12a
0342
(K12a
0342
)
A knot diagram
1
Linearized knot diagam
3 6 8 1 10 2 12 4 11 5 7 9
Solving Sequence
5,10 2,6
3 7 11 12 1 4 9 8
c
5
c
2
c
6
c
10
c
11
c
1
c
4
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.20197 × 10
404
u
155
− 1.98407 × 10
404
u
154
+ ··· + 1.03297 × 10
404
b − 1.24809 × 10
407
,
− 2.63389 × 10
406
u
155
+ 8.44260 × 10
406
u
154
+ ··· + 7.75764 × 10
406
a + 6.28696 × 10
409
,
u
156
+ u
155
+ ··· − 643u + 751i
I
u
2
= h−7283u
37
+ 6235u
36
+ ··· + 995b − 2491, 3092u
37
− 2046u
36
+ ··· + 995a + 12148,
u
38
+ 12u
36
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 194 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−1.20 × 10
404
u
155
− 1.98 × 10
404
u
154
+ · · · + 1.03 × 10
404
b − 1.25 ×
10
407
, −2.63 × 10
406
u
155
+ 8.44 × 10
406
u
154
+ · · · + 7.76 × 10
406
a + 6.29 ×
10
409
, u
156
+ u
155
+ · · · − 643u + 751i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
0.339523u
155
− 1.08830u
154
+ ··· + 1312.04u − 810.422
1.16361u
155
+ 1.92074u
154
+ ··· − 990.348u + 1208.25
a
6
=
1
u
2
a
3
=
0.887263u
155
− 0.732362u
154
+ ··· + 1494.76u − 674.462
0.803609u
155
+ 1.94703u
154
+ ··· − 1525.03u + 1352.30
a
7
=
0.240562u
155
+ 0.684041u
154
+ ··· − 624.185u + 655.447
−0.222710u
155
− 1.77408u
154
+ ··· + 1850.31u − 1384.20
a
11
=
−u
u
a
12
=
1.58683u
155
− 2.09974u
154
+ ··· + 4195.43u − 1967.02
−0.323186u
155
+ 3.07800u
154
+ ··· − 4460.22u + 2614.13
a
1
=
−0.724223u
155
− 4.21579u
154
+ ··· + 3923.98u − 2938.41
0.518971u
155
+ 2.43169u
154
+ ··· − 2514.80u + 1834.96
a
4
=
0.363334u
155
− 0.0490247u
154
+ ··· + 370.041u + 97.1690
0.721342u
155
+ 2.37469u
154
+ ··· − 1453.60u + 1335.56
a
9
=
−u
3
u
3
+ u
a
8
=
0.428023u
155
− 1.47511u
154
+ ··· + 2752.95u − 1358.47
0.845539u
155
+ 0.990339u
154
+ ··· − 279.843u + 478.958
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6.61247u
155
− 7.18823u
154
+ ··· − 439.660u − 3074.15
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
156
+ 68u
155
+ ··· + 586213058u + 32137561
c
2
, c
6
u
156
− 2u
155
+ ··· − 17042u + 5669
c
3
, c
8
u
156
− u
155
+ ··· + 6147u + 2449
c
4
u
156
− 4u
155
+ ··· − 513066u + 23269
c
5
, c
10
u
156
− u
155
+ ··· + 643u + 751
c
7
, c
11
u
156
− 3u
155
+ ··· + 107845u + 85523
c
9
u
156
− 77u
155
+ ··· − 10171145u + 564001
c
12
u
156
+ 9u
155
+ ··· − 1045u + 521
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
156
+ 60y
155
+ ··· + 29158613325391790y + 1032822827028721
c
2
, c
6
y
156
+ 68y
155
+ ··· + 586213058y + 32137561
c
3
, c
8
y
156
− 83y
155
+ ··· − 131376593y + 5997601
c
4
y
156
− 20y
155
+ ··· − 25116154598y + 541446361
c
5
, c
10
y
156
+ 77y
155
+ ··· + 10171145y + 564001
c
7
, c
11
y
156
− 105y
155
+ ··· + 830770663883y + 7314183529
c
9
y
156
+ 25y
155
+ ··· + 20263498622645y + 318097128001
c
12
y
156
+ 11y
155
+ ··· + 19725051y + 271441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314686 + 0.948049I
a = −1.122900 + 0.399488I
b = −0.05478 − 1.90960I
4.50020 + 0.21846I 0
u = 0.314686 − 0.948049I
a = −1.122900 − 0.399488I
b = −0.05478 + 1.90960I
4.50020 − 0.21846I 0
u = −0.170790 + 0.987084I
a = 0.633623 − 1.049930I
b = −0.357628 + 0.104624I
3.20120 − 1.52428I 0
u = −0.170790 − 0.987084I
a = 0.633623 + 1.049930I
b = −0.357628 − 0.104624I
3.20120 + 1.52428I 0
u = −0.389580 + 0.925758I
a = −3.06881 + 1.42393I
b = 2.74803 + 0.41625I
−0.36759 − 1.52334I 0
u = −0.389580 − 0.925758I
a = −3.06881 − 1.42393I
b = 2.74803 − 0.41625I
−0.36759 + 1.52334I 0
u = 0.764967 + 0.665148I
a = 0.30131 + 1.97652I
b = −1.77763 − 0.59009I
−8.04521 − 0.38455I 0
u = 0.764967 − 0.665148I
a = 0.30131 − 1.97652I
b = −1.77763 + 0.59009I
−8.04521 + 0.38455I 0
u = −0.287570 + 0.978275I
a = 1.141850 − 0.391800I
b = −0.447530 − 1.222970I
4.40725 − 3.47807I 0
u = −0.287570 − 0.978275I
a = 1.141850 + 0.391800I
b = −0.447530 + 1.222970I
4.40725 + 3.47807I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.379406 + 0.964078I
a = 2.31237 + 1.11954I
b = −2.06980 − 0.13247I
2.40104 − 3.09117I 0
u = 0.379406 − 0.964078I
a = 2.31237 − 1.11954I
b = −2.06980 + 0.13247I
2.40104 + 3.09117I 0
u = 0.168715 + 0.947032I
a = −0.609414 − 0.921753I
b = 0.157383 + 0.470877I
1.28269 − 2.51191I 0
u = 0.168715 − 0.947032I
a = −0.609414 + 0.921753I
b = 0.157383 − 0.470877I
1.28269 + 2.51191I 0
u = −0.620529 + 0.727479I
a = 0.916688 + 0.299057I
b = 0.575110 − 0.684533I
−2.52818 + 5.31514I 0
u = −0.620529 − 0.727479I
a = 0.916688 − 0.299057I
b = 0.575110 + 0.684533I
−2.52818 − 5.31514I 0
u = −0.192813 + 1.026250I
a = −0.1149880 − 0.0450683I
b = −0.211794 + 1.044400I
−1.75492 − 0.21945I 0
u = −0.192813 − 1.026250I
a = −0.1149880 + 0.0450683I
b = −0.211794 − 1.044400I
−1.75492 + 0.21945I 0
u = −0.967091 + 0.396088I
a = −0.07366 + 1.60101I
b = 1.82974 + 0.15178I
−2.07204 − 13.90080I 0
u = −0.967091 − 0.396088I
a = −0.07366 − 1.60101I
b = 1.82974 − 0.15178I
−2.07204 + 13.90080I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.310213 + 0.900109I
a = −1.06413 + 1.58543I
b = 1.97565 − 1.89639I
−2.43039 − 4.42948I 0
u = −0.310213 − 0.900109I
a = −1.06413 − 1.58543I
b = 1.97565 + 1.89639I
−2.43039 + 4.42948I 0
u = −0.522391 + 0.912570I
a = −0.575948 + 0.066149I
b = −0.085719 + 1.120830I
−1.95927 − 0.77778I 0
u = −0.522391 − 0.912570I
a = −0.575948 − 0.066149I
b = −0.085719 − 1.120830I
−1.95927 + 0.77778I 0
u = −0.909221 + 0.259472I
a = 0.123111 + 0.685530I
b = −0.316398 + 0.008844I
2.89929 − 2.34324I 0
u = −0.909221 − 0.259472I
a = 0.123111 − 0.685530I
b = −0.316398 − 0.008844I
2.89929 + 2.34324I 0
u = 0.327121 + 0.886426I
a = 0.21564 + 2.15420I
b = −1.73820 − 2.40526I
2.00818 + 0.26275I 0
u = 0.327121 − 0.886426I
a = 0.21564 − 2.15420I
b = −1.73820 + 2.40526I
2.00818 − 0.26275I 0
u = 0.761910 + 0.558313I
a = −0.99544 − 1.87431I
b = 1.142060 − 0.268267I
−1.75544 + 0.37427I 0
u = 0.761910 − 0.558313I
a = −0.99544 + 1.87431I
b = 1.142060 + 0.268267I
−1.75544 − 0.37427I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369426 + 0.994086I
a = −1.96669 + 1.41932I
b = 2.20930 − 0.98738I
−1.96143 + 7.05234I 0
u = −0.369426 − 0.994086I
a = −1.96669 − 1.41932I
b = 2.20930 + 0.98738I
−1.96143 − 7.05234I 0
u = −0.231301 + 0.909026I
a = 0.172950 − 0.756205I
b = 0.513443 − 0.335586I
4.28323 − 1.07875I 0
u = −0.231301 − 0.909026I
a = 0.172950 + 0.756205I
b = 0.513443 + 0.335586I
4.28323 + 1.07875I 0
u = 0.873648 + 0.340491I
a = −0.346265 + 0.707821I
b = 0.281624 − 0.173512I
0.13196 + 8.09309I 0
u = 0.873648 − 0.340491I
a = −0.346265 − 0.707821I
b = 0.281624 + 0.173512I
0.13196 − 8.09309I 0
u = −0.368759 + 0.861294I
a = −0.21879 + 3.23453I
b = 2.37621 − 2.72280I
−0.61701 + 4.67868I 0
u = −0.368759 − 0.861294I
a = −0.21879 − 3.23453I
b = 2.37621 + 2.72280I
−0.61701 − 4.67868I 0
u = 0.324965 + 1.012440I
a = 1.44767 − 0.05934I
b = −0.494335 + 0.177695I
4.69177 − 2.40977I 0
u = 0.324965 − 1.012440I
a = 1.44767 + 0.05934I
b = −0.494335 − 0.177695I
4.69177 + 2.40977I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.277751 + 0.894534I
a = 0.272369 − 0.204315I
b = −1.045410 − 0.821220I
3.59555 + 3.72788I 0
u = 0.277751 − 0.894534I
a = 0.272369 + 0.204315I
b = −1.045410 + 0.821220I
3.59555 − 3.72788I 0
u = 1.015980 + 0.348748I
a = −0.03654 + 1.55044I
b = −1.73438 + 0.30252I
1.04423 + 7.45505I 0
u = 1.015980 − 0.348748I
a = −0.03654 − 1.55044I
b = −1.73438 − 0.30252I
1.04423 − 7.45505I 0
u = 0.214175 + 1.057270I
a = −0.817825 − 1.130120I
b = 0.895341 − 0.109395I
−0.96779 + 5.37139I 0
u = 0.214175 − 1.057270I
a = −0.817825 + 1.130120I
b = 0.895341 + 0.109395I
−0.96779 − 5.37139I 0
u = 0.834858 + 0.385886I
a = 0.504327 − 1.072800I
b = 1.30683 + 0.76592I
−5.07291 − 2.27519I 0
u = 0.834858 − 0.385886I
a = 0.504327 + 1.072800I
b = 1.30683 − 0.76592I
−5.07291 + 2.27519I 0
u = 0.392121 + 1.007210I
a = 0.884957 + 1.045460I
b = −0.452494 − 1.041260I
4.37259 − 6.31285I 0
u = 0.392121 − 1.007210I
a = 0.884957 − 1.045460I
b = −0.452494 + 1.041260I
4.37259 + 6.31285I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.763974 + 0.483070I
a = −0.265987 − 1.249780I
b = −1.54989 + 0.74973I
−1.51002 − 2.90487I 0
u = −0.763974 − 0.483070I
a = −0.265987 + 1.249780I
b = −1.54989 − 0.74973I
−1.51002 + 2.90487I 0
u = −0.699502 + 0.847403I
a = −0.73555 + 1.79135I
b = 2.22784 − 0.54310I
−4.02999 + 2.67079I 0
u = −0.699502 − 0.847403I
a = −0.73555 − 1.79135I
b = 2.22784 + 0.54310I
−4.02999 − 2.67079I 0
u = −0.702976 + 0.547108I
a = 1.02977 − 2.07419I
b = −1.314950 + 0.139898I
−6.14075 − 5.00203I 0
u = −0.702976 − 0.547108I
a = 1.02977 + 2.07419I
b = −1.314950 − 0.139898I
−6.14075 + 5.00203I 0
u = −0.321932 + 1.061480I
a = −0.833564 − 0.350555I
b = −0.0635669 + 0.0950970I
4.76986 + 5.15135I 0
u = −0.321932 − 1.061480I
a = −0.833564 + 0.350555I
b = −0.0635669 − 0.0950970I
4.76986 − 5.15135I 0
u = 0.683523 + 0.554488I
a = −0.99602 − 1.73710I
b = 1.73993 + 0.19544I
−0.22944 + 4.39648I 0
u = 0.683523 − 0.554488I
a = −0.99602 + 1.73710I
b = 1.73993 − 0.19544I
−0.22944 − 4.39648I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.411070 + 1.041850I
a = −0.270836 + 0.721017I
b = −0.196903 − 0.838389I
5.49577 + 3.46244I 0
u = −0.411070 − 1.041850I
a = −0.270836 − 0.721017I
b = −0.196903 + 0.838389I
5.49577 − 3.46244I 0
u = −0.685378 + 0.540273I
a = 0.70519 − 1.42825I
b = −1.65080 + 0.27536I
0.20529 − 1.95269I 0
u = −0.685378 − 0.540273I
a = 0.70519 + 1.42825I
b = −1.65080 − 0.27536I
0.20529 + 1.95269I 0
u = 0.519236 + 1.018860I
a = 0.026199 + 0.606770I
b = 0.056375 + 0.196424I
1.34667 − 2.83958I 0
u = 0.519236 − 1.018860I
a = 0.026199 − 0.606770I
b = 0.056375 − 0.196424I
1.34667 + 2.83958I 0
u = 0.631143 + 0.576314I
a = −0.77796 − 2.45089I
b = 2.16384 + 0.11659I
1.24304 + 1.23867I 0
u = 0.631143 − 0.576314I
a = −0.77796 + 2.45089I
b = 2.16384 − 0.11659I
1.24304 − 1.23867I 0
u = 0.730028 + 0.426011I
a = 0.46514 − 1.41810I
b = 1.62643 + 0.90017I
−5.43928 + 7.39195I 0
u = 0.730028 − 0.426011I
a = 0.46514 + 1.41810I
b = 1.62643 − 0.90017I
−5.43928 − 7.39195I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.477199 + 1.051930I
a = −0.503885 + 0.648213I
b = 0.894322 − 0.618879I
3.70748 − 0.15166I 0
u = 0.477199 − 1.051930I
a = −0.503885 − 0.648213I
b = 0.894322 + 0.618879I
3.70748 + 0.15166I 0
u = −0.716845 + 0.444011I
a = 0.63771 − 1.97825I
b = −0.602540 + 0.140499I
−5.59556 + 5.07298I 0
u = −0.716845 − 0.444011I
a = 0.63771 + 1.97825I
b = −0.602540 − 0.140499I
−5.59556 − 5.07298I 0
u = −0.807265 + 0.242487I
a = 0.22546 + 1.85523I
b = 1.257880 − 0.118049I
−5.93107 − 3.05587I 0
u = −0.807265 − 0.242487I
a = 0.22546 − 1.85523I
b = 1.257880 + 0.118049I
−5.93107 + 3.05587I 0
u = −0.439023 + 1.071930I
a = 0.168515 + 0.509331I
b = −0.544178 − 0.663350I
5.25817 + 3.39113I 0
u = −0.439023 − 1.071930I
a = 0.168515 − 0.509331I
b = −0.544178 + 0.663350I
5.25817 − 3.39113I 0
u = −0.557443 + 1.020580I
a = −0.158651 + 0.981541I
b = 0.455205 − 0.018837I
−1.80516 + 7.01140I 0
u = −0.557443 − 1.020580I
a = −0.158651 − 0.981541I
b = 0.455205 + 0.018837I
−1.80516 − 7.01140I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.577409 + 1.025130I
a = −1.23261 − 2.41380I
b = 3.25283 + 1.24785I
2.60603 − 6.01858I 0
u = 0.577409 − 1.025130I
a = −1.23261 + 2.41380I
b = 3.25283 − 1.24785I
2.60603 + 6.01858I 0
u = −0.626104 + 0.534752I
a = 0.0056920 − 0.0550585I
b = 0.722902 + 0.343109I
−3.23822 − 2.34344I 0
u = −0.626104 − 0.534752I
a = 0.0056920 + 0.0550585I
b = 0.722902 − 0.343109I
−3.23822 + 2.34344I 0
u = −0.625453 + 0.519765I
a = 0.16231 − 2.25984I
b = −2.07324 + 0.50021I
0.86345 − 4.89693I 0
u = −0.625453 − 0.519765I
a = 0.16231 + 2.25984I
b = −2.07324 − 0.50021I
0.86345 + 4.89693I 0
u = −0.572499 + 1.042580I
a = 1.67007 − 2.15788I
b = −3.19405 + 0.62334I
2.41575 + 9.65210I 0
u = −0.572499 − 1.042580I
a = 1.67007 + 2.15788I
b = −3.19405 − 0.62334I
2.41575 − 9.65210I 0
u = 0.595624 + 1.031600I
a = −1.16682 − 1.91428I
b = 2.50507 + 1.26030I
1.19711 − 9.36105I 0
u = 0.595624 − 1.031600I
a = −1.16682 + 1.91428I
b = 2.50507 − 1.26030I
1.19711 + 9.36105I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.593322 + 1.034280I
a = 0.92240 − 1.48547I
b = −2.48652 + 1.39183I
−4.67986 + 9.99352I 0
u = −0.593322 − 1.034280I
a = 0.92240 + 1.48547I
b = −2.48652 − 1.39183I
−4.67986 − 9.99352I 0
u = −0.598676 + 1.039030I
a = 1.18922 − 1.79510I
b = −2.27709 + 0.95338I
1.68875 + 6.93868I 0
u = −0.598676 − 1.039030I
a = 1.18922 + 1.79510I
b = −2.27709 − 0.95338I
1.68875 − 6.93868I 0
u = 0.610139 + 1.033340I
a = −0.50259 − 1.54405I
b = 2.35284 + 1.62725I
−0.32346 − 5.55789I 0
u = 0.610139 − 1.033340I
a = −0.50259 + 1.54405I
b = 2.35284 − 1.62725I
−0.32346 + 5.55789I 0
u = 0.695051 + 0.983936I
a = 1.07951 + 1.32265I
b = −2.44418 − 0.32764I
−7.10538 − 5.12757I 0
u = 0.695051 − 0.983936I
a = 1.07951 − 1.32265I
b = −2.44418 + 0.32764I
−7.10538 + 5.12757I 0
u = 0.522378 + 1.089810I
a = −0.667224 + 0.732118I
b = 0.477953 − 0.724821I
3.26152 − 4.43525I 0
u = 0.522378 − 1.089810I
a = −0.667224 − 0.732118I
b = 0.477953 + 0.724821I
3.26152 + 4.43525I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.450080 + 0.634804I
a = −0.490028 − 0.317649I
b = −0.215712 + 0.122955I
−0.030131 − 1.277460I 0
u = 0.450080 − 0.634804I
a = −0.490028 + 0.317649I
b = −0.215712 − 0.122955I
−0.030131 + 1.277460I 0
u = 0.985195 + 0.723490I
a = 0.25473 + 1.55530I
b = −1.59947 + 0.05949I
−4.15642 − 8.44858I 0
u = 0.985195 − 0.723490I
a = 0.25473 − 1.55530I
b = −1.59947 − 0.05949I
−4.15642 + 8.44858I 0
u = −0.874131 + 0.866056I
a = −0.252868 + 1.194610I
b = 2.19417 − 0.29826I
−3.01919 + 4.59139I 0
u = −0.874131 − 0.866056I
a = −0.252868 − 1.194610I
b = 2.19417 + 0.29826I
−3.01919 − 4.59139I 0
u = 0.281693 + 1.200670I
a = −0.412752 − 0.605345I
b = 0.880298 − 0.251427I
−0.07942 − 5.37671I 0
u = 0.281693 − 1.200670I
a = −0.412752 + 0.605345I
b = 0.880298 + 0.251427I
−0.07942 + 5.37671I 0
u = −0.605742 + 1.076930I
a = 1.59470 − 1.28539I
b = −2.29188 − 0.06672I
0.27308 + 8.09103I 0
u = −0.605742 − 1.076930I
a = 1.59470 + 1.28539I
b = −2.29188 + 0.06672I
0.27308 − 8.09103I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.520380 + 1.121920I
a = 0.955421 + 0.480931I
b = −0.812013 − 0.820838I
3.38361 + 2.22304I 0
u = −0.520380 − 1.121920I
a = 0.955421 − 0.480931I
b = −0.812013 + 0.820838I
3.38361 − 2.22304I 0
u = 0.585855 + 1.090390I
a = −1.91646 − 1.21893I
b = 2.53111 − 0.33787I
−3.47988 − 12.42280I 0
u = 0.585855 − 1.090390I
a = −1.91646 + 1.21893I
b = 2.53111 + 0.33787I
−3.47988 + 12.42280I 0
u = −0.704138 + 0.290929I
a = −0.757040 − 0.812459I
b = −0.176420 + 0.892429I
0.94200 + 2.44909I 0
u = −0.704138 − 0.290929I
a = −0.757040 + 0.812459I
b = −0.176420 − 0.892429I
0.94200 − 2.44909I 0
u = −0.606842 + 1.088630I
a = 0.384191 − 0.926406I
b = −1.91223 + 1.42145I
−3.68759 + 0.00634I 0
u = −0.606842 − 1.088630I
a = 0.384191 + 0.926406I
b = −1.91223 − 1.42145I
−3.68759 − 0.00634I 0
u = 0.510897 + 1.138500I
a = −0.303510 − 0.600633I
b = 0.291658 + 0.208675I
−0.00303 − 3.85262I 0
u = 0.510897 − 1.138500I
a = −0.303510 + 0.600633I
b = 0.291658 − 0.208675I
−0.00303 + 3.85262I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.654555 + 0.332436I
a = 0.591153 − 0.783342I
b = −0.135768 + 0.815860I
1.075190 − 0.122962I 0
u = 0.654555 − 0.332436I
a = 0.591153 + 0.783342I
b = −0.135768 − 0.815860I
1.075190 + 0.122962I 0
u = 0.655003 + 0.318049I
a = −0.284407 + 0.105268I
b = 0.591088 + 0.006799I
−2.42606 − 0.70127I 0
u = 0.655003 − 0.318049I
a = −0.284407 − 0.105268I
b = 0.591088 − 0.006799I
−2.42606 + 0.70127I 0
u = −0.910786 + 0.891962I
a = −0.48384 + 1.60604I
b = 2.16993 − 0.00669I
−2.96834 + 1.90597I 0
u = −0.910786 − 0.891962I
a = −0.48384 − 1.60604I
b = 2.16993 + 0.00669I
−2.96834 − 1.90597I 0
u = 0.176825 + 1.271730I
a = −0.857305 − 0.471239I
b = 0.732823 + 0.974096I
5.56436 + 4.82435I 0
u = 0.176825 − 1.271730I
a = −0.857305 + 0.471239I
b = 0.732823 − 0.974096I
5.56436 − 4.82435I 0
u = 0.634061 + 1.125180I
a = −1.45622 − 0.86675I
b = 2.00233 − 0.38221I
−2.89210 − 3.18493I 0
u = 0.634061 − 1.125180I
a = −1.45622 + 0.86675I
b = 2.00233 + 0.38221I
−2.89210 + 3.18493I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609232 + 1.156980I
a = 0.226479 − 0.590302I
b = −0.417868 + 0.431707I
2.57819 − 13.54640I 0
u = 0.609232 − 1.156980I
a = 0.226479 + 0.590302I
b = −0.417868 − 0.431707I
2.57819 + 13.54640I 0
u = −0.597251 + 1.185190I
a = −0.115502 − 0.444116I
b = 0.368514 + 0.158468I
5.65845 + 7.80630I 0
u = −0.597251 − 1.185190I
a = −0.115502 + 0.444116I
b = 0.368514 − 0.158468I
5.65845 − 7.80630I 0
u = −0.546174 + 1.224470I
a = −1.50124 + 1.29771I
b = 3.05551 − 0.68186I
−2.96174 + 8.13583I 0
u = −0.546174 − 1.224470I
a = −1.50124 − 1.29771I
b = 3.05551 + 0.68186I
−2.96174 − 8.13583I 0
u = −0.657062 + 1.177770I
a = −1.36747 + 1.58923I
b = 3.06183 − 0.58267I
0.3293 + 19.8011I 0
u = −0.657062 − 1.177770I
a = −1.36747 − 1.58923I
b = 3.06183 + 0.58267I
0.3293 − 19.8011I 0
u = −0.100808 + 1.351960I
a = −0.533792 − 0.214465I
b = 0.23273 + 1.57802I
4.23693 − 10.48220I 0
u = −0.100808 − 1.351960I
a = −0.533792 + 0.214465I
b = 0.23273 − 1.57802I
4.23693 + 10.48220I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.881084 + 1.036760I
a = 0.438040 + 0.883985I
b = −2.20326 − 0.37361I
−3.23204 + 1.72984I 0
u = 0.881084 − 1.036760I
a = 0.438040 − 0.883985I
b = −2.20326 + 0.37361I
−3.23204 − 1.72984I 0
u = 0.658091 + 1.205700I
a = 1.31663 + 1.50523I
b = −3.07784 − 0.56855I
3.67860 − 13.47280I 0
u = 0.658091 − 1.205700I
a = 1.31663 − 1.50523I
b = −3.07784 + 0.56855I
3.67860 + 13.47280I 0
u = −0.253746 + 1.376080I
a = 0.788847 − 0.488417I
b = −1.11170 + 1.02007I
8.25173 + 1.72796I 0
u = −0.253746 − 1.376080I
a = 0.788847 + 0.488417I
b = −1.11170 − 1.02007I
8.25173 − 1.72796I 0
u = 0.510191 + 0.275897I
a = 1.02470 − 1.69924I
b = −0.160387 + 0.570498I
1.61176 − 3.82565I 0.67831 + 6.25245I
u = 0.510191 − 0.275897I
a = 1.02470 + 1.69924I
b = −0.160387 − 0.570498I
1.61176 + 3.82565I 0.67831 − 6.25245I
u = −0.546569 + 0.128274I
a = −1.49865 − 0.80037I
b = 0.075574 + 0.289173I
2.70783 + 0.36374I 3.83104 + 1.53290I
u = −0.546569 − 0.128274I
a = −1.49865 + 0.80037I
b = 0.075574 − 0.289173I
2.70783 − 0.36374I 3.83104 − 1.53290I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.18825 + 1.46944I
a = 0.454513 − 0.375637I
b = −0.15234 + 2.01768I
7.36728 + 3.23128I 0
u = 0.18825 − 1.46944I
a = 0.454513 + 0.375637I
b = −0.15234 − 2.01768I
7.36728 − 3.23128I 0
u = 0.02911 + 1.48434I
a = 1.168710 + 0.198616I
b = −2.23509 − 1.22613I
5.52859 − 1.48937I 0
u = 0.02911 − 1.48434I
a = 1.168710 − 0.198616I
b = −2.23509 + 1.22613I
5.52859 + 1.48937I 0
u = 0.382604 + 0.286600I
a = −0.729730 − 0.769814I
b = −0.245728 + 0.455420I
−0.184437 − 1.162580I −3.08681 + 5.07810I
u = 0.382604 − 0.286600I
a = −0.729730 + 0.769814I
b = −0.245728 − 0.455420I
−0.184437 + 1.162580I −3.08681 − 5.07810I
20
II. I
u
2
= h−7283u
37
+ 6235u
36
+ · · · + 995b − 2491, 3092u
37
− 2046u
36
+
· · · + 995a + 12148, u
38
+ 12u
36
+ · · · + 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
−3.10754u
37
+ 2.05628u
36
+ ··· − 17.0472u − 12.2090
7.31960u
37
− 6.26633u
36
+ ··· + 11.9628u + 2.50352
a
6
=
1
u
2
a
3
=
−2.07437u
37
− 2.67136u
36
+ ··· − 4.07940u − 7.64925
8.25930u
37
+ 1.98392u
36
+ ··· + 20.3849u + 7.23116
a
7
=
7.86734u
37
+ 1.91055u
36
+ ··· + 41.1286u − 1.23920
0.215075u
37
+ 7.88744u
36
+ ··· + 6.09447u + 9.41809
a
11
=
−u
u
a
12
=
15.1417u
37
+ 2.78191u
36
+ ··· − 5.59196u − 4.98995
1.24623u
37
− 5.77186u
36
+ ··· − 15.7236u − 6.30452
a
1
=
16.1417u
37
+ 2.78191u
36
+ ··· − 5.59196u − 4.98995
0.246231u
37
− 5.77186u
36
+ ··· − 17.7236u − 6.30452
a
4
=
−12.1759u
37
+ 9.97990u
36
+ ··· + 65.2312u + 31.7889
7.32864u
37
+ 9.02613u
36
+ ··· + 23.4995u + 4.87437
a
9
=
−u
3
u
3
+ u
a
8
=
−2.94573u
37
− 1.24523u
36
+ ··· + 21.2201u + 5.22513
7.80402u
37
+ 5.46332u
36
+ ··· + 15.3719u + 5.76482
(ii) Obstruction class = 1
(iii) Cusp Shapes =
311
995
u
37
+
33803
995
u
36
+ ··· +
120606
995
u +
13535
199
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
38
− 19u
37
+ ··· − 23u + 1
c
2
u
38
− u
37
+ ··· − u + 1
c
3
u
38
− 8u
36
+ ··· − 2u + 1
c
4
u
38
+ 7u
37
+ ··· + 7u + 1
c
5
u
38
+ 12u
36
+ ··· + 2u + 1
c
6
u
38
+ u
37
+ ··· + u + 1
c
7
u
38
− 2u
37
+ ··· − 14u
2
+ 1
c
8
u
38
− 8u
36
+ ··· + 2u + 1
c
9
u
38
+ 24u
37
+ ··· + 26u + 1
c
10
u
38
+ 12u
36
+ ··· − 2u + 1
c
11
u
38
+ 2u
37
+ ··· − 14u
2
+ 1
c
12
u
38
− 2u
37
+ ··· + 10u + 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 19y
37
+ ··· + 3y + 1
c
2
, c
6
y
38
+ 19y
37
+ ··· + 23y + 1
c
3
, c
8
y
38
− 16y
37
+ ··· − 32y + 1
c
4
y
38
− y
37
+ ··· + 19y + 1
c
5
, c
10
y
38
+ 24y
37
+ ··· + 26y + 1
c
7
, c
11
y
38
− 34y
37
+ ··· − 28y + 1
c
9
y
38
− 32y
36
+ ··· − 38y + 1
c
12
y
38
− 2y
37
+ ··· − 40y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.346633 + 0.913206I
a = −0.239791 − 0.510182I
b = −0.424762 − 0.773960I
3.48133 + 3.00418I −0.07411 + 2.12856I
u = 0.346633 − 0.913206I
a = −0.239791 + 0.510182I
b = −0.424762 + 0.773960I
3.48133 − 3.00418I −0.07411 − 2.12856I
u = 0.301513 + 0.914943I
a = 0.732917 + 0.423678I
b = 0.102967 − 0.753120I
3.41062 − 5.71924I −0.72914 + 7.89995I
u = 0.301513 − 0.914943I
a = 0.732917 − 0.423678I
b = 0.102967 + 0.753120I
3.41062 + 5.71924I −0.72914 − 7.89995I
u = −0.733903 + 0.761750I
a = −0.86783 + 1.25552I
b = 1.168020 − 0.189941I
−5.11553 + 6.68417I −4.19613 − 6.96120I
u = −0.733903 − 0.761750I
a = −0.86783 − 1.25552I
b = 1.168020 + 0.189941I
−5.11553 − 6.68417I −4.19613 + 6.96120I
u = 0.692411 + 0.628096I
a = −0.76820 − 1.59903I
b = 1.95207 + 0.24126I
0.41456 + 3.20402I −0.72082 − 2.63545I
u = 0.692411 − 0.628096I
a = −0.76820 + 1.59903I
b = 1.95207 − 0.24126I
0.41456 − 3.20402I −0.72082 + 2.63545I
u = −0.405760 + 1.013140I
a = −0.604304 + 0.119948I
b = −0.229560 − 0.210902I
4.55898 + 3.61942I 1.30393 − 4.94313I
u = −0.405760 − 1.013140I
a = −0.604304 − 0.119948I
b = −0.229560 + 0.210902I
4.55898 − 3.61942I 1.30393 + 4.94313I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.316501 + 1.083920I
a = 0.20343 + 1.52675I
b = −1.000670 − 0.920320I
0.71744 − 4.93871I 5.28229 + 3.82588I
u = 0.316501 − 1.083920I
a = 0.20343 − 1.52675I
b = −1.000670 + 0.920320I
0.71744 + 4.93871I 5.28229 − 3.82588I
u = 0.784167 + 0.841255I
a = −0.13311 + 1.69915I
b = −2.40917 − 1.11192I
−3.74428 − 4.78087I −8.45889 + 5.85278I
u = 0.784167 − 0.841255I
a = −0.13311 − 1.69915I
b = −2.40917 + 1.11192I
−3.74428 + 4.78087I −8.45889 − 5.85278I
u = −0.270191 + 0.786977I
a = 0.830494 − 0.598475I
b = 0.131868 − 0.840401I
3.51053 − 0.69885I −2.05567 − 2.41427I
u = −0.270191 − 0.786977I
a = 0.830494 + 0.598475I
b = 0.131868 + 0.840401I
3.51053 + 0.69885I −2.05567 + 2.41427I
u = 0.602124 + 1.003030I
a = −1.20083 − 2.04407I
b = 2.52189 + 0.99851I
1.55396 − 8.20858I 0. + 7.20942I
u = 0.602124 − 1.003030I
a = −1.20083 + 2.04407I
b = 2.52189 − 0.99851I
1.55396 + 8.20858I 0. − 7.20942I
u = −0.439660 + 1.095730I
a = 1.81719 − 1.68910I
b = −3.01576 + 1.14116I
−1.76589 + 8.07111I 1.68233 − 10.53606I
u = −0.439660 − 1.095730I
a = 1.81719 + 1.68910I
b = −3.01576 − 1.14116I
−1.76589 − 8.07111I 1.68233 + 10.53606I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.503608 + 1.077910I
a = 0.954334 + 0.352535I
b = −1.001150 − 0.857931I
3.76237 + 2.98497I 3.83010 − 4.26044I
u = −0.503608 − 1.077910I
a = 0.954334 − 0.352535I
b = −1.001150 + 0.857931I
3.76237 − 2.98497I 3.83010 + 4.26044I
u = 0.228552 + 0.738188I
a = 2.50537 − 0.49257I
b = −1.21116 + 1.68755I
−0.66638 + 2.56401I −1.12291 − 4.70623I
u = 0.228552 − 0.738188I
a = 2.50537 + 0.49257I
b = −1.21116 − 1.68755I
−0.66638 − 2.56401I −1.12291 + 4.70623I
u = 0.812457 + 0.921922I
a = 1.03497 + 1.43564I
b = −2.11344 + 0.45923I
−3.50761 − 1.19591I −6.34432 − 2.08353I
u = 0.812457 − 0.921922I
a = 1.03497 − 1.43564I
b = −2.11344 − 0.45923I
−3.50761 + 1.19591I −6.34432 + 2.08353I
u = −0.355743 + 0.679655I
a = 1.60153 − 2.39187I
b = −2.02823 + 1.25785I
−3.33747 − 4.69234I −6.27818 + 4.28854I
u = −0.355743 − 0.679655I
a = 1.60153 + 2.39187I
b = −2.02823 − 1.25785I
−3.33747 + 4.69234I −6.27818 − 4.28854I
u = −0.759379 + 0.994661I
a = −0.160025 + 0.962962I
b = 1.80915 − 1.19487I
−4.40408 − 0.99838I −7.00268 + 0.I
u = −0.759379 − 0.994661I
a = −0.160025 − 0.962962I
b = 1.80915 + 1.19487I
−4.40408 + 0.99838I −7.00268 + 0.I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.587859 + 0.355353I
a = −1.03266 − 1.18007I
b = −0.208703 + 0.879426I
1.69614 + 1.35708I 0.61288 − 2.76121I
u = −0.587859 − 0.355353I
a = −1.03266 + 1.18007I
b = −0.208703 − 0.879426I
1.69614 − 1.35708I 0.61288 + 2.76121I
u = 0.008225 + 1.396310I
a = −0.581533 + 0.388919I
b = 0.49580 − 1.64255I
7.31275 + 2.46224I 0
u = 0.008225 − 1.396310I
a = −0.581533 − 0.388919I
b = 0.49580 + 1.64255I
7.31275 − 2.46224I 0
u = 0.02154 + 1.45038I
a = −1.265650 − 0.113040I
b = 2.31036 + 1.03438I
5.64774 − 1.52204I 0
u = 0.02154 − 1.45038I
a = −1.265650 + 0.113040I
b = 2.31036 − 1.03438I
5.64774 + 1.52204I 0
u = −0.058020 + 0.433386I
a = −2.32631 − 2.17616I
b = 0.65045 + 1.35245I
1.27923 + 1.49890I 1.46933 − 3.64562I
u = −0.058020 − 0.433386I
a = −2.32631 + 2.17616I
b = 0.65045 − 1.35245I
1.27923 − 1.49890I 1.46933 + 3.64562I
29
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
38
− 19u
37
+ ··· − 23u + 1)
· (u
156
+ 68u
155
+ ··· + 586213058u + 32137561)
c
2
(u
38
− u
37
+ ··· − u + 1)(u
156
− 2u
155
+ ··· − 17042u + 5669)
c
3
(u
38
− 8u
36
+ ··· − 2u + 1)(u
156
− u
155
+ ··· + 6147u + 2449)
c
4
(u
38
+ 7u
37
+ ··· + 7u + 1)(u
156
− 4u
155
+ ··· − 513066u + 23269)
c
5
(u
38
+ 12u
36
+ ··· + 2u + 1)(u
156
− u
155
+ ··· + 643u + 751)
c
6
(u
38
+ u
37
+ ··· + u + 1)(u
156
− 2u
155
+ ··· − 17042u + 5669)
c
7
(u
38
− 2u
37
+ ··· − 14u
2
+ 1)(u
156
− 3u
155
+ ··· + 107845u + 85523)
c
8
(u
38
− 8u
36
+ ··· + 2u + 1)(u
156
− u
155
+ ··· + 6147u + 2449)
c
9
(u
38
+ 24u
37
+ ··· + 26u + 1)
· (u
156
− 77u
155
+ ··· − 10171145u + 564001)
c
10
(u
38
+ 12u
36
+ ··· − 2u + 1)(u
156
− u
155
+ ··· + 643u + 751)
c
11
(u
38
+ 2u
37
+ ··· − 14u
2
+ 1)(u
156
− 3u
155
+ ··· + 107845u + 85523)
c
12
(u
38
− 2u
37
+ ··· + 10u + 1)(u
156
+ 9u
155
+ ··· − 1045u + 521)
30
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
38
+ 19y
37
+ ··· + 3y + 1)
· (y
156
+ 60y
155
+ ··· + 29158613325391790y + 1032822827028721)
c
2
, c
6
(y
38
+ 19y
37
+ ··· + 23y + 1)
· (y
156
+ 68y
155
+ ··· + 586213058y + 32137561)
c
3
, c
8
(y
38
− 16y
37
+ ··· − 32y + 1)
· (y
156
− 83y
155
+ ··· − 131376593y + 5997601)
c
4
(y
38
− y
37
+ ··· + 19y + 1)
· (y
156
− 20y
155
+ ··· − 25116154598y + 541446361)
c
5
, c
10
(y
38
+ 24y
37
+ ··· + 26y + 1)
· (y
156
+ 77y
155
+ ··· + 10171145y + 564001)
c
7
, c
11
(y
38
− 34y
37
+ ··· − 28y + 1)
· (y
156
− 105y
155
+ ··· + 830770663883y + 7314183529)
c
9
(y
38
− 32y
36
+ ··· − 38y + 1)
· (y
156
+ 25y
155
+ ··· + 20263498622645y + 318097128001)
c
12
(y
38
− 2y
37
+ ··· − 40y + 1)
· (y
156
+ 11y
155
+ ··· + 19725051y + 271441)
31
