12a
0449
(K12a
0449
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 8 2 11 5 1 12 7 4
Solving Sequence
2,7
6 3
1,12
11 8 5 10 4 9
c
6
c
2
c
1
c
11
c
7
c
5
c
10
c
3
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 99197u
26
+ 483399u
25
+ ··· + 631375a − 1029892, u
27
+ u
26
+ ··· + 3u + 1i
I
u
2
= h5.33925 × 10
205
u
93
+ 1.44539 × 10
206
u
92
+ ··· + 6.46446 × 10
207
b − 5.33518 × 10
207
,
1.10034 × 10
207
u
93
− 1.28414 × 10
208
u
92
+ ··· + 1.48683 × 10
209
a − 1.01915 × 10
210
,
u
94
− 2u
93
+ ··· + 239u + 23i
I
u
3
= hb + u, 3u
12
+ 2u
11
+ 10u
10
+ 5u
9
+ 21u
8
+ 9u
7
+ 26u
6
+ 8u
5
+ 23u
4
+ 2u
3
+ 13u
2
+ a − 4u + 5,
u
14
+ u
13
+ 4u
12
+ 3u
11
+ 9u
10
+ 6u
9
+ 13u
8
+ 7u
7
+ 13u
6
+ 5u
5
+ 9u
4
+ u
3
+ 4u
2
+ 1i
I
u
4
= h−u
13
− u
12
− 4u
11
− 3u
10
− 9u
9
− 5u
8
− 13u
7
− 5u
6
− 13u
5
− 5u
4
− 9u
3
− 3u
2
+ b − 4u − 1,
3u
12
+ 2u
11
+ 10u
10
+ 5u
9
+ 21u
8
+ 6u
7
+ 27u
6
+ 3u
5
+ 24u
4
+ 4u
3
+ 12u
2
+ a + 2u + 4,
u
14
+ u
13
+ 4u
12
+ 3u
11
+ 9u
10
+ 5u
9
+ 13u
8
+ 5u
7
+ 13u
6
+ 5u
5
+ 9u
4
+ 3u
3
+ 4u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 149 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, 9.92 × 10
4
u
26
+ 4.83 × 10
5
u
25
+ · · · + 6.31 × 10
5
a − 1.03 ×
10
6
, u
27
+ u
26
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−0.157113u
26
− 0.765629u
25
+ ··· + 2.13457u + 1.63119
u
a
11
=
−0.157113u
26
− 0.765629u
25
+ ··· + 1.13457u + 1.63119
u
a
8
=
0.608516u
26
+ 0.435136u
25
+ ··· − 2.10253u + 0.842887
−u
2
a
5
=
−0.598842u
26
− 1.17770u
25
+ ··· − 1.70722u + 0.923554
−0.0912247u
26
− 0.115144u
25
+ ··· − 0.178083u + 0.112520
a
10
=
0.0162677u
26
− 0.0766074u
25
+ ··· + 3.11723u + 2.23971
u
3
+ u
a
4
=
0.0478115u
26
+ 0.779812u
25
+ ··· − 2.00245u − 1.72486
−0.0331435u
26
− 0.163559u
25
+ ··· − 0.490035u − 0.496162
a
9
=
0.128060u
26
− 0.212444u
25
+ ··· + 2.62579u + 2.11032
0.317876u
26
+ 0.232204u
25
+ ··· + 0.983732u + 0.0465033
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1220986
631375
u
26
+
62912
631375
u
25
+ ··· −
2949469
631375
u +
2743229
631375
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
27
+ 11u
26
+ ··· − u − 1
c
2
, c
6
, c
7
c
11
u
27
− u
26
+ ··· + 3u − 1
c
3
u
27
− 24u
26
+ ··· + 12672u − 1280
c
4
, c
5
, c
8
u
27
− 12u
26
+ ··· + 400u − 32
c
9
, c
12
u
27
− 6u
25
+ ··· − 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
27
+ 19y
26
+ ··· + 59y −1
c
2
, c
6
, c
7
c
11
y
27
+ 11y
26
+ ··· − y −1
c
3
y
27
− 6y
26
+ ··· − 8994816y −1638400
c
4
, c
5
, c
8
y
27
+ 24y
26
+ ··· + 9984y −1024
c
9
, c
12
y
27
− 12y
26
+ ··· + 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.746155 + 0.657899I
a = 1.92597 + 0.33252I
b = 0.746155 + 0.657899I
4.39292 − 2.39590I 7.41009 + 1.19808I
u = 0.746155 − 0.657899I
a = 1.92597 − 0.33252I
b = 0.746155 − 0.657899I
4.39292 + 2.39590I 7.41009 − 1.19808I
u = −0.281755 + 1.039740I
a = −0.45630 − 1.46633I
b = −0.281755 + 1.039740I
−3.52982 − 3.73575I −3.49881 + 4.98534I
u = −0.281755 − 1.039740I
a = −0.45630 + 1.46633I
b = −0.281755 − 1.039740I
−3.52982 + 3.73575I −3.49881 − 4.98534I
u = −0.650521 + 0.866897I
a = −2.64625 − 0.54807I
b = −0.650521 + 0.866897I
2.46186 − 3.31082I 6.75297 + 3.07336I
u = −0.650521 − 0.866897I
a = −2.64625 + 0.54807I
b = −0.650521 − 0.866897I
2.46186 + 3.31082I 6.75297 − 3.07336I
u = −0.094739 + 1.096350I
a = −1.28622 − 0.62434I
b = −0.094739 + 1.096350I
−0.64427 + 3.17091I −2.11058 − 2.29373I
u = −0.094739 − 1.096350I
a = −1.28622 + 0.62434I
b = −0.094739 − 1.096350I
−0.64427 − 3.17091I −2.11058 + 2.29373I
u = 0.176859 + 1.086480I
a = 0.839851 − 1.074650I
b = 0.176859 + 1.086480I
−5.61395 + 0.05445I −6.98172 + 0.86750I
u = 0.176859 − 1.086480I
a = 0.839851 + 1.074650I
b = 0.176859 − 1.086480I
−5.61395 − 0.05445I −6.98172 − 0.86750I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805946 + 0.753226I
a = 1.237390 + 0.449968I
b = 0.805946 + 0.753226I
10.51250 + 2.25745I 10.71549 − 2.75707I
u = 0.805946 − 0.753226I
a = 1.237390 − 0.449968I
b = 0.805946 − 0.753226I
10.51250 − 2.25745I 10.71549 + 2.75707I
u = −0.704061 + 0.941806I
a = −2.17634 + 0.20089I
b = −0.704061 + 0.941806I
1.99788 − 7.27498I 5.83290 + 8.99704I
u = −0.704061 − 0.941806I
a = −2.17634 − 0.20089I
b = −0.704061 − 0.941806I
1.99788 + 7.27498I 5.83290 − 8.99704I
u = −0.975439 + 0.658242I
a = −1.44476 + 0.02800I
b = −0.975439 + 0.658242I
12.41630 + 5.47236I 8.85634 − 1.56087I
u = −0.975439 − 0.658242I
a = −1.44476 − 0.02800I
b = −0.975439 − 0.658242I
12.41630 − 5.47236I 8.85634 + 1.56087I
u = 0.669337 + 1.009460I
a = 1.97958 − 1.21132I
b = 0.669337 + 1.009460I
8.79484 + 8.98450I 7.89641 − 7.55009I
u = 0.669337 − 1.009460I
a = 1.97958 + 1.21132I
b = 0.669337 − 1.009460I
8.79484 − 8.98450I 7.89641 + 7.55009I
u = 0.716486 + 1.064120I
a = 2.08136 − 0.43119I
b = 0.716486 + 1.064120I
2.01310 + 13.75430I 3.02468 − 10.55140I
u = 0.716486 − 1.064120I
a = 2.08136 + 0.43119I
b = 0.716486 − 1.064120I
2.01310 − 13.75430I 3.02468 + 10.55140I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.761514 + 1.146540I
a = −1.79916 − 0.64270I
b = −0.761514 + 1.146540I
9.2811 − 18.3561I 5.22196 + 9.69605I
u = −0.761514 − 1.146540I
a = −1.79916 + 0.64270I
b = −0.761514 − 1.146540I
9.2811 + 18.3561I 5.22196 − 9.69605I
u = 0.350509 + 0.506121I
a = 1.84663 + 2.87006I
b = 0.350509 + 0.506121I
4.17741 − 1.74336I 11.21417 − 1.14123I
u = 0.350509 − 0.506121I
a = 1.84663 − 2.87006I
b = 0.350509 − 0.506121I
4.17741 + 1.74336I 11.21417 + 1.14123I
u = −0.331730 + 0.517465I
a = 0.148186 + 0.163864I
b = −0.331730 + 0.517465I
0.056692 − 1.398250I 0.03091 + 4.28330I
u = −0.331730 − 0.517465I
a = 0.148186 − 0.163864I
b = −0.331730 − 0.517465I
0.056692 + 1.398250I 0.03091 − 4.28330I
u = −0.331066
a = 1.50011
b = −0.331066
1.12812 9.27040
7
II. I
u
2
= h5.34 × 10
205
u
93
+ 1.45 × 10
206
u
92
+ · · · + 6.46 × 10
207
b − 5.34 ×
10
207
, 1.10 × 10
207
u
93
− 1.28 × 10
208
u
92
+ · · · + 1.49 × 10
209
a − 1.02 ×
10
210
, u
94
− 2u
93
+ · · · + 239u + 23i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−0.00740061u
93
+ 0.0863680u
92
+ ··· + 51.8143u + 6.85450
−0.00825939u
93
− 0.0223590u
92
+ ··· − 1.25417u + 0.825308
a
11
=
0.000858782u
93
+ 0.108727u
92
+ ··· + 53.0685u + 6.02919
−0.00825939u
93
− 0.0223590u
92
+ ··· − 1.25417u + 0.825308
a
8
=
0.0508490u
93
− 0.0534431u
92
+ ··· + 3.09848u + 2.28219
−0.115309u
93
+ 0.236786u
92
+ ··· − 54.3135u − 5.24937
a
5
=
0.0291642u
93
+ 0.00380409u
92
+ ··· + 75.2003u + 11.8564
0.00448644u
93
− 0.00426952u
92
+ ··· + 14.9451u + 4.37624
a
10
=
0.199981u
93
− 0.398793u
92
+ ··· + 106.883u + 6.60078
0.0168638u
93
− 0.0892040u
92
+ ··· + 24.7190u + 1.75162
a
4
=
0.106433u
93
− 0.368537u
92
+ ··· + 31.8088u + 5.86817
−0.00383274u
93
+ 0.0445719u
92
+ ··· + 36.1222u + 5.61793
a
9
=
0.223235u
93
− 0.439512u
92
+ ··· + 110.354u + 6.95047
0.0181517u
93
− 0.0920539u
92
+ ··· + 26.5820u + 2.27200
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.344624u
93
+ 0.673277u
92
+ ··· − 238.262u − 24.6289
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
94
+ 34u
93
+ ··· + 8843u + 529
c
2
, c
6
, c
7
c
11
u
94
+ 2u
93
+ ··· − 239u + 23
c
3
(u
47
+ 12u
46
+ ··· − 6u − 1)
2
c
4
, c
5
, c
8
(u
47
+ 5u
46
+ ··· − 12u − 1)
2
c
9
, c
12
u
94
+ 9u
93
+ ··· − 745u + 137
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
94
+ 58y
93
+ ··· + 285816831y + 279841
c
2
, c
6
, c
7
c
11
y
94
+ 34y
93
+ ··· + 8843y + 529
c
3
(y
47
− 10y
46
+ ··· + 28y −1)
2
c
4
, c
5
, c
8
(y
47
+ 53y
46
+ ··· + 26y −1)
2
c
9
, c
12
y
94
− 25y
93
+ ··· + 3079859y + 18769
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637130 + 0.773918I
a = −0.692183 + 0.906681I
b = −0.760455 + 0.971795I
1.71266 − 1.57547I 0
u = 0.637130 − 0.773918I
a = −0.692183 − 0.906681I
b = −0.760455 − 0.971795I
1.71266 + 1.57547I 0
u = 0.092155 + 1.007520I
a = −0.49162 + 1.65142I
b = 0.637573 − 0.672241I
5.05720 − 3.14968I 0
u = 0.092155 − 1.007520I
a = −0.49162 − 1.65142I
b = 0.637573 + 0.672241I
5.05720 + 3.14968I 0
u = −0.124119 + 1.007900I
a = 0.499089 − 0.182116I
b = 0.594156 + 0.283061I
−1.52181 − 2.26811I 0
u = −0.124119 − 1.007900I
a = 0.499089 + 0.182116I
b = 0.594156 − 0.283061I
−1.52181 + 2.26811I 0
u = −0.913986 + 0.442783I
a = 1.255230 + 0.495106I
b = 0.634884 + 0.752287I
3.25089 + 0.51509I 0
u = −0.913986 − 0.442783I
a = 1.255230 − 0.495106I
b = 0.634884 − 0.752287I
3.25089 − 0.51509I 0
u = 0.634884 + 0.752287I
a = −0.815127 + 1.128530I
b = −0.913986 + 0.442783I
3.25089 + 0.51509I 0
u = 0.634884 − 0.752287I
a = −0.815127 − 1.128530I
b = −0.913986 − 0.442783I
3.25089 − 0.51509I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.723959 + 0.666548I
a = 1.298590 − 0.190158I
b = 0.760168 − 0.979589I
9.83692 − 3.62268I 0
u = 0.723959 − 0.666548I
a = 1.298590 + 0.190158I
b = 0.760168 + 0.979589I
9.83692 + 3.62268I 0
u = −0.661153 + 0.706858I
a = −0.703442 − 0.143437I
b = 0.290317 + 1.381150I
3.62334 + 3.92202I 0
u = −0.661153 − 0.706858I
a = −0.703442 + 0.143437I
b = 0.290317 − 1.381150I
3.62334 − 3.92202I 0
u = −0.833196 + 0.631650I
a = 1.71669 − 0.33754I
b = 0.606964 − 0.943477I
2.65918 − 4.37576I 0
u = −0.833196 − 0.631650I
a = 1.71669 + 0.33754I
b = 0.606964 + 0.943477I
2.65918 + 4.37576I 0
u = 0.863354 + 0.611884I
a = 1.23416 − 0.84596I
b = 0.689830 − 1.000820I
3.38496 − 7.87636I 0
u = 0.863354 − 0.611884I
a = 1.23416 + 0.84596I
b = 0.689830 + 1.000820I
3.38496 + 7.87636I 0
u = −0.708371 + 0.795453I
a = 1.42928 + 0.38031I
b = 1.257070 − 0.568916I
10.20390 − 4.26315I 0
u = −0.708371 − 0.795453I
a = 1.42928 − 0.38031I
b = 1.257070 + 0.568916I
10.20390 + 4.26315I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637573 + 0.672241I
a = −1.00073 + 1.59333I
b = 0.092155 − 1.007520I
5.05720 + 3.14968I 0
u = 0.637573 − 0.672241I
a = −1.00073 − 1.59333I
b = 0.092155 + 1.007520I
5.05720 − 3.14968I 0
u = −0.740716 + 0.781651I
a = −0.83398 − 1.50097I
b = −0.654991 − 0.856676I
2.49440 + 1.76606I 0
u = −0.740716 − 0.781651I
a = −0.83398 + 1.50097I
b = −0.654991 + 0.856676I
2.49440 − 1.76606I 0
u = −0.654991 + 0.856676I
a = −1.34755 − 1.06032I
b = −0.740716 − 0.781651I
2.49440 − 1.76606I 0
u = −0.654991 − 0.856676I
a = −1.34755 + 1.06032I
b = −0.740716 + 0.781651I
2.49440 + 1.76606I 0
u = 0.401950 + 1.013810I
a = −1.55687 − 0.58870I
b = −0.336611 − 0.321294I
2.42935 + 4.96654I 0
u = 0.401950 − 1.013810I
a = −1.55687 + 0.58870I
b = −0.336611 + 0.321294I
2.42935 − 4.96654I 0
u = −0.121472 + 1.096320I
a = −0.546521 − 0.666812I
b = 0.658126 + 1.028670I
3.91970 + 1.95304I 0
u = −0.121472 − 1.096320I
a = −0.546521 + 0.666812I
b = 0.658126 − 1.028670I
3.91970 − 1.95304I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.639818 + 0.916187I
a = −2.06817 + 0.47862I
b = −0.731944 − 1.122850I
1.27653 + 6.58003I 0
u = 0.639818 − 0.916187I
a = −2.06817 − 0.47862I
b = −0.731944 + 1.122850I
1.27653 − 6.58003I 0
u = 0.606964 + 0.943477I
a = −1.61070 + 0.25384I
b = −0.833196 − 0.631650I
2.65918 + 4.37576I 0
u = 0.606964 − 0.943477I
a = −1.61070 − 0.25384I
b = −0.833196 + 0.631650I
2.65918 − 4.37576I 0
u = −0.643901 + 0.586372I
a = 0.852454 + 0.957705I
b = 0.95595 + 1.14190I
8.47453 + 3.44023I 12.7382 − 7.0609I
u = −0.643901 − 0.586372I
a = 0.852454 − 0.957705I
b = 0.95595 − 1.14190I
8.47453 − 3.44023I 12.7382 + 7.0609I
u = −0.055476 + 0.853945I
a = −1.08079 + 1.19882I
b = −0.527392 − 1.090030I
−2.02252 + 3.14008I 0. − 3.52874I
u = −0.055476 − 0.853945I
a = −1.08079 − 1.19882I
b = −0.527392 + 1.090030I
−2.02252 − 3.14008I 0. + 3.52874I
u = −0.702751 + 0.916973I
a = 0.575915 + 1.023560I
b = 1.230430 + 0.381871I
9.83536 − 1.14605I 0
u = −0.702751 − 0.916973I
a = 0.575915 − 1.023560I
b = 1.230430 − 0.381871I
9.83536 + 1.14605I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.536160 + 1.037800I
a = −1.016650 + 0.539628I
b = −0.102572 − 1.209430I
−3.44884 + 6.63369I 0
u = 0.536160 − 1.037800I
a = −1.016650 − 0.539628I
b = −0.102572 + 1.209430I
−3.44884 − 6.63369I 0
u = −0.650394 + 0.982206I
a = 1.003430 + 0.482649I
b = 0.15574 − 1.44448I
2.76733 − 9.04904I 0
u = −0.650394 − 0.982206I
a = 1.003430 − 0.482649I
b = 0.15574 + 1.44448I
2.76733 + 9.04904I 0
u = −1.037900 + 0.579454I
a = −1.034890 − 0.503132I
b = −0.773853 − 1.086360I
11.0683 + 11.8523I 0
u = −1.037900 − 0.579454I
a = −1.034890 + 0.503132I
b = −0.773853 + 1.086360I
11.0683 − 11.8523I 0
u = −0.410289 + 1.124300I
a = 0.275918 − 0.697933I
b = 0.213348 + 0.722040I
−1.44718 − 2.78873I 0
u = −0.410289 − 1.124300I
a = 0.275918 + 0.697933I
b = 0.213348 − 0.722040I
−1.44718 + 2.78873I 0
u = −0.280101 + 0.745156I
a = 0.84833 + 2.25683I
b = −0.280101 − 0.745156I
0.218771 − 60.511321 + 0.10I
u = −0.280101 − 0.745156I
a = 0.84833 − 2.25683I
b = −0.280101 + 0.745156I
0.218771 − 60.511321 + 0.10I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.630527 + 1.028320I
a = 1.86730 + 0.83890I
b = 0.85518 − 1.27123I
7.16483 − 8.49251I 0
u = −0.630527 − 1.028320I
a = 1.86730 − 0.83890I
b = 0.85518 + 1.27123I
7.16483 + 8.49251I 0
u = −0.527392 + 1.090030I
a = 1.082180 + 0.360575I
b = −0.055476 − 0.853945I
−2.02252 − 3.14008I 0
u = −0.527392 − 1.090030I
a = 1.082180 − 0.360575I
b = −0.055476 + 0.853945I
−2.02252 + 3.14008I 0
u = −0.102572 + 1.209430I
a = 0.705573 + 0.853909I
b = 0.536160 − 1.037800I
−3.44884 − 6.63369I 0
u = −0.102572 − 1.209430I
a = 0.705573 − 0.853909I
b = 0.536160 + 1.037800I
−3.44884 + 6.63369I 0
u = 0.689830 + 1.000820I
a = 0.722351 − 1.083950I
b = 0.863354 − 0.611884I
3.38496 + 7.87636I 0
u = 0.689830 − 1.000820I
a = 0.722351 + 1.083950I
b = 0.863354 + 0.611884I
3.38496 − 7.87636I 0
u = 0.658126 + 1.028670I
a = −0.005505 − 0.778723I
b = −0.121472 + 1.096320I
3.91970 + 1.95304I 0
u = 0.658126 − 1.028670I
a = −0.005505 + 0.778723I
b = −0.121472 − 1.096320I
3.91970 − 1.95304I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.760455 + 0.971795I
a = 0.597484 + 0.708327I
b = 0.637130 + 0.773918I
1.71266 − 1.57547I 0
u = −0.760455 − 0.971795I
a = 0.597484 − 0.708327I
b = 0.637130 − 0.773918I
1.71266 + 1.57547I 0
u = 0.760168 + 0.979589I
a = 0.063713 − 1.039660I
b = 0.723959 − 0.666548I
9.83692 + 3.62268I 0
u = 0.760168 − 0.979589I
a = 0.063713 + 1.039660I
b = 0.723959 + 0.666548I
9.83692 − 3.62268I 0
u = 0.213348 + 0.722040I
a = 1.012610 − 0.630769I
b = −0.410289 + 1.124300I
−1.44718 − 2.78873I −3.18438 + 7.54014I
u = 0.213348 − 0.722040I
a = 1.012610 + 0.630769I
b = −0.410289 − 1.124300I
−1.44718 + 2.78873I −3.18438 − 7.54014I
u = −0.241250 + 0.704750I
a = −0.066138 + 0.253712I
b = −0.548096 + 0.386698I
0.014771 − 1.382010I 0.64027 + 2.61668I
u = −0.241250 − 0.704750I
a = −0.066138 − 0.253712I
b = −0.548096 − 0.386698I
0.014771 + 1.382010I 0.64027 − 2.61668I
u = 1.230430 + 0.381871I
a = −1.039810 + 0.167311I
b = −0.702751 + 0.916973I
9.83536 − 1.14605I 0
u = 1.230430 − 0.381871I
a = −1.039810 − 0.167311I
b = −0.702751 − 0.916973I
9.83536 + 1.14605I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.915093 + 0.919317I
a = −0.408139 + 0.257916I
b = −0.157827 + 0.143099I
7.98321 + 3.33848I 0
u = 0.915093 − 0.919317I
a = −0.408139 − 0.257916I
b = −0.157827 − 0.143099I
7.98321 − 3.33848I 0
u = −0.548096 + 0.386698I
a = 0.105708 + 0.271296I
b = −0.241250 + 0.704750I
0.014771 − 1.382010I 0.64027 + 2.61668I
u = −0.548096 − 0.386698I
a = 0.105708 − 0.271296I
b = −0.241250 − 0.704750I
0.014771 + 1.382010I 0.64027 − 2.61668I
u = −0.773853 + 1.086360I
a = −0.546735 − 0.867636I
b = −1.037900 − 0.579454I
11.0683 − 11.8523I 0
u = −0.773853 − 1.086360I
a = −0.546735 + 0.867636I
b = −1.037900 + 0.579454I
11.0683 + 11.8523I 0
u = −0.731944 + 1.122850I
a = 1.71067 + 0.45389I
b = 0.639818 − 0.916187I
1.27653 − 6.58003I 0
u = −0.731944 − 1.122850I
a = 1.71067 − 0.45389I
b = 0.639818 + 0.916187I
1.27653 + 6.58003I 0
u = 0.594156 + 0.283061I
a = 0.510319 + 0.641559I
b = −0.124119 + 1.007900I
−1.52181 − 2.26811I −0.48315 + 4.62195I
u = 0.594156 − 0.283061I
a = 0.510319 − 0.641559I
b = −0.124119 − 1.007900I
−1.52181 + 2.26811I −0.48315 − 4.62195I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.257070 + 0.568916I
a = −1.127470 − 0.179853I
b = −0.708371 − 0.795453I
10.20390 + 4.26315I 0
u = 1.257070 − 0.568916I
a = −1.127470 + 0.179853I
b = −0.708371 + 0.795453I
10.20390 − 4.26315I 0
u = 0.290317 + 1.381150I
a = −0.196459 − 0.451442I
b = −0.661153 + 0.706858I
3.62334 + 3.92202I 0
u = 0.290317 − 1.381150I
a = −0.196459 + 0.451442I
b = −0.661153 − 0.706858I
3.62334 − 3.92202I 0
u = 0.15574 + 1.44448I
a = −0.542768 + 0.721473I
b = −0.650394 − 0.982206I
2.76733 + 9.04904I 0
u = 0.15574 − 1.44448I
a = −0.542768 − 0.721473I
b = −0.650394 + 0.982206I
2.76733 − 9.04904I 0
u = 0.95595 + 1.14190I
a = −0.538804 + 0.521414I
b = −0.643901 + 0.586372I
8.47453 + 3.44023I 0
u = 0.95595 − 1.14190I
a = −0.538804 − 0.521414I
b = −0.643901 − 0.586372I
8.47453 − 3.44023I 0
u = 0.85518 + 1.27123I
a = −1.49665 + 0.59796I
b = −0.630527 − 1.028320I
7.16483 + 8.49251I 0
u = 0.85518 − 1.27123I
a = −1.49665 − 0.59796I
b = −0.630527 + 1.028320I
7.16483 − 8.49251I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.336611 + 0.321294I
a = 2.73806 − 2.77848I
b = 0.401950 − 1.013810I
2.42935 − 4.96654I 6.06415 + 7.59784I
u = −0.336611 − 0.321294I
a = 2.73806 + 2.77848I
b = 0.401950 + 1.013810I
2.42935 + 4.96654I 6.06415 − 7.59784I
u = −0.157827 + 0.143099I
a = 1.68440 + 2.40915I
b = 0.915093 + 0.919317I
7.98321 + 3.33848I −1.37117 − 6.10856I
u = −0.157827 − 0.143099I
a = 1.68440 − 2.40915I
b = 0.915093 − 0.919317I
7.98321 − 3.33848I −1.37117 + 6.10856I
20
III. I
u
3
= hb + u, 3u
12
+ 2u
11
+ · · · + a + 5, u
14
+ u
13
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−3u
12
− 2u
11
+ ··· + 4u − 5
−u
a
11
=
−3u
12
− 2u
11
+ ··· + 5u − 5
−u
a
8
=
−3u
13
− 2u
12
+ ··· − 5u + 1
−u
2
a
5
=
2u
13
+ 4u
12
+ ··· + u + 5
−u
12
− u
11
− 3u
10
− 2u
9
− 6u
8
− 3u
7
− 7u
6
− 2u
5
− 6u
4
− 2u
2
+ u − 1
a
10
=
u
13
− u
12
+ ··· + 5u − 2
−u
3
− u
a
4
=
−u
13
+ 2u
12
+ ··· − 5u + 3
−u
12
− u
11
− 3u
10
− 2u
9
− 5u
8
− 3u
7
− 5u
6
− 2u
5
− 3u
4
+ u
3
− u
2
+ 2u
a
9
=
u
13
− 2u
12
+ ··· + 5u − 3
u
12
+ u
11
+ ··· − 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
13
− 10u
12
− 33u
11
− 32u
10
− 72u
9
− 63u
8
− 101u
7
− 77u
6
−
94u
5
− 56u
4
− 57u
3
− 22u
2
− 16u − 3
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
14
− 7u
13
+ ··· − 8u + 1
c
2
, c
7
u
14
− u
13
+ ··· + 4u
2
+ 1
c
3
u
14
− 5u
13
+ ··· + 2u
3
+ 1
c
4
, c
5
u
14
− u
13
+ ··· + 2u
2
+ 1
c
6
, c
11
u
14
+ u
13
+ ··· + 4u
2
+ 1
c
8
u
14
+ u
13
+ ··· + 2u
2
+ 1
c
9
, c
12
u
14
− 2u
12
+ 2u
11
+ 5u
10
− 2u
9
− 2u
8
+ 5u
7
+ 4u
6
− 2u
5
+ 2u
3
+ u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 7y
13
+ ··· + 4y + 1
c
2
, c
6
, c
7
c
11
y
14
+ 7y
13
+ ··· + 8y + 1
c
3
y
14
− 5y
13
+ ··· − 4y
2
+ 1
c
4
, c
5
, c
8
y
14
+ 15y
13
+ ··· + 4y + 1
c
9
, c
12
y
14
− 4y
13
+ ··· − y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.835016 + 0.652956I
a = 1.082660 − 0.023516I
b = 0.835016 − 0.652956I
9.18268 − 3.72870I 6.95343 + 5.35594I
u = −0.835016 − 0.652956I
a = 1.082660 + 0.023516I
b = 0.835016 + 0.652956I
9.18268 + 3.72870I 6.95343 − 5.35594I
u = 0.385097 + 1.030810I
a = −0.713394 + 0.989090I
b = −0.385097 − 1.030810I
−2.10484 + 5.24737I 2.29092 − 7.88179I
u = 0.385097 − 1.030810I
a = −0.713394 − 0.989090I
b = −0.385097 + 1.030810I
−2.10484 − 5.24737I 2.29092 + 7.88179I
u = −0.304987 + 1.069450I
a = 1.364310 − 0.051930I
b = 0.304987 − 1.069450I
0.46853 − 6.15386I 1.00883 + 6.93248I
u = −0.304987 − 1.069450I
a = 1.364310 + 0.051930I
b = 0.304987 + 1.069450I
0.46853 + 6.15386I 1.00883 − 6.93248I
u = 0.698601 + 0.929832I
a = −1.98759 + 0.18930I
b = −0.698601 − 0.929832I
1.51835 + 5.41185I 4.65952 − 5.17870I
u = 0.698601 − 0.929832I
a = −1.98759 − 0.18930I
b = −0.698601 + 0.929832I
1.51835 − 5.41185I 4.65952 + 5.17870I
u = −0.146958 + 0.722606I
a = −2.16477 + 3.14041I
b = 0.146958 − 0.722606I
3.47331 + 1.89764I −0.76890 − 1.21220I
u = −0.146958 − 0.722606I
a = −2.16477 − 3.14041I
b = 0.146958 + 0.722606I
3.47331 − 1.89764I −0.76890 + 1.21220I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688119 + 1.111760I
a = 1.62355 + 0.83041I
b = 0.688119 − 1.111760I
6.23197 − 7.88321I 3.18752 + 4.61068I
u = −0.688119 − 1.111760I
a = 1.62355 − 0.83041I
b = 0.688119 + 1.111760I
6.23197 + 7.88321I 3.18752 − 4.61068I
u = 0.391382 + 0.565226I
a = 0.295240 + 0.912738I
b = −0.391382 − 0.565226I
0.96922 + 1.42724I 8.66869 − 4.22022I
u = 0.391382 − 0.565226I
a = 0.295240 − 0.912738I
b = −0.391382 + 0.565226I
0.96922 − 1.42724I 8.66869 + 4.22022I
25
IV.
I
u
4
= h−u
13
−u
12
+· · · +b − 1, 3u
12
+2u
11
+· · · +a + 4, u
14
+u
13
+· · · +u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−3u
12
− 2u
11
+ ··· − 2u − 4
u
13
+ u
12
+ ··· + 4u + 1
a
11
=
−u
13
− 4u
12
+ ··· − 6u − 5
u
13
+ u
12
+ ··· + 4u + 1
a
8
=
5u
13
+ 4u
12
+ ··· + 2u
2
+ 5u
−u
13
− 3u
11
+ ··· − u + 3
a
5
=
u
13
+ 5u
12
+ ··· + 4u + 6
−u
13
− 3u
12
+ ··· − 2u − 2
a
10
=
−3u
13
− 2u
12
+ ··· − 6u − 3
−2u
13
− 3u
12
+ ··· − 2u − 3
a
4
=
−u
13
+ 2u
12
+ ··· − u + 2
−u
13
− 2u
12
+ ··· − 3u − 1
a
9
=
−3u
13
− u
12
+ ··· − 6u − 2
−u
13
− 3u
12
+ ··· − 10u
2
− 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −4u
13
−8u
12
−16u
11
−26u
10
−35u
9
−50u
8
−43u
7
−64u
6
−32u
5
−65u
4
−19u
3
−36u
2
−8u−7
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
14
− 7u
13
+ ··· − 7u + 1
c
2
, c
7
u
14
− u
13
+ ··· − u + 1
c
3
(u
7
+ 2u
6
+ u
5
− 2u
4
− 2u
3
− 1)
2
c
4
, c
5
(u
7
+ 4u
5
+ 4u
3
− u
2
− 1)
2
c
6
, c
11
u
14
+ u
13
+ ··· + u + 1
c
8
(u
7
+ 4u
5
+ 4u
3
+ u
2
+ 1)
2
c
9
, c
12
u
14
− 2u
12
+ ··· + 5u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 7y
13
+ ··· + 7y + 1
c
2
, c
6
, c
7
c
11
y
14
+ 7y
13
+ ··· + 7y + 1
c
3
(y
7
− 2y
6
+ 5y
5
− 8y
4
+ 8y
3
− 4y
2
− 1)
2
c
4
, c
5
, c
8
(y
7
+ 8y
6
+ 24y
5
+ 32y
4
+ 16y
3
− y
2
− 2y −1)
2
c
9
, c
12
y
14
− 4y
13
+ ··· − 5y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.694890 + 0.719116I
a = −1.08112 + 1.11881I
b = −0.694890 + 0.719116I
2.16696 5.29110 + 0.I
u = 0.694890 − 0.719116I
a = −1.08112 − 1.11881I
b = −0.694890 − 0.719116I
2.16696 5.29110 + 0.I
u = −0.225892 + 0.801630I
a = −2.21355 − 0.57675I
b = 0.325663 + 1.155690I
1.57743 + 3.93356I 1.12375 − 3.23997I
u = −0.225892 − 0.801630I
a = −2.21355 + 0.57675I
b = 0.325663 − 1.155690I
1.57743 − 3.93356I 1.12375 + 3.23997I
u = 0.321396 + 0.763972I
a = 0.372798 − 0.905399I
b = −0.467860 + 1.112130I
−1.05108 − 2.27150I 5.46525 − 2.40329I
u = 0.321396 − 0.763972I
a = 0.372798 + 0.905399I
b = −0.467860 − 1.112130I
−1.05108 + 2.27150I 5.46525 + 2.40329I
u = −0.325663 + 1.155690I
a = 1.10062 − 1.14286I
b = 0.225892 + 0.801630I
1.57743 − 3.93356I 1.12375 + 3.23997I
u = −0.325663 − 1.155690I
a = 1.10062 + 1.14286I
b = 0.225892 − 0.801630I
1.57743 + 3.93356I 1.12375 − 3.23997I
u = 0.467860 + 1.112130I
a = 0.265542 − 0.617986I
b = −0.321396 + 0.763972I
−1.05108 + 2.27150I 5.46525 + 2.40329I
u = 0.467860 − 1.112130I
a = 0.265542 + 0.617986I
b = −0.321396 − 0.763972I
−1.05108 − 2.27150I 5.46525 − 2.40329I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.506790 + 0.539046I
a = 1.206850 + 0.713023I
b = 0.925802 + 0.984727I
8.25977 + 2.86772I 6.76546 + 6.29506I
u = −0.506790 − 0.539046I
a = 1.206850 − 0.713023I
b = 0.925802 − 0.984727I
8.25977 − 2.86772I 6.76546 − 6.29506I
u = −0.925802 + 0.984727I
a = 0.348859 + 0.683436I
b = 0.506790 + 0.539046I
8.25977 − 2.86772I 6.76546 − 6.29506I
u = −0.925802 − 0.984727I
a = 0.348859 − 0.683436I
b = 0.506790 − 0.539046I
8.25977 + 2.86772I 6.76546 + 6.29506I
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
14
− 7u
13
+ ··· − 7u + 1)(u
14
− 7u
13
+ ··· − 8u + 1)
· (u
27
+ 11u
26
+ ··· − u − 1)(u
94
+ 34u
93
+ ··· + 8843u + 529)
c
2
, c
7
(u
14
− u
13
+ ··· + 4u
2
+ 1)(u
14
− u
13
+ ··· − u + 1)
· (u
27
− u
26
+ ··· + 3u − 1)(u
94
+ 2u
93
+ ··· − 239u + 23)
c
3
((u
7
+ 2u
6
+ u
5
− 2u
4
− 2u
3
− 1)
2
)(u
14
− 5u
13
+ ··· + 2u
3
+ 1)
· (u
27
− 24u
26
+ ··· + 12672u − 1280)(u
47
+ 12u
46
+ ··· − 6u − 1)
2
c
4
, c
5
((u
7
+ 4u
5
+ 4u
3
− u
2
− 1)
2
)(u
14
− u
13
+ ··· + 2u
2
+ 1)
· (u
27
− 12u
26
+ ··· + 400u − 32)(u
47
+ 5u
46
+ ··· − 12u − 1)
2
c
6
, c
11
(u
14
+ u
13
+ ··· + u + 1)(u
14
+ u
13
+ ··· + 4u
2
+ 1)
· (u
27
− u
26
+ ··· + 3u − 1)(u
94
+ 2u
93
+ ··· − 239u + 23)
c
8
((u
7
+ 4u
5
+ 4u
3
+ u
2
+ 1)
2
)(u
14
+ u
13
+ ··· + 2u
2
+ 1)
· (u
27
− 12u
26
+ ··· + 400u − 32)(u
47
+ 5u
46
+ ··· − 12u − 1)
2
c
9
, c
12
(u
14
− 2u
12
+ ··· + 5u + 1)
· (u
14
− 2u
12
+ 2u
11
+ 5u
10
− 2u
9
− 2u
8
+ 5u
7
+ 4u
6
− 2u
5
+ 2u
3
+ u + 1)
· (u
27
− 6u
25
+ ··· − 6u − 1)(u
94
+ 9u
93
+ ··· − 745u + 137)
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
14
+ 7y
13
+ ··· + 7y + 1)(y
14
+ 7y
13
+ ··· + 4y + 1)
· (y
27
+ 19y
26
+ ··· + 59y −1)
· (y
94
+ 58y
93
+ ··· + 285816831y + 279841)
c
2
, c
6
, c
7
c
11
(y
14
+ 7y
13
+ ··· + 8y + 1)(y
14
+ 7y
13
+ ··· + 7y + 1)
· (y
27
+ 11y
26
+ ··· − y −1)(y
94
+ 34y
93
+ ··· + 8843y + 529)
c
3
((y
7
− 2y
6
+ ··· − 4y
2
− 1)
2
)(y
14
− 5y
13
+ ··· − 4y
2
+ 1)
· (y
27
− 6y
26
+ ··· − 8994816y −1638400)
· (y
47
− 10y
46
+ ··· + 28y −1)
2
c
4
, c
5
, c
8
(y
7
+ 8y
6
+ 24y
5
+ 32y
4
+ 16y
3
− y
2
− 2y −1)
2
· (y
14
+ 15y
13
+ ··· + 4y + 1)(y
27
+ 24y
26
+ ··· + 9984y −1024)
· (y
47
+ 53y
46
+ ··· + 26y −1)
2
c
9
, c
12
(y
14
− 4y
13
+ ··· − 5y + 1)(y
14
− 4y
13
+ ··· − y + 1)
· (y
27
− 12y
26
+ ··· + 8y −1)(y
94
− 25y
93
+ ··· + 3079859y + 18769)
32
