12a
0364
(K12a
0364
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 11 2 12 1 7 5 10 4
Solving Sequence
2,6 3,9
4 7 10 1 8 12 11 5
c
2
c
3
c
6
c
9
c
1
c
8
c
12
c
11
c
5
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.06101 × 10
668
u
182
+ 1.45399 × 10
669
u
181
+ ··· + 3.50750 × 10
668
b + 1.63631 × 10
672
,
4.31223 × 10
671
u
182
+ 1.20316 × 10
672
u
181
+ ··· + 3.97400 × 10
671
a + 1.18875 × 10
675
,
u
183
+ u
182
+ ··· + 4256u + 1133i
I
u
2
= h24823104u
41
19103471u
40
+ ··· + 3944339b 19426104,
10847937u
41
23370443u
40
+ ··· + 3944339a + 1833879, u
42
+ 11u
40
+ ··· u + 1i
* 2 irreducible components of dim
C
= 0, with total 225 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
= h3.06 × 10
668
u
182
+ 1.45 × 10
669
u
181
+ · · · + 3.51 × 10
668
b + 1.64 ×
10
672
, 4.31 × 10
671
u
182
+ 1.20 × 10
672
u
181
+ · · · + 3.97 × 10
671
a + 1.19 ×
10
675
, u
183
+ u
182
+ · · · + 4256u + 1133i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
1.08511u
182
3.02757u
181
+ ··· 7046.61u 2991.31
0.872703u
182
4.14537u
181
+ ··· 13315.2u 4665.18
a
4
=
1.12129u
182
+ 0.925627u
181
+ ··· + 4093.75u + 1132.16
1.05786u
182
+ 1.82765u
181
+ ··· + 6881.98u + 2201.09
a
7
=
u
u
a
10
=
0.139695u
182
1.77491u
181
+ ··· 5689.73u 2039.58
2.09751u
182
2.89272u
181
+ ··· 11958.4u 3713.44
a
1
=
u
2
+ 1
u
4
a
8
=
0.320040u
182
2.23656u
181
+ ··· 7280.85u 2535.00
1.70018u
182
2.74137u
181
+ ··· 10716.3u 3390.53
a
12
=
0.323583u
182
0.355194u
181
+ ··· 1218.60u 260.576
2.31378u
182
1.07817u
181
+ ··· 5843.16u 1298.01
a
11
=
0.0734871u
182
+ 2.24058u
181
+ ··· + 6864.55u + 2639.36
3.39552u
182
+ 1.13443u
181
+ ··· 496.042u + 1175.34
a
5
=
1.99923u
182
+ 1.23701u
181
+ ··· + 6552.84u + 1660.68
1.79503u
182
4.25068u
181
+ ··· 10911.1u 4668.15
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1.45862u
182
+ 0.408690u
181
+ ··· + 1561.89u + 128.705
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
183
+ 77u
182
+ ··· 46277120u 1283689
c
2
, c
6
u
183
u
182
+ ··· + 4256u 1133
c
3
u
183
+ u
182
+ ··· + 31u 3
c
4
u
183
+ 3u
182
+ ··· + 555350u 53533
c
5
, c
10
u
183
+ u
182
+ ··· 173u 59
c
7
u
183
2u
182
+ ··· + 334697u 27379
c
8
u
183
5u
182
+ ··· 6926u 485
c
9
u
183
+ 7u
182
+ ··· + 1157925u 194803
c
11
u
183
87u
182
+ ··· + 82911u 3481
c
12
u
183
+ 16u
182
+ ··· 199u 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
183
+ 65y
182
+ ··· 180776219221564y 1647857448721
c
2
, c
6
y
183
+ 77y
182
+ ··· 46277120y 1283689
c
3
y
183
17y
182
+ ··· + 67y 9
c
4
y
183
+ 11y
182
+ ··· 122436449664y 2865782089
c
5
, c
10
y
183
87y
182
+ ··· + 82911y 3481
c
7
y
183
28y
182
+ ··· 2771494231y 749609641
c
8
y
183
29y
182
+ ··· 40132714y 235225
c
9
y
183
11y
182
+ ··· 18463850066073y 37948208809
c
11
y
183
+ 33y
182
+ ··· + 364826579y 12117361
c
12
y
183
+ 10y
182
+ ··· 2819y 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.002506 + 1.001090I
a = 0.301136 + 1.067720I
b = 0.015541 + 0.450831I
2.35185 1.36074I 0
u = 0.002506 1.001090I
a = 0.301136 1.067720I
b = 0.015541 0.450831I
2.35185 + 1.36074I 0
u = 0.657408 + 0.760366I
a = 0.640158 0.397181I
b = 0.0807366 + 0.0498924I
3.94780 1.03684I 0
u = 0.657408 0.760366I
a = 0.640158 + 0.397181I
b = 0.0807366 0.0498924I
3.94780 + 1.03684I 0
u = 0.907481 + 0.395088I
a = 0.975120 0.368474I
b = 0.023349 0.616263I
1.78380 + 1.10430I 0
u = 0.907481 0.395088I
a = 0.975120 + 0.368474I
b = 0.023349 + 0.616263I
1.78380 1.10430I 0
u = 0.346743 + 0.922544I
a = 1.94060 + 0.03413I
b = 2.05091 0.63156I
2.22716 + 1.66256I 0
u = 0.346743 0.922544I
a = 1.94060 0.03413I
b = 2.05091 + 0.63156I
2.22716 1.66256I 0
u = 0.832406 + 0.580904I
a = 0.816072 1.107820I
b = 0.21102 1.46237I
5.69571 + 6.18009I 0
u = 0.832406 0.580904I
a = 0.816072 + 1.107820I
b = 0.21102 + 1.46237I
5.69571 6.18009I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.445854 + 0.912506I
a = 0.250178 + 0.647036I
b = 0.582212 0.638228I
4.07840 + 1.74509I 0
u = 0.445854 0.912506I
a = 0.250178 0.647036I
b = 0.582212 + 0.638228I
4.07840 1.74509I 0
u = 0.550473 + 0.855625I
a = 1.58869 + 0.29474I
b = 1.47188 + 2.18116I
3.11251 0.85633I 0
u = 0.550473 0.855625I
a = 1.58869 0.29474I
b = 1.47188 2.18116I
3.11251 + 0.85633I 0
u = 0.550724 + 0.859621I
a = 1.54212 1.93111I
b = 0.40476 1.59933I
3.09891 3.55549I 0
u = 0.550724 0.859621I
a = 1.54212 + 1.93111I
b = 0.40476 + 1.59933I
3.09891 + 3.55549I 0
u = 0.539399 + 0.794949I
a = 1.32069 1.68704I
b = 1.17697 2.20251I
6.50793 + 1.54821I 0
u = 0.539399 0.794949I
a = 1.32069 + 1.68704I
b = 1.17697 + 2.20251I
6.50793 1.54821I 0
u = 0.100235 + 1.035900I
a = 0.418216 + 0.328869I
b = 0.218597 1.065900I
6.21715 0.49274I 0
u = 0.100235 1.035900I
a = 0.418216 0.328869I
b = 0.218597 + 1.065900I
6.21715 + 0.49274I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.747476 + 0.729954I
a = 1.42324 + 0.66409I
b = 0.32911 + 2.22620I
2.50612 1.04846I 0
u = 0.747476 0.729954I
a = 1.42324 0.66409I
b = 0.32911 2.22620I
2.50612 + 1.04846I 0
u = 0.557270 + 0.773086I
a = 2.28692 + 1.27034I
b = 1.14776 + 1.11615I
0.232614 + 0.596001I 0
u = 0.557270 0.773086I
a = 2.28692 1.27034I
b = 1.14776 1.11615I
0.232614 0.596001I 0
u = 0.627455 + 0.716670I
a = 2.33890 + 0.93316I
b = 0.807083 + 1.028980I
2.26284 6.40383I 0
u = 0.627455 0.716670I
a = 2.33890 0.93316I
b = 0.807083 1.028980I
2.26284 + 6.40383I 0
u = 0.728434 + 0.611027I
a = 1.24633 0.73003I
b = 0.482467 1.183330I
7.15615 + 1.84565I 0
u = 0.728434 0.611027I
a = 1.24633 + 0.73003I
b = 0.482467 + 1.183330I
7.15615 1.84565I 0
u = 0.433567 + 0.963298I
a = 1.84915 0.03503I
b = 1.84761 1.03237I
3.99443 + 3.51059I 0
u = 0.433567 0.963298I
a = 1.84915 + 0.03503I
b = 1.84761 + 1.03237I
3.99443 3.51059I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.931814 + 0.508864I
a = 0.913621 1.050700I
b = 0.474141 1.264530I
0.02127 9.16097I 0
u = 0.931814 0.508864I
a = 0.913621 + 1.050700I
b = 0.474141 + 1.264530I
0.02127 + 9.16097I 0
u = 0.986706 + 0.407027I
a = 0.636220 + 0.399246I
b = 0.065403 + 0.890735I
4.94639 + 5.58121I 0
u = 0.986706 0.407027I
a = 0.636220 0.399246I
b = 0.065403 0.890735I
4.94639 5.58121I 0
u = 0.654680 + 0.844531I
a = 1.20925 + 0.95465I
b = 1.196920 + 0.684125I
0.61558 2.54624I 0
u = 0.654680 0.844531I
a = 1.20925 0.95465I
b = 1.196920 0.684125I
0.61558 + 2.54624I 0
u = 0.731449 + 0.571623I
a = 1.53574 + 1.48199I
b = 0.37856 + 1.76760I
0.37741 5.71633I 0
u = 0.731449 0.571623I
a = 1.53574 1.48199I
b = 0.37856 1.76760I
0.37741 + 5.71633I 0
u = 0.516145 + 0.771156I
a = 0.952646 + 0.811885I
b = 0.324158 0.327902I
0.53621 + 2.32801I 0
u = 0.516145 0.771156I
a = 0.952646 0.811885I
b = 0.324158 + 0.327902I
0.53621 2.32801I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.926464 + 0.046019I
a = 0.367772 0.284571I
b = 0.358099 0.222420I
3.54138 + 2.83842I 0
u = 0.926464 0.046019I
a = 0.367772 + 0.284571I
b = 0.358099 + 0.222420I
3.54138 2.83842I 0
u = 0.012896 + 1.073490I
a = 0.737068 0.531654I
b = 0.405083 + 0.417015I
0.32963 + 5.18055I 0
u = 0.012896 1.073490I
a = 0.737068 + 0.531654I
b = 0.405083 0.417015I
0.32963 5.18055I 0
u = 0.568689 + 0.915928I
a = 0.82583 1.67184I
b = 0.74892 2.67127I
0.69467 5.11406I 0
u = 0.568689 0.915928I
a = 0.82583 + 1.67184I
b = 0.74892 + 2.67127I
0.69467 + 5.11406I 0
u = 0.619160 + 0.882815I
a = 0.462784 0.132943I
b = 1.094350 + 0.862174I
3.61626 + 6.02592I 0
u = 0.619160 0.882815I
a = 0.462784 + 0.132943I
b = 1.094350 0.862174I
3.61626 6.02592I 0
u = 0.543038 + 0.933500I
a = 0.257256 + 0.203403I
b = 0.434241 0.990715I
1.09057 6.62662I 0
u = 0.543038 0.933500I
a = 0.257256 0.203403I
b = 0.434241 + 0.990715I
1.09057 + 6.62662I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.707658 + 0.818823I
a = 1.55822 + 0.50718I
b = 0.78450 + 2.51756I
3.25753 + 4.56073I 0
u = 0.707658 0.818823I
a = 1.55822 0.50718I
b = 0.78450 2.51756I
3.25753 4.56073I 0
u = 0.757720 + 0.507649I
a = 0.865308 + 0.335743I
b = 0.357419 + 1.226330I
2.79108 2.17795I 0
u = 0.757720 0.507649I
a = 0.865308 0.335743I
b = 0.357419 1.226330I
2.79108 + 2.17795I 0
u = 0.765290 + 0.777732I
a = 0.313788 0.283363I
b = 0.764073 + 0.447255I
1.24383 2.75337I 0
u = 0.765290 0.777732I
a = 0.313788 + 0.283363I
b = 0.764073 0.447255I
1.24383 + 2.75337I 0
u = 0.642154 + 0.885034I
a = 0.605908 0.137387I
b = 0.1325530 0.0361140I
0.97256 2.56913I 0
u = 0.642154 0.885034I
a = 0.605908 + 0.137387I
b = 0.1325530 + 0.0361140I
0.97256 + 2.56913I 0
u = 0.595783 + 0.918335I
a = 1.67611 + 1.20857I
b = 1.09082 + 1.56018I
6.04330 + 2.97947I 0
u = 0.595783 0.918335I
a = 1.67611 1.20857I
b = 1.09082 1.56018I
6.04330 2.97947I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.029805 + 1.094630I
a = 0.088335 + 0.419086I
b = 0.622284 0.818090I
5.69385 4.53725I 0
u = 0.029805 1.094630I
a = 0.088335 0.419086I
b = 0.622284 + 0.818090I
5.69385 + 4.53725I 0
u = 0.720237 + 0.833458I
a = 0.323093 0.535044I
b = 0.886760 + 0.556851I
3.94229 0.87080I 0
u = 0.720237 0.833458I
a = 0.323093 + 0.535044I
b = 0.886760 0.556851I
3.94229 + 0.87080I 0
u = 0.754844 + 0.804416I
a = 0.315687 + 0.638489I
b = 0.019468 + 1.338820I
4.36353 0.84859I 0
u = 0.754844 0.804416I
a = 0.315687 0.638489I
b = 0.019468 1.338820I
4.36353 + 0.84859I 0
u = 0.782981 + 0.783214I
a = 1.076580 + 0.514922I
b = 0.976505 0.481147I
0.11595 4.26403I 0
u = 0.782981 0.783214I
a = 1.076580 0.514922I
b = 0.976505 + 0.481147I
0.11595 + 4.26403I 0
u = 0.348230 + 0.819536I
a = 1.22288 1.43888I
b = 1.72181 1.72458I
2.13854 + 0.82162I 0
u = 0.348230 0.819536I
a = 1.22288 + 1.43888I
b = 1.72181 + 1.72458I
2.13854 0.82162I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.972199 + 0.546222I
a = 0.905079 1.011520I
b = 0.59293 1.36816I
2.2484 + 14.7363I 0
u = 0.972199 0.546222I
a = 0.905079 + 1.011520I
b = 0.59293 + 1.36816I
2.2484 14.7363I 0
u = 0.926293 + 0.626932I
a = 0.718099 + 0.500561I
b = 0.068622 + 1.369810I
5.25177 0.84623I 0
u = 0.926293 0.626932I
a = 0.718099 0.500561I
b = 0.068622 1.369810I
5.25177 + 0.84623I 0
u = 0.644364 + 0.601015I
a = 1.27594 + 1.84739I
b = 0.24025 + 1.69818I
1.74748 + 0.50069I 0
u = 0.644364 0.601015I
a = 1.27594 1.84739I
b = 0.24025 1.69818I
1.74748 0.50069I 0
u = 1.005530 + 0.493859I
a = 0.855579 0.487436I
b = 0.221917 0.783760I
3.95772 6.48113I 0
u = 1.005530 0.493859I
a = 0.855579 + 0.487436I
b = 0.221917 + 0.783760I
3.95772 + 6.48113I 0
u = 0.680848 + 0.895509I
a = 2.02301 1.39181I
b = 0.08403 2.24040I
3.01635 9.89154I 0
u = 0.680848 0.895509I
a = 2.02301 + 1.39181I
b = 0.08403 + 2.24040I
3.01635 + 9.89154I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.293861 + 1.092740I
a = 0.275776 + 0.887136I
b = 1.057290 0.147130I
5.37966 + 0.54573I 0
u = 0.293861 1.092740I
a = 0.275776 0.887136I
b = 1.057290 + 0.147130I
5.37966 0.54573I 0
u = 0.614405 + 0.950872I
a = 0.69550 1.46015I
b = 0.47805 2.61113I
1.54033 + 11.29370I 0
u = 0.614405 0.950872I
a = 0.69550 + 1.46015I
b = 0.47805 + 2.61113I
1.54033 11.29370I 0
u = 0.406869 + 0.762225I
a = 0.517813 0.465383I
b = 1.46685 + 0.25108I
2.26522 2.73823I 0
u = 0.406869 0.762225I
a = 0.517813 + 0.465383I
b = 1.46685 0.25108I
2.26522 + 2.73823I 0
u = 0.706734 + 0.897618I
a = 0.565162 0.517095I
b = 0.477838 0.337322I
3.72711 + 6.31023I 0
u = 0.706734 0.897618I
a = 0.565162 + 0.517095I
b = 0.477838 + 0.337322I
3.72711 6.31023I 0
u = 0.602287 + 0.971494I
a = 1.48413 0.29604I
b = 0.82135 1.38664I
1.18792 4.46977I 0
u = 0.602287 0.971494I
a = 1.48413 + 0.29604I
b = 0.82135 + 1.38664I
1.18792 + 4.46977I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.440159 + 0.730665I
a = 1.49175 + 0.11182I
b = 1.44488 + 1.55039I
2.20716 2.85779I 0
u = 0.440159 0.730665I
a = 1.49175 0.11182I
b = 1.44488 1.55039I
2.20716 + 2.85779I 0
u = 0.066321 + 1.145210I
a = 0.173277 + 1.057000I
b = 0.366641 + 0.617366I
2.18553 1.55193I 0
u = 0.066321 1.145210I
a = 0.173277 1.057000I
b = 0.366641 0.617366I
2.18553 + 1.55193I 0
u = 0.571600 + 0.996567I
a = 1.28701 1.25303I
b = 0.21402 1.44820I
1.09499 + 7.05040I 0
u = 0.571600 0.996567I
a = 1.28701 + 1.25303I
b = 0.21402 + 1.44820I
1.09499 7.05040I 0
u = 0.182935 + 0.825630I
a = 1.09557 1.16253I
b = 1.94970 1.15239I
1.04922 6.70990I 0
u = 0.182935 0.825630I
a = 1.09557 + 1.16253I
b = 1.94970 + 1.15239I
1.04922 + 6.70990I 0
u = 0.734748 + 0.893581I
a = 1.40870 0.16123I
b = 0.685157 0.691738I
4.09264 + 6.47599I 0
u = 0.734748 0.893581I
a = 1.40870 + 0.16123I
b = 0.685157 + 0.691738I
4.09264 6.47599I 0
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.425821 + 0.724945I
a = 1.61129 + 0.01796I
b = 0.401842 + 1.054020I
2.22001 0.03158I 0
u = 0.425821 0.724945I
a = 1.61129 0.01796I
b = 0.401842 1.054020I
2.22001 + 0.03158I 0
u = 0.500021 + 1.055210I
a = 1.46816 + 0.96083I
b = 1.60403 + 1.24379I
3.47825 4.06656I 0
u = 0.500021 1.055210I
a = 1.46816 0.96083I
b = 1.60403 1.24379I
3.47825 + 4.06656I 0
u = 0.536497 + 1.041030I
a = 1.80577 0.29656I
b = 1.50259 1.80856I
3.77068 + 6.27330I 0
u = 0.536497 1.041030I
a = 1.80577 + 0.29656I
b = 1.50259 + 1.80856I
3.77068 6.27330I 0
u = 0.625977 + 1.008080I
a = 2.27038 0.60756I
b = 2.14868 1.97553I
2.94141 5.50909I 0
u = 0.625977 1.008080I
a = 2.27038 + 0.60756I
b = 2.14868 + 1.97553I
2.94141 + 5.50909I 0
u = 0.256991 + 1.163570I
a = 0.366759 + 0.971787I
b = 1.229430 + 0.181151I
3.93847 + 4.09185I 0
u = 0.256991 1.163570I
a = 0.366759 0.971787I
b = 1.229430 0.181151I
3.93847 4.09185I 0
15
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.754021 + 0.287387I
a = 1.07649 1.18000I
b = 0.034614 0.751200I
1.74947 5.45439I 0
u = 0.754021 0.287387I
a = 1.07649 + 1.18000I
b = 0.034614 + 0.751200I
1.74947 + 5.45439I 0
u = 0.693187 + 0.972666I
a = 1.92085 1.00783I
b = 0.55058 2.22183I
1.76365 + 6.53880I 0
u = 0.693187 0.972666I
a = 1.92085 + 1.00783I
b = 0.55058 + 2.22183I
1.76365 6.53880I 0
u = 0.581428 + 1.048690I
a = 0.98044 + 1.14657I
b = 0.80086 + 1.75516I
5.82744 + 3.18112I 0
u = 0.581428 1.048690I
a = 0.98044 1.14657I
b = 0.80086 1.75516I
5.82744 3.18112I 0
u = 0.564537 + 1.063780I
a = 1.82335 0.39956I
b = 1.37094 2.09985I
1.86512 11.45180I 0
u = 0.564537 1.063780I
a = 1.82335 + 0.39956I
b = 1.37094 + 2.09985I
1.86512 + 11.45180I 0
u = 0.174384 + 1.208110I
a = 0.524593 + 0.137775I
b = 0.320091 + 1.012060I
6.60576 2.51542I 0
u = 0.174384 1.208110I
a = 0.524593 0.137775I
b = 0.320091 1.012060I
6.60576 + 2.51542I 0
16
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.651991 + 1.036130I
a = 2.17446 0.68534I
b = 1.90939 2.32363I
1.74039 + 11.02230I 0
u = 0.651991 1.036130I
a = 2.17446 + 0.68534I
b = 1.90939 + 2.32363I
1.74039 11.02230I 0
u = 1.120770 + 0.511977I
a = 0.218490 0.312685I
b = 0.508258 + 0.256981I
0.07891 3.60178I 0
u = 1.120770 0.511977I
a = 0.218490 + 0.312685I
b = 0.508258 0.256981I
0.07891 + 3.60178I 0
u = 0.568498 + 1.094660I
a = 1.57377 + 0.76408I
b = 1.70332 + 1.39301I
4.01703 + 10.33240I 0
u = 0.568498 1.094660I
a = 1.57377 0.76408I
b = 1.70332 1.39301I
4.01703 10.33240I 0
u = 0.286438 + 1.203250I
a = 0.463832 + 0.372551I
b = 0.391616 + 1.153900I
4.85145 3.50894I 0
u = 0.286438 1.203250I
a = 0.463832 0.372551I
b = 0.391616 1.153900I
4.85145 + 3.50894I 0
u = 1.201630 + 0.366700I
a = 0.227274 0.364806I
b = 0.398790 + 0.251327I
1.21805 + 8.43185I 0
u = 1.201630 0.366700I
a = 0.227274 + 0.364806I
b = 0.398790 0.251327I
1.21805 8.43185I 0
17
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.163361 + 0.722347I
a = 0.17044 + 1.68096I
b = 0.554933 0.439499I
3.60569 + 0.91408I 0
u = 0.163361 0.722347I
a = 0.17044 1.68096I
b = 0.554933 + 0.439499I
3.60569 0.91408I 0
u = 0.887416 + 0.897545I
a = 0.876365 + 0.557933I
b = 1.185220 0.447285I
0.484505 + 0.801877I 0
u = 0.887416 0.897545I
a = 0.876365 0.557933I
b = 1.185220 + 0.447285I
0.484505 0.801877I 0
u = 0.679377 + 1.064960I
a = 1.75357 + 0.61628I
b = 1.44551 + 1.61863I
4.22031 11.83660I 0
u = 0.679377 1.064960I
a = 1.75357 0.61628I
b = 1.44551 1.61863I
4.22031 + 11.83660I 0
u = 0.614405 + 1.108390I
a = 1.15925 0.81638I
b = 0.64869 1.31796I
0.95377 + 7.38140I 0
u = 0.614405 1.108390I
a = 1.15925 + 0.81638I
b = 0.64869 + 1.31796I
0.95377 7.38140I 0
u = 0.048543 + 1.286710I
a = 0.179118 0.247357I
b = 0.188381 + 0.663010I
6.90319 6.80569I 0
u = 0.048543 1.286710I
a = 0.179118 + 0.247357I
b = 0.188381 0.663010I
6.90319 + 6.80569I 0
18
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.741752 + 1.062770I
a = 0.638047 + 0.391667I
b = 1.080460 + 0.126837I
0.73666 1.74573I 0
u = 0.741752 1.062770I
a = 0.638047 0.391667I
b = 1.080460 0.126837I
0.73666 + 1.74573I 0
u = 0.743358 + 1.068010I
a = 1.40354 0.56029I
b = 0.73904 1.54332I
3.89033 5.27299I 0
u = 0.743358 1.068010I
a = 1.40354 + 0.56029I
b = 0.73904 + 1.54332I
3.89033 + 5.27299I 0
u = 0.685622 + 0.062792I
a = 1.26008 1.09590I
b = 0.266208 0.336374I
0.922578 + 0.048130I 0
u = 0.685622 0.062792I
a = 1.26008 + 1.09590I
b = 0.266208 + 0.336374I
0.922578 0.048130I 0
u = 0.169187 + 0.659747I
a = 1.92803 + 1.62798I
b = 0.028611 + 1.086390I
1.92712 2.23063I 0
u = 0.169187 0.659747I
a = 1.92803 1.62798I
b = 0.028611 1.086390I
1.92712 + 2.23063I 0
u = 0.691667 + 1.124390I
a = 1.68925 + 0.55794I
b = 1.61313 + 1.80059I
1.9117 + 15.1089I 0
u = 0.691667 1.124390I
a = 1.68925 0.55794I
b = 1.61313 1.80059I
1.9117 15.1089I 0
19
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.113932 + 1.315720I
a = 0.035196 0.297355I
b = 0.389075 + 0.552433I
5.23347 + 12.43860I 0
u = 0.113932 1.315720I
a = 0.035196 + 0.297355I
b = 0.389075 0.552433I
5.23347 12.43860I 0
u = 0.663157 + 1.153060I
a = 0.962363 + 0.608426I
b = 0.96558 + 1.50778I
0.47354 6.87486I 0
u = 0.663157 1.153060I
a = 0.962363 0.608426I
b = 0.96558 1.50778I
0.47354 + 6.87486I 0
u = 0.468880 + 1.250480I
a = 0.507304 + 0.343123I
b = 0.680719 + 0.729966I
3.49916 2.93925I 0
u = 0.468880 1.250480I
a = 0.507304 0.343123I
b = 0.680719 0.729966I
3.49916 + 2.93925I 0
u = 0.719720 + 1.129520I
a = 1.70723 + 0.52583I
b = 1.57114 + 1.91853I
0.4317 20.9045I 0
u = 0.719720 1.129520I
a = 1.70723 0.52583I
b = 1.57114 1.91853I
0.4317 + 20.9045I 0
u = 0.838840 + 1.052250I
a = 0.695315 + 0.500346I
b = 1.317710 0.059726I
0.00586 + 5.83011I 0
u = 0.838840 1.052250I
a = 0.695315 0.500346I
b = 1.317710 + 0.059726I
0.00586 5.83011I 0
20
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.679859 + 1.168940I
a = 1.166050 0.597194I
b = 0.88191 1.39736I
2.63445 11.59730I 0
u = 0.679859 1.168940I
a = 1.166050 + 0.597194I
b = 0.88191 + 1.39736I
2.63445 + 11.59730I 0
u = 0.715483 + 1.150510I
a = 1.074610 + 0.526236I
b = 1.05007 + 1.58204I
1.93145 + 12.69900I 0
u = 0.715483 1.150510I
a = 1.074610 0.526236I
b = 1.05007 1.58204I
1.93145 12.69900I 0
u = 0.356069 + 1.313130I
a = 0.441378 + 0.312510I
b = 0.670233 + 0.413618I
3.00371 2.12483I 0
u = 0.356069 1.313130I
a = 0.441378 0.312510I
b = 0.670233 0.413618I
3.00371 + 2.12483I 0
u = 0.461444 + 0.430420I
a = 0.872894 0.243124I
b = 0.092223 + 0.808916I
2.31438 0.06014I 0
u = 0.461444 0.430420I
a = 0.872894 + 0.243124I
b = 0.092223 0.808916I
2.31438 + 0.06014I 0
u = 0.245412 + 0.547747I
a = 3.24858 + 1.25026I
b = 0.098916 + 1.285710I
0.09375 + 7.04987I 0. 7.90849I
u = 0.245412 0.547747I
a = 3.24858 1.25026I
b = 0.098916 1.285710I
0.09375 7.04987I 0. + 7.90849I
21
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.536888 + 0.260481I
a = 2.04301 0.26542I
b = 0.482652 + 1.129620I
0.06937 + 6.93748I 4.00000 6.68296I
u = 0.536888 0.260481I
a = 2.04301 + 0.26542I
b = 0.482652 1.129620I
0.06937 6.93748I 4.00000 + 6.68296I
u = 0.06137 + 1.44383I
a = 0.077666 + 0.257321I
b = 0.156272 0.130436I
2.13345 + 1.87687I 0
u = 0.06137 1.44383I
a = 0.077666 0.257321I
b = 0.156272 + 0.130436I
2.13345 1.87687I 0
u = 0.450150 + 0.260377I
a = 1.99999 + 0.36343I
b = 0.508367 + 0.934477I
1.94064 2.06419I 0.46983 + 2.36152I
u = 0.450150 0.260377I
a = 1.99999 0.36343I
b = 0.508367 0.934477I
1.94064 + 2.06419I 0.46983 2.36152I
u = 0.305881 + 0.404271I
a = 1.22384 + 2.52004I
b = 0.976394 + 0.446525I
0.86266 4.29940I 4.39227 + 7.53740I
u = 0.305881 0.404271I
a = 1.22384 2.52004I
b = 0.976394 0.446525I
0.86266 + 4.29940I 4.39227 7.53740I
u = 0.464626
a = 0.745919
b = 0.383953
0.878667 11.1150
u = 0.20168 + 1.53495I
a = 0.035560 + 0.170255I
b = 0.055628 + 0.623909I
3.99142 2.96540I 0
22
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.20168 1.53495I
a = 0.035560 0.170255I
b = 0.055628 0.623909I
3.99142 + 2.96540I 0
u = 0.318767 + 0.317698I
a = 0.52218 + 2.34710I
b = 0.728595 + 0.621611I
2.45495 0.21803I 0.535482 + 0.281744I
u = 0.318767 0.317698I
a = 0.52218 2.34710I
b = 0.728595 0.621611I
2.45495 + 0.21803I 0.535482 0.281744I
23
II. I
u
2
= h2.48 × 10
7
u
41
1.91 × 10
7
u
40
+ · · · + 3.94 × 10
6
b 1.94 × 10
7
, 1.08 ×
10
7
u
41
2.34×10
7
u
40
+· · · +3.94×10
6
a+1.83×10
6
, u
42
+11u
40
+· · ·u +1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
2.75025u
41
+ 5.92506u
40
+ ··· + 4.56550u 0.464939
6.29335u
41
+ 4.84326u
40
+ ··· 8.67531u + 4.92506
a
4
=
10.8206u
41
+ 9.12531u
40
+ ··· 3.47298u + 9.32568
8.50296u
41
+ 3.54988u
40
+ ··· 0.304710u + 9.12531
a
7
=
u
u
a
10
=
0.0728852u
41
+ 4.18160u
40
+ ··· + 2.10420u 1.54674
3.47021u
41
+ 3.09980u
40
+ ··· 11.1366u + 3.84326
a
1
=
u
2
+ 1
u
4
a
8
=
0.0728852u
41
+ 4.18160u
40
+ ··· + 3.10420u 1.54674
6.92724u
41
+ 6.63540u
40
+ ··· 14.2453u + 7.02486
a
12
=
3.45329u
41
5.81424u
40
+ ··· + 12.8848u 8.71909
2.47177u
41
+ 1.47911u
40
+ ··· + 8.66963u + 1.03117
a
11
=
1.55056u
41
+ 0.591649u
40
+ ··· + 10.4025u + 3.51094
0.666025u
41
+ 1.91470u
40
+ ··· 1.94694u + 3.34665
a
5
=
2.59689u
41
3.27679u
40
+ ··· + 7.61969u + 0.118711
4.28962u
41
0.428211u
40
+ ··· 0.566875u + 1.18748
(ii) Obstruction class = 1
(iii) Cusp Shapes =
65427262
3944339
u
41
+
4960727
3944339
u
40
+ ···
17347683
563477
u
25550128
3944339
24
(iv) u-Polynomials at the component
25
Crossings u-Polynomials at each crossing
c
1
u
42
22u
41
+ ··· 15u + 1
c
2
u
42
+ 11u
40
+ ··· u + 1
c
3
u
42
10u
40
+ ··· + 4u + 1
c
4
u
42
2u
40
+ ··· u + 1
c
5
u
42
13u
40
+ ··· 4u + 1
c
6
u
42
+ 11u
40
+ ··· + u + 1
c
7
u
42
+ u
41
+ ··· + 10u + 1
c
8
u
42
2u
40
+ ··· + 5u + 1
c
9
u
42
+ 14u
41
+ ··· + 100u + 5
c
10
u
42
13u
40
+ ··· + 4u + 1
c
11
u
42
26u
41
+ ··· 16u + 1
c
12
u
42
3u
41
+ ··· 4u + 1
26
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
+ 2y
41
+ ··· + 27y + 1
c
2
, c
6
y
42
+ 22y
41
+ ··· + 15y + 1
c
3
y
42
20y
41
+ ··· + 8y + 1
c
4
y
42
4y
41
+ ··· 5y + 1
c
5
, c
10
y
42
26y
41
+ ··· 16y + 1
c
7
y
42
+ 5y
41
+ ··· 34y + 1
c
8
y
42
4y
41
+ ··· + y + 1
c
9
y
42
+ 10y
41
+ ··· + 360y + 25
c
11
y
42
6y
41
+ ··· + 84y + 1
c
12
y
42
9y
41
+ ··· + 2y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.670458 + 0.713555I
a = 0.973164 + 0.142027I
b = 0.79476 + 1.70582I
3.53244 + 3.09675I 8.80493 3.18234I
u = 0.670458 0.713555I
a = 0.973164 0.142027I
b = 0.79476 1.70582I
3.53244 3.09675I 8.80493 + 3.18234I
u = 0.765369 + 0.681061I
a = 0.290687 + 0.798138I
b = 0.249516 + 0.168749I
0.24970 2.93248I 0.78372 + 3.20918I
u = 0.765369 0.681061I
a = 0.290687 0.798138I
b = 0.249516 0.168749I
0.24970 + 2.93248I 0.78372 3.20918I
u = 0.181479 + 1.016510I
a = 0.397246 + 0.442301I
b = 0.807929 0.774630I
4.84099 1.24138I 1.82984 + 5.05876I
u = 0.181479 1.016510I
a = 0.397246 0.442301I
b = 0.807929 + 0.774630I
4.84099 + 1.24138I 1.82984 5.05876I
u = 0.659509 + 0.654424I
a = 1.62696 + 0.05983I
b = 0.83118 + 1.89065I
3.55715 0.72991I 11.18768 + 1.45522I
u = 0.659509 0.654424I
a = 1.62696 0.05983I
b = 0.83118 1.89065I
3.55715 + 0.72991I 11.18768 1.45522I
u = 0.782153 + 0.467085I
a = 0.362792 + 0.743012I
b = 0.113135 0.357342I
1.33161 + 7.62899I 5.62238 7.51224I
u = 0.782153 0.467085I
a = 0.362792 0.743012I
b = 0.113135 + 0.357342I
1.33161 7.62899I 5.62238 + 7.51224I
29
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.531701 + 0.731373I
a = 1.45615 + 1.62975I
b = 1.14820 + 1.82542I
6.53602 + 1.27696I 7.1168 + 13.7607I
u = 0.531701 0.731373I
a = 1.45615 1.62975I
b = 1.14820 1.82542I
6.53602 1.27696I 7.1168 13.7607I
u = 0.512783 + 0.689247I
a = 2.16896 + 1.74741I
b = 0.85634 + 1.82804I
0.88350 + 1.12586I 3.95962 4.39017I
u = 0.512783 0.689247I
a = 2.16896 1.74741I
b = 0.85634 1.82804I
0.88350 1.12586I 3.95962 + 4.39017I
u = 0.105492 + 1.142710I
a = 0.615136 + 0.421279I
b = 1.055090 0.420890I
3.47572 3.47512I 0.89011 + 1.91027I
u = 0.105492 1.142710I
a = 0.615136 0.421279I
b = 1.055090 + 0.420890I
3.47572 + 3.47512I 0.89011 1.91027I
u = 0.760232 + 0.863900I
a = 0.780387 + 0.639712I
b = 0.908836 + 0.017677I
0.24497 2.81726I 0. + 3.73854I
u = 0.760232 0.863900I
a = 0.780387 0.639712I
b = 0.908836 0.017677I
0.24497 + 2.81726I 0. 3.73854I
u = 0.551182 + 1.012470I
a = 1.14574 1.32473I
b = 1.03048 1.82842I
5.57913 + 3.09875I 11.19527 3.15161I
u = 0.551182 1.012470I
a = 1.14574 + 1.32473I
b = 1.03048 + 1.82842I
5.57913 3.09875I 11.19527 + 3.15161I
30
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.572223 + 1.015750I
a = 1.67614 1.08196I
b = 1.41264 2.15996I
2.01487 5.56271I 2.72621 + 6.98267I
u = 0.572223 1.015750I
a = 1.67614 + 1.08196I
b = 1.41264 + 2.15996I
2.01487 + 5.56271I 2.72621 6.98267I
u = 0.667591 + 0.978214I
a = 1.50276 0.95929I
b = 0.24454 1.45204I
2.71125 8.31111I 5.35759 + 9.33828I
u = 0.667591 0.978214I
a = 1.50276 + 0.95929I
b = 0.24454 + 1.45204I
2.71125 + 8.31111I 5.35759 9.33828I
u = 0.523883 + 0.619357I
a = 2.69588 + 1.20336I
b = 0.67112 + 1.81429I
0.89552 6.58153I 6.70168 + 5.42352I
u = 0.523883 0.619357I
a = 2.69588 1.20336I
b = 0.67112 1.81429I
0.89552 + 6.58153I 6.70168 5.42352I
u = 0.145604 + 0.788646I
a = 0.25633 + 1.90984I
b = 0.460282 0.035005I
3.94604 0.19498I 4.57927 1.41449I
u = 0.145604 0.788646I
a = 0.25633 1.90984I
b = 0.460282 + 0.035005I
3.94604 + 0.19498I 4.57927 + 1.41449I
u = 0.590563 + 1.047720I
a = 1.64541 1.05105I
b = 1.12474 2.38885I
0.53960 + 11.18960I 4.00000 10.67377I
u = 0.590563 1.047720I
a = 1.64541 + 1.05105I
b = 1.12474 + 2.38885I
0.53960 11.18960I 4.00000 + 10.67377I
31
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.663997 + 1.017430I
a = 1.57665 1.07372I
b = 0.29062 2.00669I
2.43664 + 5.93494I 7.76279 4.79880I
u = 0.663997 1.017430I
a = 1.57665 + 1.07372I
b = 0.29062 + 2.00669I
2.43664 5.93494I 7.76279 + 4.79880I
u = 0.036945 + 0.778472I
a = 1.86422 + 1.34579I
b = 1.082220 0.107037I
1.93192 + 3.63918I 2.78083 4.14568I
u = 0.036945 0.778472I
a = 1.86422 1.34579I
b = 1.082220 + 0.107037I
1.93192 3.63918I 2.78083 + 4.14568I
u = 0.546682 + 0.425527I
a = 0.751887 0.503336I
b = 0.960506 0.354893I
2.96144 + 1.74006I 6.97083 + 0.25058I
u = 0.546682 0.425527I
a = 0.751887 + 0.503336I
b = 0.960506 + 0.354893I
2.96144 1.74006I 6.97083 0.25058I
u = 0.015468 + 1.309640I
a = 0.129270 + 0.659065I
b = 0.267455 + 0.537072I
1.63389 + 1.59592I 13.25426 + 0.I
u = 0.015468 1.309640I
a = 0.129270 0.659065I
b = 0.267455 0.537072I
1.63389 1.59592I 13.25426 + 0.I
u = 0.459986 + 0.489536I
a = 0.410194 1.224130I
b = 1.289730 0.084097I
2.48373 4.43340I 6.59955 + 7.64683I
u = 0.459986 0.489536I
a = 0.410194 + 1.224130I
b = 1.289730 + 0.084097I
2.48373 + 4.43340I 6.59955 7.64683I
32
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.19796 + 1.53436I
a = 0.0391256 0.1159400I
b = 0.016441 0.575361I
4.03906 2.89466I 0
u = 0.19796 1.53436I
a = 0.0391256 + 0.1159400I
b = 0.016441 + 0.575361I
4.03906 + 2.89466I 0
33
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
42
22u
41
+ ··· 15u + 1)
· (u
183
+ 77u
182
+ ··· 46277120u 1283689)
c
2
(u
42
+ 11u
40
+ ··· u + 1)(u
183
u
182
+ ··· + 4256u 1133)
c
3
(u
42
10u
40
+ ··· + 4u + 1)(u
183
+ u
182
+ ··· + 31u 3)
c
4
(u
42
2u
40
+ ··· u + 1)(u
183
+ 3u
182
+ ··· + 555350u 53533)
c
5
(u
42
13u
40
+ ··· 4u + 1)(u
183
+ u
182
+ ··· 173u 59)
c
6
(u
42
+ 11u
40
+ ··· + u + 1)(u
183
u
182
+ ··· + 4256u 1133)
c
7
(u
42
+ u
41
+ ··· + 10u + 1)(u
183
2u
182
+ ··· + 334697u 27379)
c
8
(u
42
2u
40
+ ··· + 5u + 1)(u
183
5u
182
+ ··· 6926u 485)
c
9
(u
42
+ 14u
41
+ ··· + 100u + 5)
· (u
183
+ 7u
182
+ ··· + 1157925u 194803)
c
10
(u
42
13u
40
+ ··· + 4u + 1)(u
183
+ u
182
+ ··· 173u 59)
c
11
(u
42
26u
41
+ ··· 16u + 1)(u
183
87u
182
+ ··· + 82911u 3481)
c
12
(u
42
3u
41
+ ··· 4u + 1)(u
183
+ 16u
182
+ ··· 199u 7)
34
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
42
+ 2y
41
+ ··· + 27y + 1)
· (y
183
+ 65y
182
+ ··· 180776219221564y 1647857448721)
c
2
, c
6
(y
42
+ 22y
41
+ ··· + 15y + 1)
· (y
183
+ 77y
182
+ ··· 46277120y 1283689)
c
3
(y
42
20y
41
+ ··· + 8y + 1)(y
183
17y
182
+ ··· + 67y 9)
c
4
(y
42
4y
41
+ ··· 5y + 1)
· (y
183
+ 11y
182
+ ··· 122436449664y 2865782089)
c
5
, c
10
(y
42
26y
41
+ ··· 16y + 1)(y
183
87y
182
+ ··· + 82911y 3481)
c
7
(y
42
+ 5y
41
+ ··· 34y + 1)
· (y
183
28y
182
+ ··· 2771494231y 749609641)
c
8
(y
42
4y
41
+ ··· + y + 1)(y
183
29y
182
+ ··· 4.01327 × 10
7
y 235225)
c
9
(y
42
+ 10y
41
+ ··· + 360y + 25)
· (y
183
11y
182
+ ··· 18463850066073y 37948208809)
c
11
(y
42
6y
41
+ ··· + 84y + 1)
· (y
183
+ 33y
182
+ ··· + 364826579y 12117361)
c
12
(y
42
9y
41
+ ··· + 2y + 1)(y
183
+ 10y
182
+ ··· 2819y 49)
35