12a
1252
(K12a
1252
)
A knot diagram
1
Linearized knot diagam
5 7 8 10 12 2 11 4 1 3 6 9
Solving Sequence
2,6
7
3,11
8 12 5 1 10 4 9
c
6
c
2
c
7
c
11
c
5
c
1
c
10
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.05887 × 10
810
u
147
− 2.27511 × 10
810
u
146
+ ··· + 8.89868 × 10
809
b + 7.85959 × 10
811
,
4.95430 × 10
810
u
147
− 1.09395 × 10
811
u
146
+ ··· + 7.11894 × 10
810
a + 2.23800 × 10
812
,
u
148
− 3u
147
+ ··· + 1664u − 64i
I
u
2
= h−3.69653 × 10
27
u
31
+ 1.94930 × 10
27
u
30
+ ··· + 1.18072 × 10
28
b + 3.70363 × 10
28
,
1.05394 × 10
28
u
31
− 9.29787 × 10
27
u
30
+ ··· + 1.18072 × 10
28
a − 1.82165 × 10
29
, u
32
− u
31
+ ··· − 32u + 4i
I
u
3
= hb + 1, a + 2, u + 1i
* 3 irreducible components of dim
C
= 0, with total 181 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
= h1.06 × 10
810
u
147
− 2.28 × 10
810
u
146
+ · · · + 8.90 × 10
809
b + 7.86 ×
10
811
, 4.95 × 10
810
u
147
− 1.09 × 10
811
u
146
+ · · · + 7.12 × 10
810
a + 2.24 ×
10
812
, u
148
− 3u
147
+ · · · + 1664u − 64i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−0.695932u
147
+ 1.53668u
146
+ ··· + 1076.78u − 31.4373
−1.18992u
147
+ 2.55668u
146
+ ··· + 2177.36u − 88.3231
a
8
=
0.858311u
147
− 1.88226u
146
+ ··· − 1494.64u + 53.2154
−0.532878u
147
+ 1.17822u
146
+ ··· + 1069.01u − 42.7677
a
12
=
0.493986u
147
− 1.02000u
146
+ ··· − 1100.58u + 56.8858
−1.18992u
147
+ 2.55668u
146
+ ··· + 2177.36u − 88.3231
a
5
=
−0.625260u
147
+ 1.36525u
146
+ ··· + 1031.38u − 32.9940
−0.0734242u
147
+ 0.157657u
146
+ ··· − 160.009u + 6.08635
a
1
=
0.906475u
147
− 1.94690u
146
+ ··· − 1819.41u + 78.0628
−1.02336u
147
+ 2.25345u
146
+ ··· + 1988.38u − 80.5304
a
10
=
0.345697u
147
− 0.716800u
146
+ ··· − 861.448u + 46.6551
−1.48200u
147
+ 3.18936u
146
+ ··· + 2732.24u − 110.645
a
4
=
−1.01014u
147
+ 2.19116u
146
+ ··· + 1778.97u − 69.2538
0.887000u
147
− 1.95334u
146
+ ··· − 1752.90u + 70.5881
a
9
=
0.601293u
147
− 1.26852u
146
+ ··· − 1162.24u + 53.7405
−0.984196u
147
+ 2.14628u
146
+ ··· + 1887.69u − 76.4534
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.98535u
147
+ 4.27263u
146
+ ··· + 9435.88u − 379.745
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
148
+ 7u
147
+ ··· + 309248u − 8192
c
2
, c
6
u
148
− 3u
147
+ ··· + 1664u − 64
c
3
, c
8
u
148
− 53u
146
+ ··· − 69528u − 5398
c
4
u
148
+ 12u
147
+ ··· + 890247u + 39209
c
5
, c
11
u
148
+ 12u
147
+ ··· − 190801u + 15047
c
7
u
148
+ 8u
147
+ ··· − 1488u + 352
c
9
, c
12
u
148
− 2u
147
+ ··· + 5011u + 1511
c
10
u
148
+ 8u
147
+ ··· + 92u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
148
− 29y
147
+ ··· − 82061557760y + 67108864
c
2
, c
6
y
148
− 97y
147
+ ··· − 472064y + 4096
c
3
, c
8
y
148
− 106y
147
+ ··· − 7039344540y + 29138404
c
4
y
148
− 86y
147
+ ··· − 56591966597y + 1537345681
c
5
, c
11
y
148
− 6y
147
+ ··· − 1680126787y + 226412209
c
7
y
148
+ 26y
147
+ ··· + 1328384y + 123904
c
9
, c
12
y
148
− 74y
147
+ ··· − 53825165y + 2283121
c
10
y
148
− 92y
147
+ ··· − 7376y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.998975
a = −9.00379
b = −8.88000
−3.29196 0
u = −1.001280 + 0.121814I
a = −1.55091 − 0.67592I
b = −0.397573 + 1.291550I
−2.95378 + 4.74648I 0
u = −1.001280 − 0.121814I
a = −1.55091 + 0.67592I
b = −0.397573 − 1.291550I
−2.95378 − 4.74648I 0
u = 0.979532 + 0.265553I
a = 2.17297 − 0.50429I
b = 1.266910 − 0.019396I
−1.46182 + 0.19004I 0
u = 0.979532 − 0.265553I
a = 2.17297 + 0.50429I
b = 1.266910 + 0.019396I
−1.46182 − 0.19004I 0
u = −0.978560 + 0.088689I
a = 1.54103 + 0.03967I
b = 0.320832 − 1.245260I
−0.848601 + 0.712057I 0
u = −0.978560 − 0.088689I
a = 1.54103 − 0.03967I
b = 0.320832 + 1.245260I
−0.848601 − 0.712057I 0
u = 1.02679
a = −5.67154
b = −5.52076
1.90434 0
u = −0.487555 + 0.838326I
a = −0.243061 − 0.400109I
b = 0.446349 + 0.109960I
−3.53924 + 3.38613I 0
u = −0.487555 − 0.838326I
a = −0.243061 + 0.400109I
b = 0.446349 − 0.109960I
−3.53924 − 3.38613I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.541062 + 0.800143I
a = −0.426118 + 0.485811I
b = 0.420514 + 1.349730I
3.71420 − 5.73870I 0
u = −0.541062 − 0.800143I
a = −0.426118 − 0.485811I
b = 0.420514 − 1.349730I
3.71420 + 5.73870I 0
u = −0.824577 + 0.627928I
a = 1.54458 + 0.15924I
b = 0.678655 − 1.119070I
5.34251 + 4.21313I 0
u = −0.824577 − 0.627928I
a = 1.54458 − 0.15924I
b = 0.678655 + 1.119070I
5.34251 − 4.21313I 0
u = −0.146305 + 0.950013I
a = −0.439846 + 0.517499I
b = 0.00412 − 1.45152I
6.77113 − 4.33030I 0
u = −0.146305 − 0.950013I
a = −0.439846 − 0.517499I
b = 0.00412 + 1.45152I
6.77113 + 4.33030I 0
u = 0.193329 + 1.021940I
a = −0.1056660 − 0.0729260I
b = −0.424250 + 0.779453I
−0.32151 + 3.67859I 0
u = 0.193329 − 1.021940I
a = −0.1056660 + 0.0729260I
b = −0.424250 − 0.779453I
−0.32151 − 3.67859I 0
u = 0.967582 + 0.428688I
a = 1.039380 + 0.808691I
b = 0.193773 + 0.932549I
4.48473 + 0.64595I 0
u = 0.967582 − 0.428688I
a = 1.039380 − 0.808691I
b = 0.193773 − 0.932549I
4.48473 − 0.64595I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.046890 + 0.179815I
a = 1.46586 − 0.74459I
b = 0.428562 + 0.858984I
−3.97448 − 1.36858I 0
u = 1.046890 − 0.179815I
a = 1.46586 + 0.74459I
b = 0.428562 − 0.858984I
−3.97448 + 1.36858I 0
u = −0.905840 + 0.070464I
a = 1.77744 − 0.57611I
b = 0.189820 − 1.036770I
−0.581103 + 0.163298I 0
u = −0.905840 − 0.070464I
a = 1.77744 + 0.57611I
b = 0.189820 + 1.036770I
−0.581103 − 0.163298I 0
u = 0.657331 + 0.874331I
a = −0.155952 + 0.147906I
b = 0.132803 − 1.051790I
3.70098 − 1.00312I 0
u = 0.657331 − 0.874331I
a = −0.155952 − 0.147906I
b = 0.132803 + 1.051790I
3.70098 + 1.00312I 0
u = −1.090600 + 0.085057I
a = −0.403894 − 0.573903I
b = −0.256619 + 1.059350I
−3.25785 − 1.75417I 0
u = −1.090600 − 0.085057I
a = −0.403894 + 0.573903I
b = −0.256619 − 1.059350I
−3.25785 + 1.75417I 0
u = 0.045113 + 0.902363I
a = −0.279687 + 0.249075I
b = −0.20404 − 1.47487I
7.46086 − 1.02746I 0
u = 0.045113 − 0.902363I
a = −0.279687 − 0.249075I
b = −0.20404 + 1.47487I
7.46086 + 1.02746I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.964435 + 0.528760I
a = −1.65767 + 0.23378I
b = −0.82904 + 1.40310I
2.41645 + 10.70490I 0
u = −0.964435 − 0.528760I
a = −1.65767 − 0.23378I
b = −0.82904 − 1.40310I
2.41645 − 10.70490I 0
u = −1.11321
a = −1.34445
b = −0.817667
−2.09828 0
u = 0.978688 + 0.531377I
a = 1.49089 − 0.22737I
b = 0.019577 + 0.817614I
−1.73665 − 1.00946I 0
u = 0.978688 − 0.531377I
a = 1.49089 + 0.22737I
b = 0.019577 − 0.817614I
−1.73665 + 1.00946I 0
u = −0.796699 + 0.798526I
a = 0.090951 − 0.497407I
b = −0.414434 − 1.219000I
5.48629 + 1.19754I 0
u = −0.796699 − 0.798526I
a = 0.090951 + 0.497407I
b = −0.414434 + 1.219000I
5.48629 − 1.19754I 0
u = 0.855690 + 0.022334I
a = −0.501243 + 0.405395I
b = −0.12349 + 1.74194I
6.12738 − 2.39401I 0
u = 0.855690 − 0.022334I
a = −0.501243 − 0.405395I
b = −0.12349 − 1.74194I
6.12738 + 2.39401I 0
u = 1.122970 + 0.221520I
a = −1.67603 − 0.00043I
b = −0.456779 − 1.151730I
0.78672 − 4.82195I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.122970 − 0.221520I
a = −1.67603 + 0.00043I
b = −0.456779 + 1.151730I
0.78672 + 4.82195I 0
u = 1.132960 + 0.184979I
a = 2.11105 − 0.02549I
b = 0.606686 + 1.175000I
−1.91226 − 9.97599I 0
u = 1.132960 − 0.184979I
a = 2.11105 + 0.02549I
b = 0.606686 − 1.175000I
−1.91226 + 9.97599I 0
u = −0.167696 + 0.830715I
a = 0.719297 − 0.441119I
b = −0.108840 + 1.254980I
6.82116 − 1.26098I 0
u = −0.167696 − 0.830715I
a = 0.719297 + 0.441119I
b = −0.108840 − 1.254980I
6.82116 + 1.26098I 0
u = 1.097170 + 0.393643I
a = −1.055370 − 0.836704I
b = −0.161125 − 1.329870I
4.01216 − 3.42781I 0
u = 1.097170 − 0.393643I
a = −1.055370 + 0.836704I
b = −0.161125 + 1.329870I
4.01216 + 3.42781I 0
u = 1.162530 + 0.110552I
a = −0.49055 − 1.75992I
b = −0.24297 − 2.33015I
1.71213 + 0.89613I 0
u = 1.162530 − 0.110552I
a = −0.49055 + 1.75992I
b = −0.24297 + 2.33015I
1.71213 − 0.89613I 0
u = 0.043024 + 0.822795I
a = 0.308023 − 0.064297I
b = 0.349503 + 1.298690I
7.34364 − 4.71295I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.043024 − 0.822795I
a = 0.308023 + 0.064297I
b = 0.349503 − 1.298690I
7.34364 + 4.71295I 0
u = 0.925161 + 0.734034I
a = −1.226640 + 0.581528I
b = −0.423764 − 0.656324I
3.16791 − 5.15859I 0
u = 0.925161 − 0.734034I
a = −1.226640 − 0.581528I
b = −0.423764 + 0.656324I
3.16791 + 5.15859I 0
u = 0.793129 + 0.169532I
a = −2.03048 + 0.46907I
b = −0.213641 + 0.686279I
3.05592 − 3.90355I 0
u = 0.793129 − 0.169532I
a = −2.03048 − 0.46907I
b = −0.213641 − 0.686279I
3.05592 + 3.90355I 0
u = −0.795481 + 0.119193I
a = −1.91223 + 1.13449I
b = 0.165990 + 0.828092I
−2.36738 − 3.50678I 0
u = −0.795481 − 0.119193I
a = −1.91223 − 1.13449I
b = 0.165990 − 0.828092I
−2.36738 + 3.50678I 0
u = 0.281703 + 0.739427I
a = 0.236624 − 0.047229I
b = −0.463989 + 1.181300I
1.33669 + 4.28399I 0
u = 0.281703 − 0.739427I
a = 0.236624 + 0.047229I
b = −0.463989 − 1.181300I
1.33669 − 4.28399I 0
u = −1.158890 + 0.347160I
a = 1.153150 + 0.597580I
b = 1.21867 + 0.75437I
−4.90081 + 2.57699I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.158890 − 0.347160I
a = 1.153150 − 0.597580I
b = 1.21867 − 0.75437I
−4.90081 − 2.57699I 0
u = 1.154930 + 0.430914I
a = 1.70525 + 0.25632I
b = 0.77052 + 1.25304I
−1.35304 − 8.69049I 0
u = 1.154930 − 0.430914I
a = 1.70525 − 0.25632I
b = 0.77052 − 1.25304I
−1.35304 + 8.69049I 0
u = −0.024414 + 1.242440I
a = −0.101884 − 0.168785I
b = −0.417637 + 1.323890I
5.0171 + 13.4094I 0
u = −0.024414 − 1.242440I
a = −0.101884 + 0.168785I
b = −0.417637 − 1.323890I
5.0171 − 13.4094I 0
u = 0.761704 + 1.000990I
a = −0.090886 − 0.422053I
b = 0.198590 + 0.667003I
−0.20951 + 4.22417I 0
u = 0.761704 − 1.000990I
a = −0.090886 + 0.422053I
b = 0.198590 − 0.667003I
−0.20951 − 4.22417I 0
u = 1.161310 + 0.494248I
a = −1.396410 − 0.171798I
b = −0.417239 − 1.192050I
1.54271 − 4.31838I 0
u = 1.161310 − 0.494248I
a = −1.396410 + 0.171798I
b = −0.417239 + 1.192050I
1.54271 + 4.31838I 0
u = −1.264180 + 0.035145I
a = −1.295710 + 0.380986I
b = −0.813677 + 0.191919I
−2.11744 − 0.27476I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.264180 − 0.035145I
a = −1.295710 − 0.380986I
b = −0.813677 − 0.191919I
−2.11744 + 0.27476I 0
u = 0.731870
a = 2.81710
b = 0.223688
−2.40966 0
u = 0.545625 + 0.480160I
a = 0.792980 + 0.027976I
b = 0.565064 − 0.123977I
3.27041 + 0.51628I 0
u = 0.545625 − 0.480160I
a = 0.792980 − 0.027976I
b = 0.565064 + 0.123977I
3.27041 − 0.51628I 0
u = 0.706244 + 0.159648I
a = 2.26520 − 0.46593I
b = −0.229498 − 0.619494I
0.22308 − 9.03211I 0
u = 0.706244 − 0.159648I
a = 2.26520 + 0.46593I
b = −0.229498 + 0.619494I
0.22308 + 9.03211I 0
u = −1.236630 + 0.367556I
a = −1.325800 − 0.143074I
b = −1.125180 − 0.151997I
−0.39143 + 7.36342I 0
u = −1.236630 − 0.367556I
a = −1.325800 + 0.143074I
b = −1.125180 + 0.151997I
−0.39143 − 7.36342I 0
u = −1.293790 + 0.016628I
a = 1.34357 + 1.04717I
b = 0.906865 + 0.487435I
−4.14275 + 4.35163I 0
u = −1.293790 − 0.016628I
a = 1.34357 − 1.04717I
b = 0.906865 − 0.487435I
−4.14275 − 4.35163I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.259140 + 0.339361I
a = 1.60009 + 0.18659I
b = 1.50955 − 0.01803I
−3.96389 + 12.46680I 0
u = −1.259140 − 0.339361I
a = 1.60009 − 0.18659I
b = 1.50955 + 0.01803I
−3.96389 − 12.46680I 0
u = 0.018190 + 1.311240I
a = 0.100602 + 0.127253I
b = 0.312202 − 1.219180I
7.58151 + 6.81855I 0
u = 0.018190 − 1.311240I
a = 0.100602 − 0.127253I
b = 0.312202 + 1.219180I
7.58151 − 6.81855I 0
u = 1.293850 + 0.262453I
a = 1.105250 + 0.064065I
b = 0.835200 − 0.060936I
−4.85576 − 3.29651I 0
u = 1.293850 − 0.262453I
a = 1.105250 − 0.064065I
b = 0.835200 + 0.060936I
−4.85576 + 3.29651I 0
u = 1.110710 + 0.736036I
a = −1.070280 + 0.296553I
b = −0.123917 − 1.331670I
0.79405 − 3.24013I 0
u = 1.110710 − 0.736036I
a = −1.070280 − 0.296553I
b = −0.123917 + 1.331670I
0.79405 + 3.24013I 0
u = −1.256460 + 0.462101I
a = −1.46740 + 0.58071I
b = −0.166590 + 0.934241I
3.40222 + 6.01608I 0
u = −1.256460 − 0.462101I
a = −1.46740 − 0.58071I
b = −0.166590 − 0.934241I
3.40222 − 6.01608I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.356080 + 0.033968I
a = −0.210703 + 1.315800I
b = −0.284359 + 0.384223I
−6.46626 − 1.53022I 0
u = 1.356080 − 0.033968I
a = −0.210703 − 1.315800I
b = −0.284359 − 0.384223I
−6.46626 + 1.53022I 0
u = 1.326900 + 0.328141I
a = −1.205220 + 0.188834I
b = −1.177380 + 0.012184I
−8.88511 − 7.19016I 0
u = 1.326900 − 0.328141I
a = −1.205220 − 0.188834I
b = −1.177380 − 0.012184I
−8.88511 + 7.19016I 0
u = 0.456630 + 1.298970I
a = −0.091367 + 0.222731I
b = −0.044328 − 1.116070I
3.81077 − 1.17505I 0
u = 0.456630 − 1.298970I
a = −0.091367 − 0.222731I
b = −0.044328 + 1.116070I
3.81077 + 1.17505I 0
u = −1.284210 + 0.502551I
a = 1.50771 − 0.54607I
b = 0.164050 − 1.242770I
3.17597 + 9.56394I 0
u = −1.284210 − 0.502551I
a = 1.50771 + 0.54607I
b = 0.164050 + 1.242770I
3.17597 − 9.56394I 0
u = −1.316010 + 0.422732I
a = −1.63121 + 0.55445I
b = −0.75000 + 1.20772I
3.13156 + 9.26884I 0
u = −1.316010 − 0.422732I
a = −1.63121 − 0.55445I
b = −0.75000 − 1.20772I
3.13156 − 9.26884I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.338820 + 0.443912I
a = 1.53098 − 0.68187I
b = 0.50883 − 1.40431I
3.13625 + 5.88804I 0
u = −1.338820 − 0.443912I
a = 1.53098 + 0.68187I
b = 0.50883 + 1.40431I
3.13625 − 5.88804I 0
u = 1.389110 + 0.248197I
a = −0.686632 + 0.093548I
b = −0.756625 + 0.484787I
−7.60449 + 1.53250I 0
u = 1.389110 − 0.248197I
a = −0.686632 − 0.093548I
b = −0.756625 − 0.484787I
−7.60449 − 1.53250I 0
u = 1.28538 + 0.59896I
a = 1.375410 − 0.010157I
b = 0.777058 + 1.034200I
−3.70009 − 9.54538I 0
u = 1.28538 − 0.59896I
a = 1.375410 + 0.010157I
b = 0.777058 − 1.034200I
−3.70009 + 9.54538I 0
u = −1.43342 + 0.04162I
a = 0.212483 + 1.055430I
b = 0.293308 + 0.767339I
−4.48949 − 1.91087I 0
u = −1.43342 − 0.04162I
a = 0.212483 − 1.055430I
b = 0.293308 − 0.767339I
−4.48949 + 1.91087I 0
u = 0.272735 + 0.473195I
a = 0.66028 − 1.54048I
b = −0.698261 − 0.342449I
0.30681 − 9.18810I 0. + 7.87469I
u = 0.272735 − 0.473195I
a = 0.66028 + 1.54048I
b = −0.698261 + 0.342449I
0.30681 + 9.18810I 0. − 7.87469I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45172 + 0.34735I
a = 0.486718 + 0.179530I
b = 0.606051 + 0.077812I
−5.51503 + 1.40723I 0
u = −1.45172 − 0.34735I
a = 0.486718 − 0.179530I
b = 0.606051 − 0.077812I
−5.51503 − 1.40723I 0
u = −0.505474
a = −3.41984
b = −1.08169
−2.11691 −2.33680
u = 1.18740 + 0.91560I
a = 0.645734 − 0.378474I
b = 0.341396 + 1.294290I
−1.62535 − 5.06069I 0
u = 1.18740 − 0.91560I
a = 0.645734 + 0.378474I
b = 0.341396 − 1.294290I
−1.62535 + 5.06069I 0
u = −1.37346 + 0.62175I
a = −1.246160 + 0.076721I
b = −0.57463 + 1.38599I
−4.57713 + 13.33340I 0
u = −1.37346 − 0.62175I
a = −1.246160 − 0.076721I
b = −0.57463 − 1.38599I
−4.57713 − 13.33340I 0
u = −0.11525 + 1.50803I
a = −0.026629 − 0.311960I
b = 0.301052 + 1.161610I
−0.50561 − 6.47180I 0
u = −0.11525 − 1.50803I
a = −0.026629 + 0.311960I
b = 0.301052 − 1.161610I
−0.50561 + 6.47180I 0
u = 0.233046 + 0.428128I
a = −0.225094 + 0.890786I
b = −1.010910 + 0.576812I
0.47288 − 3.03099I 0. + 4.98012I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.233046 − 0.428128I
a = −0.225094 − 0.890786I
b = −1.010910 − 0.576812I
0.47288 + 3.03099I 0. − 4.98012I
u = 1.39794 + 0.59199I
a = 1.40083 + 0.29721I
b = 0.66660 + 1.45106I
0.5957 − 19.7827I 0
u = 1.39794 − 0.59199I
a = 1.40083 − 0.29721I
b = 0.66660 − 1.45106I
0.5957 + 19.7827I 0
u = 1.39220 + 0.62459I
a = −1.298500 − 0.238662I
b = −0.59972 − 1.32552I
3.31483 − 13.47540I 0
u = 1.39220 − 0.62459I
a = −1.298500 + 0.238662I
b = −0.59972 + 1.32552I
3.31483 + 13.47540I 0
u = −1.37574 + 0.66868I
a = −0.920405 − 0.062597I
b = −0.570218 + 0.989043I
−6.02833 + 3.51010I 0
u = −1.37574 − 0.66868I
a = −0.920405 + 0.062597I
b = −0.570218 − 0.989043I
−6.02833 − 3.51010I 0
u = −1.40293 + 0.61925I
a = 1.096460 − 0.163641I
b = 0.466410 − 1.266650I
−1.17104 + 8.05759I 0
u = −1.40293 − 0.61925I
a = 1.096460 + 0.163641I
b = 0.466410 + 1.266650I
−1.17104 − 8.05759I 0
u = 1.54859 + 0.06380I
a = 0.087473 + 1.242880I
b = −0.090189 + 0.935616I
−3.84919 + 2.91875I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54859 − 0.06380I
a = 0.087473 − 1.242880I
b = −0.090189 − 0.935616I
−3.84919 − 2.91875I 0
u = 0.114152 + 0.427480I
a = 0.37862 + 2.16441I
b = 0.465593 + 0.332487I
3.47120 − 3.96057I −0.76088 + 5.49022I
u = 0.114152 − 0.427480I
a = 0.37862 − 2.16441I
b = 0.465593 − 0.332487I
3.47120 + 3.96057I −0.76088 − 5.49022I
u = 0.430417
a = 1.95398
b = 1.13867
3.11867 11.3360
u = −0.374119 + 0.157315I
a = −2.48685 + 2.77992I
b = 0.198397 + 0.115965I
−1.15794 + 2.86780I −8.1906 − 15.4182I
u = −0.374119 − 0.157315I
a = −2.48685 − 2.77992I
b = 0.198397 − 0.115965I
−1.15794 − 2.86780I −8.1906 + 15.4182I
u = −0.221579 + 0.335225I
a = −0.465697 + 1.006490I
b = −0.195530 + 0.347109I
−0.258193 + 0.948961I −5.03205 − 6.93675I
u = −0.221579 − 0.335225I
a = −0.465697 − 1.006490I
b = −0.195530 − 0.347109I
−0.258193 − 0.948961I −5.03205 + 6.93675I
u = 1.67500 + 0.34258I
a = −0.401335 − 0.530466I
b = −0.115990 − 1.336160I
3.26870 − 2.85344I 0
u = 1.67500 − 0.34258I
a = −0.401335 + 0.530466I
b = −0.115990 + 1.336160I
3.26870 + 2.85344I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171975 + 0.207533I
a = −1.76616 + 2.61003I
b = 0.477496 + 0.853959I
−1.80489 + 0.70629I −3.75596 + 0.77630I
u = −0.171975 − 0.207533I
a = −1.76616 − 2.61003I
b = 0.477496 − 0.853959I
−1.80489 − 0.70629I −3.75596 − 0.77630I
u = −1.41222 + 1.09290I
a = 0.450345 − 0.043560I
b = 0.006493 − 0.947333I
3.20492 + 1.23648I 0
u = −1.41222 − 1.09290I
a = 0.450345 + 0.043560I
b = 0.006493 + 0.947333I
3.20492 − 1.23648I 0
u = −1.53614 + 1.03100I
a = −0.353023 + 0.191300I
b = 0.167074 + 1.015640I
0.71957 − 5.92465I 0
u = −1.53614 − 1.03100I
a = −0.353023 − 0.191300I
b = 0.167074 − 1.015640I
0.71957 + 5.92465I 0
u = 0.0449647 + 0.0386777I
a = 9.8557 − 13.3234I
b = −0.629229 + 0.034065I
−1.93499 + 0.04260I −5.84770 + 0.18610I
u = 0.0449647 − 0.0386777I
a = 9.8557 + 13.3234I
b = −0.629229 − 0.034065I
−1.93499 − 0.04260I −5.84770 − 0.18610I
19
II.
I
u
2
= h−3.70×10
27
u
31
+1.95×10
27
u
30
+· · ·+1.18×10
28
b+3.70×10
28
, 1.05×
10
28
u
31
−9.30×10
27
u
30
+· · ·+1.18×10
28
a−1.82×10
29
, u
32
−u
31
+· · ·−32u+4i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−0.892625u
31
+ 0.787473u
30
+ ··· − 72.7200u + 15.4282
0.313073u
31
− 0.165094u
30
+ ··· + 18.0166u − 3.13675
a
8
=
0.269708u
31
− 0.223395u
30
+ ··· + 20.7150u + 1.40618
−0.115266u
31
− 0.132082u
30
+ ··· + 5.04831u − 1.60378
a
12
=
−1.20570u
31
+ 0.952567u
30
+ ··· − 90.7367u + 18.5650
0.313073u
31
− 0.165094u
30
+ ··· + 18.0166u − 3.13675
a
5
=
−0.0576021u
31
− 0.162207u
30
+ ··· + 18.1224u − 6.40769
−0.502394u
31
+ 0.0201067u
30
+ ··· − 25.2754u + 4.41217
a
1
=
−0.784210u
31
+ 0.480099u
30
+ ··· − 47.3400u + 8.78576
0.0803291u
31
+ 0.0181257u
30
+ ··· + 2.47781u − 0.326669
a
10
=
−1.22228u
31
+ 0.723669u
30
+ ··· − 79.4422u + 15.9922
0.144459u
31
− 0.175097u
30
+ ··· + 13.4667u − 2.12691
a
4
=
0.246671u
31
− 0.202763u
30
+ ··· + 26.2725u − 1.32167
−0.433277u
31
+ 0.306649u
30
+ ··· − 20.9282u + 2.85911
a
9
=
−0.511610u
31
+ 0.364549u
30
+ ··· − 34.6526u + 8.45934
0.0210628u
31
+ 0.0266265u
30
+ ··· − 2.60628u + 0.382990
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16776350410579283533434547811
2951805926757894053797541338
u
31
−
984837912925122273368138546
1475902963378947026898770669
u
30
+
··· +
285880812023794591010467485726
1475902963378947026898770669
u −
49130089448924623249282354989
1475902963378947026898770669
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
32
− 4u
30
+ ··· + 4u − 1
c
2
u
32
+ u
31
+ ··· + 32u + 4
c
3
u
32
+ u
31
+ ··· − 29u − 5
c
4
u
32
− 2u
31
+ ··· − 10u − 1
c
5
u
32
− 2u
31
+ ··· + 8u
2
− 1
c
6
u
32
− u
31
+ ··· − 32u + 4
c
7
u
32
+ 8u
30
+ ··· − 2u + 1
c
8
u
32
− u
31
+ ··· + 29u − 5
c
9
u
32
+ 4u
31
+ ··· + 8u + 1
c
10
u
32
− 6u
31
+ ··· − 4u − 1
c
11
u
32
+ 2u
31
+ ··· + 8u
2
− 1
c
12
u
32
− 4u
31
+ ··· − 8u + 1
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− 8y
31
+ ··· − 108y + 1
c
2
, c
6
y
32
− 23y
31
+ ··· − 384y + 16
c
3
, c
8
y
32
− 25y
31
+ ··· − 2041y + 25
c
4
y
32
− 32y
31
+ ··· − 262y + 1
c
5
, c
11
y
32
− 4y
31
+ ··· − 16y + 1
c
7
y
32
+ 16y
31
+ ··· + 8y + 1
c
9
, c
12
y
32
− 12y
31
+ ··· − 22y + 1
c
10
y
32
− 26y
31
+ ··· + 4y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.989035
a = −2.74822
b = −2.18636
−3.31580 −20.3770
u = 1.02792
a = 5.14338
b = 4.91861
1.92614 139.610
u = −0.888724 + 0.614899I
a = 1.61692 + 0.61350I
b = 0.412116 − 0.770259I
3.62543 + 5.41670I 3.89177 − 11.06584I
u = −0.888724 − 0.614899I
a = 1.61692 − 0.61350I
b = 0.412116 + 0.770259I
3.62543 − 5.41670I 3.89177 + 11.06584I
u = −1.081340 + 0.365801I
a = −2.25275 + 0.06142I
b = −0.702549 + 0.980578I
−0.49714 + 10.70130I −4.28218 − 10.76152I
u = −1.081340 − 0.365801I
a = −2.25275 − 0.06142I
b = −0.702549 − 0.980578I
−0.49714 − 10.70130I −4.28218 + 10.76152I
u = 0.872148 + 0.741704I
a = 0.788226 − 0.802935I
b = 0.352112 + 1.231850I
−1.18585 − 5.35254I −2.31772 + 8.85992I
u = 0.872148 − 0.741704I
a = 0.788226 + 0.802935I
b = 0.352112 − 1.231850I
−1.18585 + 5.35254I −2.31772 − 8.85992I
u = 0.019492 + 0.793963I
a = −0.639434 + 0.223382I
b = −0.058380 − 1.364100I
7.22725 − 3.03526I 1.60721 + 2.24653I
u = 0.019492 − 0.793963I
a = −0.639434 − 0.223382I
b = −0.058380 + 1.364100I
7.22725 + 3.03526I 1.60721 − 2.24653I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.718754
a = −3.15670
b = −0.730490
−2.78642 −20.7790
u = 1.153630 + 0.627666I
a = −1.216750 + 0.164373I
b = −0.184062 − 1.338370I
0.84249 − 2.90689I −4.00000 − 7.68903I
u = 1.153630 − 0.627666I
a = −1.216750 − 0.164373I
b = −0.184062 + 1.338370I
0.84249 + 2.90689I −4.00000 + 7.68903I
u = 0.630297
a = −1.30578
b = −1.14501
2.80744 −15.0600
u = −0.866790 + 1.062590I
a = 0.194823 + 0.024285I
b = −0.185375 − 0.992785I
3.18382 + 0.42893I −4.00000 + 5.66853I
u = −0.866790 − 1.062590I
a = 0.194823 − 0.024285I
b = −0.185375 + 0.992785I
3.18382 − 0.42893I −4.00000 − 5.66853I
u = −1.306560 + 0.417683I
a = 1.56250 − 0.67934I
b = 0.444831 − 1.186090I
3.16143 + 7.53864I −4.00000 − 6.54870I
u = −1.306560 − 0.417683I
a = 1.56250 + 0.67934I
b = 0.444831 + 1.186090I
3.16143 − 7.53864I −4.00000 + 6.54870I
u = 1.385550 + 0.017479I
a = −0.236043 − 1.084400I
b = −0.265120 − 0.145374I
−5.23935 + 2.46952I −8.95373 − 2.59121I
u = 1.385550 − 0.017479I
a = −0.236043 + 1.084400I
b = −0.265120 + 0.145374I
−5.23935 − 2.46952I −8.95373 + 2.59121I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.396670 + 0.117559I
a = 0.015588 + 0.457847I
b = 0.306974 + 0.090803I
−4.93719 + 1.05608I −6.78147 + 3.24845I
u = −1.396670 − 0.117559I
a = 0.015588 − 0.457847I
b = 0.306974 − 0.090803I
−4.93719 − 1.05608I −6.78147 − 3.24845I
u = 0.465997 + 0.299877I
a = −0.63375 − 1.40333I
b = 0.12655 − 1.58705I
7.05657 − 2.62192I 4.69024 + 4.09449I
u = 0.465997 − 0.299877I
a = −0.63375 + 1.40333I
b = 0.12655 + 1.58705I
7.05657 + 2.62192I 4.69024 − 4.09449I
u = 1.44852 + 0.05682I
a = 0.098223 + 1.333720I
b = −0.148844 + 0.831205I
−5.56128 + 2.25902I −8.88971 − 3.82266I
u = 1.44852 − 0.05682I
a = 0.098223 − 1.333720I
b = −0.148844 − 0.831205I
−5.56128 − 2.25902I −8.88971 + 3.82266I
u = −0.91980 + 1.13013I
a = −0.269359 − 0.145641I
b = 0.288978 + 1.015440I
0.25423 − 6.25148I −4.00000 + 10.69821I
u = −0.91980 − 1.13013I
a = −0.269359 + 0.145641I
b = 0.288978 − 1.015440I
0.25423 + 6.25148I −4.00000 − 10.69821I
u = 1.39313 + 0.84915I
a = −0.570702 − 0.138273I
b = −0.226166 − 1.155230I
3.68457 − 2.27679I 0
u = 1.39313 − 0.84915I
a = −0.570702 + 0.138273I
b = −0.226166 + 1.155230I
3.68457 + 2.27679I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.246218 + 0.146936I
a = −0.42383 − 4.10183I
b = 0.410556 + 0.500219I
−1.06107 + 2.42797I −3.75720 + 1.85924I
u = 0.246218 − 0.146936I
a = −0.42383 + 4.10183I
b = 0.410556 − 0.500219I
−1.06107 − 2.42797I −3.75720 − 1.85924I
28
III. I
u
3
= hb + 1, a + 2, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
11
=
−2
−1
a
8
=
−1
0
a
12
=
−1
−1
a
5
=
0
−1
a
1
=
0
−1
a
10
=
−1
−1
a
4
=
1
0
a
9
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
8
u
c
2
, c
7
, c
9
c
10
, c
11
u − 1
c
4
, c
5
, c
6
c
12
u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
8
y
c
2
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y −1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −2.00000
b = −1.00000
−3.28987 −12.0000
32
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
32
− 4u
30
+ ··· + 4u − 1)(u
148
+ 7u
147
+ ··· + 309248u − 8192)
c
2
(u − 1)(u
32
+ u
31
+ ··· + 32u + 4)(u
148
− 3u
147
+ ··· + 1664u − 64)
c
3
u(u
32
+ u
31
+ ··· − 29u − 5)(u
148
− 53u
146
+ ··· − 69528u − 5398)
c
4
(u + 1)(u
32
− 2u
31
+ ··· − 10u − 1)
· (u
148
+ 12u
147
+ ··· + 890247u + 39209)
c
5
(u + 1)(u
32
− 2u
31
+ ··· + 8u
2
− 1)
· (u
148
+ 12u
147
+ ··· − 190801u + 15047)
c
6
(u + 1)(u
32
− u
31
+ ··· − 32u + 4)(u
148
− 3u
147
+ ··· + 1664u − 64)
c
7
(u − 1)(u
32
+ 8u
30
+ ··· − 2u + 1)(u
148
+ 8u
147
+ ··· − 1488u + 352)
c
8
u(u
32
− u
31
+ ··· + 29u − 5)(u
148
− 53u
146
+ ··· − 69528u − 5398)
c
9
(u − 1)(u
32
+ 4u
31
+ ··· + 8u + 1)(u
148
− 2u
147
+ ··· + 5011u + 1511)
c
10
(u − 1)(u
32
− 6u
31
+ ··· − 4u − 1)(u
148
+ 8u
147
+ ··· + 92u − 8)
c
11
(u − 1)(u
32
+ 2u
31
+ ··· + 8u
2
− 1)
· (u
148
+ 12u
147
+ ··· − 190801u + 15047)
c
12
(u + 1)(u
32
− 4u
31
+ ··· − 8u + 1)(u
148
− 2u
147
+ ··· + 5011u + 1511)
33
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
32
− 8y
31
+ ··· − 108y + 1)
· (y
148
− 29y
147
+ ··· − 82061557760y + 67108864)
c
2
, c
6
(y −1)(y
32
− 23y
31
+ ··· − 384y + 16)
· (y
148
− 97y
147
+ ··· − 472064y + 4096)
c
3
, c
8
y(y
32
− 25y
31
+ ··· − 2041y + 25)
· (y
148
− 106y
147
+ ··· − 7039344540y + 29138404)
c
4
(y −1)(y
32
− 32y
31
+ ··· − 262y + 1)
· (y
148
− 86y
147
+ ··· − 56591966597y + 1537345681)
c
5
, c
11
(y −1)(y
32
− 4y
31
+ ··· − 16y + 1)
· (y
148
− 6y
147
+ ··· − 1680126787y + 226412209)
c
7
(y −1)(y
32
+ 16y
31
+ ··· + 8y + 1)
· (y
148
+ 26y
147
+ ··· + 1328384y + 123904)
c
9
, c
12
(y −1)(y
32
− 12y
31
+ ··· − 22y + 1)
· (y
148
− 74y
147
+ ··· − 53825165y + 2283121)
c
10
(y −1)(y
32
− 26y
31
+ ··· + 4y + 1)(y
148
− 92y
147
+ ··· − 7376y + 64)
34
