12n
0513
(K12n
0513
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 11 4 11 5 1 8 7
Solving Sequence
4,8 5,11
9 10 12 3 7 1 6 2
c
4
c
8
c
9
c
11
c
3
c
7
c
12
c
6
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.11455 × 10
216
u
83
− 1.22374 × 10
217
u
82
+ ··· + 1.43757 × 10
217
b − 1.08508 × 10
217
,
− 1.59930 × 10
217
u
83
− 4.98714 × 10
217
u
82
+ ··· + 1.43757 × 10
217
a − 1.15733 × 10
218
,
u
84
+ 3u
83
+ ··· + 6u − 1i
I
u
2
= h−2270u
21
− 3510u
20
+ ··· + 61b − 3235, −7325u
21
− 11232u
20
+ ··· + 61a − 11023,
u
22
+ 2u
21
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 106 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−4.11 × 10
216
u
83
− 1.22 × 10
217
u
82
+ · · · + 1.44 × 10
217
b − 1.09 ×
10
217
, −1.60 × 10
217
u
83
− 4.99 × 10
217
u
82
+ · · · + 1.44 × 10
217
a − 1.16 ×
10
218
, u
84
+ 3u
83
+ · · · + 6u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
1.11250u
83
+ 3.46914u
82
+ ··· − 73.5902u + 8.05058
0.286216u
83
+ 0.851258u
82
+ ··· − 7.95580u + 0.754799
a
9
=
2.00350u
83
+ 6.21549u
82
+ ··· − 103.174u + 8.32630
0.383700u
83
+ 1.12001u
82
+ ··· − 7.13407u + 0.363188
a
10
=
1.72740u
83
+ 5.47297u
82
+ ··· − 95.2664u + 8.16810
0.342545u
83
+ 1.03274u
82
+ ··· − 7.92489u + 0.448974
a
12
=
1.11250u
83
+ 3.46914u
82
+ ··· − 73.5902u + 8.05058
0.252151u
83
+ 0.812685u
82
+ ··· − 8.27842u + 0.623153
a
3
=
0.118293u
83
+ 0.140322u
82
+ ··· + 28.7740u + 14.3613
0.136975u
83
+ 0.450890u
82
+ ··· + 0.649097u + 1.21041
a
7
=
u
u
a
1
=
1.06394u
83
+ 3.26827u
82
+ ··· − 73.1824u + 8.12599
0.203595u
83
+ 0.611813u
82
+ ··· − 7.87055u + 0.698566
a
6
=
1.61980u
83
+ 5.09548u
82
+ ··· − 94.0400u + 7.96311
0.0171652u
83
+ 0.125743u
82
+ ··· − 8.77587u + 0.619271
a
2
=
−1.37298u
83
− 4.14238u
82
+ ··· + 83.9230u + 0.293934
−0.122114u
83
− 0.296643u
82
+ ··· + 4.05853u + 0.483833
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.46226u
83
− 4.71452u
82
+ ··· + 33.6541u − 9.62565
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
84
+ 35u
83
+ ··· + 55u + 1
c
2
, c
5
u
84
+ u
83
+ ··· + 9u − 1
c
3
u
84
+ 2u
83
+ ··· − 3150u − 863
c
4
, c
7
u
84
+ 3u
83
+ ··· + 6u − 1
c
6
u
84
+ u
83
+ ··· − 4996204u − 2395607
c
8
, c
11
u
84
− 10u
83
+ ··· + 8180u + 3952
c
9
u
84
+ 34u
82
+ ··· + 1301846276u + 241946651
c
10
u
84
− 10u
83
+ ··· − 248u + 1
c
12
u
84
− 4u
83
+ ··· − 28586236u + 7588717
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
84
+ 37y
83
+ ··· + 1781y + 1
c
2
, c
5
y
84
− 35y
83
+ ··· − 55y + 1
c
3
y
84
+ 12y
83
+ ··· + 9189498y + 744769
c
4
, c
7
y
84
− 21y
83
+ ··· + 48y + 1
c
6
y
84
+ 53y
83
+ ··· − 69359144214586y + 5738932898449
c
8
, c
11
y
84
− 84y
83
+ ··· − 1119037552y + 15618304
c
9
y
84
+ 68y
83
+ ··· + 1815122488070227036y + 58538181930115801
c
10
y
84
+ 12y
83
+ ··· − 58496y + 1
c
12
y
84
+ 64y
83
+ ··· − 298596197402654y + 57588625706089
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.900153 + 0.297981I
a = 0.152850 − 0.484510I
b = 1.277690 − 0.223754I
−0.21302 − 4.33780I 0
u = 0.900153 − 0.297981I
a = 0.152850 + 0.484510I
b = 1.277690 + 0.223754I
−0.21302 + 4.33780I 0
u = −0.721646 + 0.828109I
a = −0.479477 − 1.213880I
b = −0.562940 − 0.435217I
2.62706 + 3.30026I 0
u = −0.721646 − 0.828109I
a = −0.479477 + 1.213880I
b = −0.562940 + 0.435217I
2.62706 − 3.30026I 0
u = 0.898980 + 0.044549I
a = 0.520925 − 1.086290I
b = 1.39226 − 1.50003I
−0.92412 − 1.22946I −12.54684 + 0.I
u = 0.898980 − 0.044549I
a = 0.520925 + 1.086290I
b = 1.39226 + 1.50003I
−0.92412 + 1.22946I −12.54684 + 0.I
u = −0.881658 + 0.085784I
a = −0.628035 + 1.224740I
b = −1.12816 + 2.00117I
−1.65718 − 5.58665I −13.05862 + 4.36644I
u = −0.881658 − 0.085784I
a = −0.628035 − 1.224740I
b = −1.12816 − 2.00117I
−1.65718 + 5.58665I −13.05862 − 4.36644I
u = −0.780154 + 0.371808I
a = 0.156738 − 0.240422I
b = −0.771810 + 0.080467I
−0.0845697 − 0.1001390I −9.69562 + 0.I
u = −0.780154 − 0.371808I
a = 0.156738 + 0.240422I
b = −0.771810 − 0.080467I
−0.0845697 + 0.1001390I −9.69562 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826574 + 0.108876I
a = 0.648654 + 0.935247I
b = −0.312333 + 0.007656I
0.214695 − 0.733341I −9.75722 − 1.67126I
u = −0.826574 − 0.108876I
a = 0.648654 − 0.935247I
b = −0.312333 − 0.007656I
0.214695 + 0.733341I −9.75722 + 1.67126I
u = −0.870921 + 0.787220I
a = −0.60547 − 1.61811I
b = −1.43008 − 1.28544I
5.63391 + 7.36950I 0
u = −0.870921 − 0.787220I
a = −0.60547 + 1.61811I
b = −1.43008 + 1.28544I
5.63391 − 7.36950I 0
u = −0.917337 + 0.733359I
a = −1.35773 − 0.70979I
b = −1.61122 − 0.13239I
5.47056 − 1.58629I 0
u = −0.917337 − 0.733359I
a = −1.35773 + 0.70979I
b = −1.61122 + 0.13239I
5.47056 + 1.58629I 0
u = −0.698347 + 0.435308I
a = 1.19604 − 1.25661I
b = −0.330618 − 1.054550I
−3.52883 + 2.77312I −15.4506 − 6.7979I
u = −0.698347 − 0.435308I
a = 1.19604 + 1.25661I
b = −0.330618 + 1.054550I
−3.52883 − 2.77312I −15.4506 + 6.7979I
u = −0.071228 + 0.808709I
a = 0.684407 − 0.392922I
b = −0.667491 + 0.370099I
2.08277 + 3.57421I −4.77531 − 3.69472I
u = −0.071228 − 0.808709I
a = 0.684407 + 0.392922I
b = −0.667491 − 0.370099I
2.08277 − 3.57421I −4.77531 + 3.69472I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.882596 + 0.809217I
a = 0.76923 − 1.57559I
b = 1.68260 − 1.03445I
6.12462 − 2.40868I 0
u = 0.882596 − 0.809217I
a = 0.76923 + 1.57559I
b = 1.68260 + 1.03445I
6.12462 + 2.40868I 0
u = 0.919192 + 0.775802I
a = 1.27737 − 0.97215I
b = 1.77985 − 0.24242I
6.00052 − 3.56886I 0
u = 0.919192 − 0.775802I
a = 1.27737 + 0.97215I
b = 1.77985 + 0.24242I
6.00052 + 3.56886I 0
u = −0.131087 + 0.779739I
a = −0.618512 − 0.563874I
b = 0.623447 + 0.478283I
2.93571 + 1.52852I −2.60851 − 2.55303I
u = −0.131087 − 0.779739I
a = −0.618512 + 0.563874I
b = 0.623447 − 0.478283I
2.93571 − 1.52852I −2.60851 + 2.55303I
u = −0.532846 + 0.536929I
a = −0.110446 − 0.772642I
b = 1.039160 − 0.278861I
1.53936 + 3.45140I −4.45971 − 6.29986I
u = −0.532846 − 0.536929I
a = −0.110446 + 0.772642I
b = 1.039160 + 0.278861I
1.53936 − 3.45140I −4.45971 + 6.29986I
u = 0.743015 + 0.118915I
a = −1.08667 + 1.31261I
b = 0.311075 + 0.036329I
−1.00616 + 6.17268I −13.15706 − 1.64571I
u = 0.743015 − 0.118915I
a = −1.08667 − 1.31261I
b = 0.311075 − 0.036329I
−1.00616 − 6.17268I −13.15706 + 1.64571I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.608571 + 0.441527I
a = −0.116760 − 0.757237I
b = −1.50360 − 0.59788I
−0.30762 − 8.50634I −8.7735 + 11.8688I
u = 0.608571 − 0.441527I
a = −0.116760 + 0.757237I
b = −1.50360 + 0.59788I
−0.30762 + 8.50634I −8.7735 − 11.8688I
u = −0.763077 + 1.009160I
a = 0.290491 + 1.008800I
b = 1.26873 + 0.94425I
5.88830 + 7.20760I 0
u = −0.763077 − 1.009160I
a = 0.290491 − 1.008800I
b = 1.26873 − 0.94425I
5.88830 − 7.20760I 0
u = 0.718688
a = −1.57675
b = 0.296620
−5.24836 −19.9760
u = 0.935696 + 0.904486I
a = 0.732618 − 1.149590I
b = 1.70260 − 0.35455I
4.37832 − 3.33219I 0
u = 0.935696 − 0.904486I
a = 0.732618 + 1.149590I
b = 1.70260 + 0.35455I
4.37832 + 3.33219I 0
u = 0.795821 + 1.049650I
a = −0.428636 + 0.975134I
b = −1.31864 + 0.60090I
8.06712 − 0.99861I 0
u = 0.795821 − 1.049650I
a = −0.428636 − 0.975134I
b = −1.31864 − 0.60090I
8.06712 + 0.99861I 0
u = −0.483252 + 0.480273I
a = 1.88640 − 2.27246I
b = −0.558902 − 1.166930I
0.09901 + 7.96107I −7.32121 − 11.83227I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.483252 − 0.480273I
a = 1.88640 + 2.27246I
b = −0.558902 + 1.166930I
0.09901 − 7.96107I −7.32121 + 11.83227I
u = −0.616946 + 0.250802I
a = −0.74826 + 1.21205I
b = −0.19427 + 1.83238I
−3.45151 + 0.05717I −15.3703 − 3.3052I
u = −0.616946 − 0.250802I
a = −0.74826 − 1.21205I
b = −0.19427 − 1.83238I
−3.45151 − 0.05717I −15.3703 + 3.3052I
u = −0.799101 + 1.075390I
a = 0.589749 + 0.783838I
b = 0.951424 + 0.130937I
1.72718 − 2.24494I 0
u = −0.799101 − 1.075390I
a = 0.589749 − 0.783838I
b = 0.951424 − 0.130937I
1.72718 + 2.24494I 0
u = −0.709874 + 1.145940I
a = −0.707557 − 1.188160I
b = −1.16025 + 0.97520I
5.83263 − 0.09887I 0
u = −0.709874 − 1.145940I
a = −0.707557 + 1.188160I
b = −1.16025 − 0.97520I
5.83263 + 0.09887I 0
u = −1.113350 + 0.768279I
a = −0.620139 − 0.681105I
b = −1.55359 − 0.74336I
1.39386 + 2.74337I 0
u = −1.113350 − 0.768279I
a = −0.620139 + 0.681105I
b = −1.55359 + 0.74336I
1.39386 − 2.74337I 0
u = −1.344250 + 0.217412I
a = 0.191483 + 0.020332I
b = 0.162753 − 0.595444I
−1.31503 + 2.43238I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.344250 − 0.217412I
a = 0.191483 − 0.020332I
b = 0.162753 + 0.595444I
−1.31503 − 2.43238I 0
u = 0.816860 + 1.100600I
a = −0.723679 + 0.953539I
b = −1.42267 − 0.16761I
8.92473 + 4.08371I 0
u = 0.816860 − 1.100600I
a = −0.723679 − 0.953539I
b = −1.42267 + 0.16761I
8.92473 − 4.08371I 0
u = −0.810679 + 1.116350I
a = 0.795718 + 0.932947I
b = 1.38186 − 0.37607I
7.28558 − 10.07310I 0
u = −0.810679 − 1.116350I
a = 0.795718 − 0.932947I
b = 1.38186 + 0.37607I
7.28558 + 10.07310I 0
u = 0.452766 + 0.404638I
a = −1.47433 − 2.68024I
b = 0.535538 − 1.093260I
1.00688 − 2.77629I −4.92596 + 6.43001I
u = 0.452766 − 0.404638I
a = −1.47433 + 2.68024I
b = 0.535538 + 1.093260I
1.00688 + 2.77629I −4.92596 − 6.43001I
u = 0.805308 + 1.153490I
a = 0.670849 − 1.225990I
b = 1.62167 + 0.83385I
6.06561 − 4.85072I 0
u = 0.805308 − 1.153490I
a = 0.670849 + 1.225990I
b = 1.62167 − 0.83385I
6.06561 + 4.85072I 0
u = 0.572850 + 0.113813I
a = 0.31165 − 1.93224I
b = 0.522800 − 1.239640I
−0.74994 − 2.26614I −2.36898 + 2.26109I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.572850 − 0.113813I
a = 0.31165 + 1.93224I
b = 0.522800 + 1.239640I
−0.74994 + 2.26614I −2.36898 − 2.26109I
u = −1.10949 + 0.90861I
a = 0.575846 + 0.933832I
b = 1.43129 + 0.81182I
0.73551 + 9.43744I 0
u = −1.10949 − 0.90861I
a = 0.575846 − 0.933832I
b = 1.43129 − 0.81182I
0.73551 − 9.43744I 0
u = 1.12332 + 0.90477I
a = −0.794206 + 0.775788I
b = −1.384030 + 0.239354I
7.03396 − 6.13444I 0
u = 1.12332 − 0.90477I
a = −0.794206 − 0.775788I
b = −1.384030 − 0.239354I
7.03396 + 6.13444I 0
u = 1.11834 + 0.91483I
a = −0.698998 + 1.111010I
b = −1.93787 + 0.75793I
7.93180 − 11.37730I 0
u = 1.11834 − 0.91483I
a = −0.698998 − 1.111010I
b = −1.93787 − 0.75793I
7.93180 + 11.37730I 0
u = 1.44736
a = −0.363781
b = −0.569357
−7.28072 0
u = −1.12433 + 0.91467I
a = 0.648636 + 1.173700I
b = 2.02318 + 0.93554I
6.2467 + 17.4034I 0
u = −1.12433 − 0.91467I
a = 0.648636 − 1.173700I
b = 2.02318 − 0.93554I
6.2467 − 17.4034I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16723 + 0.87243I
a = 0.832601 + 0.550806I
b = 1.073570 − 0.015326I
4.64251 − 0.27243I 0
u = −1.16723 − 0.87243I
a = 0.832601 − 0.550806I
b = 1.073570 + 0.015326I
4.64251 + 0.27243I 0
u = 1.46004 + 0.25246I
a = −0.241739 − 0.095073I
b = −0.433386 − 0.864185I
−3.27457 − 7.84836I 0
u = 1.46004 − 0.25246I
a = −0.241739 + 0.095073I
b = −0.433386 + 0.864185I
−3.27457 + 7.84836I 0
u = 0.360098 + 0.364687I
a = 0.126184 − 0.361675I
b = −1.58298 + 0.61850I
−3.32779 − 1.11831I −1.97095 + 8.18187I
u = 0.360098 − 0.364687I
a = 0.126184 + 0.361675I
b = −1.58298 − 0.61850I
−3.32779 + 1.11831I −1.97095 − 8.18187I
u = 1.09967 + 1.02790I
a = 0.499291 − 1.100540I
b = 2.35471 − 0.43931I
5.16143 − 2.94606I 0
u = 1.09967 − 1.02790I
a = 0.499291 + 1.100540I
b = 2.35471 + 0.43931I
5.16143 + 2.94606I 0
u = −0.483190
a = 0.389799
b = −0.350552
−0.728767 −13.5780
u = 1.54161
a = −0.494347
b = −0.315152
−7.66030 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.18837 + 0.98534I
a = −0.407590 − 1.019860I
b = −2.35923 − 0.86528I
4.38461 + 7.76770I 0
u = −1.18837 − 0.98534I
a = −0.407590 + 1.019860I
b = −2.35923 + 0.86528I
4.38461 − 7.76770I 0
u = 0.0562391 + 0.1093170I
a = 3.31304 − 10.80210I
b = 0.057086 − 0.925377I
2.98085 − 2.73185I −6.71068 + 3.58075I
u = 0.0562391 − 0.1093170I
a = 3.31304 + 10.80210I
b = 0.057086 + 0.925377I
2.98085 + 2.73185I −6.71068 − 3.58075I
13
II. I
u
2
= h−2270u
21
− 3510u
20
+ · · · + 61b − 3235, −7325u
21
− 11232u
20
+
· · · + 61a − 11023, u
22
+ 2u
21
+ · · · + 3u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
120.082u
21
+ 184.131u
20
+ ··· + 171.852u + 180.705
37.2131u
21
+ 57.5410u
20
+ ··· + 54.0164u + 53.0328
a
9
=
−46.2295u
21
− 62.9672u
20
+ ··· − 125.787u − 80.5738
64.6721u
21
+ 100.475u
20
+ ··· + 82.5902u + 95.1803
a
10
=
−128.098u
21
− 187.557u
20
+ ··· − 250.623u − 205.246
38.2131u
21
+ 59.5410u
20
+ ··· + 47.0164u + 56.0328
a
12
=
120.082u
21
+ 184.131u
20
+ ··· + 171.852u + 180.705
−u
21
− 2u
20
+ ··· + 6u − 3
a
3
=
−21.8361u
21
− 22.7377u
20
+ ··· − 148.295u − 87.5902
−44.0492u
21
− 58.2787u
20
+ ··· − 139.311u − 93.6230
a
7
=
u
u
a
1
=
158.295u
21
+ 243.672u
20
+ ··· + 218.869u + 236.738
37.2131u
21
+ 57.5410u
20
+ ··· + 53.0164u + 53.0328
a
6
=
−110.902u
21
− 163.443u
20
+ ··· − 206.377u − 175.754
19.0656u
21
+ 29.7049u
20
+ ··· + 20.0820u + 30.1639
a
2
=
−85.3279u
21
− 120.525u
20
+ ··· − 226.410u − 175.820
13.3607u
21
+ 25.3770u
20
+ ··· − 12.0492u + 11.9016
(ii) Obstruction class = 1
(iii) Cusp Shapes =
24462
61
u
21
+
34979
61
u
20
+ ··· +
60315
61
u +
46454
61
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
22
− 12u
21
+ ··· − 14u + 1
c
2
u
22
− 6u
20
+ ··· − 4u + 1
c
3
u
22
− u
21
+ ··· − 5u + 1
c
4
u
22
+ 2u
21
+ ··· + 3u + 1
c
5
u
22
− 6u
20
+ ··· + 4u + 1
c
6
u
22
− 4u
21
+ ··· − u + 1
c
7
u
22
− 2u
21
+ ··· − 3u + 1
c
8
u
22
+ 15u
21
+ ··· + 71u + 7
c
9
u
22
+ u
21
+ ··· + 85u + 25
c
10
u
22
− 7u
21
+ ··· − 3u + 1
c
11
u
22
− 15u
21
+ ··· − 71u + 7
c
12
u
22
− 7u
21
+ ··· − 145u + 25
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 4y
21
+ ··· − 34y + 1
c
2
, c
5
y
22
− 12y
21
+ ··· − 14y + 1
c
3
y
22
− 5y
21
+ ··· − 5y + 1
c
4
, c
7
y
22
− 14y
21
+ ··· − 23y + 1
c
6
y
22
+ 16y
21
+ ··· − 5y + 1
c
8
, c
11
y
22
− 9y
21
+ ··· + 139y + 49
c
9
y
22
+ 15y
21
+ ··· − 1675y + 625
c
10
y
22
− y
21
+ ··· − 19y + 1
c
12
y
22
+ 7y
21
+ ··· + 3175y + 625
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.856866 + 0.225545I
a = 0.116220 − 1.077310I
b = 0.730381 − 1.204090I
−1.39247 − 2.50433I −14.5995 + 5.8291I
u = 0.856866 − 0.225545I
a = 0.116220 + 1.077310I
b = 0.730381 + 1.204090I
−1.39247 + 2.50433I −14.5995 − 5.8291I
u = 1.199800 + 0.111608I
a = 0.182768 − 0.604891I
b = 0.049347 − 1.002740I
−2.03186 − 2.81294I −12.81418 + 4.24921I
u = 1.199800 − 0.111608I
a = 0.182768 + 0.604891I
b = 0.049347 + 1.002740I
−2.03186 + 2.81294I −12.81418 − 4.24921I
u = −0.875034 + 0.884635I
a = −0.94631 − 1.18135I
b = −1.50308 + 0.02900I
4.98177 + 4.55914I −7.33008 − 6.48846I
u = −0.875034 − 0.884635I
a = −0.94631 + 1.18135I
b = −1.50308 − 0.02900I
4.98177 − 4.55914I −7.33008 + 6.48846I
u = 0.981816 + 0.815014I
a = 0.984311 − 0.726208I
b = 1.078410 + 0.042052I
3.84789 + 0.29212I −9.38873 + 0.21800I
u = 0.981816 − 0.815014I
a = 0.984311 + 0.726208I
b = 1.078410 − 0.042052I
3.84789 − 0.29212I −9.38873 − 0.21800I
u = 0.913832 + 0.921577I
a = 0.358907 − 1.181190I
b = 1.61312 − 0.84739I
3.96542 − 6.69979I −8.00000 + 5.21042I
u = 0.913832 − 0.921577I
a = 0.358907 + 1.181190I
b = 1.61312 + 0.84739I
3.96542 + 6.69979I −8.00000 − 5.21042I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.903138 + 0.946974I
a = −0.53621 − 1.31657I
b = −1.83276 − 0.47601I
4.87145 + 2.17227I −6.96260 + 2.10282I
u = −0.903138 − 0.946974I
a = −0.53621 + 1.31657I
b = −1.83276 + 0.47601I
4.87145 − 2.17227I −6.96260 − 2.10282I
u = −1.317320 + 0.174304I
a = 0.028989 − 0.518429I
b = 0.382618 − 1.170230I
−4.00357 + 8.00834I −15.9429 − 7.4079I
u = −1.317320 − 0.174304I
a = 0.028989 + 0.518429I
b = 0.382618 + 1.170230I
−4.00357 − 8.00834I −15.9429 + 7.4079I
u = 0.629269 + 0.030820I
a = 0.21465 + 2.17300I
b = 0.956578 + 0.758261I
0.31361 + 1.97050I −9.18967 − 2.78008I
u = 0.629269 − 0.030820I
a = 0.21465 − 2.17300I
b = 0.956578 − 0.758261I
0.31361 − 1.97050I −9.18967 + 2.78008I
u = −1.38946
a = −0.256953
b = 0.173681
−7.68275 −26.5880
u = −0.555921 + 0.018578I
a = 0.41900 + 2.48592I
b = −1.060200 + 0.680133I
−0.74395 − 7.07177I −11.14495 + 8.67430I
u = −0.555921 − 0.018578I
a = 0.41900 − 2.48592I
b = −1.060200 − 0.680133I
−0.74395 + 7.07177I −11.14495 − 8.67430I
u = −0.486314 + 0.175391I
a = 0.530851 − 1.103340I
b = −1.41229 − 1.14920I
−3.73858 + 0.98517I −20.7815 − 2.2138I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.486314 − 0.175391I
a = 0.530851 + 1.103340I
b = −1.41229 + 1.14920I
−3.73858 − 0.98517I −20.7815 + 2.2138I
u = −1.49824
a = −0.449376
b = −0.177933
−7.74653 −52.1880
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 12u
21
+ ··· − 14u + 1)(u
84
+ 35u
83
+ ··· + 55u + 1)
c
2
(u
22
− 6u
20
+ ··· − 4u + 1)(u
84
+ u
83
+ ··· + 9u − 1)
c
3
(u
22
− u
21
+ ··· − 5u + 1)(u
84
+ 2u
83
+ ··· − 3150u − 863)
c
4
(u
22
+ 2u
21
+ ··· + 3u + 1)(u
84
+ 3u
83
+ ··· + 6u − 1)
c
5
(u
22
− 6u
20
+ ··· + 4u + 1)(u
84
+ u
83
+ ··· + 9u − 1)
c
6
(u
22
− 4u
21
+ ··· − u + 1)(u
84
+ u
83
+ ··· − 4996204u − 2395607)
c
7
(u
22
− 2u
21
+ ··· − 3u + 1)(u
84
+ 3u
83
+ ··· + 6u − 1)
c
8
(u
22
+ 15u
21
+ ··· + 71u + 7)(u
84
− 10u
83
+ ··· + 8180u + 3952)
c
9
(u
22
+ u
21
+ ··· + 85u + 25)
· (u
84
+ 34u
82
+ ··· + 1301846276u + 241946651)
c
10
(u
22
− 7u
21
+ ··· − 3u + 1)(u
84
− 10u
83
+ ··· − 248u + 1)
c
11
(u
22
− 15u
21
+ ··· − 71u + 7)(u
84
− 10u
83
+ ··· + 8180u + 3952)
c
12
(u
22
− 7u
21
+ ··· − 145u + 25)
· (u
84
− 4u
83
+ ··· − 28586236u + 7588717)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ 4y
21
+ ··· − 34y + 1)(y
84
+ 37y
83
+ ··· + 1781y + 1)
c
2
, c
5
(y
22
− 12y
21
+ ··· − 14y + 1)(y
84
− 35y
83
+ ··· − 55y + 1)
c
3
(y
22
− 5y
21
+ ··· − 5y + 1)(y
84
+ 12y
83
+ ··· + 9189498y + 744769)
c
4
, c
7
(y
22
− 14y
21
+ ··· − 23y + 1)(y
84
− 21y
83
+ ··· + 48y + 1)
c
6
(y
22
+ 16y
21
+ ··· − 5y + 1)
· (y
84
+ 53y
83
+ ··· − 69359144214586y + 5738932898449)
c
8
, c
11
(y
22
− 9y
21
+ ··· + 139y + 49)
· (y
84
− 84y
83
+ ··· − 1119037552y + 15618304)
c
9
(y
22
+ 15y
21
+ ··· − 1675y + 625)
· (y
84
+ 68y
83
+ ··· + 1815122488070227036y + 58538181930115801)
c
10
(y
22
− y
21
+ ··· − 19y + 1)(y
84
+ 12y
83
+ ··· − 58496y + 1)
c
12
(y
22
+ 7y
21
+ ··· + 3175y + 625)
· (y
84
+ 64y
83
+ ··· − 298596197402654y + 57588625706089)
23
