 + 1.007970I
0.32910 − 3.56046I 1.95395 + 6.01185I
u = −1.41878 + 0.21917I
a = 0
b = 0.369732 − 0.377747I
5.87256 − 6.43072I 6.8570 + 13.9114I
u = −1.41878 + 0.21917I
a = 0
b = −0.512005 − 0.131324I
5.87256 − 2.37095I 9.93110 − 5.20350I
u = −1.41878 − 0.21917I
a = 0
b = 0.369732 + 0.377747I
5.87256 + 6.43072I 6.8570 − 13.9114I
u = −1.41878 − 0.21917I
a = 0
b = −0.512005 + 0.131324I
5.87256 + 2.37095I 9.93110 + 5.20350I
17
III. I
u
3
= h−2a
3
+ b − 5a − 1, a
4
− a
3
+ 3a
2
− 2a + 1, u − 1i
(i) Arc colorings
a
9
=
0
1
a
11
=
1
0
a
12
=
1
−1
a
5
=
a
2a
3
+ 5a + 1
a
10
=
1
0
a
4
=
a
2a
3
+ 4a + 1
a
8
=
a
2
2a
3
− a
2
+ 5a − 1
a
7
=
−2a
3
+ 2a
2
− 5a + 1
2a
3
− a
2
+ 5a − 1
a
1
=
−a
3
+ 3a
2
− 2a + 1
0
a
6
=
a
2
2a
3
− a
2
+ 5a − 1
a
3
=
a
3
+ a
2
+ 1
a
3
+ a
2
+ 2a + 3
a
2
=
a
3
+ a
2a
3
− a
2
+ 5a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15a
3
+ 3a
2
− 46a + 36
18
(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 + 1)
4
c
10
u
4
c
11
(u − 1)
4
c
12
u
4
+ 5u
3
+ 7u
2
+ 2u + 1
19
(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
, c
11
(y −1)
4
c
10
y
4
c
12
y
4
− 11y
3
+ 31y
2
+ 10y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.395123 + 0.506844I
b = 2.48997 + 2.74859I
1.43393 − 1.41510I 21.1644 − 23.7210I
u = 1.00000
a = 0.395123 − 0.506844I
b = 2.48997 − 2.74859I
1.43393 + 1.41510I 21.1644 + 23.7210I
u = 1.00000
a = 0.10488 + 1.55249I
b = 0.010029 + 0.381188I
8.43568 − 3.16396I 35.3356 − 15.0782I
u = 1.00000
a = 0.10488 − 1.55249I
b = 0.010029 − 0.381188I
8.43568 + 3.16396I 35.3356 + 15.0782I
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
+ u
83
+ ··· − 1664u + 101)
c
7
(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
8
u
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
84
+ 2u
83
+ ··· + 3072u + 1024)
c
9
((u + 1)
4
)(u
5
− u
4
+ ··· + u + 1)
2
(u
84
+ 7u
83
+ ··· + 19u + 1)
c
10
u
4
(u
5
+ u
4
+ ··· + u + 1)
2
(u
84
− 13u
83
+ ··· + 104u + 16)
c
11
((u − 1)
4
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
84
+ 7u
83
+ ··· + 19u + 1)
c
12
(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)
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
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
84
+ 69y
83
+ ··· − 1278338y + 10201)
c
7
(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
9
, c
11
(y −1)
4
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
84
− 49y
83
+ ··· − 211y + 1)
c
10
y
4
(y
5
+ 3y
4
+ ··· − y −1)
2
(y
84
− 21y
83
+ ··· − 19776y + 256)
c
12
(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)
23
