12a
0155
(K12a
0155
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 11 10 12 4 8 6 1 7
Solving Sequence
4,8
9 10
3,12
7 1 2 6 11 5
c
8
c
9
c
3
c
7
c
12
c
1
c
6
c
11
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.07210 × 10
79
u
73
− 4.45872 × 10
79
u
72
+ ··· + 1.81105 × 10
80
b − 5.45671 × 10
80
,
9.44926 × 10
78
u
73
+ 1.37256 × 10
79
u
72
+ ··· + 6.03683 × 10
79
a + 2.79535 × 10
80
, u
74
+ 2u
73
+ ··· + 16u + 64i
I
u
2
= h12u
8
a
2
− 12u
8
+ ··· − 283a − 196, 2u
8
a
2
+ 5u
8
a + ··· + 9a − 20,
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
u
3
= hu
11
+ 2u
9
+ 2u
7
− u
3
+ b, −u
10
+ u
9
− 3u
8
+ 2u
7
− 5u
6
+ 2u
5
− 4u
4
− 2u
2
+ a − u − 1,
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1i
I
v
1
= ha, −2v
3
+ 3v
2
+ 4b − 8v + 3, 2v
4
− v
3
+ 5v
2
+ v + 1i
* 4 irreducible components of dim
C
= 0, with total 117 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−2.07 × 10
79
u
73
− 4.46 × 10
79
u
72
+ · · · + 1.81 × 10
80
b − 5.46 ×
10
80
, 9.45 × 10
78
u
73
+ 1.37 × 10
79
u
72
+ · · · + 6.04 × 10
79
a + 2.80 ×
10
80
, u
74
+ 2u
73
+ · · · + 16u + 64i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
12
=
−0.156527u
73
− 0.227365u
72
+ ··· − 9.44771u − 4.63049
0.114414u
73
+ 0.246195u
72
+ ··· + 18.2624u + 3.01301
a
7
=
−0.0427323u
73
− 0.0222590u
72
+ ··· − 17.0843u − 2.73523
0.0558199u
73
+ 0.00860331u
72
+ ··· + 7.08355u − 20.4297
a
1
=
−0.247663u
73
− 0.406614u
72
+ ··· − 47.8687u − 2.35262
−0.0419160u
73
− 0.134596u
72
+ ··· − 19.1036u − 12.4163
a
2
=
−0.200457u
73
− 0.360919u
72
+ ··· − 39.4697u − 7.35311
0.00721908u
73
− 0.0715981u
72
+ ··· − 12.9464u − 14.2988
a
6
=
−0.0796114u
73
− 0.0728386u
72
+ ··· − 15.9420u + 4.33996
0.101084u
73
+ 0.0798881u
72
+ ··· + 11.6620u − 23.1448
a
11
=
−0.143338u
73
− 0.243103u
72
+ ··· − 20.1363u + 2.92790
−0.144745u
73
− 0.280896u
72
+ ··· − 39.7884u + 8.31570
a
5
=
−0.150768u
73
− 0.223403u
72
+ ··· − 14.3340u + 4.38601
0.0968957u
73
+ 0.183211u
72
+ ··· + 33.5347u + 6.73864
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.801859u
73
− 1.46138u
72
+ ··· − 97.4961u + 28.5646
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 40u
73
+ ··· + 177u + 16
c
2
, c
4
u
74
− 4u
73
+ ··· − 35u + 4
c
3
, c
8
u
74
+ 2u
73
+ ··· + 16u + 64
c
5
, c
6
, c
10
u
74
+ 2u
73
+ ··· + 78u + 9
c
7
, c
12
u
74
+ 2u
73
+ ··· + 54u + 9
c
9
u
74
− 24u
73
+ ··· − 103168u + 4096
c
11
u
74
− 26u
73
+ ··· − 2880u + 81
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
− 8y
73
+ ··· − 5953y + 256
c
2
, c
4
y
74
− 40y
73
+ ··· − 177y + 16
c
3
, c
8
y
74
+ 24y
73
+ ··· + 103168y + 4096
c
5
, c
6
, c
10
y
74
+ 82y
73
+ ··· − 3456y + 81
c
7
, c
12
y
74
+ 26y
73
+ ··· + 2880y + 81
c
9
y
74
+ 44y
73
+ ··· − 654376960y + 16777216
c
11
y
74
+ 58y
73
+ ··· + 591300y + 6561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.016280 + 0.056443I
a = −0.846246 − 0.233543I
b = −0.641966 − 0.915109I
−4.55260 − 4.71728I −5.48750 + 5.97757I
u = −1.016280 − 0.056443I
a = −0.846246 + 0.233543I
b = −0.641966 + 0.915109I
−4.55260 + 4.71728I −5.48750 − 5.97757I
u = 0.715978 + 0.749309I
a = −1.009060 + 0.512831I
b = −0.819433 + 1.097530I
−10.62080 + 2.16848I −8.29410 + 0.I
u = 0.715978 − 0.749309I
a = −1.009060 − 0.512831I
b = −0.819433 − 1.097530I
−10.62080 − 2.16848I −8.29410 + 0.I
u = 1.018120 + 0.241002I
a = −0.883835 − 0.063210I
b = −0.634326 − 0.779842I
−4.97717 − 0.27862I −6.77921 + 0.I
u = 1.018120 − 0.241002I
a = −0.883835 + 0.063210I
b = −0.634326 + 0.779842I
−4.97717 + 0.27862I −6.77921 + 0.I
u = 0.101684 + 0.941180I
a = −0.96039 + 1.37103I
b = 0.668786 − 0.848557I
−6.34170 + 2.58749I −5.26885 − 2.40308I
u = 0.101684 − 0.941180I
a = −0.96039 − 1.37103I
b = 0.668786 + 0.848557I
−6.34170 − 2.58749I −5.26885 + 2.40308I
u = 0.702951 + 0.605779I
a = 1.083580 − 0.777415I
b = 0.577935 − 0.892143I
−0.36424 + 2.16926I −1.33400 − 2.94106I
u = 0.702951 − 0.605779I
a = 1.083580 + 0.777415I
b = 0.577935 + 0.892143I
−0.36424 − 2.16926I −1.33400 + 2.94106I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455877 + 0.982311I
a = 0.549167 + 0.442923I
b = 0.532038 + 0.022585I
−1.99851 − 5.40155I 0
u = 0.455877 − 0.982311I
a = 0.549167 − 0.442923I
b = 0.532038 − 0.022585I
−1.99851 + 5.40155I 0
u = −0.688565 + 0.844832I
a = −2.45152 − 0.54418I
b = −0.623313 + 0.954050I
−3.63561 + 3.57244I 0
u = −0.688565 − 0.844832I
a = −2.45152 + 0.54418I
b = −0.623313 − 0.954050I
−3.63561 − 3.57244I 0
u = −0.922080 + 0.581194I
a = −0.902921 − 0.473277I
b = −0.730349 − 1.085650I
−6.70976 − 5.72717I 0
u = −0.922080 − 0.581194I
a = −0.902921 + 0.473277I
b = −0.730349 + 1.085650I
−6.70976 + 5.72717I 0
u = 0.400961 + 1.025910I
a = 0.513025 − 0.645985I
b = −0.156641 + 1.061890I
3.87862 − 1.01189I 0
u = 0.400961 − 1.025910I
a = 0.513025 + 0.645985I
b = −0.156641 − 1.061890I
3.87862 + 1.01189I 0
u = −0.039055 + 1.116760I
a = −0.491876 − 1.057740I
b = −0.338560 + 1.089190I
5.21780 + 1.15055I 0
u = −0.039055 − 1.116760I
a = −0.491876 + 1.057740I
b = −0.338560 − 1.089190I
5.21780 − 1.15055I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.686707 + 0.883279I
a = 1.136820 + 0.777943I
b = 0.710003 + 0.868137I
−3.51612 + 1.72512I 0
u = −0.686707 − 0.883279I
a = 1.136820 − 0.777943I
b = 0.710003 − 0.868137I
−3.51612 − 1.72512I 0
u = −0.780808 + 0.406319I
a = 1.069120 − 0.412845I
b = 0.132045 − 0.962513I
−0.190732 − 0.765674I 0.883971 + 0.910639I
u = −0.780808 − 0.406319I
a = 1.069120 + 0.412845I
b = 0.132045 + 0.962513I
−0.190732 + 0.765674I 0.883971 − 0.910639I
u = 0.868207 + 0.709119I
a = −1.316090 + 0.047838I
b = −0.932909 − 0.593077I
−8.22620 − 0.36510I 0
u = 0.868207 − 0.709119I
a = −1.316090 − 0.047838I
b = −0.932909 + 0.593077I
−8.22620 + 0.36510I 0
u = −0.773522 + 0.832238I
a = −1.388560 + 0.057416I
b = −1.017760 + 0.654828I
−11.98240 + 4.46440I 0
u = −0.773522 − 0.832238I
a = −1.388560 − 0.057416I
b = −1.017760 − 0.654828I
−11.98240 − 4.46440I 0
u = −0.923574 + 0.692893I
a = 1.084650 + 0.825348I
b = 0.628177 + 0.990952I
−3.34148 − 6.33239I 0
u = −0.923574 − 0.692893I
a = 1.084650 − 0.825348I
b = 0.628177 − 0.990952I
−3.34148 + 6.33239I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.643430 + 0.541266I
a = 0.11958 + 1.53542I
b = −0.096809 + 0.216360I
−3.46513 + 1.05609I −11.55620 − 0.54689I
u = 0.643430 − 0.541266I
a = 0.11958 − 1.53542I
b = −0.096809 − 0.216360I
−3.46513 − 1.05609I −11.55620 + 0.54689I
u = 0.251058 + 1.133180I
a = −1.05747 + 0.95104I
b = −0.431302 − 1.095140I
4.59696 − 6.09538I 0
u = 0.251058 − 1.133180I
a = −1.05747 − 0.95104I
b = −0.431302 + 1.095140I
4.59696 + 6.09538I 0
u = 0.680178 + 0.965059I
a = 2.06174 − 1.01173I
b = 0.733930 + 1.124350I
−9.95050 − 7.53602I 0
u = 0.680178 − 0.965059I
a = 2.06174 + 1.01173I
b = 0.733930 − 1.124350I
−9.95050 + 7.53602I 0
u = −0.760147 + 0.919939I
a = 0.363285 + 1.114770I
b = 0.972224 + 0.550351I
−11.71740 + 1.32226I 0
u = −0.760147 − 0.919939I
a = 0.363285 − 1.114770I
b = 0.972224 − 0.550351I
−11.71740 − 1.32226I 0
u = 0.785310 + 0.041797I
a = 1.032650 − 0.688989I
b = 0.336202 − 0.946046I
0.75306 + 2.46584I 1.27659 − 6.33944I
u = 0.785310 − 0.041797I
a = 1.032650 + 0.688989I
b = 0.336202 + 0.946046I
0.75306 − 2.46584I 1.27659 + 6.33944I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.669060 + 1.015260I
a = −2.02541 + 0.47750I
b = −0.619534 − 1.034680I
0.81052 − 7.48437I 0
u = 0.669060 − 1.015260I
a = −2.02541 − 0.47750I
b = −0.619534 + 1.034680I
0.81052 + 7.48437I 0
u = −0.602047 + 1.071410I
a = 0.540817 + 0.305119I
b = −0.091548 − 1.090250I
1.71998 + 5.88464I 0
u = −0.602047 − 1.071410I
a = 0.540817 − 0.305119I
b = −0.091548 + 1.090250I
1.71998 − 5.88464I 0
u = −0.962055 + 0.769007I
a = −1.407370 − 0.115629I
b = −0.982890 + 0.515422I
−11.46460 − 4.27058I 0
u = −0.962055 − 0.769007I
a = −1.407370 + 0.115629I
b = −0.982890 − 0.515422I
−11.46460 + 4.27058I 0
u = 1.018000 + 0.713154I
a = −0.877403 + 0.545175I
b = −0.723054 + 1.145040I
−9.5271 + 10.4754I 0
u = 1.018000 − 0.713154I
a = −0.877403 − 0.545175I
b = −0.723054 − 1.145040I
−9.5271 − 10.4754I 0
u = −0.322053 + 1.215640I
a = −0.289638 − 0.522660I
b = 0.510459 + 0.750000I
−0.063900 − 0.320410I 0
u = −0.322053 − 1.215640I
a = −0.289638 + 0.522660I
b = 0.510459 − 0.750000I
−0.063900 + 0.320410I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.757308 + 1.014150I
a = 0.521716 − 0.835498I
b = 0.980452 − 0.466162I
−7.29295 − 5.66257I 0
u = 0.757308 − 1.014150I
a = 0.521716 + 0.835498I
b = 0.980452 + 0.466162I
−7.29295 + 5.66257I 0
u = 0.141074 + 1.267450I
a = 0.314381 − 1.040930I
b = 0.549097 + 0.971551I
0.71079 − 3.98529I 0
u = 0.141074 − 1.267450I
a = 0.314381 + 1.040930I
b = 0.549097 − 0.971551I
0.71079 + 3.98529I 0
u = −0.257906 + 0.673206I
a = 0.875017 − 0.842641I
b = 0.362715 − 0.412513I
−0.25584 + 1.43316I −2.89373 − 4.25664I
u = −0.257906 − 0.673206I
a = 0.875017 + 0.842641I
b = 0.362715 + 0.412513I
−0.25584 − 1.43316I −2.89373 + 4.25664I
u = 0.512625 + 1.186330I
a = −0.180598 + 0.307148I
b = 0.462194 − 0.608975I
−1.73996 − 5.08791I 0
u = 0.512625 − 1.186330I
a = −0.180598 − 0.307148I
b = 0.462194 + 0.608975I
−1.73996 + 5.08791I 0
u = −0.766224 + 1.056700I
a = −2.02146 − 0.26151I
b = −0.666344 + 1.052100I
−2.19593 + 12.55800I 0
u = −0.766224 − 1.056700I
a = −2.02146 + 0.26151I
b = −0.666344 − 1.052100I
−2.19593 − 12.55800I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.334080 + 1.262000I
a = 0.739927 + 1.023500I
b = 0.574354 − 1.047070I
−0.23035 + 9.53465I 0
u = −0.334080 − 1.262000I
a = 0.739927 − 1.023500I
b = 0.574354 + 1.047070I
−0.23035 − 9.53465I 0
u = −0.726282 + 1.091930I
a = 1.77788 + 0.71191I
b = 0.700817 − 1.164010I
−5.15120 + 11.77850I 0
u = −0.726282 − 1.091930I
a = 1.77788 − 0.71191I
b = 0.700817 + 1.164010I
−5.15120 − 11.77850I 0
u = −0.817220 + 1.044540I
a = 0.714742 + 0.868490I
b = 1.041650 + 0.454586I
−10.5690 + 10.7948I 0
u = −0.817220 − 1.044540I
a = 0.714742 − 0.868490I
b = 1.041650 − 0.454586I
−10.5690 − 10.7948I 0
u = 0.810773 + 1.098430I
a = 1.85420 − 0.50706I
b = 0.716271 + 1.194250I
−8.2766 − 17.1352I 0
u = 0.810773 − 1.098430I
a = 1.85420 + 0.50706I
b = 0.716271 − 1.194250I
−8.2766 + 17.1352I 0
u = −0.189049 + 0.597095I
a = 2.34091 + 2.24975I
b = −0.233253 − 0.857584I
−0.892082 − 1.083450I 4.37786 − 0.74207I
u = −0.189049 − 0.597095I
a = 2.34091 − 2.24975I
b = −0.233253 + 0.857584I
−0.892082 + 1.083450I 4.37786 + 0.74207I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.022832 + 0.605905I
a = 1.015490 − 0.770054I
b = 0.451799 − 0.569597I
−0.20066 + 1.45515I −0.46303 − 4.13714I
u = −0.022832 − 0.605905I
a = 1.015490 + 0.770054I
b = 0.451799 + 0.569597I
−0.20066 − 1.45515I −0.46303 + 4.13714I
u = 0.057884 + 0.497232I
a = −1.161350 − 0.318274I
b = −0.901151 − 0.915137I
−8.05648 − 3.30418I 5.21911 + 6.27707I
u = 0.057884 − 0.497232I
a = −1.161350 + 0.318274I
b = −0.901151 + 0.915137I
−8.05648 + 3.30418I 5.21911 − 6.27707I
12
II. I
u
2
= h12u
8
a
2
− 12u
8
+ · · · − 283a − 196, 2u
8
a
2
+ 5u
8
a + · · · + 9a −
20, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
12
=
a
−0.0424028a
2
u
8
+ 0.0424028u
8
+ ··· + a + 0.692580
a
7
=
0.0424028a
2
u
8
− 0.0424028u
8
+ ··· − 0.307420a
2
+ 1.30742
0.0424028a
2
u
8
− 0.0424028u
8
+ ··· − 0.307420a
2
+ 1.30742
a
1
=
u
2
+ 1
u
2
a
2
=
u
6
+ u
4
+ 2u
2
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
6
=
0.0848057a
2
u
8
− 0.0848057u
8
+ ··· − 0.614841a
2
+ 2.61484
0.127208a
2
u
8
− 0.127208u
8
+ ··· − a + 1.92226
a
11
=
0.0424028a
2
u
8
− 0.0424028u
8
+ ··· + 2a − 0.692580
0.0424028a
2
u
8
− 0.0424028u
8
+ ··· + 2a + 1.30742
a
5
=
u
4
+ u
2
+ 1
u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
7
− 4u
6
+ 4u
5
− 4u
4
+ 8u
3
− 4u
2
− 6
13
(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)
3
c
2
, c
4
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
c
3
, c
8
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
3
c
5
, c
6
, c
7
c
10
, c
12
u
27
+ 9u
25
+ ··· + u + 1
c
9
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
3
c
11
u
27
− 18u
26
+ ··· + 13u + 1
14
(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)
3
c
2
, c
4
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
3
c
3
, c
8
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
3
c
5
, c
6
, c
7
c
10
, c
12
y
27
+ 18y
26
+ ··· + 13y −1
c
9
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
3
c
11
y
27
− 18y
26
+ ··· + 265y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = 0.824898 − 1.007270I
b = 0.277934 + 1.206900I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = −0.140343 + 0.966856I
a = −0.429022 − 0.227708I
b = −0.658031 − 0.118772I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = −0.140343 + 0.966856I
a = 1.61297 + 0.63923I
b = 0.380097 − 1.088130I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = −0.140343 − 0.966856I
a = 0.824898 + 1.007270I
b = 0.277934 − 1.206900I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = −0.140343 − 0.966856I
a = −0.429022 + 0.227708I
b = −0.658031 + 0.118772I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = −0.140343 − 0.966856I
a = 1.61297 − 0.63923I
b = 0.380097 + 1.088130I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = −0.628449 + 0.875112I
a = −0.725227 − 0.503645I
b = 0.082565 + 1.353850I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.628449 + 0.875112I
a = −0.666708 − 1.013420I
b = −0.663930 − 0.542279I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.628449 + 0.875112I
a = 1.94244 − 0.11561I
b = 0.581364 − 0.811567I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.628449 − 0.875112I
a = −0.725227 + 0.503645I
b = 0.082565 − 1.353850I
−0.61694 − 2.45442I −2.32792 + 2.91298I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.628449 − 0.875112I
a = −0.666708 + 1.013420I
b = −0.663930 + 0.542279I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = −0.628449 − 0.875112I
a = 1.94244 + 0.11561I
b = 0.581364 + 0.811567I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.796005 + 0.733148I
a = −1.263760 + 0.143919I
b = −0.021021 − 1.362970I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = 0.796005 + 0.733148I
a = −0.81256 + 1.34091I
b = −0.617263 + 0.715712I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = 0.796005 + 0.733148I
a = 1.93616 + 0.21716I
b = 0.638283 + 0.647255I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = 0.796005 − 0.733148I
a = −1.263760 − 0.143919I
b = −0.021021 + 1.362970I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = 0.796005 − 0.733148I
a = −0.81256 − 1.34091I
b = −0.617263 − 0.715712I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = 0.796005 − 0.733148I
a = 1.93616 − 0.21716I
b = 0.638283 − 0.647255I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = 0.728966 + 0.986295I
a = −0.877277 + 0.977536I
b = −0.774180 + 0.585725I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.728966 + 0.986295I
a = −0.598365 + 0.132184I
b = 0.08677 − 1.42529I
−3.59813 − 7.08493I −5.57680 + 5.91335I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.728966 + 0.986295I
a = 1.86581 + 0.16138I
b = 0.687410 + 0.839570I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.728966 − 0.986295I
a = −0.877277 − 0.977536I
b = −0.774180 − 0.585725I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = 0.728966 − 0.986295I
a = −0.598365 − 0.132184I
b = 0.08677 + 1.42529I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = 0.728966 − 0.986295I
a = 1.86581 − 0.16138I
b = 0.687410 − 0.839570I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.512358
a = 1.42282
b = 0.247373
−1.19845 −8.65230
u = −0.512358
a = −4.52078 + 3.95478I
b = −0.123686 + 1.022690I
−1.19845 −8.65230
u = −0.512358
a = −4.52078 − 3.95478I
b = −0.123686 − 1.022690I
−1.19845 −8.65230
18
III. I
u
3
= hu
11
+ 2u
9
+ 2u
7
− u
3
+ b, −u
10
+ u
9
+ · · · + a − 1, u
12
+ 3u
10
+
5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
12
=
u
10
− u
9
+ 3u
8
− 2u
7
+ 5u
6
− 2u
5
+ 4u
4
+ 2u
2
+ u + 1
−u
11
− 2u
9
− 2u
7
+ u
3
a
7
=
−u
10
− u
9
− 3u
8
− 2u
7
− 5u
6
− 2u
5
− 4u
4
− 2u
2
+ u
1
a
1
=
u
11
+ 2u
9
+ 2u
7
− u
3
0
a
2
=
−u
7
− 2u
5
− 2u
3
−u
7
− u
5
+ u
a
6
=
−u
10
− 3u
8
− 5u
6
+ u
5
− 4u
4
+ 2u
3
− 2u
2
+ 2u
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u + 1
a
11
=
−u
11
+ u
10
− 3u
9
+ 3u
8
− 4u
7
+ 5u
6
− 2u
5
+ 4u
4
+ u
3
+ 2u
2
+ u + 1
−u
11
− 2u
9
− 2u
7
+ u
3
a
5
=
u
9
+ 2u
7
+ 3u
5
+ 2u
3
+ u
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
10
+ 12u
8
+ 16u
6
+ 8u
4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
8
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
, c
6
, c
7
c
10
, c
12
(u
2
+ 1)
6
c
11
(u + 1)
12
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
3
, c
8
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
5
, c
6
, c
7
c
10
, c
12
(y + 1)
12
c
11
(y −1)
12
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295542 + 1.002190I
a = 0.272397 + 1.266420I
b = − 1.000000I
1.89061 − 0.92430I 1.71672 + 0.79423I
u = 0.295542 − 1.002190I
a = 0.272397 − 1.266420I
b = 1.000000I
1.89061 + 0.92430I 1.71672 − 0.79423I
u = −0.295542 + 1.002190I
a = 1.266420 + 0.272397I
b = − 1.000000I
1.89061 + 0.92430I 1.71672 − 0.79423I
u = −0.295542 − 1.002190I
a = 1.266420 − 0.272397I
b = 1.000000I
1.89061 − 0.92430I 1.71672 + 0.79423I
u = 0.664531 + 0.428243I
a = 0.79605 + 2.11811I
b = 1.000000I
−1.89061 + 0.92430I −5.71672 − 0.79423I
u = 0.664531 − 0.428243I
a = 0.79605 − 2.11811I
b = − 1.000000I
−1.89061 − 0.92430I −5.71672 + 0.79423I
u = −0.664531 + 0.428243I
a = −2.11811 − 0.79605I
b = 1.000000I
−1.89061 − 0.92430I −5.71672 + 0.79423I
u = −0.664531 − 0.428243I
a = −2.11811 + 0.79605I
b = − 1.000000I
−1.89061 + 0.92430I −5.71672 − 0.79423I
u = 0.558752 + 1.073950I
a = 0.950374 + 0.167130I
b = 1.000000I
− 5.69302I −2.00000 + 5.51057I
u = 0.558752 − 1.073950I
a = 0.950374 − 0.167130I
b = − 1.000000I
5.69302I −2.00000 − 5.51057I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.558752 + 1.073950I
a = −0.167130 − 0.950374I
b = 1.000000I
5.69302I −2.00000 − 5.51057I
u = −0.558752 − 1.073950I
a = −0.167130 + 0.950374I
b = − 1.000000I
− 5.69302I −2.00000 + 5.51057I
23
IV. I
v
1
= ha, −2v
3
+ 3v
2
+ 4b − 8v + 3, 2v
4
− v
3
+ 5v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
10
=
1
0
a
3
=
v
0
a
12
=
0
1
2
v
3
−
3
4
v
2
+ 2v −
3
4
a
7
=
1
3
2
v
3
−
5
4
v
2
+
7
2
v +
1
4
a
1
=
−
1
2
v
3
+
3
4
v
2
− 2v +
3
4
2v
3
− v
2
+ 5v + 1
a
2
=
−
1
2
v
3
+
3
4
v
2
− v +
3
4
2v
3
− v
2
+ 5v + 1
a
6
=
−
3
2
v
3
+
5
4
v
2
−
7
2
v +
3
4
3
2
v
3
−
5
4
v
2
+
7
2
v +
1
4
a
11
=
−
3
2
v
3
+
1
4
v
2
− 3v −
7
4
v
2
−
1
2
v +
5
2
a
5
=
1
2
v
3
−
3
4
v
2
+ 2v −
3
4
−2v
3
+ v
2
− 5v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2v
3
− 14
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
, c
9
u
4
c
4
(u + 1)
4
c
5
, c
6
, c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
7
u
4
+ u
3
+ u
2
+ 1
c
10
u
4
− u
3
+ 3u
2
− 2u + 1
c
12
u
4
− u
3
+ u
2
+ 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
8
, c
9
y
4
c
5
, c
6
, c
10
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
7
, c
12
y
4
+ y
3
+ 3y
2
+ 2y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.130534 + 0.427872I
a = 0
b = −0.851808 + 0.911292I
−8.43568 + 3.16396I −14.13894 + 0.11292I
v = −0.130534 − 0.427872I
a = 0
b = −0.851808 − 0.911292I
−8.43568 − 3.16396I −14.13894 − 0.11292I
v = 0.38053 + 1.53420I
a = 0
b = 0.351808 + 0.720342I
−1.43393 − 1.41510I −8.73606 + 5.88934I
v = 0.38053 − 1.53420I
a = 0
b = 0.351808 − 0.720342I
−1.43393 + 1.41510I −8.73606 − 5.88934I
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
3
· (u
74
+ 40u
73
+ ··· + 177u + 16)
c
2
(u − 1)
4
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
· (u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
· (u
74
− 4u
73
+ ··· − 35u + 4)
c
3
, c
8
u
4
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
3
· (u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
74
+ 2u
73
+ ··· + 16u + 64)
c
4
(u + 1)
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
· (u
74
− 4u
73
+ ··· − 35u + 4)
c
5
, c
6
((u
2
+ 1)
6
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
27
+ 9u
25
+ ··· + u + 1)
· (u
74
+ 2u
73
+ ··· + 78u + 9)
c
7
((u
2
+ 1)
6
)(u
4
+ u
3
+ u
2
+ 1)(u
27
+ 9u
25
+ ··· + u + 1)
· (u
74
+ 2u
73
+ ··· + 54u + 9)
c
9
u
4
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
3
· (u
74
− 24u
73
+ ··· − 103168u + 4096)
c
10
((u
2
+ 1)
6
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
27
+ 9u
25
+ ··· + u + 1)
· (u
74
+ 2u
73
+ ··· + 78u + 9)
c
11
((u + 1)
12
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
27
− 18u
26
+ ··· + 13u + 1)
· (u
74
− 26u
73
+ ··· − 2880u + 81)
c
12
((u
2
+ 1)
6
)(u
4
− u
3
+ u
2
+ 1)(u
27
+ 9u
25
+ ··· + u + 1)
· (u
74
+ 2u
73
+ ··· + 54u + 9)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
4
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
3
· (y
74
− 8y
73
+ ··· − 5953y + 256)
c
2
, c
4
(y − 1)
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
· (y
74
− 40y
73
+ ··· − 177y + 16)
c
3
, c
8
y
4
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
· (y
74
+ 24y
73
+ ··· + 103168y + 4096)
c
5
, c
6
, c
10
((y + 1)
12
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
27
+ 18y
26
+ ··· + 13y − 1)
· (y
74
+ 82y
73
+ ··· − 3456y + 81)
c
7
, c
12
((y + 1)
12
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
27
+ 18y
26
+ ··· + 13y − 1)
· (y
74
+ 26y
73
+ ··· + 2880y + 81)
c
9
y
4
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
· (y
74
+ 44y
73
+ ··· − 654376960y + 16777216)
c
11
((y − 1)
12
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
27
− 18y
26
+ ··· + 265y − 1)
· (y
74
+ 58y
73
+ ··· + 591300y + 6561)
29
