12a
0766
(K12a
0766
)
A knot diagram
1
Linearized knot diagam
3 8 10 11 1 12 2 6 5 4 7 9
Solving Sequence
3,10
4 11
5,8
2 1 6 7 9 12
c
3
c
10
c
4
c
2
c
1
c
5
c
7
c
9
c
12
c
6
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.13361 × 10
216
u
128
− 2.24626 × 10
216
u
127
+ ··· + 5.09830 × 10
216
b + 8.25708 × 10
217
,
− 5.76761 × 10
217
u
128
+ 1.76555 × 10
218
u
127
+ ··· + 2.19227 × 10
218
a − 3.76892 × 10
218
,
u
129
− 57u
127
+ ··· + 378u + 43i
I
u
2
= h2u
22
− 20u
20
+ ··· − 7u
2
+ b, −3u
23
− 3u
22
+ ··· + a + 4, u
24
− 12u
22
+ ··· − 2u + 1i
I
u
3
= hb + 1, a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 154 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
= h2.13 × 10
216
u
128
− 2.25 × 10
216
u
127
+ · · · + 5.10 × 10
216
b + 8.26 ×
10
217
, −5.77 × 10
217
u
128
+ 1.77 × 10
218
u
127
+ · · · + 2.19 × 10
218
a − 3.77 ×
10
218
, u
129
− 57u
127
+ · · · + 378u + 43i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
11
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
0.263089u
128
− 0.805353u
127
+ ··· + 42.7132u + 1.71919
−0.418495u
128
+ 0.440590u
127
+ ··· − 138.953u − 16.1957
a
2
=
0.467938u
128
− 0.812760u
127
+ ··· + 28.7148u + 7.66234
−0.705149u
128
+ 0.785581u
127
+ ··· − 30.0980u − 6.28193
a
1
=
−0.237211u
128
− 0.0271790u
127
+ ··· − 1.38322u + 1.38042
−0.705149u
128
+ 0.785581u
127
+ ··· − 30.0980u − 6.28193
a
6
=
0.755620u
128
− 0.177142u
127
+ ··· + 47.3681u + 1.03645
−0.0305009u
128
− 0.0755006u
127
+ ··· − 2.33441u + 1.39110
a
7
=
−0.0733243u
128
− 0.511720u
127
+ ··· + 60.5543u + 8.77827
0.587856u
128
− 0.0941282u
127
+ ··· + 75.5430u + 9.18933
a
9
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
12
=
0.448679u
128
− 0.802998u
127
+ ··· + 8.13708u + 4.46535
−0.545577u
128
+ 0.686006u
127
+ ··· − 3.01559u − 2.16240
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.688840u
128
− 1.19440u
127
+ ··· − 15.5285u − 16.6790
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
129
+ 58u
128
+ ··· + 1112505u + 85849
c
2
, c
7
u
129
− 29u
127
+ ··· + 259u + 293
c
3
, c
4
, c
10
u
129
− 57u
127
+ ··· + 378u + 43
c
5
u
129
+ 3u
128
+ ··· − 40u + 1
c
6
, c
11
u
129
+ u
128
+ ··· + 76623u + 52995
c
8
u
129
− 9u
128
+ ··· − 40u + 1
c
9
u
129
− 3u
128
+ ··· + 20927496u + 1128105
c
12
u
129
+ 4u
128
+ ··· − 146894u − 14831
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
129
+ 38y
128
+ ··· + 16755519645y −7370050801
c
2
, c
7
y
129
− 58y
128
+ ··· + 1112505y −85849
c
3
, c
4
, c
10
y
129
− 114y
128
+ ··· − 32126y −1849
c
5
y
129
− 5y
128
+ ··· + 90y −1
c
6
, c
11
y
129
+ 89y
128
+ ··· − 89198342211y −2808470025
c
8
y
129
− 13y
128
+ ··· + 10y −1
c
9
y
129
+ 41y
128
+ ··· + 17191577913966y −1272620891025
c
12
y
129
− 34y
128
+ ··· + 16675400862y −219958561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.949751 + 0.312486I
a = −0.245150 − 1.217980I
b = −0.053229 + 0.489319I
−1.37418 − 3.62180I 0
u = −0.949751 − 0.312486I
a = −0.245150 + 1.217980I
b = −0.053229 − 0.489319I
−1.37418 + 3.62180I 0
u = 0.381049 + 0.913700I
a = −0.512439 − 1.315800I
b = −1.031630 + 0.528294I
−5.02675 + 4.64385I 0
u = 0.381049 − 0.913700I
a = −0.512439 + 1.315800I
b = −1.031630 − 0.528294I
−5.02675 − 4.64385I 0
u = −0.866089 + 0.420234I
a = −0.442386 + 1.197430I
b = −0.333734 − 0.814259I
−1.03335 + 4.34050I 0
u = −0.866089 − 0.420234I
a = −0.442386 − 1.197430I
b = −0.333734 + 0.814259I
−1.03335 − 4.34050I 0
u = 0.683065 + 0.677856I
a = −0.361680 − 0.409401I
b = 1.013710 + 0.399081I
−3.98667 + 0.69907I 0
u = 0.683065 − 0.677856I
a = −0.361680 + 0.409401I
b = 1.013710 − 0.399081I
−3.98667 − 0.69907I 0
u = −1.012930 + 0.246613I
a = 0.575278 + 0.469381I
b = 0.972479 − 0.530189I
1.40813 + 4.17445I 0
u = −1.012930 − 0.246613I
a = 0.575278 − 0.469381I
b = 0.972479 + 0.530189I
1.40813 − 4.17445I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.120180 + 1.042100I
a = 0.587260 − 0.370386I
b = 0.951327 + 0.351873I
−6.36332 − 1.31649I 0
u = 0.120180 − 1.042100I
a = 0.587260 + 0.370386I
b = 0.951327 − 0.351873I
−6.36332 + 1.31649I 0
u = 0.930564 + 0.535062I
a = 0.232044 + 0.420312I
b = −1.139950 − 0.597740I
−3.39947 − 9.60540I 0
u = 0.930564 − 0.535062I
a = 0.232044 − 0.420312I
b = −1.139950 + 0.597740I
−3.39947 + 9.60540I 0
u = 0.258275 + 0.852940I
a = 1.04567 + 1.25372I
b = 1.173070 − 0.639730I
−5.4770 + 14.4708I 0
u = 0.258275 − 0.852940I
a = 1.04567 − 1.25372I
b = 1.173070 + 0.639730I
−5.4770 − 14.4708I 0
u = 1.137320 + 0.022675I
a = −0.161520 − 0.175917I
b = 0.596067 + 0.326746I
2.31439 + 0.13029I 0
u = 1.137320 − 0.022675I
a = −0.161520 + 0.175917I
b = 0.596067 − 0.326746I
2.31439 − 0.13029I 0
u = 1.102490 + 0.358833I
a = 0.052065 + 1.356020I
b = 1.263830 − 0.200178I
−6.13755 − 1.11746I 0
u = 1.102490 − 0.358833I
a = 0.052065 − 1.356020I
b = 1.263830 + 0.200178I
−6.13755 + 1.11746I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.246164 + 0.794294I
a = −0.386614 + 0.196484I
b = 0.370391 − 0.944177I
−3.02843 − 8.71041I 0
u = −0.246164 − 0.794294I
a = −0.386614 − 0.196484I
b = 0.370391 + 0.944177I
−3.02843 + 8.71041I 0
u = −0.283413 + 0.756145I
a = 0.266452 − 0.756504I
b = −0.452930 + 0.551945I
−3.38000 − 0.26645I 0
u = −0.283413 − 0.756145I
a = 0.266452 + 0.756504I
b = −0.452930 − 0.551945I
−3.38000 + 0.26645I 0
u = −0.034989 + 0.800453I
a = 1.36090 − 0.58764I
b = 0.996535 − 0.319770I
−6.92317 + 1.00814I −12.18026 + 0.I
u = −0.034989 − 0.800453I
a = 1.36090 + 0.58764I
b = 0.996535 + 0.319770I
−6.92317 − 1.00814I −12.18026 + 0.I
u = 0.126930 + 0.784165I
a = −1.149040 − 0.097972I
b = −1.342670 − 0.116692I
−9.11009 + 5.26813I −8.05145 − 5.13781I
u = 0.126930 − 0.784165I
a = −1.149040 + 0.097972I
b = −1.342670 + 0.116692I
−9.11009 − 5.26813I −8.05145 + 5.13781I
u = −0.187496 + 0.764059I
a = −1.73126 + 1.16904I
b = −1.055730 − 0.571772I
−1.05862 − 8.07165I 0. + 8.98454I
u = −0.187496 − 0.764059I
a = −1.73126 − 1.16904I
b = −1.055730 + 0.571772I
−1.05862 + 8.07165I 0. − 8.98454I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.030500 + 0.640829I
a = −0.216380 − 1.198020I
b = −1.027760 + 0.456095I
−3.59587 + 7.09073I 0
u = 1.030500 − 0.640829I
a = −0.216380 + 1.198020I
b = −1.027760 − 0.456095I
−3.59587 − 7.09073I 0
u = −1.220350 + 0.209824I
a = 0.240259 + 1.184820I
b = 1.132200 − 0.505673I
−2.05649 + 2.37182I 0
u = −1.220350 − 0.209824I
a = 0.240259 − 1.184820I
b = 1.132200 + 0.505673I
−2.05649 − 2.37182I 0
u = −1.239870 + 0.079195I
a = 0.079776 + 0.181516I
b = −1.308510 + 0.359200I
−0.76367 + 4.11159I 0
u = −1.239870 − 0.079195I
a = 0.079776 − 0.181516I
b = −1.308510 − 0.359200I
−0.76367 − 4.11159I 0
u = −0.305571 + 0.691387I
a = 1.31729 − 1.56690I
b = 0.935225 + 0.280011I
−3.19789 − 3.11388I −6.21792 + 5.42458I
u = −0.305571 − 0.691387I
a = 1.31729 + 1.56690I
b = 0.935225 − 0.280011I
−3.19789 + 3.11388I −6.21792 − 5.42458I
u = 1.237240 + 0.189888I
a = −0.121801 − 0.109652I
b = 0.987710 + 0.333102I
2.27384 + 0.38414I 0
u = 1.237240 − 0.189888I
a = −0.121801 + 0.109652I
b = 0.987710 − 0.333102I
2.27384 − 0.38414I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.235239 + 0.703017I
a = 0.404597 − 0.343920I
b = −0.473645 − 0.664736I
0.65019 + 3.24933I 1.31667 − 4.26581I
u = 0.235239 − 0.703017I
a = 0.404597 + 0.343920I
b = −0.473645 + 0.664736I
0.65019 − 3.24933I 1.31667 + 4.26581I
u = −1.233480 + 0.335060I
a = −0.732802 + 0.658777I
b = −1.062360 − 0.337000I
−3.23505 − 5.10584I 0
u = −1.233480 − 0.335060I
a = −0.732802 − 0.658777I
b = −1.062360 + 0.337000I
−3.23505 + 5.10584I 0
u = 0.641954 + 0.273036I
a = −0.142359 + 0.908731I
b = 0.640329 − 0.603514I
2.32665 + 0.32348I 5.25845 − 1.82103I
u = 0.641954 − 0.273036I
a = −0.142359 − 0.908731I
b = 0.640329 + 0.603514I
2.32665 − 0.32348I 5.25845 + 1.82103I
u = −1.285400 + 0.213367I
a = −0.93465 + 2.85309I
b = −0.934262 − 0.427913I
0.654419 − 1.065000I 0
u = −1.285400 − 0.213367I
a = −0.93465 − 2.85309I
b = −0.934262 + 0.427913I
0.654419 + 1.065000I 0
u = −1.288580 + 0.195899I
a = 1.43230 − 1.20557I
b = −0.982426 + 0.963915I
3.71266 + 0.80569I 0
u = −1.288580 − 0.195899I
a = 1.43230 + 1.20557I
b = −0.982426 − 0.963915I
3.71266 − 0.80569I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.285080 + 0.242605I
a = −0.325908 + 0.834995I
b = 0.254221 − 0.713807I
0.53289 + 2.24449I 0
u = 1.285080 − 0.242605I
a = −0.325908 − 0.834995I
b = 0.254221 + 0.713807I
0.53289 − 2.24449I 0
u = −1.288460 + 0.230065I
a = −1.86772 + 1.35606I
b = 0.605807 − 0.633999I
0.45040 − 4.03098I 0
u = −1.288460 − 0.230065I
a = −1.86772 − 1.35606I
b = 0.605807 + 0.633999I
0.45040 + 4.03098I 0
u = −0.232760 + 0.633710I
a = 1.50550 − 1.36661I
b = 1.270070 + 0.569449I
−3.18629 − 6.33519I −3.14862 + 12.03347I
u = −0.232760 − 0.633710I
a = 1.50550 + 1.36661I
b = 1.270070 − 0.569449I
−3.18629 + 6.33519I −3.14862 − 12.03347I
u = −1.303760 + 0.250568I
a = 0.42423 − 2.11325I
b = 1.101360 + 0.686491I
2.99432 − 6.05078I 0
u = −1.303760 − 0.250568I
a = 0.42423 + 2.11325I
b = 1.101360 − 0.686491I
2.99432 + 6.05078I 0
u = 0.051728 + 0.663678I
a = −1.51687 − 0.44769I
b = −1.024090 + 0.575987I
−1.22613 + 2.75786I −2.65450 − 2.60934I
u = 0.051728 − 0.663678I
a = −1.51687 + 0.44769I
b = −1.024090 − 0.575987I
−1.22613 − 2.75786I −2.65450 + 2.60934I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.107918 + 0.656610I
a = −1.25879 + 2.14517I
b = −1.061850 − 0.537149I
−5.38016 − 5.47743I −9.82084 + 6.44409I
u = −0.107918 − 0.656610I
a = −1.25879 − 2.14517I
b = −1.061850 + 0.537149I
−5.38016 + 5.47743I −9.82084 − 6.44409I
u = −0.660616 + 0.073556I
a = 0.618520 − 1.253390I
b = 0.895989 + 0.597110I
1.57071 − 4.30992I 4.28889 + 6.85006I
u = −0.660616 − 0.073556I
a = 0.618520 + 1.253390I
b = 0.895989 − 0.597110I
1.57071 + 4.30992I 4.28889 − 6.85006I
u = 1.313710 + 0.241466I
a = −0.780841 − 0.440678I
b = −1.068580 − 0.182131I
1.08249 + 4.90601I 0
u = 1.313710 − 0.241466I
a = −0.780841 + 0.440678I
b = −1.068580 + 0.182131I
1.08249 − 4.90601I 0
u = 1.289040 + 0.356639I
a = −0.041263 − 0.873175I
b = −0.943221 − 0.301307I
−2.79875 + 3.16373I 0
u = 1.289040 − 0.356639I
a = −0.041263 + 0.873175I
b = −0.943221 + 0.301307I
−2.79875 − 3.16373I 0
u = 1.331160 + 0.228298I
a = 0.12635 − 2.10173I
b = −0.783896 + 1.071910I
4.30701 + 6.39294I 0
u = 1.331160 − 0.228298I
a = 0.12635 + 2.10173I
b = −0.783896 − 1.071910I
4.30701 − 6.39294I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.340690 + 0.174728I
a = −1.074840 − 0.818066I
b = 0.441055 + 0.970931I
4.93415 + 0.07314I 0
u = 1.340690 − 0.174728I
a = −1.074840 + 0.818066I
b = 0.441055 − 0.970931I
4.93415 − 0.07314I 0
u = 1.347990 + 0.123766I
a = 2.47858 + 0.55625I
b = −0.829918 − 0.381993I
1.08424 − 2.31644I 0
u = 1.347990 − 0.123766I
a = 2.47858 − 0.55625I
b = −0.829918 + 0.381993I
1.08424 + 2.31644I 0
u = −1.264160 + 0.488046I
a = −0.149323 − 0.190707I
b = −0.827861 + 0.220619I
−2.13885 − 4.09392I 0
u = −1.264160 − 0.488046I
a = −0.149323 + 0.190707I
b = −0.827861 − 0.220619I
−2.13885 + 4.09392I 0
u = 1.338380 + 0.267903I
a = −0.30424 + 2.95672I
b = 1.015670 − 0.585199I
−0.80604 + 8.84631I 0
u = 1.338380 − 0.267903I
a = −0.30424 − 2.95672I
b = 1.015670 + 0.585199I
−0.80604 − 8.84631I 0
u = −0.014498 + 0.634879I
a = 0.965550 + 0.059490I
b = −0.411697 − 0.598157I
−3.51388 + 0.94620I −5.93034 − 0.85000I
u = −0.014498 − 0.634879I
a = 0.965550 − 0.059490I
b = −0.411697 + 0.598157I
−3.51388 − 0.94620I −5.93034 + 0.85000I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.341020 + 0.325292I
a = −0.319508 − 0.763984I
b = 1.399080 − 0.055416I
−4.49309 − 9.26298I 0
u = −1.341020 − 0.325292I
a = −0.319508 + 0.763984I
b = 1.399080 + 0.055416I
−4.49309 + 9.26298I 0
u = −0.046328 + 0.601989I
a = 3.03271 + 0.58825I
b = 0.957541 − 0.270349I
−3.21632 − 1.82438I −7.37850 + 2.56071I
u = −0.046328 − 0.601989I
a = 3.03271 − 0.58825I
b = 0.957541 + 0.270349I
−3.21632 + 1.82438I −7.37850 − 2.56071I
u = −1.383490 + 0.203364I
a = 0.77665 − 1.26093I
b = −0.068033 + 0.886656I
5.67947 − 3.84340I 0
u = −1.383490 − 0.203364I
a = 0.77665 + 1.26093I
b = −0.068033 − 0.886656I
5.67947 + 3.84340I 0
u = 0.286197 + 0.523035I
a = −0.693003 − 0.555111I
b = −0.343974 + 0.639364I
0.27805 + 1.47291I 2.31189 − 3.55895I
u = 0.286197 − 0.523035I
a = −0.693003 + 0.555111I
b = −0.343974 − 0.639364I
0.27805 − 1.47291I 2.31189 + 3.55895I
u = 1.398270 + 0.126201I
a = −1.31607 − 0.81801I
b = 1.055110 + 0.696789I
3.72771 − 1.60223I 0
u = 1.398270 − 0.126201I
a = −1.31607 + 0.81801I
b = 1.055110 − 0.696789I
3.72771 + 1.60223I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.385930 + 0.258089I
a = 0.08055 − 2.26566I
b = −1.30652 + 0.64174I
1.95632 + 9.61573I 0
u = 1.385930 − 0.258089I
a = 0.08055 + 2.26566I
b = −1.30652 − 0.64174I
1.95632 − 9.61573I 0
u = 1.376150 + 0.318704I
a = 0.62793 + 2.22037I
b = 1.090750 − 0.600637I
3.89259 + 11.99520I 0
u = 1.376150 − 0.318704I
a = 0.62793 − 2.22037I
b = 1.090750 + 0.600637I
3.89259 − 11.99520I 0
u = −1.397690 + 0.206523I
a = 0.23606 − 1.56090I
b = 0.382058 + 0.827988I
5.64023 − 4.18276I 0
u = −1.397690 − 0.206523I
a = 0.23606 + 1.56090I
b = 0.382058 − 0.827988I
5.64023 + 4.18276I 0
u = −1.38908 + 0.28476I
a = −1.119860 + 0.514843I
b = 0.446373 − 0.753770I
5.80637 − 6.84590I 0
u = −1.38908 − 0.28476I
a = −1.119860 − 0.514843I
b = 0.446373 + 0.753770I
5.80637 + 6.84590I 0
u = 1.42371 + 0.02338I
a = 0.81141 + 1.82550I
b = −0.959007 − 0.705674I
7.97409 − 4.11261I 0
u = 1.42371 − 0.02338I
a = 0.81141 − 1.82550I
b = −0.959007 + 0.705674I
7.97409 + 4.11261I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42793 + 0.07169I
a = 0.83963 + 1.73453I
b = −0.708158 − 0.760697I
8.71683 − 1.42435I 0
u = −1.42793 − 0.07169I
a = 0.83963 − 1.73453I
b = −0.708158 + 0.760697I
8.71683 + 1.42435I 0
u = −0.462513 + 0.332703I
a = 0.380139 + 0.296075I
b = −1.120650 + 0.546857I
−2.04857 + 3.24927I −1.31395 − 2.13875I
u = −0.462513 − 0.332703I
a = 0.380139 − 0.296075I
b = −1.120650 − 0.546857I
−2.04857 − 3.24927I −1.31395 + 2.13875I
u = −0.062807 + 0.564581I
a = 0.447226 − 0.373579I
b = 0.856584 + 0.981455I
−0.13828 − 3.48408I −4.17456 + 6.37397I
u = −0.062807 − 0.564581I
a = 0.447226 + 0.373579I
b = 0.856584 − 0.981455I
−0.13828 + 3.48408I −4.17456 − 6.37397I
u = 1.40597 + 0.32561I
a = 1.11586 + 1.04697I
b = −0.417371 − 0.998080I
2.22103 + 12.76300I 0
u = 1.40597 − 0.32561I
a = 1.11586 − 1.04697I
b = −0.417371 + 0.998080I
2.22103 − 12.76300I 0
u = 1.42730 + 0.29068I
a = −0.23713 − 1.95978I
b = −0.989534 + 0.413380I
2.35464 + 6.74741I 0
u = 1.42730 − 0.29068I
a = −0.23713 + 1.95978I
b = −0.989534 − 0.413380I
2.35464 − 6.74741I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42268 + 0.33037I
a = −0.933547 − 1.033410I
b = 0.591135 + 0.709360I
2.07597 + 4.27513I 0
u = 1.42268 − 0.33037I
a = −0.933547 + 1.033410I
b = 0.591135 − 0.709360I
2.07597 − 4.27513I 0
u = −1.42028 + 0.35130I
a = −0.13660 + 2.23521I
b = −1.181510 − 0.674850I
−0.1426 − 18.8140I 0
u = −1.42028 − 0.35130I
a = −0.13660 − 2.23521I
b = −1.181510 + 0.674850I
−0.1426 + 18.8140I 0
u = 0.283349 + 0.453426I
a = −0.833098 − 0.166446I
b = 0.027745 + 0.713970I
0.451489 + 1.313460I 4.43011 − 5.18918I
u = 0.283349 − 0.453426I
a = −0.833098 + 0.166446I
b = 0.027745 − 0.713970I
0.451489 − 1.313460I 4.43011 + 5.18918I
u = 1.49176 + 0.01117I
a = −0.40095 + 1.69312I
b = 0.605739 − 0.736610I
6.66225 − 3.55941I 0
u = 1.49176 − 0.01117I
a = −0.40095 − 1.69312I
b = 0.605739 + 0.736610I
6.66225 + 3.55941I 0
u = −1.45922 + 0.38895I
a = −0.04132 − 1.98850I
b = 1.021220 + 0.619356I
0.78262 − 9.39430I 0
u = −1.45922 − 0.38895I
a = −0.04132 + 1.98850I
b = 1.021220 − 0.619356I
0.78262 + 9.39430I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49938 + 0.21106I
a = 1.182780 − 0.621147I
b = −0.852786 + 0.326083I
3.02808 − 3.76961I 0
u = −1.49938 − 0.21106I
a = 1.182780 + 0.621147I
b = −0.852786 − 0.326083I
3.02808 + 3.76961I 0
u = −0.471922
a = −0.923633
b = −0.896592
−1.83682 −3.53830
u = −0.211913 + 0.419594I
a = −0.149374 + 1.219750I
b = −0.542353 + 0.689988I
0.15758 + 2.13562I 0.765701 − 1.016074I
u = −0.211913 − 0.419594I
a = −0.149374 − 1.219750I
b = −0.542353 − 0.689988I
0.15758 − 2.13562I 0.765701 + 1.016074I
u = −1.54866 + 0.03684I
a = −0.87285 − 1.46188I
b = 1.013370 + 0.617331I
5.42233 − 8.72251I 0
u = −1.54866 − 0.03684I
a = −0.87285 + 1.46188I
b = 1.013370 − 0.617331I
5.42233 + 8.72251I 0
u = −0.171390 + 0.265251I
a = −3.61939 − 1.83440I
b = 1.024380 − 0.332569I
−3.72652 + 3.87879I −6.37269 − 2.76527I
u = −0.171390 − 0.265251I
a = −3.61939 + 1.83440I
b = 1.024380 + 0.332569I
−3.72652 − 3.87879I −6.37269 + 2.76527I
17
II. I
u
2
=
h2u
22
−20u
20
+· · ·−7u
2
+b, −3u
23
−3u
22
+· · ·+a+4, u
24
−12u
22
+· · ·−2u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
11
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
3u
23
+ 3u
22
+ ··· + 3u − 4
−2u
22
+ 20u
20
+ ··· − 6u
3
+ 7u
2
a
2
=
−u
23
+ 10u
21
+ ··· − u
2
+ 6u
3u
23
− 32u
21
+ ··· + 2u − 1
a
1
=
2u
23
− 22u
21
+ ··· + 8u − 1
3u
23
− 32u
21
+ ··· + 2u − 1
a
6
=
2u
22
+ u
21
+ ··· − 2u − 2
u
22
− 11u
20
+ ··· − u − 1
a
7
=
u
22
+ u
21
+ ··· − 2u − 3
−u
23
− u
22
+ ··· − 2u − 1
a
9
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
12
=
u
23
− 12u
21
+ ··· + 7u − 1
3u
23
− 32u
21
+ ··· + 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −5u
23
−2u
22
+52u
21
+13u
20
−228u
19
−26u
18
+527u
17
−5u
16
−631u
15
+75u
14
+232u
13
−
36u
12
+296u
11
−150u
10
−345u
9
+229u
8
+105u
7
−104u
6
−33u
5
+16u
4
+36u
3
−22u
2
−4u+4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 12u
23
+ ··· − 15u + 1
c
2
u
24
− 6u
22
+ ··· + u + 1
c
3
, c
4
u
24
− 12u
22
+ ··· − 2u + 1
c
5
u
24
− u
23
+ ··· + 2u
3
+ 1
c
6
u
24
+ 10u
22
+ ··· − u + 1
c
7
u
24
− 6u
22
+ ··· − u + 1
c
8
u
24
+ 3u
23
+ ··· − 2u
2
+ 1
c
9
u
24
+ 4u
22
+ ··· + 2u + 1
c
10
u
24
− 12u
22
+ ··· + 2u + 1
c
11
u
24
+ 10u
22
+ ··· + u + 1
c
12
u
24
− 4u
23
+ ··· − 6u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 12y
23
+ ··· + 5y + 1
c
2
, c
7
y
24
− 12y
23
+ ··· − 15y + 1
c
3
, c
4
, c
10
y
24
− 24y
23
+ ··· + 12y + 1
c
5
y
24
− 7y
23
+ ··· − 4y
2
+ 1
c
6
, c
11
y
24
+ 20y
23
+ ··· + 21y + 1
c
8
y
24
− 3y
23
+ ··· − 4y + 1
c
9
y
24
+ 8y
23
+ ··· + 8y + 1
c
12
y
24
− 12y
23
+ ··· − 12y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.068651 + 0.929424I
a = −0.779468 − 0.069325I
b = −0.919955 + 0.342426I
−5.90696 + 1.40699I −0.05401 − 5.04118I
u = −0.068651 − 0.929424I
a = −0.779468 + 0.069325I
b = −0.919955 − 0.342426I
−5.90696 − 1.40699I −0.05401 + 5.04118I
u = −1.169690 + 0.336481I
a = 0.118835 − 0.515687I
b = 1.023000 + 0.327982I
−2.71990 − 5.96107I −2.03566 + 9.01778I
u = −1.169690 − 0.336481I
a = 0.118835 + 0.515687I
b = 1.023000 − 0.327982I
−2.71990 + 5.96107I −2.03566 − 9.01778I
u = −1.216630 + 0.130232I
a = −0.817041 − 0.399318I
b = −1.160540 + 0.376595I
−1.09013 + 3.04838I −1.88313 − 2.66207I
u = −1.216630 − 0.130232I
a = −0.817041 + 0.399318I
b = −1.160540 − 0.376595I
−1.09013 − 3.04838I −1.88313 + 2.66207I
u = 1.249520 + 0.073520I
a = 1.42032 + 0.82987I
b = −0.649867 + 0.185310I
1.068270 − 0.560706I −1.91586 + 1.84291I
u = 1.249520 − 0.073520I
a = 1.42032 − 0.82987I
b = −0.649867 − 0.185310I
1.068270 + 0.560706I −1.91586 − 1.84291I
u = 1.231740 + 0.410206I
a = 0.463258 + 0.212630I
b = 0.838774 + 0.283314I
−1.97455 + 3.43328I 0.001801 + 0.732890I
u = 1.231740 − 0.410206I
a = 0.463258 − 0.212630I
b = 0.838774 − 0.283314I
−1.97455 − 3.43328I 0.001801 − 0.732890I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.324470 + 0.572839I
a = 0.78856 − 2.18880I
b = 1.095880 + 0.468311I
−3.77922 − 5.20044I −5.17463 + 7.04376I
u = −0.324470 − 0.572839I
a = 0.78856 + 2.18880I
b = 1.095880 − 0.468311I
−3.77922 + 5.20044I −5.17463 − 7.04376I
u = 1.335640 + 0.131798I
a = −1.49295 − 0.94299I
b = 0.927331 + 0.901413I
4.76519 − 1.46228I 8.75844 + 4.53633I
u = 1.335640 − 0.131798I
a = −1.49295 + 0.94299I
b = 0.927331 − 0.901413I
4.76519 + 1.46228I 8.75844 − 4.53633I
u = −1.382630 + 0.158548I
a = 0.06907 − 1.77420I
b = 0.706472 + 0.869930I
5.39705 − 5.11184I 5.06340 + 6.86539I
u = −1.382630 − 0.158548I
a = 0.06907 + 1.77420I
b = 0.706472 − 0.869930I
5.39705 + 5.11184I 5.06340 − 6.86539I
u = 1.41196 + 0.28189I
a = 0.12280 − 2.23498I
b = −1.118650 + 0.593449I
1.78373 + 8.57178I 0.47705 − 5.72602I
u = 1.41196 − 0.28189I
a = 0.12280 + 2.23498I
b = −1.118650 − 0.593449I
1.78373 − 8.57178I 0.47705 + 5.72602I
u = −1.44505 + 0.20614I
a = 1.13988 − 1.06214I
b = −0.565803 + 0.404626I
3.88649 − 4.27371I 5.08249 + 4.87114I
u = −1.44505 − 0.20614I
a = 1.13988 + 1.06214I
b = −0.565803 − 0.404626I
3.88649 + 4.27371I 5.08249 − 4.87114I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.312652 + 0.364008I
a = −1.53580 − 2.12958I
b = 0.651268 + 0.301680I
−1.97511 + 1.86915I 0.15434 − 3.03982I
u = 0.312652 − 0.364008I
a = −1.53580 + 2.12958I
b = 0.651268 − 0.301680I
−1.97511 − 1.86915I 0.15434 + 3.03982I
u = 0.065601 + 0.351466I
a = −1.49746 + 0.80113I
b = −0.827907 + 0.854306I
0.54513 + 3.18351I 5.52576 − 4.38971I
u = 0.065601 − 0.351466I
a = −1.49746 − 0.80113I
b = −0.827907 − 0.854306I
0.54513 − 3.18351I 5.52576 + 4.38971I
23
III. I
u
3
= hb + 1, a + 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
−1
a
4
=
1
−1
a
11
=
−1
0
a
5
=
0
−1
a
8
=
−1
−1
a
2
=
0
−1
a
1
=
−1
−1
a
6
=
1
0
a
7
=
−1
0
a
9
=
0
−1
a
12
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
10
u + 1
c
6
, c
9
, c
11
u
c
12
u − 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
10
, c
12
y −1
c
6
, c
9
, c
11
y
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = −1.00000
−1.64493 −6.00000
27
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
24
− 12u
23
+ ··· − 15u + 1)
· (u
129
+ 58u
128
+ ··· + 1112505u + 85849)
c
2
(u + 1)(u
24
− 6u
22
+ ··· + u + 1)(u
129
− 29u
127
+ ··· + 259u + 293)
c
3
, c
4
(u + 1)(u
24
− 12u
22
+ ··· − 2u + 1)(u
129
− 57u
127
+ ··· + 378u + 43)
c
5
(u + 1)(u
24
− u
23
+ ··· + 2u
3
+ 1)(u
129
+ 3u
128
+ ··· − 40u + 1)
c
6
u(u
24
+ 10u
22
+ ··· − u + 1)(u
129
+ u
128
+ ··· + 76623u + 52995)
c
7
(u + 1)(u
24
− 6u
22
+ ··· − u + 1)(u
129
− 29u
127
+ ··· + 259u + 293)
c
8
(u + 1)(u
24
+ 3u
23
+ ··· − 2u
2
+ 1)(u
129
− 9u
128
+ ··· − 40u + 1)
c
9
u(u
24
+ 4u
22
+ ··· + 2u + 1)
· (u
129
− 3u
128
+ ··· + 20927496u + 1128105)
c
10
(u + 1)(u
24
− 12u
22
+ ··· + 2u + 1)(u
129
− 57u
127
+ ··· + 378u + 43)
c
11
u(u
24
+ 10u
22
+ ··· + u + 1)(u
129
+ u
128
+ ··· + 76623u + 52995)
c
12
(u − 1)(u
24
− 4u
23
+ ··· − 6u
2
+ 1)
· (u
129
+ 4u
128
+ ··· − 146894u − 14831)
28
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
24
+ 12y
23
+ ··· + 5y + 1)
· (y
129
+ 38y
128
+ ··· + 16755519645y −7370050801)
c
2
, c
7
(y −1)(y
24
− 12y
23
+ ··· − 15y + 1)
· (y
129
− 58y
128
+ ··· + 1112505y −85849)
c
3
, c
4
, c
10
(y −1)(y
24
− 24y
23
+ ··· + 12y + 1)
· (y
129
− 114y
128
+ ··· − 32126y −1849)
c
5
(y −1)(y
24
− 7y
23
+ ··· − 4y
2
+ 1)(y
129
− 5y
128
+ ··· + 90y −1)
c
6
, c
11
y(y
24
+ 20y
23
+ ··· + 21y + 1)
· (y
129
+ 89y
128
+ ··· − 89198342211y −2808470025)
c
8
(y −1)(y
24
− 3y
23
+ ··· − 4y + 1)(y
129
− 13y
128
+ ··· + 10y −1)
c
9
y(y
24
+ 8y
23
+ ··· + 8y + 1)
· (y
129
+ 41y
128
+ ··· + 17191577913966y −1272620891025)
c
12
(y −1)(y
24
− 12y
23
+ ··· − 12y + 1)
· (y
129
− 34y
128
+ ··· + 16675400862y −219958561)
29
