12a
0490
(K12a
0490
)
A knot diagram
1
Linearized knot diagam
3 6 12 8 2 10 5 11 1 7 4 9
Solving Sequence
4,8 5,11
9 12 1 3 7 10 6 2
c
4
c
8
c
11
c
12
c
3
c
7
c
10
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u,
250936582341786u
28
− 122066524221929u
27
+ ··· + 148804454046473a − 98424746117489,
u
29
− u
28
+ ··· + 2u + 1i
I
u
2
= h−1.05564 × 10
344
u
87
+ 9.79310 × 10
344
u
86
+ ··· + 1.52446 × 10
344
b + 3.97004 × 10
347
,
− 5.49731 × 10
346
u
87
+ 3.25834 × 10
347
u
86
+ ··· + 1.25158 × 10
347
a + 5.74130 × 10
349
,
u
88
− 5u
87
+ ··· + 3584u + 821i
I
u
3
= hb + u, −u
11
+ u
10
− 7u
9
+ 7u
8
− 22u
7
+ 20u
6
− 38u
5
+ 30u
4
− 36u
3
+ 23u
2
+ a − 16u + 7,
u
14
− u
13
+ 8u
12
− 7u
11
+ 28u
10
− 21u
9
+ 55u
8
− 35u
7
+ 64u
6
− 34u
5
+ 42u
4
− 18u
3
+ 12u
2
− 4u − 1i
* 3 irreducible components of dim
C
= 0, with total 131 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
= hb − u, 2.51 × 10
14
u
28
− 1.22 × 10
14
u
27
+ · · · + 1.49 × 10
14
a − 9.84 ×
10
13
, u
29
− u
28
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
−1.68635u
28
+ 0.820315u
27
+ ··· − 0.162655u + 0.661437
u
a
9
=
2.67746u
28
− 0.133672u
27
+ ··· − 1.06713u + 0.714235
−1.08667u
28
− 0.0581082u
27
+ ··· − 2.41842u − 0.866036
a
12
=
−1.68635u
28
+ 0.820315u
27
+ ··· − 1.16266u + 0.661437
u
a
1
=
2.38291u
28
+ 0.0817397u
27
+ ··· − 2.92353u + 0.0907982
−1.36536u
28
+ 0.339734u
27
+ ··· − 2.62020u − 1.13818
a
3
=
0.866036u
28
− 1.95270u
27
+ ··· − 4.03414u − 0.686351
−u
2
a
7
=
u
u
3
+ u
a
10
=
−1.40957u
28
+ 0.932959u
27
+ ··· − 0.204858u + 0.940177
0.250397u
28
− 0.395790u
27
+ ··· − 0.0978403u − 0.110687
a
6
=
−1.70921u
28
+ 1.67866u
27
+ ··· + 6.16797u + 1.12970
−0.197996u
28
− 0.326044u
27
+ ··· − 1.09569u − 0.941452
a
2
=
0.525755u
28
− 0.0225068u
27
+ ··· − 7.84043u − 1.04956
−0.197996u
28
− 0.326044u
27
+ ··· − 1.09569u − 0.941452
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
566288427861444
148804454046473
u
28
−
861558207456155
148804454046473
u
27
+ ··· −
4146887141209843
148804454046473
u −
3721831975657214
148804454046473
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 11u
28
+ ··· + 4736u + 256
c
2
, c
5
u
29
+ 11u
28
+ ··· + 192u + 16
c
3
, c
4
, c
7
c
11
u
29
− u
28
+ ··· + 2u + 1
c
6
, c
9
, c
10
c
12
u
29
− u
28
+ ··· + 4u + 1
c
8
u
29
− 28u
28
+ ··· − 6144u + 2048
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 13y
28
+ ··· + 9166848y − 65536
c
2
, c
5
y
29
− 11y
28
+ ··· + 4736y − 256
c
3
, c
4
, c
7
c
11
y
29
+ 23y
28
+ ··· + 20y − 1
c
6
, c
9
, c
10
c
12
y
29
− 21y
28
+ ··· + 16y − 1
c
8
y
29
− 4y
28
+ ··· − 31457280y − 4194304
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.943671 + 0.254326I
a = 1.002260 − 0.565360I
b = 0.943671 + 0.254326I
−6.98851 + 7.38189I −18.4807 − 4.8783I
u = 0.943671 − 0.254326I
a = 1.002260 + 0.565360I
b = 0.943671 − 0.254326I
−6.98851 − 7.38189I −18.4807 + 4.8783I
u = −0.931114 + 0.157675I
a = −1.095410 − 0.365233I
b = −0.931114 + 0.157675I
−5.01123 − 1.88675I −17.5811 + 0.8407I
u = −0.931114 − 0.157675I
a = −1.095410 + 0.365233I
b = −0.931114 − 0.157675I
−5.01123 + 1.88675I −17.5811 − 0.8407I
u = −0.382213 + 0.987155I
a = −0.742302 − 0.002124I
b = −0.382213 + 0.987155I
1.88723 + 3.15225I −8.02900 − 4.43437I
u = −0.382213 − 0.987155I
a = −0.742302 + 0.002124I
b = −0.382213 − 0.987155I
1.88723 − 3.15225I −8.02900 + 4.43437I
u = 0.048532 + 1.085820I
a = −2.00236 − 1.54010I
b = 0.048532 + 1.085820I
0.49844 − 7.80036I −10.28673 + 6.90769I
u = 0.048532 − 1.085820I
a = −2.00236 + 1.54010I
b = 0.048532 − 1.085820I
0.49844 + 7.80036I −10.28673 − 6.90769I
u = 0.080324 + 1.107540I
a = 1.71771 − 0.28078I
b = 0.080324 + 1.107540I
4.67366 + 1.54454I −5.37934 − 3.77559I
u = 0.080324 − 1.107540I
a = 1.71771 + 0.28078I
b = 0.080324 − 1.107540I
4.67366 − 1.54454I −5.37934 + 3.77559I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.537814 + 0.473191I
a = 0.64181 + 1.26516I
b = 0.537814 + 0.473191I
−2.87090 + 3.41002I −17.4789 − 2.4204I
u = 0.537814 − 0.473191I
a = 0.64181 − 1.26516I
b = 0.537814 − 0.473191I
−2.87090 − 3.41002I −17.4789 + 2.4204I
u = 0.464520 + 1.279870I
a = 1.55204 − 0.50969I
b = 0.464520 + 1.279870I
−3.93836 − 8.89106I −15.2442 + 6.9531I
u = 0.464520 − 1.279870I
a = 1.55204 + 0.50969I
b = 0.464520 − 1.279870I
−3.93836 + 8.89106I −15.2442 − 6.9531I
u = −0.128639 + 1.359520I
a = −0.86220 − 2.02768I
b = −0.128639 + 1.359520I
5.82172 + 4.48234I −14.8090 − 6.0213I
u = −0.128639 − 1.359520I
a = −0.86220 + 2.02768I
b = −0.128639 − 1.359520I
5.82172 − 4.48234I −14.8090 + 6.0213I
u = 0.254997 + 1.384100I
a = 0.889760 − 0.491762I
b = 0.254997 + 1.384100I
9.13257 − 0.76587I −4.66197 − 1.18942I
u = 0.254997 − 1.384100I
a = 0.889760 + 0.491762I
b = 0.254997 − 1.384100I
9.13257 + 0.76587I −4.66197 + 1.18942I
u = −0.33115 + 1.41930I
a = −0.822163 − 0.477668I
b = −0.33115 + 1.41930I
8.79150 + 6.45231I −4.82568 − 4.60766I
u = −0.33115 − 1.41930I
a = −0.822163 + 0.477668I
b = −0.33115 − 1.41930I
8.79150 − 6.45231I −4.82568 + 4.60766I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.497017 + 0.157040I
a = 2.59708 − 1.03005I
b = 0.497017 + 0.157040I
−10.64620 − 0.03192I −29.1555 + 7.5854I
u = 0.497017 − 0.157040I
a = 2.59708 + 1.03005I
b = 0.497017 − 0.157040I
−10.64620 + 0.03192I −29.1555 − 7.5854I
u = −0.51917 + 1.42010I
a = −1.160960 − 0.482236I
b = −0.51917 + 1.42010I
3.16273 + 12.79870I −10.04451 − 6.89203I
u = −0.51917 − 1.42010I
a = −1.160960 + 0.482236I
b = −0.51917 − 1.42010I
3.16273 − 12.79870I −10.04451 + 6.89203I
u = 0.57303 + 1.43212I
a = 1.124520 − 0.387229I
b = 0.57303 + 1.43212I
0.7116 − 19.0153I −12.0000 + 9.9067I
u = 0.57303 − 1.43212I
a = 1.124520 + 0.387229I
b = 0.57303 − 1.43212I
0.7116 + 19.0153I −12.0000 − 9.9067I
u = −0.441008 + 0.034064I
a = 0.225680 + 0.493763I
b = −0.441008 + 0.034064I
−0.743051 + 0.035864I −12.27916 + 0.21691I
u = −0.441008 − 0.034064I
a = 0.225680 − 0.493763I
b = −0.441008 − 0.034064I
−0.743051 − 0.035864I −12.27916 − 0.21691I
u = −0.333214
a = 0.869115
b = −0.333214
−0.737681 −13.2750
7
II. I
u
2
= h−1.06 × 10
344
u
87
+ 9.79 × 10
344
u
86
+ · · · + 1.52 × 10
344
b + 3.97 ×
10
347
, −5.50 × 10
346
u
87
+ 3.26 × 10
347
u
86
+ · · · + 1.25 × 10
347
a + 5.74 ×
10
349
, u
88
− 5u
87
+ · · · + 3584u + 821i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
0.439229u
87
− 2.60338u
86
+ ··· − 1546.53u − 458.724
0.692469u
87
− 6.42398u
86
+ ··· − 11147.5u − 2604.23
a
9
=
−0.518913u
87
+ 1.96411u
86
+ ··· − 2137.91u − 428.380
0.867957u
87
− 4.16018u
86
+ ··· + 1075.10u + 82.6704
a
12
=
−0.253240u
87
+ 3.82061u
86
+ ··· + 9601.01u + 2145.50
0.692469u
87
− 6.42398u
86
+ ··· − 11147.5u − 2604.23
a
1
=
−0.0184597u
87
+ 2.48755u
86
+ ··· + 9882.72u + 2145.17
0.231469u
87
− 3.79527u
86
+ ··· − 10084.6u − 2265.64
a
3
=
−12.5530u
87
+ 62.9597u
86
+ ··· − 3353.00u + 1681.05
12.4523u
87
− 61.5883u
86
+ ··· + 6410.79u − 966.838
a
7
=
u
u
3
+ u
a
10
=
−0.564831u
87
+ 5.00806u
86
+ ··· + 8142.29u + 1879.73
1.00653u
87
− 7.68993u
86
+ ··· − 9921.01u − 2393.09
a
6
=
−1.49311u
87
+ 18.0746u
86
+ ··· + 41278.3u + 9450.89
2.02163u
87
− 20.5931u
86
+ ··· − 40530.9u − 9364.41
a
2
=
−6.88891u
87
+ 31.1111u
86
+ ··· − 14992.8u − 1995.33
7.09278u
87
− 32.1612u
86
+ ··· + 14767.1u + 1898.83
(ii) Obstruction class = −1
(iii) Cusp Shapes = −27.8190u
87
+ 141.290u
86
+ ··· + 723.380u + 5434.35
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
44
+ 20u
43
+ ··· − 16u + 1)
2
c
2
, c
5
(u
44
− 4u
43
+ ··· − 6u + 1)
2
c
3
, c
4
, c
7
c
11
u
88
− 5u
87
+ ··· + 3584u + 821
c
6
, c
9
, c
10
c
12
u
88
− 7u
87
+ ··· + 6072u + 2143
c
8
(u
44
+ 13u
43
+ ··· + 2u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
44
+ 12y
43
+ ··· − 304y + 1)
2
c
2
, c
5
(y
44
− 20y
43
+ ··· + 16y + 1)
2
c
3
, c
4
, c
7
c
11
y
88
+ 63y
87
+ ··· + 24336392y + 674041
c
6
, c
9
, c
10
c
12
y
88
− 53y
87
+ ··· − 51150136y + 4592449
c
8
(y
44
+ 11y
43
+ ··· + 18y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395638 + 0.897674I
a = −0.966465 + 0.057775I
b = −0.889235 + 0.045072I
−1.85154 − 1.07596I 0
u = 0.395638 − 0.897674I
a = −0.966465 − 0.057775I
b = −0.889235 − 0.045072I
−1.85154 + 1.07596I 0
u = 0.073867 + 0.973400I
a = 0.201414 − 0.380588I
b = 1.09574 + 3.02407I
0.24162 + 2.29469I 0
u = 0.073867 − 0.973400I
a = 0.201414 + 0.380588I
b = 1.09574 − 3.02407I
0.24162 − 2.29469I 0
u = 0.073294 + 0.968958I
a = −0.480856 − 0.007306I
b = −1.96092 + 1.07676I
−0.04172 − 1.45400I 0
u = 0.073294 − 0.968958I
a = −0.480856 + 0.007306I
b = −1.96092 − 1.07676I
−0.04172 + 1.45400I 0
u = −0.038949 + 1.035690I
a = 0.343018 − 0.118947I
b = 2.59996 + 1.95864I
−0.35467 − 2.14659I 0
u = −0.038949 − 1.035690I
a = 0.343018 + 0.118947I
b = 2.59996 − 1.95864I
−0.35467 + 2.14659I 0
u = 0.955388 + 0.102547I
a = 0.855043 − 0.861822I
b = 0.405184 − 1.151540I
−7.65072 + 3.83591I 0
u = 0.955388 − 0.102547I
a = 0.855043 + 0.861822I
b = 0.405184 + 1.151540I
−7.65072 − 3.83591I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.834509 + 0.426099I
a = −0.262631 + 0.915377I
b = −0.240202 + 0.346289I
−2.67980 + 3.03789I 0
u = 0.834509 − 0.426099I
a = −0.262631 − 0.915377I
b = −0.240202 − 0.346289I
−2.67980 − 3.03789I 0
u = 0.050002 + 1.064780I
a = 0.65309 + 1.56196I
b = 0.03049 − 1.42468I
3.12667 − 3.60717I 0
u = 0.050002 − 1.064780I
a = 0.65309 − 1.56196I
b = 0.03049 + 1.42468I
3.12667 + 3.60717I 0
u = 0.055190 + 1.073230I
a = −1.52665 + 1.47024I
b = −0.213176 − 1.345590I
4.81705 − 2.76241I 0
u = 0.055190 − 1.073230I
a = −1.52665 − 1.47024I
b = −0.213176 + 1.345590I
4.81705 + 2.76241I 0
u = −0.889235 + 0.045072I
a = 0.439046 + 0.972185I
b = 0.395638 + 0.897674I
−1.85154 − 1.07596I 0
u = −0.889235 − 0.045072I
a = 0.439046 − 0.972185I
b = 0.395638 − 0.897674I
−1.85154 + 1.07596I 0
u = 0.647480 + 0.909082I
a = 0.024179 + 0.846346I
b = −0.199072 − 0.252945I
−2.15599 − 3.18535I 0
u = 0.647480 − 0.909082I
a = 0.024179 − 0.846346I
b = −0.199072 + 0.252945I
−2.15599 + 3.18535I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.178775 + 0.837971I
a = −0.319898 + 0.723642I
b = −0.592632 − 0.388560I
−0.386166 − 0.237422I 0
u = −0.178775 − 0.837971I
a = −0.319898 − 0.723642I
b = −0.592632 + 0.388560I
−0.386166 + 0.237422I 0
u = −0.328506 + 1.104140I
a = −0.095113 + 0.833518I
b = 0.015522 − 0.689347I
−0.747511 − 0.306015I 0
u = −0.328506 − 1.104140I
a = −0.095113 − 0.833518I
b = 0.015522 + 0.689347I
−0.747511 + 0.306015I 0
u = −0.100279 + 0.833670I
a = 2.36321 − 0.00085I
b = 0.447405 − 1.151160I
−0.63675 + 7.68993I 0
u = −0.100279 − 0.833670I
a = 2.36321 + 0.00085I
b = 0.447405 + 1.151160I
−0.63675 − 7.68993I 0
u = −1.153470 + 0.179310I
a = −0.747986 + 0.443896I
b = −0.486604 + 1.201200I
−1.78617 + 6.93892I 0
u = −1.153470 − 0.179310I
a = −0.747986 − 0.443896I
b = −0.486604 − 1.201200I
−1.78617 − 6.93892I 0
u = −0.701991 + 0.444562I
a = 1.17696 − 0.84810I
b = 0.516282 − 1.154410I
−0.31349 + 8.13644I 0
u = −0.701991 − 0.444562I
a = 1.17696 + 0.84810I
b = 0.516282 + 1.154410I
−0.31349 − 8.13644I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.024127 + 1.204100I
a = 0.686741 + 0.070014I
b = 0.304156 + 0.429506I
3.28142 + 1.60364I 0
u = −0.024127 − 1.204100I
a = 0.686741 − 0.070014I
b = 0.304156 − 0.429506I
3.28142 − 1.60364I 0
u = 0.405184 + 1.151540I
a = 0.814636 − 0.499504I
b = 0.955388 − 0.102547I
−7.65072 − 3.83591I 0
u = 0.405184 − 1.151540I
a = 0.814636 + 0.499504I
b = 0.955388 + 0.102547I
−7.65072 + 3.83591I 0
u = −0.383405 + 1.159460I
a = 0.861897 − 0.051187I
b = 0.508261 − 0.130931I
2.08931 + 3.53746I 0
u = −0.383405 − 1.159460I
a = 0.861897 + 0.051187I
b = 0.508261 + 0.130931I
2.08931 − 3.53746I 0
u = 0.447405 + 1.151160I
a = −1.55621 − 0.39958I
b = −0.100279 − 0.833670I
−0.63675 − 7.68993I 0
u = 0.447405 − 1.151160I
a = −1.55621 + 0.39958I
b = −0.100279 + 0.833670I
−0.63675 + 7.68993I 0
u = −0.333877 + 1.193500I
a = −0.578142 + 0.203628I
b = −0.095833 + 0.719086I
2.00913 + 3.28257I 0
u = −0.333877 − 1.193500I
a = −0.578142 − 0.203628I
b = −0.095833 − 0.719086I
2.00913 − 3.28257I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.516282 + 1.154410I
a = −0.952479 − 0.036873I
b = −0.701991 − 0.444562I
−0.31349 − 8.13644I 0
u = 0.516282 − 1.154410I
a = −0.952479 + 0.036873I
b = −0.701991 + 0.444562I
−0.31349 + 8.13644I 0
u = −0.095833 + 0.719086I
a = −1.026620 + 0.206353I
b = −0.333877 + 1.193500I
2.00913 + 3.28257I −12.00000 + 0.I
u = −0.095833 − 0.719086I
a = −1.026620 − 0.206353I
b = −0.333877 − 1.193500I
2.00913 − 3.28257I −12.00000 + 0.I
u = 0.510456 + 1.178910I
a = 0.717263 − 0.320490I
b = 1.301060 + 0.116336I
−4.09684 − 12.57490I 0
u = 0.510456 − 1.178910I
a = 0.717263 + 0.320490I
b = 1.301060 − 0.116336I
−4.09684 + 12.57490I 0
u = −0.592632 + 0.388560I
a = 0.955615 − 0.044076I
b = −0.178775 − 0.837971I
−0.386166 + 0.237422I −12.00000 + 0.I
u = −0.592632 − 0.388560I
a = 0.955615 + 0.044076I
b = −0.178775 + 0.837971I
−0.386166 − 0.237422I −12.00000 + 0.I
u = −0.486604 + 1.201200I
a = −0.688975 − 0.372898I
b = −1.153470 + 0.179310I
−1.78617 + 6.93892I 0
u = −0.486604 − 1.201200I
a = −0.688975 + 0.372898I
b = −1.153470 − 0.179310I
−1.78617 − 6.93892I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.301060 + 0.116336I
a = 0.613773 + 0.469300I
b = 0.510456 + 1.178910I
−4.09684 − 12.57490I 0
u = 1.301060 − 0.116336I
a = 0.613773 − 0.469300I
b = 0.510456 − 1.178910I
−4.09684 + 12.57490I 0
u = 0.015522 + 0.689347I
a = 0.520249 + 1.301450I
b = −0.328506 − 1.104140I
−0.747511 + 0.306015I −12.00000 + 0.I
u = 0.015522 − 0.689347I
a = 0.520249 − 1.301450I
b = −0.328506 + 1.104140I
−0.747511 − 0.306015I −12.00000 + 0.I
u = 0.285680 + 1.286210I
a = −1.097630 + 0.495754I
b = −0.56605 − 1.46741I
6.43432 − 6.56301I 0
u = 0.285680 − 1.286210I
a = −1.097630 − 0.495754I
b = −0.56605 + 1.46741I
6.43432 + 6.56301I 0
u = −0.213176 + 1.345590I
a = 1.31992 + 1.02616I
b = 0.055190 − 1.073230I
4.81705 + 2.76241I 0
u = −0.213176 − 1.345590I
a = 1.31992 − 1.02616I
b = 0.055190 + 1.073230I
4.81705 − 2.76241I 0
u = −0.491215 + 1.284550I
a = 1.058670 + 0.203604I
b = 0.680102 − 1.206280I
1.92815 + 6.09693I 0
u = −0.491215 − 1.284550I
a = 1.058670 − 0.203604I
b = 0.680102 + 1.206280I
1.92815 − 6.09693I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680102 + 1.206280I
a = −1.069720 + 0.044812I
b = −0.491215 − 1.284550I
1.92815 − 6.09693I 0
u = 0.680102 − 1.206280I
a = −1.069720 − 0.044812I
b = −0.491215 + 1.284550I
1.92815 + 6.09693I 0
u = −0.328429 + 1.350810I
a = 1.008230 + 0.432064I
b = 0.66120 − 1.48553I
4.98438 + 11.81130I 0
u = −0.328429 − 1.350810I
a = 1.008230 − 0.432064I
b = 0.66120 + 1.48553I
4.98438 − 11.81130I 0
u = 0.03049 + 1.42468I
a = −0.567160 + 1.132320I
b = 0.050002 − 1.064780I
3.12667 + 3.60717I 0
u = 0.03049 − 1.42468I
a = −0.567160 − 1.132320I
b = 0.050002 + 1.064780I
3.12667 − 3.60717I 0
u = −0.326282 + 0.449657I
a = −1.29823 − 1.02321I
b = −0.31384 + 1.56248I
0.36905 + 2.88717I −18.5219 − 5.6422I
u = −0.326282 − 0.449657I
a = −1.29823 + 1.02321I
b = −0.31384 − 1.56248I
0.36905 − 2.88717I −18.5219 + 5.6422I
u = 0.304156 + 0.429506I
a = 1.16885 + 1.06258I
b = −0.024127 + 1.204100I
3.28142 + 1.60364I −4.45910 − 2.86227I
u = 0.304156 − 0.429506I
a = 1.16885 − 1.06258I
b = −0.024127 − 1.204100I
3.28142 − 1.60364I −4.45910 + 2.86227I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.508261 + 0.130931I
a = −0.98451 − 1.75118I
b = −0.383405 − 1.159460I
2.08931 − 3.53746I −7.63620 + 3.64913I
u = 0.508261 − 0.130931I
a = −0.98451 + 1.75118I
b = −0.383405 + 1.159460I
2.08931 + 3.53746I −7.63620 − 3.64913I
u = −0.56605 + 1.46741I
a = 0.971128 + 0.273618I
b = 0.285680 − 1.286210I
6.43432 + 6.56301I 0
u = −0.56605 − 1.46741I
a = 0.971128 − 0.273618I
b = 0.285680 + 1.286210I
6.43432 − 6.56301I 0
u = −0.240202 + 0.346289I
a = 2.09505 + 0.30603I
b = 0.834509 + 0.426099I
−2.67980 + 3.03789I −17.8249 − 5.9672I
u = −0.240202 − 0.346289I
a = 2.09505 − 0.30603I
b = 0.834509 − 0.426099I
−2.67980 − 3.03789I −17.8249 + 5.9672I
u = −0.31384 + 1.56248I
a = −0.262929 − 0.512752I
b = −0.326282 + 0.449657I
0.36905 + 2.88717I 0
u = −0.31384 − 1.56248I
a = −0.262929 + 0.512752I
b = −0.326282 − 0.449657I
0.36905 − 2.88717I 0
u = 0.66120 + 1.48553I
a = −0.914234 + 0.208865I
b = −0.328429 − 1.350810I
4.98438 − 11.81130I 0
u = 0.66120 − 1.48553I
a = −0.914234 − 0.208865I
b = −0.328429 + 1.350810I
4.98438 + 11.81130I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.199072 + 0.252945I
a = 0.05673 + 2.93523I
b = 0.647480 − 0.909082I
−2.15599 + 3.18535I −16.4226 − 4.3884I
u = −0.199072 − 0.252945I
a = 0.05673 − 2.93523I
b = 0.647480 + 0.909082I
−2.15599 − 3.18535I −16.4226 + 4.3884I
u = −1.96092 + 1.07676I
a = −0.089326 + 0.188830I
b = 0.073294 + 0.968958I
−0.04172 − 1.45400I 0
u = −1.96092 − 1.07676I
a = −0.089326 − 0.188830I
b = 0.073294 − 0.968958I
−0.04172 + 1.45400I 0
u = 1.09574 + 3.02407I
a = 0.0899031 − 0.0948497I
b = 0.073867 + 0.973400I
0.24162 + 2.29469I 0
u = 1.09574 − 3.02407I
a = 0.0899031 + 0.0948497I
b = 0.073867 − 0.973400I
0.24162 − 2.29469I 0
u = 2.59996 + 1.95864I
a = 0.0934743 + 0.0680048I
b = −0.038949 + 1.035690I
−0.35467 − 2.14659I 0
u = 2.59996 − 1.95864I
a = 0.0934743 − 0.0680048I
b = −0.038949 − 1.035690I
−0.35467 + 2.14659I 0
19
III. I
u
3
= hb + u, −u
11
+ u
10
+ · · · + a + 7, u
14
− u
13
+ · · · − 4u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
u
11
− u
10
+ ··· + 16u − 7
−u
a
9
=
−4u
13
+ 4u
12
+ ··· − 24u + 11
u
13
− u
12
+ ··· − 7u
2
+ u
a
12
=
u
11
− u
10
+ ··· + 17u − 7
−u
a
1
=
−4u
13
+ 4u
12
+ ··· − 23u + 11
u
13
− 2u
12
+ ··· − 10u
2
+ u
a
3
=
u
12
− u
11
+ ··· − 7u + 1
−u
2
a
7
=
u
u
3
+ u
a
10
=
u
12
+ 5u
10
+ ··· + 15u − 7
−u
12
+ u
11
+ ··· + 2u + 1
a
6
=
u
13
− 2u
12
+ ··· + 31u − 10
u
12
− u
11
+ ··· + 7u
2
− 2u
a
2
=
−2u
13
+ 3u
12
+ ··· − 30u + 12
−u
12
+ u
11
+ ··· − 7u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −4u
13
−u
12
−28u
11
−7u
10
−82u
9
−27u
8
−130u
7
−53u
6
−119u
5
−45u
4
−66u
3
−5u
2
−23u+6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 6u
13
+ ··· − 13u + 1
c
2
u
14
+ 2u
13
+ ··· + 3u + 1
c
3
, c
7
u
14
+ u
13
+ ··· + 4u − 1
c
4
, c
11
u
14
− u
13
+ ··· − 4u − 1
c
5
u
14
− 2u
13
+ ··· − 3u + 1
c
6
, c
9
u
14
− u
13
+ ··· + 6u
2
− 1
c
8
u
14
− 9u
13
+ ··· + 15u − 1
c
10
, c
12
u
14
+ u
13
+ ··· + 6u
2
− 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
+ 10y
13
+ ··· − 21y + 1
c
2
, c
5
y
14
− 6y
13
+ ··· − 13y + 1
c
3
, c
4
, c
7
c
11
y
14
+ 15y
13
+ ··· − 40y + 1
c
6
, c
9
, c
10
c
12
y
14
− 13y
13
+ ··· − 12y + 1
c
8
y
14
− 5y
13
+ ··· − 29y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.494303 + 0.948206I
a = −0.338246 + 0.404754I
b = −0.494303 − 0.948206I
1.02409 − 2.16166I −11.75755 + 0.70501I
u = 0.494303 − 0.948206I
a = −0.338246 − 0.404754I
b = −0.494303 + 0.948206I
1.02409 + 2.16166I −11.75755 − 0.70501I
u = −0.403796 + 1.012310I
a = 1.96277 − 0.70590I
b = 0.403796 − 1.012310I
−0.83998 + 9.12624I −13.7432 − 11.8895I
u = −0.403796 − 1.012310I
a = 1.96277 + 0.70590I
b = 0.403796 + 1.012310I
−0.83998 − 9.12624I −13.7432 + 11.8895I
u = −0.385160 + 1.187760I
a = 0.204583 + 0.322059I
b = 0.385160 − 1.187760I
0.46872 − 2.66919I −10.42920 + 4.04963I
u = −0.385160 − 1.187760I
a = 0.204583 − 0.322059I
b = 0.385160 + 1.187760I
0.46872 + 2.66919I −10.42920 − 4.04963I
u = 0.141069 + 1.315050I
a = −1.06420 + 2.01626I
b = −0.141069 − 1.315050I
6.31414 − 4.36226I 1.13088 + 3.35215I
u = 0.141069 − 1.315050I
a = −1.06420 − 2.01626I
b = −0.141069 + 1.315050I
6.31414 + 4.36226I 1.13088 − 3.35215I
u = 0.569251 + 1.216470I
a = −1.045770 + 0.078978I
b = −0.569251 − 1.216470I
3.10148 − 6.42639I −6.16249 + 6.22632I
u = 0.569251 − 1.216470I
a = −1.045770 − 0.078978I
b = −0.569251 + 1.216470I
3.10148 + 6.42639I −6.16249 − 6.22632I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.080538 + 1.411260I
a = 0.032468 + 0.269326I
b = 0.080538 − 1.411260I
−0.61736 + 1.76932I −9.28138 − 4.00219I
u = −0.080538 − 1.411260I
a = 0.032468 − 0.269326I
b = 0.080538 + 1.411260I
−0.61736 − 1.76932I −9.28138 + 4.00219I
u = 0.484377
a = −1.32520
b = −0.484377
−1.88989 −21.1800
u = −0.154632
a = −10.1780
b = 0.154632
−10.4326 9.66530
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
− 6u
13
+ ··· − 13u + 1)(u
29
+ 11u
28
+ ··· + 4736u + 256)
· (u
44
+ 20u
43
+ ··· − 16u + 1)
2
c
2
(u
14
+ 2u
13
+ ··· + 3u + 1)(u
29
+ 11u
28
+ ··· + 192u + 16)
· (u
44
− 4u
43
+ ··· − 6u + 1)
2
c
3
, c
7
(u
14
+ u
13
+ ··· + 4u − 1)(u
29
− u
28
+ ··· + 2u + 1)
· (u
88
− 5u
87
+ ··· + 3584u + 821)
c
4
, c
11
(u
14
− u
13
+ ··· − 4u − 1)(u
29
− u
28
+ ··· + 2u + 1)
· (u
88
− 5u
87
+ ··· + 3584u + 821)
c
5
(u
14
− 2u
13
+ ··· − 3u + 1)(u
29
+ 11u
28
+ ··· + 192u + 16)
· (u
44
− 4u
43
+ ··· − 6u + 1)
2
c
6
, c
9
(u
14
− u
13
+ ··· + 6u
2
− 1)(u
29
− u
28
+ ··· + 4u + 1)
· (u
88
− 7u
87
+ ··· + 6072u + 2143)
c
8
(u
14
− 9u
13
+ ··· + 15u − 1)(u
29
− 28u
28
+ ··· − 6144u + 2048)
· (u
44
+ 13u
43
+ ··· + 2u + 1)
2
c
10
, c
12
(u
14
+ u
13
+ ··· + 6u
2
− 1)(u
29
− u
28
+ ··· + 4u + 1)
· (u
88
− 7u
87
+ ··· + 6072u + 2143)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
14
+ 10y
13
+ ··· − 21y + 1)(y
29
+ 13y
28
+ ··· + 9166848y − 65536)
· (y
44
+ 12y
43
+ ··· − 304y + 1)
2
c
2
, c
5
(y
14
− 6y
13
+ ··· − 13y + 1)(y
29
− 11y
28
+ ··· + 4736y − 256)
· (y
44
− 20y
43
+ ··· + 16y + 1)
2
c
3
, c
4
, c
7
c
11
(y
14
+ 15y
13
+ ··· − 40y + 1)(y
29
+ 23y
28
+ ··· + 20y − 1)
· (y
88
+ 63y
87
+ ··· + 24336392y + 674041)
c
6
, c
9
, c
10
c
12
(y
14
− 13y
13
+ ··· − 12y + 1)(y
29
− 21y
28
+ ··· + 16y − 1)
· (y
88
− 53y
87
+ ··· − 51150136y + 4592449)
c
8
(y
14
− 5y
13
+ ··· − 29y + 1)
· (y
29
− 4y
28
+ ··· − 31457280y − 4194304)
· (y
44
+ 11y
43
+ ··· + 18y + 1)
2
26
