12a
0318
(K12a
0318
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 9 1 5 7 12 4 10
Solving Sequence
6,9
7
3,10
2 1 5 8 4 12 11
c
6
c
9
c
2
c
1
c
5
c
8
c
3
c
12
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.25817 × 10
400
u
103
+ 6.06573 × 10
400
u
102
+ ··· + 2.71520 × 10
400
b − 4.51803 × 10
402
,
3.84894 × 10
400
u
103
− 1.79264 × 10
401
u
102
+ ··· + 3.39400 × 10
400
a + 2.41261 × 10
403
,
u
104
− 6u
103
+ ··· − 8175u − 625i
I
u
2
= h25a
4
− 5a
3
+ 2a
2
+ 4b + 11a + 3, 25a
5
− 5a
4
+ 2a
3
+ 6a
2
+ 5a − 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 109 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−1.26 × 10
400
u
103
+ 6.07 × 10
400
u
102
+ · · · + 2.72 × 10
400
b − 4.52 ×
10
402
, 3.85 × 10
400
u
103
− 1.79 × 10
401
u
102
+ · · · + 3.39 × 10
400
a + 2.41 ×
10
403
, u
104
− 6u
103
+ · · · − 8175u − 625i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
−u
2
a
3
=
−1.13404u
103
+ 5.28179u
102
+ ··· − 8692.58u − 710.844
0.463381u
103
− 2.23399u
102
+ ··· + 2498.84u + 166.397
a
10
=
u
−u
3
+ u
a
2
=
−0.670662u
103
+ 3.04780u
102
+ ··· − 6193.74u − 544.447
0.463381u
103
− 2.23399u
102
+ ··· + 2498.84u + 166.397
a
1
=
1.07459u
103
− 5.59952u
102
+ ··· − 3167.52u − 538.320
−1.25102u
103
+ 5.81009u
102
+ ··· − 8824.16u − 651.600
a
5
=
0.714651u
103
− 3.81450u
102
+ ··· − 3127.85u − 359.311
−1.30915u
103
+ 6.22051u
102
+ ··· − 7633.41u − 537.319
a
8
=
−0.384925u
103
+ 2.58489u
102
+ ··· + 15388.0u + 1690.93
−0.867986u
103
+ 3.89150u
102
+ ··· − 6473.36u − 445.958
a
4
=
−0.591519u
103
+ 2.65264u
102
+ ··· − 7469.87u − 752.274
−0.496111u
103
+ 2.31885u
102
+ ··· − 3046.93u − 227.266
a
12
=
−0.349150u
103
+ 1.07505u
102
+ ··· − 11968.9u − 1158.87
−0.178604u
103
+ 0.831504u
102
+ ··· − 1466.07u − 104.748
a
11
=
1.68396u
103
− 9.20013u
102
+ ··· − 12447.3u − 1482.86
−0.498847u
103
+ 2.24348u
102
+ ··· − 4062.81u − 346.564
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.235557u
103
+ 1.17647u
102
+ ··· + 281.718u − 57.7009
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
+ 42u
103
+ ··· + 5u + 1
c
2
, c
5
u
104
+ 2u
103
+ ··· + u − 1
c
3
u
104
+ u
103
+ ··· + 128000u + 20000
c
4
, c
11
u
104
− 2u
103
+ ··· + 3u − 1
c
6
, c
9
u
104
+ 6u
103
+ ··· + 8175u − 625
c
7
25(25u
104
+ 125u
103
+ ··· − 5.04359 × 10
7
u − 1.75923 × 10
8
)
c
8
25(25u
104
+ 50u
103
+ ··· + 4032879u + 1554593)
c
10
, c
12
u
104
+ 30u
103
+ ··· − 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 42y
103
+ ··· + 83y + 1
c
2
, c
5
y
104
− 42y
103
+ ··· − 5y + 1
c
3
y
104
− 33y
103
+ ··· − 16280000000y + 400000000
c
4
, c
11
y
104
+ 30y
103
+ ··· − 5y + 1
c
6
, c
9
y
104
− 86y
103
+ ··· − 30394375y + 390625
c
7
625(625y
104
− 87275y
103
+ ··· − 7.63958 × 10
17
y + 3.09488 × 10
16
)
c
8
625
· (625y
104
+ 16400y
103
+ ··· − 21479676158875y + 2416759395649)
c
10
, c
12
y
104
+ 90y
103
+ ··· − 173y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.013930 + 0.053074I
a = 0.84563 + 5.97337I
b = −0.875152 − 0.542840I
0.55238 − 2.15431I 0
u = −1.013930 − 0.053074I
a = 0.84563 − 5.97337I
b = −0.875152 + 0.542840I
0.55238 + 2.15431I 0
u = 1.034930 + 0.092377I
a = 0.432529 − 0.375380I
b = −1.43461 + 0.15241I
−4.20552 + 4.60588I 0
u = 1.034930 − 0.092377I
a = 0.432529 + 0.375380I
b = −1.43461 − 0.15241I
−4.20552 − 4.60588I 0
u = −0.920741 + 0.125206I
a = −1.26152 − 3.17105I
b = −0.819156 − 0.413304I
4.48936 + 0.62293I 0
u = −0.920741 − 0.125206I
a = −1.26152 + 3.17105I
b = −0.819156 + 0.413304I
4.48936 − 0.62293I 0
u = 0.025348 + 1.078690I
a = 0.414738 − 0.689098I
b = 1.022060 + 0.609154I
−2.41249 − 7.33475I 0
u = 0.025348 − 1.078690I
a = 0.414738 + 0.689098I
b = 1.022060 − 0.609154I
−2.41249 + 7.33475I 0
u = −1.070450 + 0.147466I
a = −0.076939 − 0.239125I
b = −0.140596 − 0.243052I
1.177780 − 0.779255I 0
u = −1.070450 − 0.147466I
a = −0.076939 + 0.239125I
b = −0.140596 + 0.243052I
1.177780 + 0.779255I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.110220 + 0.892342I
a = −0.914702 − 1.076450I
b = −1.003870 + 0.038005I
0.18628 − 5.77200I 0
u = 0.110220 − 0.892342I
a = −0.914702 + 1.076450I
b = −1.003870 − 0.038005I
0.18628 + 5.77200I 0
u = −0.867570 + 0.211578I
a = 1.23556 + 2.33717I
b = 0.801312 + 0.374759I
4.32881 − 5.13184I 0
u = −0.867570 − 0.211578I
a = 1.23556 − 2.33717I
b = 0.801312 − 0.374759I
4.32881 + 5.13184I 0
u = −0.716194 + 0.516260I
a = 0.058650 − 0.780537I
b = −0.439288 − 0.400367I
4.70460 + 0.58481I 0
u = −0.716194 − 0.516260I
a = 0.058650 + 0.780537I
b = −0.439288 + 0.400367I
4.70460 − 0.58481I 0
u = −0.134970 + 0.860713I
a = 0.305814 + 0.661002I
b = 0.532236 − 0.624590I
−1.02515 − 2.43506I 0
u = −0.134970 − 0.860713I
a = 0.305814 − 0.661002I
b = 0.532236 + 0.624590I
−1.02515 + 2.43506I 0
u = 0.755968 + 0.378816I
a = 0.009408 − 0.920023I
b = −1.187370 + 0.198303I
−4.14345 + 4.96463I 0
u = 0.755968 − 0.378816I
a = 0.009408 + 0.920023I
b = −1.187370 − 0.198303I
−4.14345 − 4.96463I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.15916
a = −0.248154
b = 1.39516
−0.196484 0
u = −0.234959 + 0.795544I
a = −0.790804 + 0.597039I
b = −0.992648 − 0.590040I
0.32570 − 4.74919I 0
u = −0.234959 − 0.795544I
a = −0.790804 − 0.597039I
b = −0.992648 + 0.590040I
0.32570 + 4.74919I 0
u = 0.031293 + 0.813655I
a = 0.98332 + 1.14454I
b = 0.973040 − 0.042367I
0.753256 + 0.017776I 0
u = 0.031293 − 0.813655I
a = 0.98332 − 1.14454I
b = 0.973040 + 0.042367I
0.753256 − 0.017776I 0
u = 0.400031 + 0.699404I
a = −0.568973 − 1.153310I
b = −1.058270 + 0.115697I
−5.49838 − 1.03204I 0
u = 0.400031 − 0.699404I
a = −0.568973 + 1.153310I
b = −1.058270 − 0.115697I
−5.49838 + 1.03204I 0
u = −0.608735 + 0.525411I
a = −0.166435 + 0.966502I
b = 0.490251 + 0.429515I
4.41771 − 5.22605I 0
u = −0.608735 − 0.525411I
a = −0.166435 − 0.966502I
b = 0.490251 − 0.429515I
4.41771 + 5.22605I 0
u = −0.517612 + 0.557275I
a = −0.267475 − 0.044433I
b = −0.631086 + 0.547783I
1.42679 − 0.09115I 8.32769 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.517612 − 0.557275I
a = −0.267475 + 0.044433I
b = −0.631086 − 0.547783I
1.42679 + 0.09115I 8.32769 + 0.I
u = 1.249050 + 0.091321I
a = −0.63785 − 1.27059I
b = 0.541821 + 1.005770I
3.02371 − 1.07462I 0
u = 1.249050 − 0.091321I
a = −0.63785 + 1.27059I
b = 0.541821 − 1.005770I
3.02371 + 1.07462I 0
u = 1.230010 + 0.257322I
a = −0.18469 + 1.76690I
b = 1.122190 − 0.745710I
1.24341 + 5.25068I 0
u = 1.230010 − 0.257322I
a = −0.18469 − 1.76690I
b = 1.122190 + 0.745710I
1.24341 − 5.25068I 0
u = −0.714203
a = −0.630403
b = −0.398199
1.03446 10.5160
u = −0.501535 + 1.223320I
a = −0.021136 − 0.607600I
b = −0.613344 + 0.675383I
5.49142 − 0.54714I 0
u = −0.501535 − 1.223320I
a = −0.021136 + 0.607600I
b = −0.613344 − 0.675383I
5.49142 + 0.54714I 0
u = −0.391187 + 1.267150I
a = 0.044961 + 0.643911I
b = 0.598753 − 0.683955I
5.05098 − 6.49860I 0
u = −0.391187 − 1.267150I
a = 0.044961 − 0.643911I
b = 0.598753 + 0.683955I
5.05098 + 6.49860I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.327230 + 0.025075I
a = −0.20990 − 1.43950I
b = 1.169970 + 0.711145I
8.34639 + 1.35481I 0
u = 1.327230 − 0.025075I
a = −0.20990 + 1.43950I
b = 1.169970 − 0.711145I
8.34639 − 1.35481I 0
u = 1.299360 + 0.322093I
a = 0.106462 + 0.307157I
b = 1.284080 − 0.060470I
4.83167 + 3.98855I 0
u = 1.299360 − 0.322093I
a = 0.106462 − 0.307157I
b = 1.284080 + 0.060470I
4.83167 − 3.98855I 0
u = −1.157470 + 0.677359I
a = −0.43424 + 1.62457I
b = −0.918558 − 0.625354I
2.25024 − 5.42318I 0
u = −1.157470 − 0.677359I
a = −0.43424 − 1.62457I
b = −0.918558 + 0.625354I
2.25024 + 5.42318I 0
u = −1.247090 + 0.519183I
a = 0.653265 − 0.592996I
b = −0.753696 + 0.620768I
2.75612 − 0.51612I 0
u = −1.247090 − 0.519183I
a = 0.653265 + 0.592996I
b = −0.753696 − 0.620768I
2.75612 + 0.51612I 0
u = 1.293830 + 0.393590I
a = −0.149281 − 0.351146I
b = −1.270650 + 0.063796I
4.02286 + 10.36490I 0
u = 1.293830 − 0.393590I
a = −0.149281 + 0.351146I
b = −1.270650 − 0.063796I
4.02286 − 10.36490I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.366010 + 0.033928I
a = 0.001319 − 0.235797I
b = −0.015035 − 0.391381I
6.33487 − 2.95650I 0
u = −1.366010 − 0.033928I
a = 0.001319 + 0.235797I
b = −0.015035 + 0.391381I
6.33487 + 2.95650I 0
u = −0.532280 + 0.337940I
a = 1.072810 + 0.907460I
b = 0.641319 + 0.116720I
−0.95235 − 1.78350I −2.07327 + 5.75596I
u = −0.532280 − 0.337940I
a = 1.072810 − 0.907460I
b = 0.641319 − 0.116720I
−0.95235 + 1.78350I −2.07327 − 5.75596I
u = 1.325390 + 0.351138I
a = −0.775024 − 1.068110I
b = 0.561537 + 0.938182I
3.49061 + 6.69572I 0
u = 1.325390 − 0.351138I
a = −0.775024 + 1.068110I
b = 0.561537 − 0.938182I
3.49061 − 6.69572I 0
u = 1.373980 + 0.047061I
a = 0.15734 − 1.49974I
b = −1.155940 + 0.715392I
9.36202 + 5.02654I 0
u = 1.373980 − 0.047061I
a = 0.15734 + 1.49974I
b = −1.155940 − 0.715392I
9.36202 − 5.02654I 0
u = 1.380450 + 0.205876I
a = 0.668151 + 1.119090I
b = −0.541182 − 0.958954I
7.11860 + 2.72109I 0
u = 1.380450 − 0.205876I
a = 0.668151 − 1.119090I
b = −0.541182 + 0.958954I
7.11860 − 2.72109I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.399670 + 0.162927I
a = −0.419135 + 1.168260I
b = 0.473091 − 0.966081I
10.46890 + 7.48108I 0
u = 1.399670 − 0.162927I
a = −0.419135 − 1.168260I
b = 0.473091 + 0.966081I
10.46890 − 7.48108I 0
u = −1.386420 + 0.266585I
a = −0.25593 − 1.81404I
b = 0.869849 + 0.621736I
3.35689 − 2.65952I 0
u = −1.386420 − 0.266585I
a = −0.25593 + 1.81404I
b = 0.869849 − 0.621736I
3.35689 + 2.65952I 0
u = 1.37389 + 0.33988I
a = 0.02125 − 1.72170I
b = −1.118940 + 0.720663I
5.34196 + 8.84585I 0
u = 1.37389 − 0.33988I
a = 0.02125 + 1.72170I
b = −1.118940 − 0.720663I
5.34196 − 8.84585I 0
u = −0.28820 + 1.38713I
a = −0.446882 + 0.904495I
b = −1.003300 − 0.636591I
4.34614 − 5.65703I 0
u = −0.28820 − 1.38713I
a = −0.446882 − 0.904495I
b = −1.003300 + 0.636591I
4.34614 + 5.65703I 0
u = 1.34330 + 0.47281I
a = 0.05769 + 1.81023I
b = 1.105550 − 0.715397I
1.81081 + 12.75050I 0
u = 1.34330 − 0.47281I
a = 0.05769 − 1.81023I
b = 1.105550 + 0.715397I
1.81081 − 12.75050I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43078 + 0.09268I
a = 0.463511 − 1.152510I
b = −0.487227 + 0.966447I
11.40100 + 1.10913I 0
u = 1.43078 − 0.09268I
a = 0.463511 + 1.152510I
b = −0.487227 − 0.966447I
11.40100 − 1.10913I 0
u = −0.18781 + 1.43114I
a = 0.413662 − 0.884510I
b = 1.010510 + 0.637829I
3.84645 − 11.63360I 0
u = −0.18781 − 1.43114I
a = 0.413662 + 0.884510I
b = 1.010510 − 0.637829I
3.84645 + 11.63360I 0
u = −1.44555 + 0.08629I
a = −0.74940 + 1.33777I
b = 0.823412 − 0.622826I
3.50118 + 2.22683I 0
u = −1.44555 − 0.08629I
a = −0.74940 − 1.33777I
b = 0.823412 + 0.622826I
3.50118 − 2.22683I 0
u = 0.190949 + 0.516496I
a = 0.0145879 − 0.0144478I
b = 1.031680 + 0.541785I
−2.05610 − 2.20533I −3.33452 − 0.09970I
u = 0.190949 − 0.516496I
a = 0.0145879 + 0.0144478I
b = 1.031680 − 0.541785I
−2.05610 + 2.20533I −3.33452 + 0.09970I
u = 0.345318 + 0.335466I
a = 0.12836 + 1.71447I
b = 1.029410 − 0.244500I
−1.96391 + 1.11544I −1.55787 − 1.47213I
u = 0.345318 − 0.335466I
a = 0.12836 − 1.71447I
b = 1.029410 + 0.244500I
−1.96391 − 1.11544I −1.55787 + 1.47213I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.370544 + 0.231620I
a = 0.30459 + 1.57062I
b = 0.178701 − 0.619565I
0.02077 + 2.00050I −0.12885 − 4.33329I
u = 0.370544 − 0.231620I
a = 0.30459 − 1.57062I
b = 0.178701 + 0.619565I
0.02077 − 2.00050I −0.12885 + 4.33329I
u = 1.51573 + 0.42036I
a = 0.698231 + 0.961625I
b = −0.536978 − 0.923935I
11.80750 + 6.14222I 0
u = 1.51573 − 0.42036I
a = 0.698231 − 0.961625I
b = −0.536978 + 0.923935I
11.80750 − 6.14222I 0
u = 1.50371 + 0.47064I
a = −0.717795 − 0.941657I
b = 0.538804 + 0.918861I
10.9616 + 12.4442I 0
u = 1.50371 − 0.47064I
a = −0.717795 + 0.941657I
b = 0.538804 − 0.918861I
10.9616 − 12.4442I 0
u = −0.422179 + 0.033106I
a = −4.10481 − 1.84710I
b = −0.946056 + 0.550739I
3.70136 + 4.72366I 5.70262 − 6.08247I
u = −0.422179 − 0.033106I
a = −4.10481 + 1.84710I
b = −0.946056 − 0.550739I
3.70136 − 4.72366I 5.70262 + 6.08247I
u = 1.51283 + 0.51617I
a = −0.14872 − 1.71406I
b = −1.112300 + 0.702932I
10.0427 + 12.1163I 0
u = 1.51283 − 0.51617I
a = −0.14872 + 1.71406I
b = −1.112300 − 0.702932I
10.0427 − 12.1163I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50426 + 0.56043I
a = 0.17208 + 1.73252I
b = 1.109870 − 0.701364I
9.2104 + 18.3996I 0
u = 1.50426 − 0.56043I
a = 0.17208 − 1.73252I
b = 1.109870 + 0.701364I
9.2104 − 18.3996I 0
u = −0.275966 + 0.081922I
a = 5.36153 + 2.17952I
b = 0.942019 − 0.553208I
3.44019 − 0.96910I 4.29951 − 0.42121I
u = −0.275966 − 0.081922I
a = 5.36153 − 2.17952I
b = 0.942019 + 0.553208I
3.44019 + 0.96910I 4.29951 + 0.42121I
u = −0.258260 + 0.055783I
a = 2.30549 − 2.00942I
b = 0.703307 − 0.430355I
−0.81820 + 1.73592I −0.97741 − 5.34079I
u = −0.258260 − 0.055783I
a = 2.30549 + 2.00942I
b = 0.703307 + 0.430355I
−0.81820 − 1.73592I −0.97741 + 5.34079I
u = −1.67498 + 0.83826I
a = −0.128673 + 1.344690I
b = −0.905498 − 0.666581I
8.57816 − 8.03076I 0
u = −1.67498 − 0.83826I
a = −0.128673 − 1.344690I
b = −0.905498 + 0.666581I
8.57816 + 8.03076I 0
u = −1.78021 + 0.60840I
a = 0.370721 − 0.903073I
b = −0.781342 + 0.678105I
8.95454 − 2.83317I 0
u = −1.78021 − 0.60840I
a = 0.370721 + 0.903073I
b = −0.781342 − 0.678105I
8.95454 + 2.83317I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.72719 + 0.74945I
a = 0.080288 − 1.352320I
b = 0.898221 + 0.667170I
8.74433 − 1.97763I 0
u = −1.72719 − 0.74945I
a = 0.080288 + 1.352320I
b = 0.898221 − 0.667170I
8.74433 + 1.97763I 0
u = −1.82306 + 0.51731I
a = −0.372352 + 0.949139I
b = 0.790607 − 0.677284I
9.07102 + 3.21849I 0
u = −1.82306 − 0.51731I
a = −0.372352 − 0.949139I
b = 0.790607 + 0.677284I
9.07102 − 3.21849I 0
15
II.
I
u
2
= h25a
4
− 5a
3
+ 2a
2
+ 4b + 11a + 3, 25a
5
− 5a
4
+ 2a
3
+ 6a
2
+ 5a − 1, u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
−1
a
7
=
1
−1
a
3
=
a
−
25
4
a
4
+
5
4
a
3
+ ··· −
11
4
a −
3
4
a
10
=
−1
0
a
2
=
−
25
4
a
4
+
5
4
a
3
+ ··· −
7
4
a −
3
4
−
25
4
a
4
+
5
4
a
3
+ ··· −
11
4
a −
3
4
a
1
=
−
125
16
a
4
+
5
8
a
2
− 3a −
13
16
75
16
a
4
+
5
8
a
3
+ ··· +
15
8
a +
5
16
a
5
=
−
25
16
a
4
−
5
4
a
3
+ ··· +
1
4
a −
5
16
−
25
16
a
4
−
5
4
a
3
+ ··· +
3
4
a −
25
16
a
8
=
−
25
16
a
4
−
5
8
a
3
+
1
8
a +
1
16
−
1
2
a −
1
2
a
4
=
a
−
25
4
a
4
+
5
4
a
3
+ ··· −
11
4
a −
3
4
a
12
=
−
25
8
a
4
+
5
8
a
3
+ ··· −
9
8
a −
1
2
75
16
a
4
+
5
8
a
3
+ ··· +
15
8
a +
5
16
a
11
=
−
1
2
a −
1
2
−
25
8
a
4
+
15
4
a
3
+ ··· +
3
4
a −
3
8
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
525
16
a
4
+
105
4
a
3
−
139
8
a
2
+
27
4
a −
13
16
16
(iv) u-Polynomials at the component
17
Crossings u-Polynomials at each crossing
c
1
u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1
c
2
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
3
u
5
c
4
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
5
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
6
(u + 1)
5
c
7
25(25u
5
− 3u
3
+ 2u
2
− 2u + 1)
c
8
25(25u
5
− 25u
4
− 17u
3
+ 10u
2
+ 7u + 1)
c
9
(u − 1)
5
c
10
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
11
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
12
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
18
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1
c
2
, c
5
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
3
y
5
c
4
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
6
, c
9
(y −1)
5
c
7
625(625y
5
− 150y
4
− 91y
3
+ 8y
2
− 1)
c
8
625(625y
5
− 1475y
4
+ 1139y
3
− 288y
2
+ 29y −1)
c
10
, c
12
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.495386 + 0.635674I
b = −0.309916 − 0.549911I
1.31583 − 1.53058I 4.90490 + 5.44833I
u = −1.00000
a = 0.495386 − 0.635674I
b = −0.309916 + 0.549911I
1.31583 + 1.53058I 4.90490 − 5.44833I
u = −1.00000
a = −0.478118 + 0.378961I
b = 1.41878 − 0.21917I
−4.22763 + 4.40083I 1.0936 + 16.2687I
u = −1.00000
a = −0.478118 − 0.378961I
b = 1.41878 + 0.21917I
−4.22763 − 4.40083I 1.0936 − 16.2687I
u = −1.00000
a = 0.165464
b = −1.21774
−0.756147 −0.0769970
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1)(u
104
+ 42u
103
+ ··· + 5u + 1)
c
2
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
104
+ 2u
103
+ ··· + u − 1)
c
3
u
5
(u
104
+ u
103
+ ··· + 128000u + 20000)
c
4
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
104
− 2u
103
+ ··· + 3u − 1)
c
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
104
+ 2u
103
+ ··· + u − 1)
c
6
((u + 1)
5
)(u
104
+ 6u
103
+ ··· + 8175u − 625)
c
7
625(25u
5
− 3u
3
+ 2u
2
− 2u + 1)
· (25u
104
+ 125u
103
+ ··· − 50435872u − 175922653)
c
8
625(25u
5
− 25u
4
− 17u
3
+ 10u
2
+ 7u + 1)
· (25u
104
+ 50u
103
+ ··· + 4032879u + 1554593)
c
9
((u − 1)
5
)(u
104
+ 6u
103
+ ··· + 8175u − 625)
c
10
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
104
+ 30u
103
+ ··· − 5u + 1)
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
104
− 2u
103
+ ··· + 3u − 1)
c
12
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
104
+ 30u
103
+ ··· − 5u + 1)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1)(y
104
+ 42y
103
+ ··· + 83y + 1)
c
2
, c
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
104
− 42y
103
+ ··· − 5y + 1)
c
3
y
5
(y
104
− 33y
103
+ ··· − 1.62800 × 10
10
y + 4.00000 × 10
8
)
c
4
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
104
+ 30y
103
+ ··· − 5y + 1)
c
6
, c
9
((y −1)
5
)(y
104
− 86y
103
+ ··· − 3.03944 × 10
7
y + 390625)
c
7
390625(625y
5
− 150y
4
− 91y
3
+ 8y
2
− 1)
· (625y
104
− 8.73 × 10
4
y
103
+ ··· − 7.64 × 10
17
y + 3.09 × 10
16
)
c
8
390625(625y
5
− 1475y
4
+ 1139y
3
− 288y
2
+ 29y −1)
· (625y
104
+ 16400y
103
+ ··· − 21479676158875y + 2416759395649)
c
10
, c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
104
+ 90y
103
+ ··· − 173y + 1)
23
