12a
0045
(K12a
0045
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 4 11 6 12 1 8 10
Solving Sequence
8,12
11
4,7
3 6 9 10 1 5 2
c
11
c
7
c
3
c
6
c
8
c
9
c
12
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.73886 × 10
473
u
111
+ 7.36133 × 10
473
u
110
+ ··· + 8.44755 × 10
472
b + 1.17690 × 10
476
,
1.22830 × 10
474
u
111
− 5.19087 × 10
474
u
110
+ ··· + 3.37902 × 10
473
a − 8.06591 × 10
476
,
u
112
− 5u
111
+ ··· − 5632u + 512i
I
u
2
= h−3u
7
+ u
6
+ 4u
5
− 3u
4
− 6u
3
+ 2u
2
+ b + 3u − 4, 4u
7
− 2u
6
− 5u
5
+ 5u
4
+ 7u
3
− 4u
2
+ a − 3u + 6,
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
I
u
3
= h−2a
2
u − 3a
2
+ 3au + b + 4a − u − 1, a
3
− 2a
2
u − au + a − 2u + 1, u
2
+ u − 1i
I
v
1
= ha, 4v
8
+ 372v
7
− 2334v
6
+ 5550v
5
− 4357v
4
− 2618v
3
+ 3887v
2
+ 683b + 3400v −4863,
v
9
− 7v
8
+ 20v
7
− 25v
6
+ 5v
5
+ 15v
4
− 22v
2
+ 13v + 1i
* 4 irreducible components of dim
C
= 0, with total 135 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−1.74 × 10
473
u
111
+ 7.36 × 10
473
u
110
+ · · · + 8.45 × 10
472
b + 1.18 ×
10
476
, 1.23 × 10
474
u
111
− 5.19 × 10
474
u
110
+ · · · + 3.38 × 10
473
a − 8.07 ×
10
476
, u
112
− 5u
111
+ · · · − 5632u + 512i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
−3.63508u
111
+ 15.3621u
110
+ ··· − 23290.3u + 2387.06
2.05842u
111
− 8.71416u
110
+ ··· + 13450.9u − 1393.18
a
7
=
−u
−u
3
+ u
a
3
=
−3.30996u
111
+ 14.0045u
110
+ ··· − 21203.9u + 2169.87
1.97006u
111
− 8.31889u
110
+ ··· + 12707.2u − 1313.20
a
6
=
0.332016u
111
− 1.18364u
110
+ ··· + 480.594u − 16.2789
1.32667u
111
− 5.42552u
110
+ ··· + 7647.22u − 780.729
a
9
=
1.36761u
111
− 5.57410u
110
+ ··· + 7412.94u − 742.249
1.52926u
111
− 6.40481u
110
+ ··· + 9333.98u − 953.908
a
10
=
2.89687u
111
− 11.9789u
110
+ ··· + 16746.9u − 1696.16
1.52926u
111
− 6.40481u
110
+ ··· + 9333.98u − 953.908
a
1
=
2.89687u
111
− 11.9789u
110
+ ··· + 16746.9u − 1696.16
0.611834u
111
− 2.49689u
110
+ ··· + 3293.45u − 328.877
a
5
=
−1.44617u
111
+ 6.03016u
110
+ ··· − 9202.34u + 961.399
0.0147551u
111
− 0.115461u
110
+ ··· + 564.279u − 65.6250
a
2
=
−4.30037u
111
+ 18.0843u
110
+ ··· − 27250.0u + 2800.12
1.91947u
111
− 8.15999u
110
+ ··· + 12820.5u − 1331.36
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18.1068u
111
+ 78.6391u
110
+ ··· − 135248.u + 14140.7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
112
+ 52u
111
+ ··· + 6550u + 1
c
2
, c
4
u
112
− 12u
111
+ ··· + 78u + 1
c
3
, c
6
u
112
− 4u
111
+ ··· − 1664u + 256
c
5
, c
8
u
112
+ 3u
111
+ ··· − 224u − 64
c
7
, c
11
u
112
− 5u
111
+ ··· − 5632u + 512
c
9
, c
10
, c
12
u
112
+ 14u
111
+ ··· + 171u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
112
+ 28y
111
+ ··· − 43105022y + 1
c
2
, c
4
y
112
− 52y
111
+ ··· − 6550y + 1
c
3
, c
6
y
112
+ 60y
111
+ ··· − 3784704y + 65536
c
5
, c
8
y
112
+ 47y
111
+ ··· − 185344y + 4096
c
7
, c
11
y
112
− 69y
111
+ ··· − 75235328y + 262144
c
9
, c
10
, c
12
y
112
− 110y
111
+ ··· − 28983y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.987913 + 0.168924I
a = −0.918537 + 0.380378I
b = −0.882679 + 0.639952I
2.30876 + 3.35064I 0
u = 0.987913 − 0.168924I
a = −0.918537 − 0.380378I
b = −0.882679 − 0.639952I
2.30876 − 3.35064I 0
u = 0.112659 + 0.958754I
a = 0.550334 − 0.341976I
b = −1.17922 + 1.72177I
1.95897 − 0.23517I 0
u = 0.112659 − 0.958754I
a = 0.550334 + 0.341976I
b = −1.17922 − 1.72177I
1.95897 + 0.23517I 0
u = −0.941698 + 0.193747I
a = 0.549932 − 0.881492I
b = 0.117151 − 0.720063I
4.85807 + 1.15903I 0
u = −0.941698 − 0.193747I
a = 0.549932 + 0.881492I
b = 0.117151 + 0.720063I
4.85807 − 1.15903I 0
u = 0.922599 + 0.202041I
a = −0.591409 − 0.833431I
b = −0.525947 − 0.138764I
0.14318 + 1.74876I 0
u = 0.922599 − 0.202041I
a = −0.591409 + 0.833431I
b = −0.525947 + 0.138764I
0.14318 − 1.74876I 0
u = −0.989073 + 0.373226I
a = 0.231341 + 0.278025I
b = 1.082440 + 0.064268I
−0.37121 − 2.19836I 0
u = −0.989073 − 0.373226I
a = 0.231341 − 0.278025I
b = 1.082440 − 0.064268I
−0.37121 + 2.19836I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.052080 + 0.121562I
a = −0.628103 − 1.234560I
b = −0.62631 + 1.29964I
5.22079 − 3.15983I 0
u = −1.052080 − 0.121562I
a = −0.628103 + 1.234560I
b = −0.62631 − 1.29964I
5.22079 + 3.15983I 0
u = −0.263231 + 1.038520I
a = 1.031050 − 0.733739I
b = −1.21393 + 1.06445I
5.66523 + 4.88950I 0
u = −0.263231 − 1.038520I
a = 1.031050 + 0.733739I
b = −1.21393 − 1.06445I
5.66523 − 4.88950I 0
u = 0.919842 + 0.048399I
a = 1.46700 + 0.26858I
b = 0.767029 + 1.031570I
−1.49378 + 1.54613I 0
u = 0.919842 − 0.048399I
a = 1.46700 − 0.26858I
b = 0.767029 − 1.031570I
−1.49378 − 1.54613I 0
u = 0.313988 + 1.041330I
a = 2.16348 − 0.54755I
b = −3.12911 + 2.53870I
0.16000 − 2.10599I 0
u = 0.313988 − 1.041330I
a = 2.16348 + 0.54755I
b = −3.12911 − 2.53870I
0.16000 + 2.10599I 0
u = 0.859832 + 0.236554I
a = −0.32071 + 2.46620I
b = −0.76197 − 1.63661I
−0.994600 − 0.244702I 0
u = 0.859832 − 0.236554I
a = −0.32071 − 2.46620I
b = −0.76197 + 1.63661I
−0.994600 + 0.244702I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.645211 + 0.908882I
a = 0.406074 − 0.178808I
b = −0.402066 − 1.027180I
−4.31644 − 4.47828I 0
u = −0.645211 − 0.908882I
a = 0.406074 + 0.178808I
b = −0.402066 + 1.027180I
−4.31644 + 4.47828I 0
u = 1.103470 + 0.161706I
a = 0.356874 − 0.708417I
b = 1.169370 + 0.176941I
−0.13349 + 1.76727I 0
u = 1.103470 − 0.161706I
a = 0.356874 + 0.708417I
b = 1.169370 − 0.176941I
−0.13349 − 1.76727I 0
u = −0.869520 + 0.018980I
a = 0.669734 − 0.947495I
b = 0.19478 + 1.72833I
4.29062 − 2.64667I 0
u = −0.869520 − 0.018980I
a = 0.669734 + 0.947495I
b = 0.19478 − 1.72833I
4.29062 + 2.64667I 0
u = −0.097707 + 1.131780I
a = −1.26124 + 0.65545I
b = 1.86008 − 1.30770I
7.06933 − 0.77487I 0
u = −0.097707 − 1.131780I
a = −1.26124 − 0.65545I
b = 1.86008 + 1.30770I
7.06933 + 0.77487I 0
u = 1.062140 + 0.446911I
a = −0.744235 − 1.049370I
b = 1.011560 + 0.521470I
3.05226 + 7.00346I 0
u = 1.062140 − 0.446911I
a = −0.744235 + 1.049370I
b = 1.011560 − 0.521470I
3.05226 − 7.00346I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.116720 + 0.299470I
a = 0.66546 + 1.25680I
b = −0.756923 − 0.431765I
4.78310 + 1.56650I 0
u = 1.116720 − 0.299470I
a = 0.66546 − 1.25680I
b = −0.756923 + 0.431765I
4.78310 − 1.56650I 0
u = −0.106096 + 0.835679I
a = −1.71103 − 0.38039I
b = 1.45697 + 0.32666I
−2.60168 + 8.03413I 0
u = −0.106096 − 0.835679I
a = −1.71103 + 0.38039I
b = 1.45697 − 0.32666I
−2.60168 − 8.03413I 0
u = −1.074420 + 0.471048I
a = 0.48698 + 2.05471I
b = 2.14483 − 1.48985I
−2.53810 − 4.23062I 0
u = −1.074420 − 0.471048I
a = 0.48698 − 2.05471I
b = 2.14483 + 1.48985I
−2.53810 + 4.23062I 0
u = 0.750829 + 0.302715I
a = 0.640656 − 1.016480I
b = 0.600724 − 0.528679I
−1.53487 + 7.70823I 0
u = 0.750829 − 0.302715I
a = 0.640656 + 1.016480I
b = 0.600724 + 0.528679I
−1.53487 − 7.70823I 0
u = −0.404340 + 0.667214I
a = −2.16675 − 0.27634I
b = 1.38716 + 1.41067I
−4.57208 − 0.19764I 0
u = −0.404340 − 0.667214I
a = −2.16675 + 0.27634I
b = 1.38716 − 1.41067I
−4.57208 + 0.19764I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.562718 + 0.536308I
a = −0.119967 + 0.522623I
b = 0.699792 + 0.611127I
−1.65451 − 1.50529I 0
u = −0.562718 − 0.536308I
a = −0.119967 − 0.522623I
b = 0.699792 − 0.611127I
−1.65451 + 1.50529I 0
u = 0.323687 + 1.179730I
a = −0.409973 + 0.354108I
b = 0.60376 − 2.00524I
1.24304 − 4.46857I 0
u = 0.323687 − 1.179730I
a = −0.409973 − 0.354108I
b = 0.60376 + 2.00524I
1.24304 + 4.46857I 0
u = −0.962683 + 0.788038I
a = −0.260779 − 0.039002I
b = −0.405012 + 0.743652I
−3.38522 − 1.66545I 0
u = −0.962683 − 0.788038I
a = −0.260779 + 0.039002I
b = −0.405012 − 0.743652I
−3.38522 + 1.66545I 0
u = −0.287462 + 0.691754I
a = 0.593994 − 0.634266I
b = −0.811368 − 0.733768I
−4.17219 + 2.32119I 0
u = −0.287462 − 0.691754I
a = 0.593994 + 0.634266I
b = −0.811368 + 0.733768I
−4.17219 − 2.32119I 0
u = 1.014560 + 0.732117I
a = 0.215744 + 0.187366I
b = −0.010991 + 0.513589I
1.05711 + 6.04270I 0
u = 1.014560 − 0.732117I
a = 0.215744 − 0.187366I
b = −0.010991 − 0.513589I
1.05711 − 6.04270I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.161230 + 0.475817I
a = −0.277099 − 0.217089I
b = −1.200030 + 0.265794I
−1.50046 − 6.83730I 0
u = −1.161230 − 0.475817I
a = −0.277099 + 0.217089I
b = −1.200030 − 0.265794I
−1.50046 + 6.83730I 0
u = 0.447908 + 0.581740I
a = −1.18928 − 0.85724I
b = 0.364030 − 0.116853I
1.18207 − 2.86004I 0
u = 0.447908 − 0.581740I
a = −1.18928 + 0.85724I
b = 0.364030 + 0.116853I
1.18207 + 2.86004I 0
u = 1.284600 + 0.081267I
a = 0.17262 − 1.57344I
b = 0.216790 − 0.027700I
4.50061 + 1.87825I 0
u = 1.284600 − 0.081267I
a = 0.17262 + 1.57344I
b = 0.216790 + 0.027700I
4.50061 − 1.87825I 0
u = 0.814984 + 1.000110I
a = −0.255947 + 0.372325I
b = −0.65284 − 1.48503I
0.256128 + 0.215496I 0
u = 0.814984 − 1.000110I
a = −0.255947 − 0.372325I
b = −0.65284 + 1.48503I
0.256128 − 0.215496I 0
u = 1.061310 + 0.734995I
a = 0.231002 − 0.484171I
b = 1.28384 + 0.99105I
−0.08758 − 3.32486I 0
u = 1.061310 − 0.734995I
a = 0.231002 + 0.484171I
b = 1.28384 − 0.99105I
−0.08758 + 3.32486I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140581 + 0.678756I
a = 1.92559 + 0.47607I
b = −1.116120 − 0.595282I
−0.07044 + 3.09882I 0
u = −0.140581 − 0.678756I
a = 1.92559 − 0.47607I
b = −1.116120 + 0.595282I
−0.07044 − 3.09882I 0
u = 0.480520 + 0.491232I
a = 0.479661 + 0.474885I
b = −1.358880 − 0.118546I
1.19166 − 0.82959I 0
u = 0.480520 − 0.491232I
a = 0.479661 − 0.474885I
b = −1.358880 + 0.118546I
1.19166 + 0.82959I 0
u = 0.664039 + 0.056295I
a = −2.16392 − 2.68234I
b = 1.22695 + 1.89143I
−0.844006 + 0.123701I 16.1538 − 18.4285I
u = 0.664039 − 0.056295I
a = −2.16392 + 2.68234I
b = 1.22695 − 1.89143I
−0.844006 − 0.123701I 16.1538 + 18.4285I
u = −1.264170 + 0.444282I
a = −0.14613 − 1.65167I
b = −1.87414 + 0.52156I
3.43374 − 7.46948I 0
u = −1.264170 − 0.444282I
a = −0.14613 + 1.65167I
b = −1.87414 − 0.52156I
3.43374 + 7.46948I 0
u = −1.305310 + 0.328556I
a = 0.89998 − 1.79680I
b = −0.91086 − 1.12171I
5.51452 − 2.03742I 0
u = −1.305310 − 0.328556I
a = 0.89998 + 1.79680I
b = −0.91086 + 1.12171I
5.51452 + 2.03742I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.277820 + 1.323270I
a = −1.62486 + 0.15415I
b = 3.25584 − 1.48744I
6.13010 − 4.83002I 0
u = 0.277820 − 1.323270I
a = −1.62486 − 0.15415I
b = 3.25584 + 1.48744I
6.13010 + 4.83002I 0
u = 1.362900 + 0.209748I
a = 0.02427 + 1.55962I
b = −0.574884 + 0.351957I
2.55654 + 7.34989I 0
u = 1.362900 − 0.209748I
a = 0.02427 − 1.55962I
b = −0.574884 − 0.351957I
2.55654 − 7.34989I 0
u = 1.338470 + 0.333318I
a = −0.877831 + 0.950009I
b = −2.01412 − 1.14375I
10.99310 − 0.43900I 0
u = 1.338470 − 0.333318I
a = −0.877831 − 0.950009I
b = −2.01412 + 1.14375I
10.99310 + 0.43900I 0
u = −1.316050 + 0.429456I
a = 0.944070 − 0.591573I
b = 0.66430 − 1.46767I
6.42012 − 4.59902I 0
u = −1.316050 − 0.429456I
a = 0.944070 + 0.591573I
b = 0.66430 + 1.46767I
6.42012 + 4.59902I 0
u = 0.610427
a = 0.610429
b = −0.200993
0.859712 11.9150
u = 1.286140 + 0.548627I
a = −0.443252 + 0.043811I
b = −1.048490 − 0.319033I
5.53294 + 5.70610I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.286140 − 0.548627I
a = −0.443252 − 0.043811I
b = −1.048490 + 0.319033I
5.53294 − 5.70610I 0
u = −1.310080 + 0.531274I
a = −0.03910 + 1.65684I
b = 2.16792 − 0.22426I
1.11481 − 13.24070I 0
u = −1.310080 − 0.531274I
a = −0.03910 − 1.65684I
b = 2.16792 + 0.22426I
1.11481 + 13.24070I 0
u = −1.28436 + 0.61419I
a = 0.742337 − 1.065820I
b = −1.41432 − 0.47830I
8.88079 − 10.89320I 0
u = −1.28436 − 0.61419I
a = 0.742337 + 1.065820I
b = −1.41432 + 0.47830I
8.88079 + 10.89320I 0
u = 1.28360 + 0.62427I
a = −0.52411 + 1.93638I
b = −3.41369 − 1.15161I
3.26019 + 8.19420I 0
u = 1.28360 − 0.62427I
a = −0.52411 − 1.93638I
b = −3.41369 + 1.15161I
3.26019 − 8.19420I 0
u = −1.41781 + 0.19610I
a = −1.080480 + 0.444312I
b = −1.41301 + 1.02495I
7.77601 − 0.27066I 0
u = −1.41781 − 0.19610I
a = −1.080480 − 0.444312I
b = −1.41301 − 1.02495I
7.77601 + 0.27066I 0
u = 0.38913 + 1.38262I
a = 1.62101 + 0.04014I
b = −3.56558 + 1.43739I
4.02685 − 10.51750I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.38913 − 1.38262I
a = 1.62101 − 0.04014I
b = −3.56558 − 1.43739I
4.02685 + 10.51750I 0
u = −0.549537 + 0.083222I
a = 0.274559 − 0.934457I
b = −0.19496 + 2.94085I
4.16876 − 2.73247I 34.1878 − 1.6499I
u = −0.549537 − 0.083222I
a = 0.274559 + 0.934457I
b = −0.19496 − 2.94085I
4.16876 + 2.73247I 34.1878 + 1.6499I
u = 1.37781 + 0.43660I
a = 0.718387 − 1.203630I
b = 2.36665 + 1.01786I
11.96300 + 6.19123I 0
u = 1.37781 − 0.43660I
a = 0.718387 + 1.203630I
b = 2.36665 − 1.01786I
11.96300 − 6.19123I 0
u = 0.182434 + 0.518573I
a = 1.66248 + 0.93649I
b = −0.473030 − 0.208731I
1.99985 + 1.66123I 2.31051 − 3.78283I
u = 0.182434 − 0.518573I
a = 1.66248 − 0.93649I
b = −0.473030 + 0.208731I
1.99985 − 1.66123I 2.31051 + 3.78283I
u = −1.37397 + 0.53912I
a = −0.631049 + 1.262440I
b = 1.48385 + 0.78634I
11.21670 − 5.22488I 0
u = −1.37397 − 0.53912I
a = −0.631049 − 1.262440I
b = 1.48385 − 0.78634I
11.21670 + 5.22488I 0
u = 1.32163 + 0.66916I
a = 0.428382 + 0.007783I
b = 0.979772 + 0.650539I
4.46415 + 11.08430I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.32163 − 0.66916I
a = 0.428382 − 0.007783I
b = 0.979772 − 0.650539I
4.46415 − 11.08430I 0
u = 1.38900 + 0.70279I
a = 0.13070 − 1.64504I
b = 3.33755 + 0.49016I
9.7116 + 11.9730I 0
u = 1.38900 − 0.70279I
a = 0.13070 + 1.64504I
b = 3.33755 − 0.49016I
9.7116 − 11.9730I 0
u = 1.37841 + 0.77274I
a = 0.06128 + 1.66829I
b = −3.52485 − 0.31007I
7.2346 + 18.0734I 0
u = 1.37841 − 0.77274I
a = 0.06128 − 1.66829I
b = −3.52485 + 0.31007I
7.2346 − 18.0734I 0
u = −1.58390
a = −2.28456
b = −3.83094
7.84469 0
u = −1.67053 + 0.32452I
a = 0.03761 + 1.53472I
b = 1.94736 + 1.83024I
12.87440 − 1.42369I 0
u = −1.67053 − 0.32452I
a = 0.03761 − 1.53472I
b = 1.94736 − 1.83024I
12.87440 + 1.42369I 0
u = −1.77832 + 0.22948I
a = −0.32455 − 1.46958I
b = −2.20973 − 2.18426I
11.74710 + 4.07589I 0
u = −1.77832 − 0.22948I
a = −0.32455 + 1.46958I
b = −2.20973 + 2.18426I
11.74710 − 4.07589I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.104682
a = −3.89166
b = 8.91953
0.460815 373.120
u = 0.0766424
a = −7.27868
b = 0.661524
−1.20372 −8.99900
16
II. I
u
2
= h−3u
7
+ u
6
+ · · · + b − 4, 4u
7
− 2u
6
+ · · · + a + 6, u
8
− u
7
− u
6
+
2u
5
+ u
4
− 2u
3
+ 2u − 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
−4u
7
+ 2u
6
+ 5u
5
− 5u
4
− 7u
3
+ 4u
2
+ 3u − 6
3u
7
− u
6
− 4u
5
+ 3u
4
+ 6u
3
− 2u
2
− 3u + 4
a
7
=
−u
−u
3
+ u
a
3
=
−4u
7
+ 2u
6
+ 5u
5
− 5u
4
− 7u
3
+ 4u
2
+ 3u − 6
3u
7
− u
6
− 4u
5
+ 3u
4
+ 6u
3
− 2u
2
− 3u + 4
a
6
=
−u
−u
3
+ u
a
9
=
u
3
u
5
− u
3
+ u
a
10
=
u
5
+ u
u
5
− u
3
+ u
a
1
=
u
5
+ u
u
7
− u
5
+ 2u
3
− u
a
5
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
2
=
−4u
7
+ 2u
6
+ 6u
5
− 5u
4
− 7u
3
+ 4u
2
+ 4u − 6
4u
7
− u
6
− 5u
5
+ 3u
4
+ 8u
3
− 2u
2
− 4u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 44u
7
− 15u
6
− 58u
5
+ 53u
4
+ 78u
3
− 42u
2
− 28u + 73
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
6
u
8
c
4
(u + 1)
8
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
7
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
8
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
9
, c
10
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
11
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
12
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
6
y
8
c
5
, c
8
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
7
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
9
, c
10
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = 1.145920 + 0.510212I
b = −1.80990 + 0.33963I
−0.604279 − 1.131230I 0.744211 − 0.553382I
u = 0.570868 − 0.730671I
a = 1.145920 − 0.510212I
b = −1.80990 − 0.33963I
−0.604279 + 1.131230I 0.744211 + 0.553382I
u = −0.855237 + 0.665892I
a = −0.315815 + 0.718986I
b = 1.043770 − 0.152194I
−3.80435 − 2.57849I −2.39106 + 4.72239I
u = −0.855237 − 0.665892I
a = −0.315815 − 0.718986I
b = 1.043770 + 0.152194I
−3.80435 + 2.57849I −2.39106 − 4.72239I
u = −1.09818
a = 0.755058
b = 0.155540
4.85780 8.45210
u = 1.031810 + 0.655470I
a = 0.069364 + 0.543055I
b = −0.759875 − 0.104398I
0.73474 + 6.44354I 0.47538 − 9.99765I
u = 1.031810 − 0.655470I
a = 0.069364 − 0.543055I
b = −0.759875 + 0.104398I
0.73474 − 6.44354I 0.47538 + 9.99765I
u = 0.603304
a = −4.55399
b = 2.89645
−0.799899 60.8910
20
III.
I
u
3
= h−2a
2
u−3a
2
+3au+b+4a−u−1, a
3
−2a
2
u−au+a−2u+1, u
2
+u−1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
11
=
1
−u + 1
a
4
=
a
2a
2
u + 3a
2
− 3au − 4a + u + 1
a
7
=
−u
−u + 1
a
3
=
a
2
u + a
2
− a + u
2a
2
u + 2a
2
− au − 4a + 2u
a
6
=
0
2a
2
u + 3a
2
− au − 2a − u − 1
a
9
=
0
u
a
10
=
u
u
a
1
=
u
u − 1
a
5
=
0
2a
2
u + 3a
2
− au − 2a − u − 1
a
2
=
a
2
u + a
2
− a + u
2a
2
u + 2a
2
− 2a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 19a
2
u + 23a
2
− 17au − 29a + 3u + 1
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
9
, c
10
(u
2
− u − 1)
3
c
11
, c
12
(u
2
+ u − 1)
3
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
8
y
6
c
7
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
3
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 1.08457
b = 0.251717
−0.126494 0.874100
u = 0.618034
a = 0.075747 + 0.460350I
b = 0.30119 − 2.39951I
4.01109 + 2.82812I −7.3018 − 15.7639I
u = 0.618034
a = 0.075747 − 0.460350I
b = 0.30119 + 2.39951I
4.01109 − 2.82812I −7.3018 + 15.7639I
u = −1.61803
a = −0.198308 + 1.205210I
b = −0.453796 + 1.142220I
11.90680 − 2.82812I 7.38403 + 1.90115I
u = −1.61803
a = −0.198308 − 1.205210I
b = −0.453796 − 1.142220I
11.90680 + 2.82812I 7.38403 − 1.90115I
u = −1.61803
a = −2.83945
b = −4.94651
7.76919 −62.0390
24
IV. I
v
1
= ha, 4v
8
+ 372v
7
+ · · · + 683b − 4863, v
9
− 7v
8
+ · · · + 13v + 1i
(i) Arc colorings
a
8
=
v
0
a
12
=
1
0
a
11
=
1
0
a
4
=
0
−0.00585652v
8
− 0.544656v
7
+ ··· − 4.97804v + 7.12006
a
7
=
v
0
a
3
=
−0.565154v
8
+ 3.44070v
7
+ ··· + 7.61933v + 0.585652
−0.00585652v
8
− 0.544656v
7
+ ··· − 4.97804v + 7.12006
a
6
=
v
0.595900v
8
− 3.58126v
7
+ ··· − 7.48463v + 3.28404
a
9
=
−1.00439v
8
+ 5.59151v
7
+ ··· + 9.26647v + 0.590044
1
a
10
=
−1.00439v
8
+ 5.59151v
7
+ ··· + 9.26647v + 1.59004
1
a
1
=
1.00439v
8
− 5.59151v
7
+ ··· − 9.26647v −0.590044
−1
a
5
=
−1.00439v
8
+ 5.59151v
7
+ ··· + 9.26647v + 0.590044
0.00585652v
8
− 0.455344v
7
+ ··· − 3.02196v + 3.87994
a
2
=
0.569546v
8
− 3.03221v
7
+ ··· − 3.88580v −0.175695
0.00585652v
8
− 0.455344v
7
+ ··· − 3.02196v + 3.87994
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
8299
683
v
8
+
59404
683
v
7
−
175193
683
v
6
+
233079
683
v
5
−
71022
683
v
4
−
122802
683
v
3
+
17898
683
v
2
+
188382
683
v −
131415
683
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
7
, c
11
u
9
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
9
, c
10
(u + 1)
9
c
12
(u − 1)
9
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
6
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
5
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
, c
11
y
9
c
9
, c
10
, c
12
(y −1)
9
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.763784 + 0.496693I
a = 0
b = −0.449406 + 0.973624I
3.42837 − 2.09337I 7.68972 + 3.82038I
v = −0.763784 − 0.496693I
a = 0
b = −0.449406 − 0.973624I
3.42837 + 2.09337I 7.68972 − 3.82038I
v = 1.072290 + 0.815867I
a = 0
b = −0.764470 − 0.234457I
1.02799 − 2.45442I 5.04100 + 1.69416I
v = 1.072290 − 0.815867I
a = 0
b = −0.764470 + 0.234457I
1.02799 + 2.45442I 5.04100 − 1.69416I
v = 1.353070 + 0.224375I
a = 0
b = 0.485105 − 0.622283I
−2.72642 − 1.33617I −1.56769 + 0.26615I
v = 1.353070 − 0.224375I
a = 0
b = 0.485105 + 0.622283I
−2.72642 + 1.33617I −1.56769 − 0.26615I
v = −0.0689118
a = 0
b = 7.43498
0.446489 −211.240
v = 1.87288 + 1.26938I
a = 0
b = 0.511281 + 0.180088I
−1.95319 − 7.08493I 0.45449 + 1.34000I
v = 1.87288 − 1.26938I
a = 0
b = 0.511281 − 0.180088I
−1.95319 + 7.08493I 0.45449 − 1.34000I
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
(u
3
− u
2
+ 2u − 1)
2
· (u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
112
+ 52u
111
+ ··· + 6550u + 1)
c
2
(u − 1)
8
(u
3
+ u
2
− 1)
2
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
112
− 12u
111
+ ··· + 78u + 1)
c
3
u
8
(u
3
− u
2
+ 2u − 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
112
− 4u
111
+ ··· − 1664u + 256)
c
4
(u + 1)
8
(u
3
− u
2
+ 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
112
− 12u
111
+ ··· + 78u + 1)
c
5
u
6
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
112
+ 3u
111
+ ··· − 224u − 64)
c
6
u
8
(u
3
+ u
2
+ 2u + 1)
2
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
112
− 4u
111
+ ··· − 1664u + 256)
c
7
u
9
(u
2
− u − 1)
3
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
112
− 5u
111
+ ··· − 5632u + 512)
c
8
u
6
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
112
+ 3u
111
+ ··· − 224u − 64)
c
9
, c
10
(u + 1)
9
(u
2
− u − 1)
3
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
112
+ 14u
111
+ ··· + 171u − 1)
c
11
u
9
(u
2
+ u − 1)
3
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
112
− 5u
111
+ ··· − 5632u + 512)
c
12
(u − 1)
9
(u
2
+ u − 1)
3
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
112
+ 14u
111
+ ··· + 171u − 1)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
(y
3
+ 3y
2
+ 2y −1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
112
+ 28y
111
+ ··· − 43105022y + 1)
c
2
, c
4
(y −1)
8
(y
3
− y
2
+ 2y −1)
2
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
112
− 52y
111
+ ··· − 6550y + 1)
c
3
, c
6
y
8
(y
3
+ 3y
2
+ 2y −1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
112
+ 60y
111
+ ··· − 3784704y + 65536)
c
5
, c
8
y
6
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
112
+ 47y
111
+ ··· − 185344y + 4096)
c
7
, c
11
y
9
(y
2
− 3y + 1)
3
(y
8
− 3y
7
+ ··· − 4y + 1)
· (y
112
− 69y
111
+ ··· − 75235328y + 262144)
c
9
, c
10
, c
12
(y −1)
9
(y
2
− 3y + 1)
3
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
112
− 110y
111
+ ··· − 28983y + 1)
30
