12a
0982
(K12a
0982
)
A knot diagram
1
Linearized knot diagam
4 6 11 9 2 10 12 1 5 3 8 7
Solving Sequence
2,5
6
3,9
10 7 11 4 1 8 12
c
5
c
2
c
9
c
6
c
10
c
4
c
1
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h396741557u
70
− 2705520519u
69
+ ··· + 3439853568b + 8641755965218,
120849802046u
70
− 453217535127u
69
+ ··· + 16303759294464a − 3531490614456158,
u
71
− 8u
70
+ ··· + 300422u − 28438i
I
u
2
= h−a
2
+ b − a, a
3
+ 2a
2
+ a + 1, u + 1i
I
u
3
= hb
6
a
3
+ 3b
5
a
2
+ ··· − a
2
+ 1, u + 1i
I
v
1
= ha, b
9
− 3b
7
− b
6
+ 3b
5
+ 2b
4
− b
3
− b
2
+ 1, v − 1i
I
v
2
= ha, b + 1, v − 1i
* 4 irreducible components of dim
C
= 0, with total 84 representations.
* 1 irreducible components of dim
C
= 1
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
= h3.97 × 10
8
u
70
− 2.71 × 10
9
u
69
+ · · · + 3.44 × 10
9
b + 8.64 ×
10
12
, 1.21 × 10
11
u
70
− 4.53 × 10
11
u
69
+ · · · + 1.63 × 10
13
a − 3.53 ×
10
15
, u
71
− 8u
70
+ · · · + 300422u − 28438i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−0.00741239u
70
+ 0.0277983u
69
+ ··· − 1878.55u + 216.606
−0.115337u
70
+ 0.786522u
69
+ ··· + 24797.7u − 2512.25
a
10
=
−0.122749u
70
+ 0.814320u
69
+ ··· + 22919.2u − 2295.64
−0.115337u
70
+ 0.786522u
69
+ ··· + 24797.7u − 2512.25
a
7
=
−0.000272721u
70
− 0.00335184u
69
+ ··· − 1221.87u + 147.123
−0.00543439u
70
+ 0.0380903u
69
+ ··· + 1475.66u − 154.612
a
11
=
0.0189981u
70
− 0.0965360u
69
+ ··· + 527.401u − 91.8508
0.0592586u
70
− 0.423571u
69
+ ··· − 15810.2u + 1629.10
a
4
=
−0.00520879u
70
+ 0.0363631u
69
+ ··· + 1412.36u − 149.354
−0.000436995u
70
+ 0.00302753u
69
+ ··· + 98.9193u − 9.63599
a
1
=
−0.00169434u
70
+ 0.0103657u
69
+ ··· + 9.95932u + 5.55905
0.00278897u
70
− 0.0175826u
69
+ ··· − 319.666u + 29.2856
a
8
=
−0.0850548u
70
+ 0.573329u
69
+ ··· + 17746.1u − 1797.14
0.0303146u
70
− 0.166206u
69
+ ··· + 680.125u − 139.988
a
12
=
0.00146179u
70
+ 0.0124218u
69
+ ··· + 2863.44u − 314.383
0.0395988u
70
− 0.254642u
69
+ ··· − 5850.13u + 567.179
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
1064976745
5159780352
u
70
+
767202109
573308928
u
69
+ ··· +
3030931480757
95551488
u −
3956494938221
1289945088
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
64(64u
71
− 64u
70
+ ··· + 8937u + 2889)
c
2
, c
5
u
71
− 8u
70
+ ··· + 300422u − 28438
c
3
, c
10
27(27u
71
− 54u
70
+ ··· − 3u + 1)
c
4
, c
9
27(27u
71
+ 54u
70
+ ··· + u + 1)
c
6
64(64u
71
− 64u
70
+ ··· − 1629153u + 409509)
c
7
, c
11
, c
12
u
71
+ 4u
70
+ ··· − 370u − 46
c
8
u
71
− 4u
70
+ ··· + 559616u − 400384
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
4096(4096y
71
− 61440y
70
+ ··· − 1.34847 × 10
9
y − 8346321)
c
2
, c
5
y
71
− 48y
70
+ ··· + 17125572968y − 808719844
c
3
, c
10
729(729y
71
− 36450y
70
+ ··· + 37y − 1)
c
4
, c
9
729(729y
71
− 30618y
70
+ ··· + 21y − 1)
c
6
4096
· (4096y
71
+ 45056y
70
+ ··· − 296794641861y − 167697621081)
c
7
, c
11
, c
12
y
71
+ 60y
70
+ ··· + 31744y − 2116
c
8
y
71
− 20y
70
+ ··· + 1087647252480y − 160307347456
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.819521 + 0.520466I
a = −1.58110 − 0.82078I
b = 1.007920 − 0.102626I
1.42180 − 0.53019I 7.50103 + 0.I
u = 0.819521 − 0.520466I
a = −1.58110 + 0.82078I
b = 1.007920 + 0.102626I
1.42180 + 0.53019I 7.50103 + 0.I
u = 0.307366 + 0.904911I
a = −1.51865 − 0.42035I
b = 1.289990 + 0.173842I
3.63707 − 1.17327I 6.61182 + 2.79470I
u = 0.307366 − 0.904911I
a = −1.51865 + 0.42035I
b = 1.289990 − 0.173842I
3.63707 + 1.17327I 6.61182 − 2.79470I
u = −1.023520 + 0.258526I
a = 0.981518 + 0.240605I
b = 0.499246 − 0.339591I
−5.41474 + 1.54205I 0
u = −1.023520 − 0.258526I
a = 0.981518 − 0.240605I
b = 0.499246 + 0.339591I
−5.41474 − 1.54205I 0
u = 0.238590 + 0.854323I
a = 1.48171 + 0.51225I
b = −1.307940 − 0.307987I
6.49722 + 2.98352I 9.50430 − 2.12816I
u = 0.238590 − 0.854323I
a = 1.48171 − 0.51225I
b = −1.307940 + 0.307987I
6.49722 − 2.98352I 9.50430 + 2.12816I
u = −0.855012
a = −0.981809
b = −0.440716
−1.39100 −8.59610
u = 0.198592 + 0.831468I
a = −1.42804 − 0.58646I
b = 1.306230 + 0.409174I
1.79097 + 6.98426I 4.65978 − 4.42101I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.198592 − 0.831468I
a = −1.42804 + 0.58646I
b = 1.306230 − 0.409174I
1.79097 − 6.98426I 4.65978 + 4.42101I
u = 1.043630 + 0.483780I
a = 1.17256 + 1.02006I
b = −1.101410 + 0.343596I
0.41067 − 3.97609I 0
u = 1.043630 − 0.483780I
a = 1.17256 − 1.02006I
b = −1.101410 − 0.343596I
0.41067 + 3.97609I 0
u = 0.806567 + 0.251561I
a = 2.38122 + 1.29998I
b = −0.812636 + 0.100931I
−3.76855 + 2.19613I 4.10036 + 1.67133I
u = 0.806567 − 0.251561I
a = 2.38122 − 1.29998I
b = −0.812636 − 0.100931I
−3.76855 − 2.19613I 4.10036 − 1.67133I
u = 0.003104 + 1.180770I
a = −1.63766 + 0.18150I
b = 1.269310 − 0.443202I
−1.89620 − 11.83840I 0
u = 0.003104 − 1.180770I
a = −1.63766 − 0.18150I
b = 1.269310 + 0.443202I
−1.89620 + 11.83840I 0
u = 1.121410 + 0.371453I
a = −0.809362 − 1.145630I
b = 0.863451 − 0.606425I
−5.56497 − 4.82283I 0
u = 1.121410 − 0.371453I
a = −0.809362 + 1.145630I
b = 0.863451 + 0.606425I
−5.56497 + 4.82283I 0
u = −0.427132 + 1.105310I
a = 1.151040 − 0.328481I
b = −0.633967 + 0.380733I
−8.07843 − 1.77357I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.427132 − 1.105310I
a = 1.151040 + 0.328481I
b = −0.633967 − 0.380733I
−8.07843 + 1.77357I 0
u = −0.203322 + 0.786463I
a = −0.533965 + 0.617042I
b = −0.037932 − 0.812366I
−5.83653 + 7.27865I −2.90503 − 6.03696I
u = −0.203322 − 0.786463I
a = −0.533965 − 0.617042I
b = −0.037932 + 0.812366I
−5.83653 − 7.27865I −2.90503 + 6.03696I
u = 0.038011 + 1.227680I
a = 1.58064 − 0.10527I
b = −1.243880 + 0.351826I
3.50101 − 7.48635I 0
u = 0.038011 − 1.227680I
a = 1.58064 + 0.10527I
b = −1.243880 − 0.351826I
3.50101 + 7.48635I 0
u = 1.136630 + 0.503317I
a = 1.051110 + 0.933094I
b = −1.319570 + 0.469175I
1.03634 − 3.89122I 0
u = 1.136630 − 0.503317I
a = 1.051110 − 0.933094I
b = −1.319570 − 0.469175I
1.03634 + 3.89122I 0
u = −0.222221 + 0.715337I
a = 0.443100 − 0.394812I
b = 0.142675 + 0.651594I
−0.58395 + 3.83218I 1.42180 − 6.56695I
u = −0.222221 − 0.715337I
a = 0.443100 + 0.394812I
b = 0.142675 − 0.651594I
−0.58395 − 3.83218I 1.42180 + 6.56695I
u = −0.469846 + 0.575519I
a = −0.827718 + 0.004464I
b = −0.069504 − 0.209872I
−1.67748 + 0.48526I −3.97187 − 0.02534I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.469846 − 0.575519I
a = −0.827718 − 0.004464I
b = −0.069504 + 0.209872I
−1.67748 − 0.48526I −3.97187 + 0.02534I
u = 1.164080 + 0.480686I
a = −1.023570 − 0.923509I
b = 1.36556 − 0.62461I
3.63673 − 7.83371I 0
u = 1.164080 − 0.480686I
a = −1.023570 + 0.923509I
b = 1.36556 + 0.62461I
3.63673 + 7.83371I 0
u = 1.176630 + 0.469379I
a = 1.016250 + 0.906931I
b = −1.37700 + 0.72719I
−1.20902 − 11.72950I 0
u = 1.176630 − 0.469379I
a = 1.016250 − 0.906931I
b = −1.37700 − 0.72719I
−1.20902 + 11.72950I 0
u = −1.26923
a = 0.443176
b = 0.935561
0.778487 0
u = −1.264160 + 0.118796I
a = −0.472558 − 0.253843I
b = −0.948987 + 0.156256I
−3.27989 − 3.71425I 0
u = −1.264160 − 0.118796I
a = −0.472558 + 0.253843I
b = −0.948987 − 0.156256I
−3.27989 + 3.71425I 0
u = −1.030390 + 0.798282I
a = 1.203360 − 0.169041I
b = −0.490852 − 0.311467I
−7.90006 − 2.14329I 0
u = −1.030390 − 0.798282I
a = 1.203360 + 0.169041I
b = −0.490852 + 0.311467I
−7.90006 + 2.14329I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.313050 + 0.189953I
a = 0.508616 − 0.502988I
b = 0.018161 − 0.445336I
−6.06596 − 3.98545I 0
u = 1.313050 − 0.189953I
a = 0.508616 + 0.502988I
b = 0.018161 + 0.445336I
−6.06596 + 3.98545I 0
u = 1.303700 + 0.351874I
a = 0.242962 + 0.221817I
b = −0.001995 + 1.154370I
−5.18776 − 7.68710I 0
u = 1.303700 − 0.351874I
a = 0.242962 − 0.221817I
b = −0.001995 − 1.154370I
−5.18776 + 7.68710I 0
u = 1.306430 + 0.367652I
a = −0.312055 − 0.131512I
b = −0.043263 − 1.280420I
−10.4234 − 11.3766I 0
u = 1.306430 − 0.367652I
a = −0.312055 + 0.131512I
b = −0.043263 + 1.280420I
−10.4234 + 11.3766I 0
u = 1.323500 + 0.319759I
a = −0.021570 − 0.255546I
b = −0.083108 − 0.928074I
−6.84932 − 3.82914I 0
u = 1.323500 − 0.319759I
a = −0.021570 + 0.255546I
b = −0.083108 + 0.928074I
−6.84932 + 3.82914I 0
u = 0.078317 + 1.379350I
a = −1.43707 + 0.03992I
b = 1.146800 − 0.238951I
1.54772 − 2.46422I 0
u = 0.078317 − 1.379350I
a = −1.43707 − 0.03992I
b = 1.146800 + 0.238951I
1.54772 + 2.46422I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40555
a = −0.778582
b = 0.168037
−2.58753 0
u = 1.367760 + 0.356897I
a = −0.0321262 − 0.0286481I
b = 0.403541 + 0.995637I
−13.64900 − 2.75115I 0
u = 1.367760 − 0.356897I
a = −0.0321262 + 0.0286481I
b = 0.403541 − 0.995637I
−13.64900 + 2.75115I 0
u = 0.002729 + 0.571241I
a = 0.495336 + 0.006107I
b = −0.646311 − 0.485330I
−2.52284 + 1.44806I 1.52827 − 4.25124I
u = 0.002729 − 0.571241I
a = 0.495336 − 0.006107I
b = −0.646311 + 0.485330I
−2.52284 − 1.44806I 1.52827 + 4.25124I
u = −1.37654 + 0.55969I
a = 1.22908 − 0.89967I
b = −1.38400 − 0.61260I
−6.2246 + 17.9070I 0
u = −1.37654 − 0.55969I
a = 1.22908 + 0.89967I
b = −1.38400 + 0.61260I
−6.2246 − 17.9070I 0
u = −1.35829 + 0.63407I
a = −1.27343 + 0.61873I
b = 1.110910 + 0.607448I
−11.4152 + 8.4414I 0
u = −1.35829 − 0.63407I
a = −1.27343 − 0.61873I
b = 1.110910 − 0.607448I
−11.4152 − 8.4414I 0
u = −1.38933 + 0.56452I
a = −1.17586 + 0.86482I
b = 1.35926 + 0.56133I
−0.95679 + 13.67690I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38933 − 0.56452I
a = −1.17586 − 0.86482I
b = 1.35926 − 0.56133I
−0.95679 − 13.67690I 0
u = −1.40775 + 0.58245I
a = 1.126330 − 0.779757I
b = −1.292850 − 0.505115I
−3.06788 + 9.01142I 0
u = −1.40775 − 0.58245I
a = 1.126330 + 0.779757I
b = −1.292850 + 0.505115I
−3.06788 − 9.01142I 0
u = −1.48483 + 0.70442I
a = 1.039620 − 0.500059I
b = −1.084850 − 0.346532I
−3.19063 + 7.21023I 0
u = −1.48483 − 0.70442I
a = 1.039620 + 0.500059I
b = −1.084850 + 0.346532I
−3.19063 − 7.21023I 0
u = 1.69240 + 0.46527I
a = 0.637845 + 0.204538I
b = −0.881903 − 0.302981I
−6.95097 + 5.16050I 0
u = 1.69240 − 0.46527I
a = 0.637845 − 0.204538I
b = −0.881903 + 0.302981I
−6.95097 − 5.16050I 0
u = 0.211013
a = −3.68122
b = 0.689101
0.960500 11.1530
u = −1.49547 + 1.02906I
a = −1.052720 + 0.285419I
b = 0.918490 + 0.196861I
−1.46472 + 1.87001I 0
u = −1.49547 − 1.02906I
a = −1.052720 − 0.285419I
b = 0.918490 − 0.196861I
−1.46472 − 1.87001I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.92924
a = −0.701661
b = 0.768833
−2.33373 0
12
II. I
u
2
= h−a
2
+ b − a, a
3
+ 2a
2
+ a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
9
=
a
a
2
+ a
a
10
=
a
2
+ 2a
a
2
+ a
a
7
=
−a
−a
2
− a
a
11
=
a
a
2
+ a
a
4
=
−a
2
− a
−a
a
1
=
a
a
2
+ a
a
8
=
a
a
2
+ a
a
12
=
a
a
2
+ a
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
9
, c
10
u
3
− u − 1
c
2
, c
5
(u + 1)
3
c
6
u
3
− 2u
2
+ u − 1
c
7
, c
8
, c
11
c
12
u
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
9
, c
10
y
3
− 2y
2
+ y − 1
c
2
, c
5
(y − 1)
3
c
6
y
3
− 2y
2
− 3y − 1
c
7
, c
8
, c
11
c
12
y
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.122561 + 0.744862I
b = −0.662359 + 0.562280I
−1.64493 −6.00000
u = −1.00000
a = −0.122561 − 0.744862I
b = −0.662359 − 0.562280I
−1.64493 −6.00000
u = −1.00000
a = −1.75488
b = 1.32472
−1.64493 −6.00000
16
III. I
u
3
= hb
6
a
3
+ 3b
5
a
2
+ · · · − a
2
+ 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
9
=
a
b
a
10
=
b + a
b
a
7
=
ba + a
2
+ 1
ba + 1
a
11
=
a
b
a
4
=
ba + 1
b
2
a
1
=
−b
2
a
2
− 2ba − 1
−b
3
a − b
2
− 1
a
8
=
−b
4
a
3
− 3b
3
a
2
+ a
3
b
2
− 3b
2
a + 2a
2
b − b + 2a
−b
5
a
2
− 2b
4
a + b
3
a
2
− b
3
+ a
a
12
=
b
5
a
3
+ b
4
a
4
+ ··· + a
2
− 1
b
5
a
3
+ 3b
4
a
2
− 2b
3
a
3
+ 2b
3
a − 4b
2
a
2
+ a
3
b − 2ba + a
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4b
2
a − 4b + 4a
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
17
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
−0.531480 −3.50976 − 2.97944I
18
IV. I
v
1
= ha, b
9
− 3b
7
− b
6
+ 3b
5
+ 2b
4
− b
3
− b
2
+ 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
6
=
1
0
a
3
=
1
0
a
9
=
0
b
a
10
=
b
b
a
7
=
−b
2
+ 1
−b
2
a
11
=
0
b
a
4
=
1
b
2
a
1
=
−b
2
+ 1
−b
4
a
8
=
−b
5
+ 2b
3
− b
−b
7
+ b
5
+ b
a
12
=
b
8
− 3b
6
+ 3b
4
− 2b
2
+ 1
b
8
− 2b
6
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b
3
+ 4b + 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 6u
8
+ 15u
7
+ 21u
6
+ 19u
5
+ 12u
4
+ 7u
3
+ 5u
2
+ 2u + 1
c
2
, c
5
u
9
c
3
, c
4
, c
6
c
9
, c
10
u
9
− 3u
7
− u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1
c
7
, c
11
, c
12
(u
3
− u
2
+ 2u − 1)
3
c
8
(u
3
+ u
2
− 1)
3
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− 6y
8
+ 11y
7
− y
6
+ 11y
5
− 40y
4
− 37y
3
− 21y
2
− 6y − 1
c
2
, c
5
y
9
c
3
, c
4
, c
6
c
9
, c
10
y
9
− 6y
8
+ 15y
7
− 21y
6
+ 19y
5
− 12y
4
+ 7y
3
− 5y
2
+ 2y − 1
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y − 1)
3
c
8
(y
3
− y
2
+ 2y − 1)
3
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.947946 + 0.524157I
−3.02413 + 2.82812I 2.49024 − 2.97945I
v = 1.00000
a = 0
b = −0.947946 − 0.524157I
−3.02413 − 2.82812I 2.49024 + 2.97945I
v = 1.00000
a = 0
b = −0.376870 + 0.700062I
−3.02413 − 2.82812I 2.49024 + 2.97945I
v = 1.00000
a = 0
b = −0.376870 − 0.700062I
−3.02413 + 2.82812I 2.49024 − 2.97945I
v = 1.00000
a = 0
b = 0.631920 + 0.444935I
1.11345 9.01951 + 0.I
v = 1.00000
a = 0
b = 0.631920 − 0.444935I
1.11345 9.01951 + 0.I
v = 1.00000
a = 0
b = −1.26384
1.11345 9.01950
v = 1.00000
a = 0
b = 1.324820 + 0.175904I
−3.02413 + 2.82812I 2.49024 − 2.97945I
v = 1.00000
a = 0
b = 1.324820 − 0.175904I
−3.02413 − 2.82812I 2.49024 + 2.97945I
22
V. I
v
2
= ha, b + 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
6
=
1
0
a
3
=
1
0
a
9
=
0
−1
a
10
=
−1
−1
a
7
=
0
−1
a
11
=
0
−1
a
4
=
1
1
a
1
=
0
−1
a
8
=
0
−1
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
10
u − 1
c
2
, c
5
, c
7
c
8
, c
11
, c
12
u
c
3
, c
4
, c
6
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
9
, c
10
y − 1
c
2
, c
5
, c
7
c
8
, c
11
, c
12
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
64(u − 1)(u
3
− u − 1)
· (u
9
+ 6u
8
+ 15u
7
+ 21u
6
+ 19u
5
+ 12u
4
+ 7u
3
+ 5u
2
+ 2u + 1)
· (64u
71
− 64u
70
+ ··· + 8937u + 2889)
c
2
, c
5
u
10
(u + 1)
3
(u
71
− 8u
70
+ ··· + 300422u − 28438)
c
3
27(u + 1)(u
3
− u − 1)(u
9
− 3u
7
− u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1)
· (27u
71
− 54u
70
+ ··· − 3u + 1)
c
4
27(u + 1)(u
3
− u − 1)(u
9
− 3u
7
− u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1)
· (27u
71
+ 54u
70
+ ··· + u + 1)
c
6
64(u + 1)(u
3
− 2u
2
+ u − 1)(u
9
− 3u
7
+ ··· − u
2
+ 1)
· (64u
71
− 64u
70
+ ··· − 1629153u + 409509)
c
7
, c
11
, c
12
u
4
(u
3
− u
2
+ 2u − 1)
3
(u
71
+ 4u
70
+ ··· − 370u − 46)
c
8
u
4
(u
3
+ u
2
− 1)
3
(u
71
− 4u
70
+ ··· + 559616u − 400384)
c
9
27(u − 1)(u
3
− u − 1)(u
9
− 3u
7
− u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1)
· (27u
71
+ 54u
70
+ ··· + u + 1)
c
10
27(u − 1)(u
3
− u − 1)(u
9
− 3u
7
− u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1)
· (27u
71
− 54u
70
+ ··· − 3u + 1)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
4096(y − 1)(y
3
− 2y
2
+ y − 1)
· (y
9
− 6y
8
+ 11y
7
− y
6
+ 11y
5
− 40y
4
− 37y
3
− 21y
2
− 6y − 1)
· (4096y
71
− 61440y
70
+ ··· − 1348468965y − 8346321)
c
2
, c
5
y
10
(y − 1)
3
(y
71
− 48y
70
+ ··· + 1.71256 × 10
10
y − 8.08720 × 10
8
)
c
3
, c
10
729(y − 1)(y
3
− 2y
2
+ y − 1)
· (y
9
− 6y
8
+ 15y
7
− 21y
6
+ 19y
5
− 12y
4
+ 7y
3
− 5y
2
+ 2y − 1)
· (729y
71
− 36450y
70
+ ··· + 37y − 1)
c
4
, c
9
729(y − 1)(y
3
− 2y
2
+ y − 1)
· (y
9
− 6y
8
+ 15y
7
− 21y
6
+ 19y
5
− 12y
4
+ 7y
3
− 5y
2
+ 2y − 1)
· (729y
71
− 30618y
70
+ ··· + 21y − 1)
c
6
4096(y − 1)(y
3
− 2y
2
− 3y − 1)
· (y
9
− 6y
8
+ 15y
7
− 21y
6
+ 19y
5
− 12y
4
+ 7y
3
− 5y
2
+ 2y − 1)
· (4096y
71
+ 45056y
70
+ ··· − 296794641861y − 167697621081)
c
7
, c
11
, c
12
y
4
(y
3
+ 3y
2
+ 2y − 1)
3
(y
71
+ 60y
70
+ ··· + 31744y − 2116)
c
8
y
4
(y
3
− y
2
+ 2y − 1)
3
· (y
71
− 20y
70
+ ··· + 1087647252480y − 160307347456)
28
