12a
0856
(K12a
0856
)
A knot diagram
1
Linearized knot diagam
4 5 9 11 10 3 12 1 6 2 8 7
Solving Sequence
7,12
8
1,4
2 9 3 6 11 5 10
c
7
c
12
c
1
c
8
c
3
c
6
c
11
c
4
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h7.12526 × 10
207
u
143
− 1.12084 × 10
208
u
142
+ ··· + 7.50129 × 10
207
b − 1.99096 × 10
208
,
1.56461 × 10
207
u
143
+ 2.57970 × 10
208
u
142
+ ··· + 4.87584 × 10
208
a + 1.63063 × 10
210
,
u
144
− 2u
143
+ ··· − 50u + 13i
I
u
2
= h−8u
27
+ 9u
26
+ ··· + 2b − 5, −u
27
+ 5u
26
+ ··· + a − 4, u
28
− u
27
+ ··· − 9u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 172 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
= h7.13 × 10
207
u
143
− 1.12 × 10
208
u
142
+ · · · + 7.50 × 10
207
b − 1.99 ×
10
208
, 1.56 × 10
207
u
143
+ 2.58 × 10
208
u
142
+ · · · + 4.88 × 10
208
a + 1.63 ×
10
210
, u
144
− 2u
143
+ · · · − 50u + 13i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
4
=
−0.0320891u
143
− 0.529079u
142
+ ··· + 51.8978u − 33.4430
−0.949871u
143
+ 1.49419u
142
+ ··· − 13.0610u + 2.65415
a
2
=
2.41193u
143
− 2.44986u
142
+ ··· − 13.7788u + 6.73154
−1.24040u
143
− 0.492406u
142
+ ··· + 58.6702u − 20.3479
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
3
=
−1.94179u
143
+ 1.00024u
142
+ ··· + 90.3581u − 53.3307
−0.242149u
143
+ 2.97935u
142
+ ··· − 70.3801u + 16.2721
a
6
=
0.318037u
143
− 2.37361u
142
+ ··· + 16.6646u + 5.50682
0.163273u
143
+ 1.25262u
142
+ ··· − 39.6022u + 9.52014
a
11
=
u
u
3
+ u
a
5
=
−1.61419u
143
− 1.49529u
142
+ ··· + 136.644u − 64.4507
−0.655868u
143
+ 5.47078u
142
+ ··· − 114.268u + 25.3417
a
10
=
−5.68102u
143
+ 12.2495u
142
+ ··· − 130.198u + 33.6185
3.80659u
143
− 5.90248u
142
+ ··· + 25.9029u − 3.68074
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.07962u
143
+ 1.78992u
142
+ ··· + 20.9985u − 23.7397
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
144
+ 12u
143
+ ··· + 667809u + 245123
c
2
u
144
− 6u
143
+ ··· + 381u + 17
c
3
u
144
− u
143
+ ··· − 3086919u + 6171839
c
4
u
144
− u
143
+ ··· + 11u + 73
c
5
, c
9
u
144
− 4u
143
+ ··· − 73u
2
+ 1
c
6
u
144
+ 3u
143
+ ··· + 10871u + 1351
c
7
, c
11
, c
12
u
144
+ 2u
143
+ ··· + 50u + 13
c
8
u
144
− 2u
143
+ ··· + 1264438u + 100009
c
10
u
144
− 8u
143
+ ··· − 325788u + 55651
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
144
− 20y
143
+ ··· + 504300454111y + 60085285129
c
2
y
144
+ 18y
143
+ ··· + 23411y + 289
c
3
y
144
+ 35y
143
+ ··· + 1367319658441467y + 38091596641921
c
4
y
144
+ 21y
143
+ ··· + 762145y + 5329
c
5
, c
9
y
144
+ 110y
143
+ ··· − 146y + 1
c
6
y
144
+ 21y
143
+ ··· + 108316509y + 1825201
c
7
, c
11
, c
12
y
144
+ 130y
143
+ ··· − 3852y + 169
c
8
y
144
− 16y
143
+ ··· + 335701233910y + 10001800081
c
10
y
144
+ 32y
143
+ ··· + 173978927610y + 3097033801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.484439 + 0.833652I
a = 0.92352 − 1.31726I
b = −0.944270 + 0.061747I
0.71833 − 4.95715I 0
u = −0.484439 − 0.833652I
a = 0.92352 + 1.31726I
b = −0.944270 − 0.061747I
0.71833 + 4.95715I 0
u = −0.205291 + 1.015960I
a = −1.12377 + 1.31874I
b = 0.820159 − 0.200524I
−0.427059 − 0.972579I 0
u = −0.205291 − 1.015960I
a = −1.12377 − 1.31874I
b = 0.820159 + 0.200524I
−0.427059 + 0.972579I 0
u = 0.476464 + 0.834498I
a = −1.07044 − 1.42369I
b = 1.023520 − 0.118162I
−4.27831 + 10.71680I 0
u = 0.476464 − 0.834498I
a = −1.07044 + 1.42369I
b = 1.023520 + 0.118162I
−4.27831 − 10.71680I 0
u = −0.046308 + 0.940124I
a = 0.66778 + 2.13397I
b = −0.012832 − 0.619127I
−4.39221 + 2.01851I 0
u = −0.046308 − 0.940124I
a = 0.66778 − 2.13397I
b = −0.012832 + 0.619127I
−4.39221 − 2.01851I 0
u = −0.428510 + 0.976666I
a = −0.870858 + 0.361395I
b = 0.481560 + 0.463855I
−0.93362 − 2.08054I 0
u = −0.428510 − 0.976666I
a = −0.870858 − 0.361395I
b = 0.481560 − 0.463855I
−0.93362 + 2.08054I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.302451 + 1.045920I
a = −0.13758 − 1.92205I
b = 0.048646 + 0.983005I
−4.65830 − 2.58703I 0
u = −0.302451 − 1.045920I
a = −0.13758 + 1.92205I
b = 0.048646 − 0.983005I
−4.65830 + 2.58703I 0
u = 0.835501 + 0.351858I
a = −0.336993 − 0.612412I
b = 1.64331 + 0.25059I
−4.67776 − 2.13375I 0
u = 0.835501 − 0.351858I
a = −0.336993 + 0.612412I
b = 1.64331 − 0.25059I
−4.67776 + 2.13375I 0
u = −0.424743 + 1.031960I
a = −0.30032 − 1.46736I
b = −0.309462 + 0.700857I
−5.06551 + 9.60123I 0
u = −0.424743 − 1.031960I
a = −0.30032 + 1.46736I
b = −0.309462 − 0.700857I
−5.06551 − 9.60123I 0
u = 0.532696 + 0.704877I
a = 0.123811 + 0.332686I
b = −0.270020 + 0.240025I
0.32838 − 1.44483I 0
u = 0.532696 − 0.704877I
a = 0.123811 − 0.332686I
b = −0.270020 − 0.240025I
0.32838 + 1.44483I 0
u = 0.402671 + 1.068910I
a = −0.02101 − 1.49837I
b = 0.381190 + 0.819710I
−0.25419 − 3.86423I 0
u = 0.402671 − 1.068910I
a = −0.02101 + 1.49837I
b = 0.381190 − 0.819710I
−0.25419 + 3.86423I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.838389 + 0.146060I
a = 0.019114 + 0.250127I
b = −1.012750 − 0.457845I
−7.80704 − 5.07775I 0
u = −0.838389 − 0.146060I
a = 0.019114 − 0.250127I
b = −1.012750 + 0.457845I
−7.80704 + 5.07775I 0
u = −0.802549 + 0.276471I
a = 0.056196 − 0.221665I
b = −1.70328 + 0.58339I
−1.07174 + 9.49563I 0
u = −0.802549 − 0.276471I
a = 0.056196 + 0.221665I
b = −1.70328 − 0.58339I
−1.07174 − 9.49563I 0
u = 0.801348 + 0.276890I
a = 0.084525 − 0.187889I
b = 1.85520 + 0.69466I
−6.0713 − 15.2379I 0
u = 0.801348 − 0.276890I
a = 0.084525 + 0.187889I
b = 1.85520 − 0.69466I
−6.0713 + 15.2379I 0
u = −0.817069 + 0.225836I
a = 0.232580 − 0.084623I
b = 0.954296 − 0.841047I
−3.23396 + 6.58116I 0
u = −0.817069 − 0.225836I
a = 0.232580 + 0.084623I
b = 0.954296 + 0.841047I
−3.23396 − 6.58116I 0
u = 0.770010 + 0.306600I
a = −0.225784 + 0.058170I
b = −0.881701 − 0.263466I
−1.02699 − 2.97737I 0
u = 0.770010 − 0.306600I
a = −0.225784 − 0.058170I
b = −0.881701 + 0.263466I
−1.02699 + 2.97737I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.324296 + 1.128410I
a = 1.63144 + 0.88501I
b = −1.38997 + 0.38453I
−3.37182 + 0.96266I 0
u = 0.324296 − 1.128410I
a = 1.63144 − 0.88501I
b = −1.38997 − 0.38453I
−3.37182 − 0.96266I 0
u = 0.508667 + 0.642306I
a = −0.45841 − 1.42683I
b = 1.277790 + 0.217856I
−3.58342 − 2.52909I 0
u = 0.508667 − 0.642306I
a = −0.45841 + 1.42683I
b = 1.277790 − 0.217856I
−3.58342 + 2.52909I 0
u = 0.793809 + 0.115009I
a = −0.274939 + 0.299235I
b = 1.197800 − 0.269573I
−3.20216 − 0.44713I 0
u = 0.793809 − 0.115009I
a = −0.274939 − 0.299235I
b = 1.197800 + 0.269573I
−3.20216 + 0.44713I 0
u = −0.752343 + 0.158889I
a = 0.172760 + 0.693918I
b = −1.281110 − 0.466597I
−7.34289 + 6.50010I −8.52338 − 6.61702I
u = −0.752343 − 0.158889I
a = 0.172760 − 0.693918I
b = −1.281110 + 0.466597I
−7.34289 − 6.50010I −8.52338 + 6.61702I
u = 0.756666 + 0.114702I
a = −0.408065 − 0.009841I
b = −1.69744 − 1.03990I
−6.44324 − 4.90939I −9.19416 + 5.96295I
u = 0.756666 − 0.114702I
a = −0.408065 + 0.009841I
b = −1.69744 + 1.03990I
−6.44324 + 4.90939I −9.19416 − 5.96295I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.705405 + 0.234610I
a = −0.402808 − 0.263173I
b = −1.89311 − 0.54996I
−6.23108 − 5.50341I −9.63772 + 6.95338I
u = 0.705405 − 0.234610I
a = −0.402808 + 0.263173I
b = −1.89311 + 0.54996I
−6.23108 + 5.50341I −9.63772 − 6.95338I
u = −0.713730 + 0.188903I
a = 0.264522 − 0.080185I
b = 1.63397 − 0.73844I
−2.84853 + 4.54527I −3.19535 − 6.40503I
u = −0.713730 − 0.188903I
a = 0.264522 + 0.080185I
b = 1.63397 + 0.73844I
−2.84853 − 4.54527I −3.19535 + 6.40503I
u = −0.101047 + 1.264280I
a = −2.22454 + 1.71769I
b = 1.92105 − 1.51333I
0.74795 − 4.42362I 0
u = −0.101047 − 1.264280I
a = −2.22454 − 1.71769I
b = 1.92105 + 1.51333I
0.74795 + 4.42362I 0
u = 0.144876 + 1.266000I
a = 1.29516 − 0.88440I
b = 0.30460 + 1.39970I
0.70441 + 3.55365I 0
u = 0.144876 − 1.266000I
a = 1.29516 + 0.88440I
b = 0.30460 − 1.39970I
0.70441 − 3.55365I 0
u = 0.164911 + 1.268170I
a = 2.36605 + 1.11555I
b = −2.46492 − 0.79841I
3.60072 − 0.38492I 0
u = 0.164911 − 1.268170I
a = 2.36605 − 1.11555I
b = −2.46492 + 0.79841I
3.60072 + 0.38492I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309929 + 0.638475I
a = −0.713504 − 0.288683I
b = 0.128784 + 0.215144I
−0.08517 − 1.57799I 2.46043 + 2.86570I
u = 0.309929 − 0.638475I
a = −0.713504 + 0.288683I
b = 0.128784 − 0.215144I
−0.08517 + 1.57799I 2.46043 − 2.86570I
u = −0.541087 + 0.456832I
a = 0.950518 − 0.141228I
b = −0.153750 + 0.347778I
−1.48008 + 1.90896I 0.10782 − 4.30726I
u = −0.541087 − 0.456832I
a = 0.950518 + 0.141228I
b = −0.153750 − 0.347778I
−1.48008 − 1.90896I 0.10782 + 4.30726I
u = 0.134061 + 0.694229I
a = 0.76342 + 1.96295I
b = −0.187826 + 0.001987I
−4.38395 + 1.97525I −5.75212 − 2.78062I
u = 0.134061 − 0.694229I
a = 0.76342 − 1.96295I
b = −0.187826 − 0.001987I
−4.38395 − 1.97525I −5.75212 + 2.78062I
u = −0.231816 + 1.281020I
a = −1.54504 + 1.16058I
b = 2.17493 − 0.40699I
−2.05842 + 3.19123I 0
u = −0.231816 − 1.281020I
a = −1.54504 − 1.16058I
b = 2.17493 + 0.40699I
−2.05842 − 3.19123I 0
u = −0.647475 + 0.251166I
a = 0.509145 + 0.324038I
b = 1.41649 + 0.53128I
−6.31893 + 1.10986I −9.87069 − 1.90455I
u = −0.647475 − 0.251166I
a = 0.509145 − 0.324038I
b = 1.41649 − 0.53128I
−6.31893 − 1.10986I −9.87069 + 1.90455I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.221526 + 1.305960I
a = −1.13191 + 2.27772I
b = 1.079640 − 0.911924I
−1.94231 + 2.79339I 0
u = −0.221526 − 1.305960I
a = −1.13191 − 2.27772I
b = 1.079640 + 0.911924I
−1.94231 − 2.79339I 0
u = −0.106764 + 1.325040I
a = −0.307376 − 0.711918I
b = −0.698393 + 1.054510I
4.71585 − 1.20350I 0
u = −0.106764 − 1.325040I
a = −0.307376 + 0.711918I
b = −0.698393 − 1.054510I
4.71585 + 1.20350I 0
u = 0.589839 + 0.261665I
a = −0.401754 − 0.186107I
b = 0.685375 + 0.364783I
−1.27712 − 1.62704I −2.28050 + 4.53291I
u = 0.589839 − 0.261665I
a = −0.401754 + 0.186107I
b = 0.685375 − 0.364783I
−1.27712 + 1.62704I −2.28050 − 4.53291I
u = 0.190785 + 1.342210I
a = −0.351655 + 0.822770I
b = 0.987081 − 0.239466I
5.18886 − 1.57086I 0
u = 0.190785 − 1.342210I
a = −0.351655 − 0.822770I
b = 0.987081 + 0.239466I
5.18886 + 1.57086I 0
u = 0.165800 + 1.350050I
a = 0.356470 − 0.324730I
b = −1.053360 + 0.262016I
4.89504 − 2.81295I 0
u = 0.165800 − 1.350050I
a = 0.356470 + 0.324730I
b = −1.053360 − 0.262016I
4.89504 + 2.81295I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.228352 + 1.344160I
a = 0.80109 + 2.98491I
b = −1.18838 − 2.38027I
4.67725 − 5.07024I 0
u = 0.228352 − 1.344160I
a = 0.80109 − 2.98491I
b = −1.18838 + 2.38027I
4.67725 + 5.07024I 0
u = 0.317730 + 1.327340I
a = −1.31560 − 1.11094I
b = 1.63846 + 0.75108I
1.31056 − 4.43134I 0
u = 0.317730 − 1.327340I
a = −1.31560 + 1.11094I
b = 1.63846 − 0.75108I
1.31056 + 4.43134I 0
u = 0.307215 + 1.334540I
a = 0.53668 + 2.61820I
b = −1.73587 − 1.73168I
−1.88662 − 8.74253I 0
u = 0.307215 − 1.334540I
a = 0.53668 − 2.61820I
b = −1.73587 + 1.73168I
−1.88662 + 8.74253I 0
u = 0.175548 + 1.361170I
a = −0.27232 − 2.95553I
b = 1.45745 + 2.33061I
2.88913 + 1.81023I 0
u = 0.175548 − 1.361170I
a = −0.27232 + 2.95553I
b = 1.45745 − 2.33061I
2.88913 − 1.81023I 0
u = 0.232817 + 1.356480I
a = −1.27934 + 1.11479I
b = −0.28186 − 1.77532I
2.12685 − 8.88426I 0
u = 0.232817 − 1.356480I
a = −1.27934 − 1.11479I
b = −0.28186 + 1.77532I
2.12685 + 8.88426I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.179507 + 1.367480I
a = 0.98913 − 2.22312I
b = −1.58512 + 1.41348I
6.97020 + 1.82589I 0
u = −0.179507 − 1.367480I
a = 0.98913 + 2.22312I
b = −1.58512 − 1.41348I
6.97020 − 1.82589I 0
u = −0.585665 + 0.195889I
a = −0.396337 − 0.192331I
b = 1.76159 − 0.82420I
−2.18899 + 6.55721I −2.36367 − 10.53063I
u = −0.585665 − 0.195889I
a = −0.396337 + 0.192331I
b = 1.76159 + 0.82420I
−2.18899 − 6.55721I −2.36367 + 10.53063I
u = −0.369732 + 1.334160I
a = 0.999324 − 0.544758I
b = −1.238170 + 0.137634I
−3.16954 − 0.73650I 0
u = −0.369732 − 1.334160I
a = 0.999324 + 0.544758I
b = −1.238170 − 0.137634I
−3.16954 + 0.73650I 0
u = 0.092976 + 1.382550I
a = −0.131750 − 1.086330I
b = 0.76682 + 1.56149I
1.51994 + 1.13170I 0
u = 0.092976 − 1.382550I
a = −0.131750 + 1.086330I
b = 0.76682 − 1.56149I
1.51994 − 1.13170I 0
u = −0.159123 + 1.378050I
a = 0.562680 − 0.319107I
b = −1.42351 + 0.79058I
3.89720 − 2.08976I 0
u = −0.159123 − 1.378050I
a = 0.562680 + 0.319107I
b = −1.42351 − 0.79058I
3.89720 + 2.08976I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220760 + 1.371420I
a = 1.011790 + 0.131945I
b = −0.072638 − 0.789139I
6.40995 + 5.60012I 0
u = −0.220760 − 1.371420I
a = 1.011790 − 0.131945I
b = −0.072638 + 0.789139I
6.40995 − 5.60012I 0
u = −0.306548 + 1.356810I
a = 1.75731 − 0.75002I
b = −2.17546 + 0.38223I
−2.55834 + 10.32380I 0
u = −0.306548 − 1.356810I
a = 1.75731 + 0.75002I
b = −2.17546 − 0.38223I
−2.55834 − 10.32380I 0
u = −0.240311 + 1.371620I
a = −1.16970 + 2.81995I
b = 1.93538 − 2.36385I
2.79316 + 9.61542I 0
u = −0.240311 − 1.371620I
a = −1.16970 − 2.81995I
b = 1.93538 + 2.36385I
2.79316 − 9.61542I 0
u = −0.602648 + 0.001439I
a = 0.701435 + 1.004830I
b = 1.67927 − 0.31381I
−6.06172 − 0.14986I −9.25778 − 0.03321I
u = −0.602648 − 0.001439I
a = 0.701435 − 1.004830I
b = 1.67927 + 0.31381I
−6.06172 + 0.14986I −9.25778 + 0.03321I
u = 0.228462 + 1.383360I
a = −0.56451 − 1.55194I
b = 0.79056 + 1.26756I
3.92636 − 4.61687I 0
u = 0.228462 − 1.383360I
a = −0.56451 + 1.55194I
b = 0.79056 − 1.26756I
3.92636 + 4.61687I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.286293 + 1.372560I
a = −0.95214 + 2.32907I
b = 1.95151 − 1.62338I
2.10234 + 8.17022I 0
u = −0.286293 − 1.372560I
a = −0.95214 − 2.32907I
b = 1.95151 + 1.62338I
2.10234 − 8.17022I 0
u = 0.567282 + 0.144042I
a = −0.66302 − 2.00906I
b = 0.14990 − 1.48278I
−2.65212 − 5.92150I −2.74444 + 9.65224I
u = 0.567282 − 0.144042I
a = −0.66302 + 2.00906I
b = 0.14990 + 1.48278I
−2.65212 + 5.92150I −2.74444 − 9.65224I
u = 0.28143 + 1.39271I
a = 1.43917 + 2.22031I
b = −2.55489 − 1.43964I
−1.05444 − 9.09052I 0
u = 0.28143 − 1.39271I
a = 1.43917 − 2.22031I
b = −2.55489 + 1.43964I
−1.05444 + 9.09052I 0
u = 0.568132 + 0.106349I
a = 0.514869 + 0.655359I
b = −1.70229 − 0.91754I
0.05998 − 2.14156I −4.51495 + 6.00689I
u = 0.568132 − 0.106349I
a = 0.514869 − 0.655359I
b = −1.70229 + 0.91754I
0.05998 + 2.14156I −4.51495 − 6.00689I
u = −0.531513 + 0.208071I
a = 0.60732 − 1.50151I
b = −0.529477 − 0.696871I
1.39825 + 2.78179I 3.69223 − 9.04451I
u = −0.531513 − 0.208071I
a = 0.60732 + 1.50151I
b = −0.529477 + 0.696871I
1.39825 − 2.78179I 3.69223 + 9.04451I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18854 + 1.42138I
a = 0.009374 − 1.074320I
b = 0.325992 + 1.109340I
4.43837 + 4.46586I 0
u = −0.18854 − 1.42138I
a = 0.009374 + 1.074320I
b = 0.325992 − 1.109340I
4.43837 − 4.46586I 0
u = 0.16719 + 1.42754I
a = −1.51427 − 1.01186I
b = 1.383820 + 0.057721I
2.78477 − 4.71286I 0
u = 0.16719 − 1.42754I
a = −1.51427 + 1.01186I
b = 1.383820 − 0.057721I
2.78477 + 4.71286I 0
u = −0.25271 + 1.41636I
a = −1.61198 + 0.75568I
b = 1.87013 + 0.21638I
−0.95147 + 4.39167I 0
u = −0.25271 − 1.41636I
a = −1.61198 − 0.75568I
b = 1.87013 − 0.21638I
−0.95147 − 4.39167I 0
u = −0.33554 + 1.40137I
a = −0.25792 + 1.67396I
b = 1.21247 − 1.35645I
1.93529 + 10.74000I 0
u = −0.33554 − 1.40137I
a = −0.25792 − 1.67396I
b = 1.21247 + 1.35645I
1.93529 − 10.74000I 0
u = −0.00046 + 1.44947I
a = −0.029667 − 0.573407I
b = −0.631891 + 0.524517I
6.69763 − 2.08158I 0
u = −0.00046 − 1.44947I
a = −0.029667 + 0.573407I
b = −0.631891 − 0.524517I
6.69763 + 2.08158I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.244572 + 0.485586I
a = −1.184440 + 0.321444I
b = 0.0439713 + 0.0995129I
−0.135288 − 1.318830I −1.57525 + 3.19258I
u = 0.244572 − 0.485586I
a = −1.184440 − 0.321444I
b = 0.0439713 − 0.0995129I
−0.135288 + 1.318830I −1.57525 − 3.19258I
u = −0.32476 + 1.42122I
a = 1.12371 − 2.10405I
b = −1.91087 + 1.38536I
4.3345 + 13.5756I 0
u = −0.32476 − 1.42122I
a = 1.12371 + 2.10405I
b = −1.91087 − 1.38536I
4.3345 − 13.5756I 0
u = 0.32397 + 1.42211I
a = −1.20536 − 2.24800I
b = 2.15419 + 1.44324I
−0.6588 − 19.3116I 0
u = 0.32397 − 1.42211I
a = −1.20536 + 2.24800I
b = 2.15419 − 1.44324I
−0.6588 + 19.3116I 0
u = 0.30949 + 1.42881I
a = 0.624801 + 1.200760I
b = −1.24453 − 0.75924I
4.50553 − 6.90107I 0
u = 0.30949 − 1.42881I
a = 0.624801 − 1.200760I
b = −1.24453 + 0.75924I
4.50553 + 6.90107I 0
u = 0.35052 + 1.43914I
a = −1.09741 − 1.76425I
b = 1.51589 + 1.03394I
0.99349 − 6.47416I 0
u = 0.35052 − 1.43914I
a = −1.09741 + 1.76425I
b = 1.51589 − 1.03394I
0.99349 + 6.47416I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03620 + 1.50860I
a = −0.384417 + 0.022533I
b = −0.193441 − 0.605626I
3.50452 + 9.51879I 0
u = 0.03620 − 1.50860I
a = −0.384417 − 0.022533I
b = −0.193441 + 0.605626I
3.50452 − 9.51879I 0
u = −0.02565 + 1.52405I
a = 0.296150 − 0.271480I
b = 0.173095 − 0.135422I
8.63364 − 3.71580I 0
u = −0.02565 − 1.52405I
a = 0.296150 + 0.271480I
b = 0.173095 + 0.135422I
8.63364 + 3.71580I 0
u = −0.350300 + 0.294411I
a = −0.65494 + 2.60181I
b = −0.182405 + 0.001264I
−1.34287 − 4.09073I 1.361715 + 0.328480I
u = −0.350300 − 0.294411I
a = −0.65494 − 2.60181I
b = −0.182405 − 0.001264I
−1.34287 + 4.09073I 1.361715 − 0.328480I
u = −0.372086 + 0.263740I
a = −0.800631 − 0.608295I
b = −1.039790 + 0.668624I
1.90228 − 0.36788I 5.99436 − 2.51246I
u = −0.372086 − 0.263740I
a = −0.800631 + 0.608295I
b = −1.039790 − 0.668624I
1.90228 + 0.36788I 5.99436 + 2.51246I
u = 0.445296 + 0.083565I
a = −0.36578 + 2.33238I
b = −0.157428 − 0.332375I
0.613113 + 0.851866I −1.28476 + 3.07098I
u = 0.445296 − 0.083565I
a = −0.36578 − 2.33238I
b = −0.157428 + 0.332375I
0.613113 − 0.851866I −1.28476 − 3.07098I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.400414 + 0.191882I
a = 1.39127 + 0.43374I
b = 1.08997 + 1.50293I
−2.03134 + 4.03831I −0.05256 + 2.68093I
u = 0.400414 − 0.191882I
a = 1.39127 − 0.43374I
b = 1.08997 − 1.50293I
−2.03134 − 4.03831I −0.05256 − 2.68093I
u = 0.11235 + 1.57442I
a = 0.298238 − 0.257865I
b = −0.113632 + 0.303865I
7.96522 − 3.66725I 0
u = 0.11235 − 1.57442I
a = 0.298238 + 0.257865I
b = −0.113632 − 0.303865I
7.96522 + 3.66725I 0
19
II. I
u
2
=
h−8u
27
+9u
26
+· · · +2b−5, −u
27
+5u
26
+· · · +a−4, u
28
−u
27
+· · · −9u
2
+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
4
=
u
27
− 5u
26
+ ··· − 19u + 4
4u
27
−
9
2
u
26
+ ··· −
5
2
u +
5
2
a
2
=
1
2
u
27
+
11
2
u
26
+ ··· + 4u +
7
2
−2u
27
− 4u
26
+ ··· + 12u − 8
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
3
=
u
27
− 5u
26
+ ··· − 21u + 4
3u
27
−
7
2
u
26
+ ··· −
5
2
u +
5
2
a
6
=
5
2
u
27
− u
26
+ ··· +
11
2
u − 1
−
9
2
u
27
+ 3u
26
+ ··· +
17
2
u − 4
a
11
=
u
u
3
+ u
a
5
=
5
2
u
27
−
21
2
u
26
+ ··· − 20u +
5
2
3u
27
− u
26
+ ··· − 5u + 5
a
10
=
−
7
2
u
27
+ 2u
26
+ ··· +
33
2
u − 7
2u
27
− 2u
26
+ ··· − 23u
3
+ 5u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 19u
27
−17u
26
+258u
25
−213u
24
+1527u
23
−1170u
22
+5136u
21
−3646u
20
+10675u
19
−
6888u
18
+ 13817u
17
− 7548u
16
+ 10302u
15
− 3377u
14
+ 2936u
13
+ 2003u
12
− 1295u
11
+
3190u
10
− 789u
9
+ 971u
8
+ 654u
7
− 416u
6
+ 752u
5
− 304u
4
+ 217u
3
− 49u
2
− 19u + 15
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 13u
27
+ ··· − 13u + 1
c
2
u
28
+ 15u
27
+ ··· + u + 1
c
3
u
28
− u
26
+ ··· + u + 1
c
4
u
28
+ 6u
26
+ ··· + u + 1
c
5
u
28
− u
27
+ ··· + 6u
2
+ 1
c
6
u
28
+ 2u
27
+ ··· − 3u + 1
c
7
u
28
− u
27
+ ··· − 9u
2
+ 1
c
8
u
28
+ u
27
+ ··· + 4u + 1
c
9
u
28
+ u
27
+ ··· + 6u
2
+ 1
c
10
u
28
+ u
27
+ ··· + 6u
2
+ 1
c
11
, c
12
u
28
+ u
27
+ ··· − 9u
2
+ 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 11y
27
+ ··· + 9y + 1
c
2
y
28
+ 9y
27
+ ··· − 15y + 1
c
3
y
28
− 2y
27
+ ··· + 25y + 1
c
4
y
28
+ 12y
27
+ ··· + 3y + 1
c
5
, c
9
y
28
+ 25y
27
+ ··· + 12y + 1
c
6
y
28
+ 8y
27
+ ··· + 3y + 1
c
7
, c
11
, c
12
y
28
+ 29y
27
+ ··· − 18y + 1
c
8
y
28
+ 7y
27
+ ··· − 20y + 1
c
10
y
28
+ 3y
27
+ ··· + 12y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.099019 + 1.101070I
a = 1.09218 + 1.78998I
b = −1.243180 − 0.474928I
−2.93576 − 0.63480I −2.85306 + 0.30472I
u = 0.099019 − 1.101070I
a = 1.09218 − 1.78998I
b = −1.243180 + 0.474928I
−2.93576 + 0.63480I −2.85306 − 0.30472I
u = −0.336272 + 1.093480I
a = −1.123310 + 0.561111I
b = 0.621514 + 0.246840I
−1.65636 − 2.14204I −4.42633 + 4.91075I
u = −0.336272 − 1.093480I
a = −1.123310 − 0.561111I
b = 0.621514 − 0.246840I
−1.65636 + 2.14204I −4.42633 − 4.91075I
u = 0.752638 + 0.348149I
a = 0.131722 + 0.706381I
b = −1.64552 − 0.23588I
−4.47474 − 2.19313I 3.30608 + 10.22120I
u = 0.752638 − 0.348149I
a = 0.131722 − 0.706381I
b = −1.64552 + 0.23588I
−4.47474 + 2.19313I 3.30608 − 10.22120I
u = 0.516440 + 0.572964I
a = −0.640847 + 0.091888I
b = 0.176016 + 0.024021I
0.49329 − 1.96254I 6.42403 + 9.07010I
u = 0.516440 − 0.572964I
a = −0.640847 − 0.091888I
b = 0.176016 − 0.024021I
0.49329 + 1.96254I 6.42403 − 9.07010I
u = −0.725668 + 0.154435I
a = 0.172636 − 0.451167I
b = 1.22815 − 0.99461I
−4.48882 + 6.00140I −6.33820 − 7.52590I
u = −0.725668 − 0.154435I
a = 0.172636 + 0.451167I
b = 1.22815 + 0.99461I
−4.48882 − 6.00140I −6.33820 + 7.52590I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.123269 + 1.312800I
a = −1.073130 − 0.268729I
b = 1.74512 + 0.52286I
4.68792 − 0.06393I 5.57659 − 0.87734I
u = 0.123269 − 1.312800I
a = −1.073130 + 0.268729I
b = 1.74512 − 0.52286I
4.68792 + 0.06393I 5.57659 + 0.87734I
u = −0.151948 + 1.349290I
a = 0.05319 − 2.07601I
b = −1.34938 + 2.23483I
2.26093 − 2.79566I 1.40081 + 5.15144I
u = −0.151948 − 1.349290I
a = 0.05319 + 2.07601I
b = −1.34938 − 2.23483I
2.26093 + 2.79566I 1.40081 − 5.15144I
u = −0.127067 + 1.358790I
a = 1.89517 − 0.10846I
b = −1.041370 − 0.241963I
2.15334 + 6.44676I 1.18886 − 7.26984I
u = −0.127067 − 1.358790I
a = 1.89517 + 0.10846I
b = −1.041370 + 0.241963I
2.15334 − 6.44676I 1.18886 + 7.26984I
u = −0.285243 + 1.363630I
a = −0.50422 + 2.26249I
b = 1.73224 − 1.89992I
0.32680 + 9.64196I −0.45509 − 9.13798I
u = −0.285243 − 1.363630I
a = −0.50422 − 2.26249I
b = 1.73224 + 1.89992I
0.32680 − 9.64196I −0.45509 + 9.13798I
u = 0.197285 + 1.384240I
a = −0.349569 − 1.311340I
b = 0.054279 + 1.054640I
5.95686 − 3.99802I 9.05109 + 2.94774I
u = 0.197285 − 1.384240I
a = −0.349569 + 1.311340I
b = 0.054279 − 1.054640I
5.95686 + 3.99802I 9.05109 − 2.94774I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.32397 + 1.41144I
a = 1.14490 + 1.82924I
b = −1.64005 − 1.07586I
1.05898 − 6.19051I 0.78900 − 1.99119I
u = 0.32397 − 1.41144I
a = 1.14490 − 1.82924I
b = −1.64005 + 1.07586I
1.05898 + 6.19051I 0.78900 + 1.99119I
u = 0.09033 + 1.57682I
a = −0.275364 + 0.128203I
b = 0.0747519 + 0.0072307I
7.90451 − 3.82235I −8.8605 + 23.2380I
u = 0.09033 − 1.57682I
a = −0.275364 − 0.128203I
b = 0.0747519 − 0.0072307I
7.90451 + 3.82235I −8.8605 − 23.2380I
u = 0.387082 + 0.161628I
a = −1.49791 − 1.39659I
b = 0.763880 + 0.206504I
0.85198 − 1.62979I 3.11094 + 3.88931I
u = 0.387082 − 0.161628I
a = −1.49791 + 1.39659I
b = 0.763880 − 0.206504I
0.85198 + 1.62979I 3.11094 − 3.88931I
u = −0.363834 + 0.027436I
a = 0.47456 + 2.75962I
b = −0.97644 + 1.13359I
−2.26930 − 4.73450I −5.41423 + 6.58008I
u = −0.363834 − 0.027436I
a = 0.47456 − 2.75962I
b = −0.97644 − 1.13359I
−2.26930 + 4.73450I −5.41423 − 6.58008I
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 13u
27
+ ··· − 13u + 1)
· (u
144
+ 12u
143
+ ··· + 667809u + 245123)
c
2
(u
28
+ 15u
27
+ ··· + u + 1)(u
144
− 6u
143
+ ··· + 381u + 17)
c
3
(u
28
− u
26
+ ··· + u + 1)(u
144
− u
143
+ ··· − 3086919u + 6171839)
c
4
(u
28
+ 6u
26
+ ··· + u + 1)(u
144
− u
143
+ ··· + 11u + 73)
c
5
(u
28
− u
27
+ ··· + 6u
2
+ 1)(u
144
− 4u
143
+ ··· − 73u
2
+ 1)
c
6
(u
28
+ 2u
27
+ ··· − 3u + 1)(u
144
+ 3u
143
+ ··· + 10871u + 1351)
c
7
(u
28
− u
27
+ ··· − 9u
2
+ 1)(u
144
+ 2u
143
+ ··· + 50u + 13)
c
8
(u
28
+ u
27
+ ··· + 4u + 1)(u
144
− 2u
143
+ ··· + 1264438u + 100009)
c
9
(u
28
+ u
27
+ ··· + 6u
2
+ 1)(u
144
− 4u
143
+ ··· − 73u
2
+ 1)
c
10
(u
28
+ u
27
+ ··· + 6u
2
+ 1)(u
144
− 8u
143
+ ··· − 325788u + 55651)
c
11
, c
12
(u
28
+ u
27
+ ··· − 9u
2
+ 1)(u
144
+ 2u
143
+ ··· + 50u + 13)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 11y
27
+ ··· + 9y + 1)
· (y
144
− 20y
143
+ ··· + 504300454111y + 60085285129)
c
2
(y
28
+ 9y
27
+ ··· − 15y + 1)(y
144
+ 18y
143
+ ··· + 23411y + 289)
c
3
(y
28
− 2y
27
+ ··· + 25y + 1)
· (y
144
+ 35y
143
+ ··· + 1367319658441467y + 38091596641921)
c
4
(y
28
+ 12y
27
+ ··· + 3y + 1)(y
144
+ 21y
143
+ ··· + 762145y + 5329)
c
5
, c
9
(y
28
+ 25y
27
+ ··· + 12y + 1)(y
144
+ 110y
143
+ ··· − 146y + 1)
c
6
(y
28
+ 8y
27
+ ··· + 3y + 1)
· (y
144
+ 21y
143
+ ··· + 108316509y + 1825201)
c
7
, c
11
, c
12
(y
28
+ 29y
27
+ ··· − 18y + 1)(y
144
+ 130y
143
+ ··· − 3852y + 169)
c
8
(y
28
+ 7y
27
+ ··· − 20y + 1)
· (y
144
− 16y
143
+ ··· + 335701233910y + 10001800081)
c
10
(y
28
+ 3y
27
+ ··· + 12y + 1)
· (y
144
+ 32y
143
+ ··· + 173978927610y + 3097033801)
27
