12a
0459
(K12a
0459
)
A knot diagram
1
Linearized knot diagam
3 6 10 12 9 2 5 11 7 1 8 4
Solving Sequence
2,6 3,10
4 7 1 11 9 5 8 12
c
2
c
3
c
6
c
1
c
10
c
9
c
5
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h7.16000 × 10
408
u
158
+ 2.81310 × 10
409
u
157
+ ··· + 2.75929 × 10
409
b + 1.24491 × 10
411
,
− 4.54199 × 10
410
u
158
− 9.85253 × 10
410
u
157
+ ··· + 1.68317 × 10
411
a + 9.52712 × 10
412
,
u
159
+ 3u
158
+ ··· + 254u + 61i
I
u
2
= h1.89088 × 10
16
u
37
+ 3.81587 × 10
16
u
36
+ ··· + 7.24163 × 10
15
b + 3.77832 × 10
16
,
1.80953 × 10
15
u
37
+ 7.77114 × 10
16
u
36
+ ··· + 2.17249 × 10
16
a + 4.07624 × 10
17
, u
38
+ 2u
37
+ ··· + 7u + 3i
* 2 irreducible components of dim
C
= 0, with total 197 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
= h7.16 × 10
408
u
158
+ 2.81 × 10
409
u
157
+ · · · + 2.76 × 10
409
b + 1.24 ×
10
411
, −4.54 × 10
410
u
158
− 9.85 × 10
410
u
157
+ · · · + 1.68 × 10
411
a + 9.53 ×
10
412
, u
159
+ 3u
158
+ · · · + 254u + 61i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
0.269847u
158
+ 0.585356u
157
+ ··· − 120.184u − 56.6022
−0.259486u
158
− 1.01950u
157
+ ··· − 145.106u − 45.1168
a
4
=
−1.65210u
158
− 10.5481u
157
+ ··· − 1632.96u − 475.800
−1.25361u
158
− 8.81070u
157
+ ··· − 1243.70u − 384.679
a
7
=
u
u
a
1
=
u
2
+ 1
−u
4
a
11
=
−0.673257u
158
− 2.06957u
157
+ ··· − 302.818u − 99.0191
−1.38391u
158
− 3.80070u
157
+ ··· − 335.208u − 87.9624
a
9
=
−0.210299u
158
− 0.627259u
157
+ ··· − 156.754u − 57.6302
−0.739633u
158
− 2.23211u
157
+ ··· − 181.676u − 46.1448
a
5
=
−0.251684u
158
− 5.77397u
157
+ ··· − 1017.29u − 340.328
−1.18463u
158
− 7.36524u
157
+ ··· − 1060.12u − 335.916
a
8
=
2.71551u
158
+ 6.99494u
157
+ ··· + 531.066u + 141.743
1.99218u
158
+ 5.00541u
157
+ ··· + 382.406u + 87.0731
a
12
=
3.02859u
158
+ 7.14838u
157
+ ··· + 521.124u + 129.485
4.07615u
158
+ 10.0795u
157
+ ··· + 726.211u + 149.463
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.54355u
158
+ 4.06187u
157
+ ··· − 159.678u − 151.190
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
159
+ 63u
158
+ ··· − 160940u − 3721
c
2
, c
6
u
159
− 3u
158
+ ··· + 254u − 61
c
3
u
159
+ 2u
158
+ ··· − 6385u − 131
c
4
, c
12
u
159
+ 6u
158
+ ··· + 329355u − 46602
c
5
u
159
− 3u
158
+ ··· − 31151u − 5272
c
7
u
159
+ 13u
158
+ ··· − 2559717451u − 258897949
c
8
, c
11
u
159
− 12u
158
+ ··· + 5916498u − 656059
c
9
u
159
+ 17u
158
+ ··· − 44446u − 5041
c
10
u
159
− 16u
158
+ ··· + 1503u − 71
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
159
+ 63y
158
+ ··· + 1061374132y −13845841
c
2
, c
6
y
159
+ 63y
158
+ ··· − 160940y −3721
c
3
y
159
− 8y
158
+ ··· + 9604635y −17161
c
4
, c
12
y
159
+ 126y
158
+ ··· + 236167644573y −2171746404
c
5
y
159
− 15y
158
+ ··· − 346128495y −27793984
c
7
y
159
+ 59y
158
+ ··· − 1286314653118589129y −67028147996406601
c
8
, c
11
y
159
+ 102y
158
+ ··· − 6052537066114y −430413411481
c
9
y
159
− 9y
158
+ ··· + 268040052y −25411681
c
10
y
159
− 18y
158
+ ··· − 151015y −5041
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.891606 + 0.451374I
a = −0.399037 − 0.880877I
b = −1.387810 + 0.079849I
−0.10649 − 4.58909I 0
u = 0.891606 − 0.451374I
a = −0.399037 + 0.880877I
b = −1.387810 − 0.079849I
−0.10649 + 4.58909I 0
u = 0.399869 + 0.927877I
a = 0.42775 − 2.20856I
b = −0.74809 − 2.12471I
−7.49146 + 2.95901I 0
u = 0.399869 − 0.927877I
a = 0.42775 + 2.20856I
b = −0.74809 + 2.12471I
−7.49146 − 2.95901I 0
u = −0.571758 + 0.834215I
a = 1.41778 − 0.73759I
b = 2.28792 − 0.39889I
1.88865 − 1.06916I 0
u = −0.571758 − 0.834215I
a = 1.41778 + 0.73759I
b = 2.28792 + 0.39889I
1.88865 + 1.06916I 0
u = 0.683602 + 0.708957I
a = 1.32111 − 0.58053I
b = 1.167530 − 0.538071I
−0.236758 − 1.021390I 0
u = 0.683602 − 0.708957I
a = 1.32111 + 0.58053I
b = 1.167530 + 0.538071I
−0.236758 + 1.021390I 0
u = 0.613617 + 0.809529I
a = −1.24201 − 1.46224I
b = −1.43474 + 0.13516I
3.28186 + 0.91601I 0
u = 0.613617 − 0.809529I
a = −1.24201 + 1.46224I
b = −1.43474 − 0.13516I
3.28186 − 0.91601I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.831614 + 0.498398I
a = 0.582103 + 0.698196I
b = 1.213780 + 0.049993I
0.93629 − 3.11773I 0
u = 0.831614 − 0.498398I
a = 0.582103 − 0.698196I
b = 1.213780 − 0.049993I
0.93629 + 3.11773I 0
u = −0.603720 + 0.758440I
a = −0.18923 + 1.77717I
b = −2.36106 + 1.11082I
−4.09868 + 4.78610I 0
u = −0.603720 − 0.758440I
a = −0.18923 − 1.77717I
b = −2.36106 − 1.11082I
−4.09868 − 4.78610I 0
u = −0.815510 + 0.510356I
a = −0.055289 − 1.063800I
b = 0.429918 − 0.267518I
0.470123 − 0.643923I 0
u = −0.815510 − 0.510356I
a = −0.055289 + 1.063800I
b = 0.429918 + 0.267518I
0.470123 + 0.643923I 0
u = −0.868748 + 0.576297I
a = 1.27606 − 0.87395I
b = 1.54440 + 0.59450I
−0.53884 + 7.54590I 0
u = −0.868748 − 0.576297I
a = 1.27606 + 0.87395I
b = 1.54440 − 0.59450I
−0.53884 − 7.54590I 0
u = −0.575233 + 0.869697I
a = 0.94013 − 2.21673I
b = 1.24916 − 1.17661I
1.77261 − 3.50082I 0
u = −0.575233 − 0.869697I
a = 0.94013 + 2.21673I
b = 1.24916 + 1.17661I
1.77261 + 3.50082I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.627251 + 0.721492I
a = 1.08372 + 2.32675I
b = 1.27777 + 1.06708I
−3.45995 − 5.36968I 0
u = 0.627251 − 0.721492I
a = 1.08372 − 2.32675I
b = 1.27777 − 1.06708I
−3.45995 + 5.36968I 0
u = 0.872842 + 0.574512I
a = −0.880043 − 0.920042I
b = −1.231380 + 0.332606I
3.92115 − 3.61044I 0
u = 0.872842 − 0.574512I
a = −0.880043 + 0.920042I
b = −1.231380 − 0.332606I
3.92115 + 3.61044I 0
u = −0.609586 + 0.849892I
a = 1.44685 − 2.54477I
b = 3.05712 − 0.70431I
0.77339 − 2.40140I 0
u = −0.609586 − 0.849892I
a = 1.44685 + 2.54477I
b = 3.05712 + 0.70431I
0.77339 + 2.40140I 0
u = −0.588733 + 0.750638I
a = −0.904183 + 0.740341I
b = −1.241650 + 0.556024I
1.21651 − 1.58917I 0
u = −0.588733 − 0.750638I
a = −0.904183 − 0.740341I
b = −1.241650 − 0.556024I
1.21651 + 1.58917I 0
u = −0.553031 + 0.767881I
a = −0.57305 + 1.84886I
b = −0.208333 + 0.772614I
−0.551910 + 1.122070I 0
u = −0.553031 − 0.767881I
a = −0.57305 − 1.84886I
b = −0.208333 − 0.772614I
−0.551910 − 1.122070I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.497138 + 0.802103I
a = 0.940684 + 0.349089I
b = −0.642794 − 0.744683I
−6.40496 + 2.25710I 0
u = 0.497138 − 0.802103I
a = 0.940684 − 0.349089I
b = −0.642794 + 0.744683I
−6.40496 − 2.25710I 0
u = 0.522717 + 0.918136I
a = −0.861764 − 0.279437I
b = 0.501977 + 0.832439I
−6.81443 + 1.89238I 0
u = 0.522717 − 0.918136I
a = −0.861764 + 0.279437I
b = 0.501977 − 0.832439I
−6.81443 − 1.89238I 0
u = 0.632740 + 0.847116I
a = −1.83466 − 2.13359I
b = −2.60512 − 1.20654I
1.39791 + 2.47477I 0
u = 0.632740 − 0.847116I
a = −1.83466 + 2.13359I
b = −2.60512 + 1.20654I
1.39791 − 2.47477I 0
u = 0.607609 + 0.711221I
a = −0.035942 + 0.740569I
b = 1.23958 + 0.90009I
1.44425 − 1.69401I 0
u = 0.607609 − 0.711221I
a = −0.035942 − 0.740569I
b = 1.23958 − 0.90009I
1.44425 + 1.69401I 0
u = 0.615466 + 0.873663I
a = −0.30344 − 1.40309I
b = −1.81053 − 1.19041I
3.08306 + 3.92462I 0
u = 0.615466 − 0.873663I
a = −0.30344 + 1.40309I
b = −1.81053 + 1.19041I
3.08306 − 3.92462I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.934127 + 0.528231I
a = −1.051730 + 0.882977I
b = −1.41419 − 0.55637I
−4.5491 + 14.0442I 0
u = −0.934127 − 0.528231I
a = −1.051730 − 0.882977I
b = −1.41419 + 0.55637I
−4.5491 − 14.0442I 0
u = −0.884763 + 0.265927I
a = −0.065974 + 0.990621I
b = −0.277394 + 0.133064I
0.067585 − 0.143772I 0
u = −0.884763 − 0.265927I
a = −0.065974 − 0.990621I
b = −0.277394 − 0.133064I
0.067585 + 0.143772I 0
u = 0.949654 + 0.508942I
a = 0.786316 + 0.857484I
b = 1.068240 − 0.317335I
1.42546 − 7.94644I 0
u = 0.949654 − 0.508942I
a = 0.786316 − 0.857484I
b = 1.068240 + 0.317335I
1.42546 + 7.94644I 0
u = −0.566757 + 0.921324I
a = −1.008770 − 0.000430I
b = −1.94280 + 0.18822I
−1.05014 − 5.62239I 0
u = −0.566757 − 0.921324I
a = −1.008770 + 0.000430I
b = −1.94280 − 0.18822I
−1.05014 + 5.62239I 0
u = −0.071453 + 1.082090I
a = −0.528626 + 0.466190I
b = 0.701369 − 0.226657I
−11.43230 + 0.10008I 0
u = −0.071453 − 1.082090I
a = −0.528626 − 0.466190I
b = 0.701369 + 0.226657I
−11.43230 − 0.10008I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.343598 + 0.842945I
a = 0.80711 − 1.83541I
b = 1.18296 − 1.98287I
−2.48699 + 1.18392I 0
u = −0.343598 − 0.842945I
a = 0.80711 + 1.83541I
b = 1.18296 + 1.98287I
−2.48699 − 1.18392I 0
u = −0.595995 + 0.919577I
a = −1.83619 + 1.92879I
b = −2.25512 − 0.32712I
−4.60052 − 9.53462I 0
u = −0.595995 − 0.919577I
a = −1.83619 − 1.92879I
b = −2.25512 + 0.32712I
−4.60052 + 9.53462I 0
u = −0.645641 + 0.628785I
a = 1.010270 − 0.702753I
b = 0.754803 + 1.111730I
−0.954940 + 0.088450I 0
u = −0.645641 − 0.628785I
a = 1.010270 + 0.702753I
b = 0.754803 − 1.111730I
−0.954940 − 0.088450I 0
u = −0.062257 + 1.101880I
a = 0.774289 + 0.733403I
b = −0.219207 + 0.885741I
−5.90968 − 1.00227I 0
u = −0.062257 − 1.101880I
a = 0.774289 − 0.733403I
b = −0.219207 − 0.885741I
−5.90968 + 1.00227I 0
u = −0.628272 + 0.908716I
a = −0.42968 + 1.46683I
b = −0.880148 + 1.051340I
0.71583 − 3.24571I 0
u = −0.628272 − 0.908716I
a = −0.42968 − 1.46683I
b = −0.880148 − 1.051340I
0.71583 + 3.24571I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.839307 + 0.294161I
a = 0.730632 − 0.193247I
b = 0.145461 − 0.690363I
−1.96454 + 3.63147I 0
u = 0.839307 − 0.294161I
a = 0.730632 + 0.193247I
b = 0.145461 + 0.690363I
−1.96454 − 3.63147I 0
u = 0.749765 + 0.825354I
a = −0.698807 + 1.067630I
b = 0.31282 + 1.42365I
−5.61660 + 0.32133I 0
u = 0.749765 − 0.825354I
a = −0.698807 − 1.067630I
b = 0.31282 − 1.42365I
−5.61660 − 0.32133I 0
u = −0.902924 + 0.660808I
a = −0.474272 + 0.497644I
b = −0.933594 − 0.010397I
2.26957 − 2.33577I 0
u = −0.902924 − 0.660808I
a = −0.474272 − 0.497644I
b = −0.933594 + 0.010397I
2.26957 + 2.33577I 0
u = 0.614092 + 0.936059I
a = 1.09199 + 1.04492I
b = 0.986717 − 0.242566I
0.77023 + 6.53892I 0
u = 0.614092 − 0.936059I
a = 1.09199 − 1.04492I
b = 0.986717 + 0.242566I
0.77023 − 6.53892I 0
u = 0.614061 + 0.939601I
a = 1.69890 + 1.00476I
b = 2.67904 + 0.70566I
−4.12502 + 10.25450I 0
u = 0.614061 − 0.939601I
a = 1.69890 − 1.00476I
b = 2.67904 − 0.70566I
−4.12502 − 10.25450I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.041450 + 0.419189I
a = −0.497265 + 0.333522I
b = 0.108138 + 0.587378I
−5.14019 + 8.67296I 0
u = 1.041450 − 0.419189I
a = −0.497265 − 0.333522I
b = 0.108138 − 0.587378I
−5.14019 − 8.67296I 0
u = −0.082693 + 1.123310I
a = −0.315749 + 0.112904I
b = 0.513951 + 0.319444I
−2.69089 − 2.42476I 0
u = −0.082693 − 1.123310I
a = −0.315749 − 0.112904I
b = 0.513951 − 0.319444I
−2.69089 + 2.42476I 0
u = −0.997319 + 0.525387I
a = 0.332017 − 0.391180I
b = 0.720221 + 0.183185I
2.63643 + 1.45962I 0
u = −0.997319 − 0.525387I
a = 0.332017 + 0.391180I
b = 0.720221 − 0.183185I
2.63643 − 1.45962I 0
u = 0.203757 + 1.109290I
a = 0.698695 + 0.024459I
b = −0.118743 − 0.669347I
−6.10046 − 0.54998I 0
u = 0.203757 − 1.109290I
a = 0.698695 − 0.024459I
b = −0.118743 + 0.669347I
−6.10046 + 0.54998I 0
u = −0.692665 + 0.521554I
a = −1.48146 + 1.30966I
b = −1.67966 − 0.21318I
−6.48598 + 1.52980I 0
u = −0.692665 − 0.521554I
a = −1.48146 − 1.30966I
b = −1.67966 + 0.21318I
−6.48598 − 1.52980I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672646 + 0.935903I
a = −0.34462 + 1.54924I
b = −0.131100 + 1.395650I
−0.89825 + 6.26091I 0
u = 0.672646 − 0.935903I
a = −0.34462 − 1.54924I
b = −0.131100 − 1.395650I
−0.89825 − 6.26091I 0
u = −0.507923 + 1.036030I
a = −0.43365 + 2.07432I
b = −2.14224 + 1.26606I
−7.83347 − 9.11034I 0
u = −0.507923 − 1.036030I
a = −0.43365 − 2.07432I
b = −2.14224 − 1.26606I
−7.83347 + 9.11034I 0
u = 0.084320 + 1.162100I
a = 0.588540 − 0.162711I
b = −0.521174 + 0.170155I
−7.16691 + 6.22962I 0
u = 0.084320 − 1.162100I
a = 0.588540 + 0.162711I
b = −0.521174 − 0.170155I
−7.16691 − 6.22962I 0
u = −0.335652 + 0.764370I
a = −1.33194 + 2.73398I
b = −1.85917 + 0.24047I
−6.44396 + 5.52006I 0
u = −0.335652 − 0.764370I
a = −1.33194 − 2.73398I
b = −1.85917 − 0.24047I
−6.44396 − 5.52006I 0
u = 0.505247 + 1.053240I
a = −0.084250 + 1.129650I
b = 0.505172 + 1.124770I
−4.46368 + 1.07446I 0
u = 0.505247 − 1.053240I
a = −0.084250 − 1.129650I
b = 0.505172 − 1.124770I
−4.46368 − 1.07446I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.214743 + 1.149270I
a = 0.128211 − 0.777716I
b = 1.037460 − 0.532001I
−10.79030 − 3.03275I 0
u = 0.214743 − 1.149270I
a = 0.128211 + 0.777716I
b = 1.037460 + 0.532001I
−10.79030 + 3.03275I 0
u = −0.329478 + 1.125570I
a = −1.41147 − 0.19219I
b = −0.564611 − 1.189060I
−8.97038 + 2.08423I 0
u = −0.329478 − 1.125570I
a = −1.41147 + 0.19219I
b = −0.564611 + 1.189060I
−8.97038 − 2.08423I 0
u = 0.573234 + 1.034610I
a = 0.66515 + 1.81424I
b = 2.00514 + 1.32017I
−3.73577 + 7.30425I 0
u = 0.573234 − 1.034610I
a = 0.66515 − 1.81424I
b = 2.00514 − 1.32017I
−3.73577 − 7.30425I 0
u = −0.626228 + 1.010830I
a = 0.585336 − 0.050441I
b = 1.185370 + 0.011923I
−1.08115 − 4.55575I 0
u = −0.626228 − 1.010830I
a = 0.585336 + 0.050441I
b = 1.185370 − 0.011923I
−1.08115 + 4.55575I 0
u = 0.553152 + 1.052900I
a = −0.78032 − 1.85728I
b = −1.28934 − 1.88716I
−8.64744 + 10.19800I 0
u = 0.553152 − 1.052900I
a = −0.78032 + 1.85728I
b = −1.28934 + 1.88716I
−8.64744 − 10.19800I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.670451 + 0.984890I
a = −0.489466 − 1.085880I
b = 0.92873 − 1.45141I
−1.96691 − 5.24950I 0
u = −0.670451 − 0.984890I
a = −0.489466 + 1.085880I
b = 0.92873 + 1.45141I
−1.96691 + 5.24950I 0
u = −0.457777 + 1.104550I
a = 0.929703 − 0.845257I
b = 1.31324 − 0.91960I
−3.73394 − 3.95029I 0
u = −0.457777 − 1.104550I
a = 0.929703 + 0.845257I
b = 1.31324 + 0.91960I
−3.73394 + 3.95029I 0
u = −0.388814 + 0.700087I
a = −0.23567 − 1.72227I
b = −0.116076 − 0.547040I
0.453064 + 0.029676I 0
u = −0.388814 − 0.700087I
a = −0.23567 + 1.72227I
b = −0.116076 + 0.547040I
0.453064 − 0.029676I 0
u = −0.623240 + 1.038110I
a = −0.73855 + 2.19114I
b = −2.03884 + 1.84794I
−7.97107 − 6.62345I 0
u = −0.623240 − 1.038110I
a = −0.73855 − 2.19114I
b = −2.03884 − 1.84794I
−7.97107 + 6.62345I 0
u = 0.114628 + 1.238640I
a = −0.772355 − 0.165121I
b = −0.463441 + 0.435036I
−6.04736 − 1.91666I 0
u = 0.114628 − 1.238640I
a = −0.772355 + 0.165121I
b = −0.463441 − 0.435036I
−6.04736 + 1.91666I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.708136 + 1.032670I
a = −0.388373 + 1.181580I
b = −1.082470 + 0.876189I
1.09638 − 3.58717I 0
u = −0.708136 − 1.032670I
a = −0.388373 − 1.181580I
b = −1.082470 − 0.876189I
1.09638 + 3.58717I 0
u = 0.219256 + 0.706031I
a = −1.73960 − 0.66953I
b = −1.51753 − 1.35320I
−6.65955 − 6.15096I 0
u = 0.219256 − 0.706031I
a = −1.73960 + 0.66953I
b = −1.51753 + 1.35320I
−6.65955 + 6.15096I 0
u = 0.777772 + 0.994883I
a = 0.796367 − 0.675047I
b = 0.218636 − 1.334040I
−6.09025 + 5.57926I 0
u = 0.777772 − 0.994883I
a = 0.796367 + 0.675047I
b = 0.218636 + 1.334040I
−6.09025 − 5.57926I 0
u = −1.247940 + 0.246837I
a = 0.042339 − 0.161157I
b = 0.075085 + 0.245060I
1.02894 − 1.15088I 0
u = −1.247940 − 0.246837I
a = 0.042339 + 0.161157I
b = 0.075085 − 0.245060I
1.02894 + 1.15088I 0
u = 0.076094 + 1.271130I
a = 0.560911 + 0.294765I
b = 0.122577 + 0.139020I
−4.97447 − 0.78694I 0
u = 0.076094 − 1.271130I
a = 0.560911 − 0.294765I
b = 0.122577 − 0.139020I
−4.97447 + 0.78694I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.066043 + 1.273770I
a = −0.451108 + 0.114589I
b = 0.453927 − 0.297525I
−11.5403 + 11.8535I 0
u = 0.066043 − 1.273770I
a = −0.451108 − 0.114589I
b = 0.453927 + 0.297525I
−11.5403 − 11.8535I 0
u = 0.662213 + 1.093830I
a = 0.65581 + 1.44233I
b = 1.41474 + 0.96411I
−0.84101 + 8.70296I 0
u = 0.662213 − 1.093830I
a = 0.65581 − 1.44233I
b = 1.41474 − 0.96411I
−0.84101 − 8.70296I 0
u = 0.693099 + 1.078350I
a = −0.51511 − 1.54099I
b = −1.71907 − 1.32929I
2.37709 + 9.41632I 0
u = 0.693099 − 1.078350I
a = −0.51511 + 1.54099I
b = −1.71907 + 1.32929I
2.37709 − 9.41632I 0
u = −0.695608 + 1.077510I
a = 0.44958 − 1.96324I
b = 1.82591 − 1.76850I
−2.06941 − 13.35370I 0
u = −0.695608 − 1.077510I
a = 0.44958 + 1.96324I
b = 1.82591 + 1.76850I
−2.06941 + 13.35370I 0
u = 0.660840 + 1.135020I
a = −0.79320 − 1.45488I
b = −1.78706 − 0.78397I
−2.17517 + 10.31870I 0
u = 0.660840 − 1.135020I
a = −0.79320 + 1.45488I
b = −1.78706 + 0.78397I
−2.17517 − 10.31870I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699736 + 1.120050I
a = −0.52746 + 1.79089I
b = −1.86336 + 1.59857I
−6.3731 − 20.0336I 0
u = −0.699736 − 1.120050I
a = −0.52746 − 1.79089I
b = −1.86336 − 1.59857I
−6.3731 + 20.0336I 0
u = −0.082018 + 1.320590I
a = 0.0961673 + 0.0711012I
b = −0.621161 − 0.145846I
−5.70638 − 5.46309I 0
u = −0.082018 − 1.320590I
a = 0.0961673 − 0.0711012I
b = −0.621161 + 0.145846I
−5.70638 + 5.46309I 0
u = 0.698089 + 1.129470I
a = 0.56404 + 1.41401I
b = 1.67719 + 1.30711I
−0.48522 + 13.96210I 0
u = 0.698089 − 1.129470I
a = 0.56404 − 1.41401I
b = 1.67719 − 1.30711I
−0.48522 − 13.96210I 0
u = −0.716426 + 1.132810I
a = 0.320924 − 1.047460I
b = 1.090520 − 0.822092I
0.74553 − 7.64812I 0
u = −0.716426 − 1.132810I
a = 0.320924 + 1.047460I
b = 1.090520 + 0.822092I
0.74553 + 7.64812I 0
u = −0.737999 + 1.123130I
a = 0.099504 − 0.680268I
b = 1.002420 − 0.822822I
−1.62771 − 5.11952I 0
u = −0.737999 − 1.123130I
a = 0.099504 + 0.680268I
b = 1.002420 + 0.822822I
−1.62771 + 5.11952I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498926 + 0.404048I
a = 0.57619 + 1.82941I
b = 1.200400 − 0.049494I
−2.11405 − 2.75941I 3.06383 + 4.92986I
u = 0.498926 − 0.404048I
a = 0.57619 − 1.82941I
b = 1.200400 + 0.049494I
−2.11405 + 2.75941I 3.06383 − 4.92986I
u = 0.353254 + 0.524132I
a = −1.98450 + 0.75608I
b = −0.65495 + 1.30072I
−6.43990 + 0.21273I 2.10466 − 2.88222I
u = 0.353254 − 0.524132I
a = −1.98450 − 0.75608I
b = −0.65495 − 1.30072I
−6.43990 − 0.21273I 2.10466 + 2.88222I
u = 0.579950 + 0.243442I
a = −1.64163 − 1.20353I
b = −0.869948 − 0.299649I
−6.67361 − 5.76857I 1.19700 + 3.98730I
u = 0.579950 − 0.243442I
a = −1.64163 + 1.20353I
b = −0.869948 + 0.299649I
−6.67361 + 5.76857I 1.19700 − 3.98730I
u = 0.574453 + 1.262280I
a = 0.031831 − 0.594807I
b = −0.204980 − 0.761417I
−8.02830 − 2.54868I 0
u = 0.574453 − 1.262280I
a = 0.031831 + 0.594807I
b = −0.204980 + 0.761417I
−8.02830 + 2.54868I 0
u = −0.673803 + 1.220830I
a = −0.428510 + 0.652156I
b = −1.22811 + 0.78321I
−2.75965 − 5.66705I 0
u = −0.673803 − 1.220830I
a = −0.428510 − 0.652156I
b = −1.22811 − 0.78321I
−2.75965 + 5.66705I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.148298 + 0.538013I
a = 1.18272 + 2.36230I
b = 1.001110 + 0.458544I
−2.03542 − 2.73997I 1.46092 + 6.56987I
u = 0.148298 − 0.538013I
a = 1.18272 − 2.36230I
b = 1.001110 − 0.458544I
−2.03542 + 2.73997I 1.46092 − 6.56987I
u = −0.528592 + 0.033707I
a = 1.07746 + 1.02503I
b = −1.050220 − 0.728367I
−5.67142 + 5.34232I 1.94062 − 3.00311I
u = −0.528592 − 0.033707I
a = 1.07746 − 1.02503I
b = −1.050220 + 0.728367I
−5.67142 − 5.34232I 1.94062 + 3.00311I
u = −0.105801 + 0.462126I
a = 1.21181 − 1.85711I
b = 0.806452 + 0.797118I
−1.237960 − 0.251521I 2.04267 − 1.76475I
u = −0.105801 − 0.462126I
a = 1.21181 + 1.85711I
b = 0.806452 − 0.797118I
−1.237960 + 0.251521I 2.04267 + 1.76475I
u = −0.411659
a = −1.64181
b = −0.0904021
1.01780 9.02240
u = −0.098178 + 0.385659I
a = −0.750766 + 0.834728I
b = 0.155455 + 0.915784I
0.53987 − 1.41440I 3.09127 + 6.46715I
u = −0.098178 − 0.385659I
a = −0.750766 − 0.834728I
b = 0.155455 − 0.915784I
0.53987 + 1.41440I 3.09127 − 6.46715I
20
II.
I
u
2
= h1.89 × 10
16
u
37
+ 3.82 × 10
16
u
36
+ · · · + 7.24 × 10
15
b + 3.78 × 10
16
, 1.81 ×
10
15
u
37
+7.77×10
16
u
36
+· · ·+2.17×10
16
a+4.08×10
17
, u
38
+2u
37
+· · ·+7u+3i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
−0.0832929u
37
− 3.57707u
36
+ ··· − 35.1519u − 18.7630
−2.61112u
37
− 5.26936u
36
+ ··· − 13.8591u − 5.21751
a
4
=
−1.46042u
37
− 4.41875u
36
+ ··· − 30.7239u − 10.2685
−1.24772u
37
− 2.76294u
36
+ ··· − 20.5806u − 7.40635
a
7
=
u
u
a
1
=
u
2
+ 1
−u
4
a
11
=
−0.898685u
37
− 4.45538u
36
+ ··· − 28.6677u − 13.7937
−5.67118u
37
− 11.2912u
36
+ ··· − 25.4961u − 6.24631
a
9
=
−1.15463u
37
− 3.68950u
36
+ ··· − 19.1918u − 8.67288
−3.68245u
37
− 5.38179u
36
+ ··· + 2.10103u + 4.87260
a
5
=
−0.224924u
37
− 2.18109u
36
+ ··· − 19.6681u − 12.6508
−0.852294u
37
− 4.02176u
36
+ ··· − 18.1714u − 10.7044
a
8
=
−0.448661u
37
− 2.86350u
36
+ ··· − 10.0284u − 4.39321
−2.39818u
37
− 4.07696u
36
+ ··· − 13.3099u − 1.91194
a
12
=
0.259530u
37
+ 0.218585u
36
+ ··· + 2.96981u + 2.40111
−0.998844u
37
− 3.13413u
36
+ ··· − 3.69804u − 0.263339
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
46300284051209689
7241625314466997
u
37
+
98055403875030441
7241625314466997
u
36
+ ···−
39251467631931458
7241625314466997
u −
44415212386419324
7241625314466997
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
38
− 16u
37
+ ··· − 89u + 9
c
2
u
38
+ 2u
37
+ ··· + 7u + 3
c
3
u
38
− u
37
+ ··· + 2u + 1
c
4
u
38
− u
37
+ ··· − 7u + 1
c
5
u
38
− 2u
37
+ ··· + 3u + 5
c
6
u
38
− 2u
37
+ ··· − 7u + 3
c
7
u
38
+ 4u
37
+ ··· − 6u + 1
c
8
u
38
+ 15u
37
+ ··· + 23u + 3
c
9
u
38
− 4u
37
+ ··· − 5u + 1
c
10
u
38
− 3u
37
+ ··· + 2u
2
+ 1
c
11
u
38
− 15u
37
+ ··· − 23u + 3
c
12
u
38
+ u
37
+ ··· + 7u + 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 8y
37
+ ··· + 89y + 81
c
2
, c
6
y
38
+ 16y
37
+ ··· + 89y + 9
c
3
y
38
+ 9y
37
+ ··· + 26y + 1
c
4
, c
12
y
38
+ 27y
37
+ ··· + 45y + 1
c
5
y
38
− 6y
37
+ ··· − 89y + 25
c
7
y
38
+ 14y
36
+ ··· + 62y + 1
c
8
, c
11
y
38
+ 19y
37
+ ··· + 263y + 9
c
9
y
38
− 20y
37
+ ··· + 5y + 1
c
10
y
38
− 13y
37
+ ··· + 4y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.892906 + 0.474049I
a = −0.543881 − 0.754852I
b = −1.211700 + 0.139841I
1.51389 − 3.94078I 9.03028 + 5.34855I
u = 0.892906 − 0.474049I
a = −0.543881 + 0.754852I
b = −1.211700 − 0.139841I
1.51389 + 3.94078I 9.03028 − 5.34855I
u = 0.594004 + 0.855655I
a = −1.70673 − 2.46179I
b = −3.00537 − 0.91058I
0.29199 + 2.34920I −3.64744 − 2.59669I
u = 0.594004 − 0.855655I
a = −1.70673 + 2.46179I
b = −3.00537 + 0.91058I
0.29199 − 2.34920I −3.64744 + 2.59669I
u = −0.119660 + 0.946619I
a = 1.57419 + 1.05120I
b = 0.134517 + 1.228940I
−8.11737 + 0.14389I −4.00888 + 0.23512I
u = −0.119660 − 0.946619I
a = 1.57419 − 1.05120I
b = 0.134517 − 1.228940I
−8.11737 − 0.14389I −4.00888 − 0.23512I
u = −0.624743 + 0.841573I
a = 1.30803 − 1.81899I
b = 2.06260 − 1.00524I
2.57134 − 2.45339I 14.6281 + 3.3793I
u = −0.624743 − 0.841573I
a = 1.30803 + 1.81899I
b = 2.06260 + 1.00524I
2.57134 + 2.45339I 14.6281 − 3.3793I
u = −0.152880 + 0.924198I
a = −0.73458 − 1.22703I
b = 0.77812 − 1.45989I
−8.06363 − 1.33130I −4.51062 + 0.49670I
u = −0.152880 − 0.924198I
a = −0.73458 + 1.22703I
b = 0.77812 + 1.45989I
−8.06363 + 1.33130I −4.51062 − 0.49670I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.580802 + 0.693592I
a = −0.725906 − 0.644062I
b = −0.844091 − 0.101811I
1.48155 + 0.28672I 10.92559 − 1.39869I
u = −0.580802 − 0.693592I
a = −0.725906 + 0.644062I
b = −0.844091 + 0.101811I
1.48155 − 0.28672I 10.92559 + 1.39869I
u = 0.643598 + 0.624322I
a = −0.259225 + 0.432239I
b = 0.375454 − 0.477948I
−4.98757 + 7.33702I 3.08491 − 6.50003I
u = 0.643598 − 0.624322I
a = −0.259225 − 0.432239I
b = 0.375454 + 0.477948I
−4.98757 − 7.33702I 3.08491 + 6.50003I
u = 0.500653 + 0.724800I
a = 1.39874 + 2.51032I
b = 2.46978 + 0.90492I
−5.37163 − 5.24450I 3.16629 + 2.91544I
u = 0.500653 − 0.724800I
a = 1.39874 − 2.51032I
b = 2.46978 − 0.90492I
−5.37163 + 5.24450I 3.16629 − 2.91544I
u = 0.542387 + 0.988587I
a = 1.52845 + 1.99838I
b = 2.59015 + 0.89227I
−6.28791 + 9.50561I 0.93292 − 9.18715I
u = 0.542387 − 0.988587I
a = 1.52845 − 1.99838I
b = 2.59015 − 0.89227I
−6.28791 − 9.50561I 0.93292 + 9.18715I
u = −0.628677 + 0.944378I
a = 0.198398 + 0.992384I
b = 0.361585 + 0.689020I
0.69924 − 5.16158I 8.52929 + 6.13893I
u = −0.628677 − 0.944378I
a = 0.198398 − 0.992384I
b = 0.361585 − 0.689020I
0.69924 + 5.16158I 8.52929 − 6.13893I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.297291 + 0.732873I
a = −0.088129 − 0.980585I
b = −0.196403 + 0.660965I
−1.29463 + 1.05866I 0.63753 − 7.22194I
u = 0.297291 − 0.732873I
a = −0.088129 + 0.980585I
b = −0.196403 − 0.660965I
−1.29463 − 1.05866I 0.63753 + 7.22194I
u = −0.348261 + 0.700215I
a = −0.98924 + 2.42809I
b = −0.89331 + 1.33268I
−1.79345 + 1.77230I 3.95525 − 1.93058I
u = −0.348261 − 0.700215I
a = −0.98924 − 2.42809I
b = −0.89331 − 1.33268I
−1.79345 − 1.77230I 3.95525 + 1.93058I
u = 0.377097 + 1.182640I
a = 0.383258 + 0.289944I
b = 0.199954 − 0.383260I
−7.24176 − 2.91426I 0.78308 + 5.40592I
u = 0.377097 − 1.182640I
a = 0.383258 − 0.289944I
b = 0.199954 + 0.383260I
−7.24176 + 2.91426I 0.78308 − 5.40592I
u = −0.530908 + 1.123200I
a = −0.749838 + 0.752634I
b = −1.61677 + 0.68323I
−3.58531 − 5.37909I −1.78970 + 6.74335I
u = −0.530908 − 1.123200I
a = −0.749838 − 0.752634I
b = −1.61677 − 0.68323I
−3.58531 + 5.37909I −1.78970 − 6.74335I
u = −1.218330 + 0.278173I
a = 0.079762 − 0.277717I
b = 0.112906 + 0.134719I
1.11970 − 1.13806I 45.7821 − 6.0056I
u = −1.218330 − 0.278173I
a = 0.079762 + 0.277717I
b = 0.112906 − 0.134719I
1.11970 + 1.13806I 45.7821 + 6.0056I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.088229 + 1.297410I
a = −0.622292 − 0.095446I
b = −0.233029 + 0.274389I
−4.69779 − 1.19929I 7.65236 + 7.47488I
u = 0.088229 − 1.297410I
a = −0.622292 + 0.095446I
b = −0.233029 − 0.274389I
−4.69779 + 1.19929I 7.65236 − 7.47488I
u = 0.677260 + 1.123800I
a = −0.59471 − 1.42221I
b = −1.52209 − 0.99311I
−0.44006 + 9.73419I 6.00000 − 9.56062I
u = 0.677260 − 1.123800I
a = −0.59471 + 1.42221I
b = −1.52209 + 0.99311I
−0.44006 − 9.73419I 6.00000 + 9.56062I
u = −0.658609 + 0.095756I
a = −0.798335 − 0.688297I
b = −0.003401 − 0.370089I
1.46725 − 0.92059I 11.98362 + 5.55999I
u = −0.658609 − 0.095756I
a = −0.798335 + 0.688297I
b = −0.003401 + 0.370089I
1.46725 + 0.92059I 11.98362 − 5.55999I
u = −0.75055 + 1.20429I
a = 0.175357 − 0.630231I
b = 0.941091 − 0.747378I
−1.67704 − 5.47366I 0. + 18.3178I
u = −0.75055 − 1.20429I
a = 0.175357 + 0.630231I
b = 0.941091 + 0.747378I
−1.67704 + 5.47366I 0. − 18.3178I
29
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
38
− 16u
37
+ ··· − 89u + 9)(u
159
+ 63u
158
+ ··· − 160940u − 3721)
c
2
(u
38
+ 2u
37
+ ··· + 7u + 3)(u
159
− 3u
158
+ ··· + 254u − 61)
c
3
(u
38
− u
37
+ ··· + 2u + 1)(u
159
+ 2u
158
+ ··· − 6385u − 131)
c
4
(u
38
− u
37
+ ··· − 7u + 1)(u
159
+ 6u
158
+ ··· + 329355u − 46602)
c
5
(u
38
− 2u
37
+ ··· + 3u + 5)(u
159
− 3u
158
+ ··· − 31151u − 5272)
c
6
(u
38
− 2u
37
+ ··· − 7u + 3)(u
159
− 3u
158
+ ··· + 254u − 61)
c
7
(u
38
+ 4u
37
+ ··· − 6u + 1)
· (u
159
+ 13u
158
+ ··· − 2559717451u − 258897949)
c
8
(u
38
+ 15u
37
+ ··· + 23u + 3)
· (u
159
− 12u
158
+ ··· + 5916498u − 656059)
c
9
(u
38
− 4u
37
+ ··· − 5u + 1)(u
159
+ 17u
158
+ ··· − 44446u − 5041)
c
10
(u
38
− 3u
37
+ ··· + 2u
2
+ 1)(u
159
− 16u
158
+ ··· + 1503u − 71)
c
11
(u
38
− 15u
37
+ ··· − 23u + 3)
· (u
159
− 12u
158
+ ··· + 5916498u − 656059)
c
12
(u
38
+ u
37
+ ··· + 7u + 1)(u
159
+ 6u
158
+ ··· + 329355u − 46602)
30
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
38
+ 8y
37
+ ··· + 89y + 81)
· (y
159
+ 63y
158
+ ··· + 1061374132y −13845841)
c
2
, c
6
(y
38
+ 16y
37
+ ··· + 89y + 9)(y
159
+ 63y
158
+ ··· − 160940y −3721)
c
3
(y
38
+ 9y
37
+ ··· + 26y + 1)(y
159
− 8y
158
+ ··· + 9604635y −17161)
c
4
, c
12
(y
38
+ 27y
37
+ ··· + 45y + 1)
· (y
159
+ 126y
158
+ ··· + 236167644573y −2171746404)
c
5
(y
38
− 6y
37
+ ··· − 89y + 25)
· (y
159
− 15y
158
+ ··· − 346128495y −27793984)
c
7
(y
38
+ 14y
36
+ ··· + 62y + 1)
· (y
159
+ 59y
158
+ ··· − 1286314653118589129y −67028147996406601)
c
8
, c
11
(y
38
+ 19y
37
+ ··· + 263y + 9)
· (y
159
+ 102y
158
+ ··· − 6052537066114y −430413411481)
c
9
(y
38
− 20y
37
+ ··· + 5y + 1)
· (y
159
− 9y
158
+ ··· + 268040052y −25411681)
c
10
(y
38
− 13y
37
+ ··· + 4y + 1)(y
159
− 18y
158
+ ··· − 151015y −5041)
31
