12a
1078
(K12a
1078
)
A knot diagram
1
Linearized knot diagam
4 7 10 11 2 9 12 3 6 1 5 8
Solving Sequence
8,12
1
5,7
11 4 2 10 3 9 6
c
12
c
7
c
11
c
4
c
1
c
10
c
3
c
8
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.42254 × 10
1026
u
182
1.43895 × 10
1026
u
181
+ ··· + 2.00299 × 10
1023
b + 6.70498 × 10
1025
,
2.27742 × 10
1027
u
182
2.16805 × 10
1027
u
181
+ ··· + 2.00299 × 10
1023
a + 1.25093 × 10
1027
,
4u
183
+ 2u
182
+ ··· 2u + 1i
I
u
2
= h3.84908 × 10
38
u
44
8.37838 × 10
37
u
43
+ ··· + 2.17731 × 10
35
b 1.13314 × 10
38
,
5.31620 × 10
38
u
44
2.05529 × 10
38
u
43
+ ··· + 2.17731 × 10
35
a 1.03891 × 10
38
, 4u
45
2u
44
+ ··· 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 228 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−1.42 × 10
1026
u
182
1.44 × 10
1026
u
181
+ · · · + 2.00 × 10
1023
b +
6.70 × 10
1025
, 2.28 × 10
1027
u
182
2.17 × 10
1027
u
181
+ · · · + 2.00 ×
10
1023
a + 1.25 × 10
1027
, 4u
183
+ 2u
182
+ · · · 2u + 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
11370.1u
182
+ 10824.1u
181
+ ··· 1274.29u 6245.32
710.207u
182
+ 718.400u
181
+ ··· + 45.9882u 334.749
a
7
=
u
u
a
11
=
9952.46u
182
+ 9437.37u
181
+ ··· 1208.38u 5503.48
2069.74u
182
+ 2066.80u
181
+ ··· + 22.0905u 1020.16
a
4
=
3805.30u
182
+ 3725.93u
181
+ ··· 166.903u 1982.81
3719.84u
182
3655.64u
181
+ ··· + 148.962u + 1917.08
a
2
=
5989.26u
182
5778.96u
181
+ ··· + 488.940u + 3208.35
558.228u
182
+ 428.115u
181
+ ··· 286.701u 435.982
a
10
=
5881.98u
182
+ 5475.97u
181
+ ··· 972.925u 3368.03
2981.75u
182
+ 2954.78u
181
+ ··· 32.4516u 1501.70
a
3
=
4703.80u
182
4514.72u
181
+ ··· + 448.847u + 2549.52
727.237u
182
836.129u
181
+ ··· 246.608u + 222.850
a
9
=
10291.8u
182
+ 9908.12u
181
+ ··· 861.800u 5561.15
584.062u
182
424.879u
181
+ ··· + 411.316u + 466.074
a
6
=
12319.2u
182
12117.3u
181
+ ··· + 361.928u + 6357.71
11019.1u
182
+ 10663.0u
181
+ ··· 782.092u 5881.84
(ii) Obstruction class = 1
(iii) Cusp Shapes = 38193.2u
182
36262.8u
181
+ ··· + 4490.93u + 21122.6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
16(16u
183
+ 252u
182
+ ··· + 449u 17)
c
2
4(4u
183
14u
182
+ ··· + 864065u 160229)
c
3
u
183
3u
182
+ ··· + 285506u 6964
c
4
, c
11
u
183
+ 5u
182
+ ··· + 1386431u + 62039
c
5
u
183
4u
182
+ ··· 17118874u 3362836
c
6
, c
9
u
183
8u
182
+ ··· 9204u + 773
c
7
, c
12
4(4u
183
2u
182
+ ··· 2u 1)
c
8
4(4u
183
2u
182
+ ··· + 4507202u 289523)
c
10
u
183
+ 6u
182
+ ··· + 5277708u + 199568
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
256(256y
183
2416y
182
+ ··· 5697y 289)
c
2
16(16y
183
+ 404y
182
+ ··· + 7.51074 × 10
11
y 2.56733 × 10
10
)
c
3
y
183
55y
182
+ ··· + 3956764060y 48497296
c
4
, c
11
y
183
121y
182
+ ··· + 995844174085y 3848837521
c
5
y
183
20y
182
+ ··· + 1169699756063260y 11308665962896
c
6
, c
9
y
183
+ 110y
182
+ ··· 36021254y 597529
c
7
, c
12
16(16y
183
1564y
182
+ ··· + 82y 1)
c
8
16(16y
183
+ 196y
182
+ ··· + 3.04473 × 10
12
y 8.38236 × 10
10
)
c
10
y
183
18y
182
+ ··· + 2408586039216y 39827386624
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.435994 + 0.892598I
a = 0.844089 + 0.425621I
b = 1.196650 + 0.717109I
2.66114 4.14393I 0
u = 0.435994 0.892598I
a = 0.844089 0.425621I
b = 1.196650 0.717109I
2.66114 + 4.14393I 0
u = 0.299647 + 0.938486I
a = 0.725434 + 0.712589I
b = 0.019019 + 0.975825I
0.93979 + 9.22059I 0
u = 0.299647 0.938486I
a = 0.725434 0.712589I
b = 0.019019 0.975825I
0.93979 9.22059I 0
u = 0.179097 + 0.961498I
a = 0.979299 + 0.643036I
b = 0.012177 + 0.515658I
1.03964 4.24096I 0
u = 0.179097 0.961498I
a = 0.979299 0.643036I
b = 0.012177 0.515658I
1.03964 + 4.24096I 0
u = 0.968063 + 0.136793I
a = 1.124980 + 0.344421I
b = 0.450543 + 0.406317I
1.60840 1.88368I 0
u = 0.968063 0.136793I
a = 1.124980 0.344421I
b = 0.450543 0.406317I
1.60840 + 1.88368I 0
u = 0.791124 + 0.673148I
a = 0.377369 + 0.292424I
b = 0.893997 0.018281I
1.37483 0.55344I 0
u = 0.791124 0.673148I
a = 0.377369 0.292424I
b = 0.893997 + 0.018281I
1.37483 + 0.55344I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.927068 + 0.493900I
a = 0.081388 + 0.179395I
b = 0.730734 0.088837I
1.27870 0.70102I 0
u = 0.927068 0.493900I
a = 0.081388 0.179395I
b = 0.730734 + 0.088837I
1.27870 + 0.70102I 0
u = 1.023140 + 0.258102I
a = 0.251436 + 0.899798I
b = 0.552228 + 0.156044I
5.93378 2.01906I 0
u = 1.023140 0.258102I
a = 0.251436 0.899798I
b = 0.552228 0.156044I
5.93378 + 2.01906I 0
u = 0.201244 + 1.044460I
a = 0.051901 0.539196I
b = 1.267020 0.259232I
0.16638 3.50169I 0
u = 0.201244 1.044460I
a = 0.051901 + 0.539196I
b = 1.267020 + 0.259232I
0.16638 + 3.50169I 0
u = 0.884541 + 0.301835I
a = 0.884826 + 0.843686I
b = 0.195765 1.292020I
1.19560 1.79116I 0
u = 0.884541 0.301835I
a = 0.884826 0.843686I
b = 0.195765 + 1.292020I
1.19560 + 1.79116I 0
u = 0.245347 + 1.037970I
a = 1.246090 0.362330I
b = 0.904434 + 0.036830I
1.37820 + 3.10134I 0
u = 0.245347 1.037970I
a = 1.246090 + 0.362330I
b = 0.904434 0.036830I
1.37820 3.10134I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.007680 + 0.351734I
a = 1.111550 0.050183I
b = 0.373220 0.770569I
1.52893 + 0.67044I 0
u = 1.007680 0.351734I
a = 1.111550 + 0.050183I
b = 0.373220 + 0.770569I
1.52893 0.67044I 0
u = 0.563418 + 0.923911I
a = 0.466978 + 0.198414I
b = 1.266650 + 0.494142I
5.96882 2.77936I 0
u = 0.563418 0.923911I
a = 0.466978 0.198414I
b = 1.266650 0.494142I
5.96882 + 2.77936I 0
u = 0.318840 + 1.038110I
a = 0.716550 0.753529I
b = 0.057847 0.951617I
4.79655 2.89380I 0
u = 0.318840 1.038110I
a = 0.716550 + 0.753529I
b = 0.057847 + 0.951617I
4.79655 + 2.89380I 0
u = 0.691890 + 0.588159I
a = 0.613586 + 0.354824I
b = 0.298548 0.446290I
1.80572 + 3.17497I 0
u = 0.691890 0.588159I
a = 0.613586 0.354824I
b = 0.298548 + 0.446290I
1.80572 3.17497I 0
u = 1.077300 + 0.189760I
a = 0.203809 + 0.380584I
b = 0.789435 1.019960I
1.54583 0.00514I 0
u = 1.077300 0.189760I
a = 0.203809 0.380584I
b = 0.789435 + 1.019960I
1.54583 + 0.00514I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.811749 + 0.390367I
a = 0.906879 0.564551I
b = 0.402641 + 0.931175I
1.10562 + 5.08781I 0
u = 0.811749 0.390367I
a = 0.906879 + 0.564551I
b = 0.402641 0.931175I
1.10562 5.08781I 0
u = 1.014490 + 0.423498I
a = 0.578315 + 0.697424I
b = 0.360178 0.895200I
1.17751 5.41890I 0
u = 1.014490 0.423498I
a = 0.578315 0.697424I
b = 0.360178 + 0.895200I
1.17751 + 5.41890I 0
u = 0.996685 + 0.488016I
a = 0.494469 0.641126I
b = 0.386486 + 0.577659I
0.01244 + 3.89579I 0
u = 0.996685 0.488016I
a = 0.494469 + 0.641126I
b = 0.386486 0.577659I
0.01244 3.89579I 0
u = 1.032780 + 0.420974I
a = 1.129910 + 0.411137I
b = 1.199630 + 0.471004I
5.41047 3.94815I 0
u = 1.032780 0.420974I
a = 1.129910 0.411137I
b = 1.199630 0.471004I
5.41047 + 3.94815I 0
u = 1.101950 + 0.288670I
a = 0.288416 0.505335I
b = 0.563293 + 1.116030I
6.33450 + 4.14277I 0
u = 1.101950 0.288670I
a = 0.288416 + 0.505335I
b = 0.563293 1.116030I
6.33450 4.14277I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.834096 + 0.109112I
a = 3.07979 0.00775I
b = 1.43386 0.77030I
0.57305 1.40697I 0
u = 0.834096 0.109112I
a = 3.07979 + 0.00775I
b = 1.43386 + 0.77030I
0.57305 + 1.40697I 0
u = 0.836413 + 0.062418I
a = 2.99172 + 0.61737I
b = 1.057480 + 0.593839I
4.69954 2.73836I 0
u = 0.836413 0.062418I
a = 2.99172 0.61737I
b = 1.057480 0.593839I
4.69954 + 2.73836I 0
u = 0.630957 + 0.550000I
a = 0.732526 0.182055I
b = 0.749114 + 0.488562I
0.58612 + 4.96450I 0
u = 0.630957 0.550000I
a = 0.732526 + 0.182055I
b = 0.749114 0.488562I
0.58612 4.96450I 0
u = 0.995413 + 0.604085I
a = 0.448626 0.325962I
b = 0.0927846 0.0130873I
0.24551 + 4.75126I 0
u = 0.995413 0.604085I
a = 0.448626 + 0.325962I
b = 0.0927846 + 0.0130873I
0.24551 4.75126I 0
u = 1.057020 + 0.521499I
a = 0.243692 1.314180I
b = 0.757740 0.296570I
0.26634 + 5.32691I 0
u = 1.057020 0.521499I
a = 0.243692 + 1.314180I
b = 0.757740 + 0.296570I
0.26634 5.32691I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.774385 + 0.242007I
a = 0.937885 + 0.332567I
b = 0.443642 1.150540I
1.62107 0.90334I 0
u = 0.774385 0.242007I
a = 0.937885 0.332567I
b = 0.443642 + 1.150540I
1.62107 + 0.90334I 0
u = 1.154430 + 0.337643I
a = 0.182258 + 0.963816I
b = 0.612179 + 0.412519I
3.48053 + 7.86335I 0
u = 1.154430 0.337643I
a = 0.182258 0.963816I
b = 0.612179 0.412519I
3.48053 7.86335I 0
u = 0.726929 + 0.324876I
a = 0.263271 0.299473I
b = 0.175979 + 0.973124I
1.41163 1.73255I 0
u = 0.726929 0.324876I
a = 0.263271 + 0.299473I
b = 0.175979 0.973124I
1.41163 + 1.73255I 0
u = 0.785385 + 0.125564I
a = 3.66711 + 0.16395I
b = 1.64059 + 0.38662I
4.18115 + 6.46744I 0
u = 0.785385 0.125564I
a = 3.66711 0.16395I
b = 1.64059 0.38662I
4.18115 6.46744I 0
u = 0.369299 + 0.700251I
a = 0.157572 + 0.892871I
b = 1.047660 0.169183I
5.08933 5.93229I 0
u = 0.369299 0.700251I
a = 0.157572 0.892871I
b = 1.047660 + 0.169183I
5.08933 + 5.93229I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.093420 + 0.525497I
a = 0.26291 + 2.03387I
b = 0.977322 + 0.284930I
4.46992 10.86910I 0
u = 1.093420 0.525497I
a = 0.26291 2.03387I
b = 0.977322 0.284930I
4.46992 + 10.86910I 0
u = 1.148310 + 0.401673I
a = 2.57107 0.49046I
b = 1.368470 0.181234I
8.69744 + 9.16930I 0
u = 1.148310 0.401673I
a = 2.57107 + 0.49046I
b = 1.368470 + 0.181234I
8.69744 9.16930I 0
u = 0.432954 + 0.648653I
a = 0.373107 1.005890I
b = 0.984194 0.292578I
0.07141 3.72785I 0
u = 0.432954 0.648653I
a = 0.373107 + 1.005890I
b = 0.984194 + 0.292578I
0.07141 + 3.72785I 0
u = 1.160210 + 0.408959I
a = 2.36187 + 0.87124I
b = 1.220010 + 0.432666I
2.86398 7.89511I 0
u = 1.160210 0.408959I
a = 2.36187 0.87124I
b = 1.220010 0.432666I
2.86398 + 7.89511I 0
u = 1.155610 + 0.425076I
a = 2.19095 1.00324I
b = 1.225060 0.567501I
3.95878 + 10.87850I 0
u = 1.155610 0.425076I
a = 2.19095 + 1.00324I
b = 1.225060 + 0.567501I
3.95878 10.87850I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.510620 + 0.568691I
a = 0.754085 + 0.628865I
b = 0.028269 + 0.827369I
2.32835 2.09541I 0
u = 0.510620 0.568691I
a = 0.754085 0.628865I
b = 0.028269 0.827369I
2.32835 + 2.09541I 0
u = 0.462933 + 0.606757I
a = 1.62969 0.29323I
b = 0.915285 0.203760I
2.02037 0.85680I 0
u = 0.462933 0.606757I
a = 1.62969 + 0.29323I
b = 0.915285 + 0.203760I
2.02037 + 0.85680I 0
u = 1.168190 + 0.406675I
a = 0.058099 0.856266I
b = 0.781953 0.489895I
0.04935 1.76185I 0
u = 1.168190 0.406675I
a = 0.058099 + 0.856266I
b = 0.781953 + 0.489895I
0.04935 + 1.76185I 0
u = 0.758589 + 0.046364I
a = 6.43651 + 0.72336I
b = 0.933852 0.056164I
1.28344 6.23630I 0
u = 0.758589 0.046364I
a = 6.43651 0.72336I
b = 0.933852 + 0.056164I
1.28344 + 6.23630I 0
u = 1.163610 + 0.435310I
a = 0.149422 + 0.146164I
b = 0.212104 + 0.761549I
2.46618 0.66784I 0
u = 1.163610 0.435310I
a = 0.149422 0.146164I
b = 0.212104 0.761549I
2.46618 + 0.66784I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.178250 + 0.394308I
a = 2.18898 + 0.55295I
b = 1.46899 + 0.47141I
4.66947 10.32320I 0
u = 1.178250 0.394308I
a = 2.18898 0.55295I
b = 1.46899 0.47141I
4.66947 + 10.32320I 0
u = 1.172400 + 0.412890I
a = 2.52642 + 0.93741I
b = 1.127020 + 0.253372I
2.83838 6.86953I 0
u = 1.172400 0.412890I
a = 2.52642 0.93741I
b = 1.127020 0.253372I
2.83838 + 6.86953I 0
u = 1.144590 + 0.515377I
a = 1.67031 + 1.08084I
b = 1.272430 + 0.159876I
7.38774 + 4.06024I 0
u = 1.144590 0.515377I
a = 1.67031 1.08084I
b = 1.272430 0.159876I
7.38774 4.06024I 0
u = 1.235570 + 0.245822I
a = 0.1300980 + 0.0298962I
b = 0.619384 + 0.925932I
4.30533 5.68525I 0
u = 1.235570 0.245822I
a = 0.1300980 0.0298962I
b = 0.619384 0.925932I
4.30533 + 5.68525I 0
u = 1.215800 + 0.338826I
a = 1.52422 0.70147I
b = 1.86632 + 0.42438I
7.49302 + 7.56242I 0
u = 1.215800 0.338826I
a = 1.52422 + 0.70147I
b = 1.86632 0.42438I
7.49302 7.56242I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.737636
a = 7.07184
b = 0.931905
2.84479 0
u = 0.676019 + 0.288627I
a = 0.440573 + 0.006647I
b = 0.741023 + 0.217066I
1.43722 0.66748I 0
u = 0.676019 0.288627I
a = 0.440573 0.006647I
b = 0.741023 0.217066I
1.43722 + 0.66748I 0
u = 1.197210 + 0.409750I
a = 1.99292 0.63256I
b = 1.42122 0.57584I
3.68508 + 8.18402I 0
u = 1.197210 0.409750I
a = 1.99292 + 0.63256I
b = 1.42122 + 0.57584I
3.68508 8.18402I 0
u = 0.393752 + 0.617992I
a = 1.63097 + 1.01161I
b = 1.071630 + 0.127140I
2.39503 + 6.32987I 0
u = 0.393752 0.617992I
a = 1.63097 1.01161I
b = 1.071630 0.127140I
2.39503 6.32987I 0
u = 0.342351 + 1.225570I
a = 0.457285 + 0.222768I
b = 1.319170 + 0.501865I
3.1050 14.5175I 0
u = 0.342351 1.225570I
a = 0.457285 0.222768I
b = 1.319170 0.501865I
3.1050 + 14.5175I 0
u = 1.191490 + 0.456262I
a = 1.92949 0.97155I
b = 1.42104 0.27469I
7.59045 4.44666I 0
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.191490 0.456262I
a = 1.92949 + 0.97155I
b = 1.42104 + 0.27469I
7.59045 + 4.44666I 0
u = 1.181640 + 0.481453I
a = 1.71341 + 1.02674I
b = 1.32595 + 0.73205I
8.9536 11.1741I 0
u = 1.181640 0.481453I
a = 1.71341 1.02674I
b = 1.32595 0.73205I
8.9536 + 11.1741I 0
u = 0.039731 + 0.713005I
a = 0.453123 0.057961I
b = 1.201940 0.147605I
4.26793 + 0.11022I 0
u = 0.039731 0.713005I
a = 0.453123 + 0.057961I
b = 1.201940 + 0.147605I
4.26793 0.11022I 0
u = 0.370607 + 0.602926I
a = 0.0770151 + 0.0774324I
b = 1.082870 + 0.431455I
0.95207 + 6.99078I 0
u = 0.370607 0.602926I
a = 0.0770151 0.0774324I
b = 1.082870 0.431455I
0.95207 6.99078I 0
u = 1.209280 + 0.456420I
a = 1.31982 0.66160I
b = 1.44690 + 0.37540I
9.15948 2.52691I 0
u = 1.209280 0.456420I
a = 1.31982 + 0.66160I
b = 1.44690 0.37540I
9.15948 + 2.52691I 0
u = 1.096100 + 0.701852I
a = 0.726296 + 0.005863I
b = 0.107506 + 1.232940I
3.61445 3.09982I 0
15
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.096100 0.701852I
a = 0.726296 0.005863I
b = 0.107506 1.232940I
3.61445 + 3.09982I 0
u = 1.228220 + 0.447011I
a = 2.07979 1.04519I
b = 1.041130 0.151390I
2.35333 + 2.06366I 0
u = 1.228220 0.447011I
a = 2.07979 + 1.04519I
b = 1.041130 + 0.151390I
2.35333 2.06366I 0
u = 1.228260 + 0.448330I
a = 1.72192 0.72860I
b = 1.43796 0.67122I
4.29641 + 7.96390I 0
u = 1.228260 0.448330I
a = 1.72192 + 0.72860I
b = 1.43796 + 0.67122I
4.29641 7.96390I 0
u = 1.190460 + 0.544327I
a = 1.36629 + 1.46671I
b = 1.105800 + 0.103015I
7.64089 + 0.90582I 0
u = 1.190460 0.544327I
a = 1.36629 1.46671I
b = 1.105800 0.103015I
7.64089 0.90582I 0
u = 1.128750 + 0.666063I
a = 0.377676 + 0.046887I
b = 0.326372 + 0.388406I
3.00457 8.90992I 0
u = 1.128750 0.666063I
a = 0.377676 0.046887I
b = 0.326372 0.388406I
3.00457 + 8.90992I 0
u = 1.113240 + 0.734851I
a = 0.679724 0.765383I
b = 1.042920 + 0.060263I
2.89140 1.80117I 0
16
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.113240 0.734851I
a = 0.679724 + 0.765383I
b = 1.042920 0.060263I
2.89140 + 1.80117I 0
u = 0.512109 + 0.423982I
a = 0.542562 + 0.299811I
b = 0.346196 + 0.406438I
1.39633 0.41385I 0
u = 0.512109 0.423982I
a = 0.542562 0.299811I
b = 0.346196 0.406438I
1.39633 + 0.41385I 0
u = 0.659068 + 0.078407I
a = 0.97221 1.33888I
b = 0.629393 0.741373I
0.59333 + 2.40562I 0
u = 0.659068 0.078407I
a = 0.97221 + 1.33888I
b = 0.629393 + 0.741373I
0.59333 2.40562I 0
u = 0.062773 + 0.653979I
a = 0.407628 + 0.952065I
b = 1.223260 + 0.520635I
5.83586 + 6.77607I 0
u = 0.062773 0.653979I
a = 0.407628 0.952065I
b = 1.223260 0.520635I
5.83586 6.77607I 0
u = 1.284550 + 0.399473I
a = 1.44996 + 0.56100I
b = 1.62880 0.08641I
4.41517 1.74291I 0
u = 1.284550 0.399473I
a = 1.44996 0.56100I
b = 1.62880 + 0.08641I
4.41517 + 1.74291I 0
u = 1.209400 + 0.593142I
a = 0.571021 0.205612I
b = 0.027888 + 1.267670I
1.8785 14.8053I 0
17
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.209400 0.593142I
a = 0.571021 + 0.205612I
b = 0.027888 1.267670I
1.8785 + 14.8053I 0
u = 0.313461 + 0.569248I
a = 0.055267 0.533115I
b = 1.064710 0.474818I
0.04406 4.58724I 0
u = 0.313461 0.569248I
a = 0.055267 + 0.533115I
b = 1.064710 + 0.474818I
0.04406 + 4.58724I 0
u = 0.449789 + 1.282540I
a = 0.460038 0.208604I
b = 1.32977 0.49680I
0.54301 + 8.13089I 0
u = 0.449789 1.282540I
a = 0.460038 + 0.208604I
b = 1.32977 + 0.49680I
0.54301 8.13089I 0
u = 0.552671 + 0.322734I
a = 1.240240 0.257184I
b = 1.019840 0.705479I
1.05335 7.56944I 0
u = 0.552671 0.322734I
a = 1.240240 + 0.257184I
b = 1.019840 + 0.705479I
1.05335 + 7.56944I 0
u = 0.233180 + 1.347250I
a = 0.33240 1.39622I
b = 0.736622 0.839707I
4.12154 3.40129I 0
u = 0.233180 1.347250I
a = 0.33240 + 1.39622I
b = 0.736622 + 0.839707I
4.12154 + 3.40129I 0
u = 1.222700 + 0.621420I
a = 0.547820 + 0.128742I
b = 0.021068 1.259930I
1.95675 + 8.82232I 0
18
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.222700 0.621420I
a = 0.547820 0.128742I
b = 0.021068 + 1.259930I
1.95675 8.82232I 0
u = 1.305040 + 0.467324I
a = 1.72002 + 0.71298I
b = 1.311810 + 0.293596I
7.15310 + 4.18475I 0
u = 1.305040 0.467324I
a = 1.72002 0.71298I
b = 1.311810 0.293596I
7.15310 4.18475I 0
u = 1.391500 + 0.090581I
a = 1.84641 0.26988I
b = 1.365490 + 0.250547I
12.73430 0.33748I 0
u = 1.391500 0.090581I
a = 1.84641 + 0.26988I
b = 1.365490 0.250547I
12.73430 + 0.33748I 0
u = 1.20352 + 0.79129I
a = 1.46918 + 1.19367I
b = 1.35988 + 0.57393I
7.69710 + 9.31848I 0
u = 1.20352 0.79129I
a = 1.46918 1.19367I
b = 1.35988 0.57393I
7.69710 9.31848I 0
u = 1.34673 + 0.57417I
a = 1.31694 + 0.61600I
b = 1.67646 + 1.10411I
5.53567 2.09330I 0
u = 1.34673 0.57417I
a = 1.31694 0.61600I
b = 1.67646 1.10411I
5.53567 + 2.09330I 0
u = 1.29737 + 0.69602I
a = 1.59511 + 0.98324I
b = 1.39424 + 0.59911I
6.1780 + 21.2684I 0
19
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.29737 0.69602I
a = 1.59511 0.98324I
b = 1.39424 0.59911I
6.1780 21.2684I 0
u = 1.44148 + 0.36244I
a = 1.69539 0.32909I
b = 0.952128 0.046267I
1.51901 + 1.31211I 0
u = 1.44148 0.36244I
a = 1.69539 + 0.32909I
b = 0.952128 + 0.046267I
1.51901 1.31211I 0
u = 1.30033 + 0.73150I
a = 1.53044 0.99996I
b = 1.38345 0.59236I
2.3154 15.2107I 0
u = 1.30033 0.73150I
a = 1.53044 + 0.99996I
b = 1.38345 + 0.59236I
2.3154 + 15.2107I 0
u = 1.49171 + 0.07947I
a = 1.72674 + 0.03755I
b = 1.367180 + 0.274051I
7.93556 + 3.58223I 0
u = 1.49171 0.07947I
a = 1.72674 0.03755I
b = 1.367180 0.274051I
7.93556 3.58223I 0
u = 1.52066 + 0.07524I
a = 1.49492 + 0.16602I
b = 0.975463 + 0.098321I
2.02827 1.74408I 0
u = 1.52066 0.07524I
a = 1.49492 0.16602I
b = 0.975463 0.098321I
2.02827 + 1.74408I 0
u = 1.28579 + 0.82078I
a = 1.24424 0.74116I
b = 1.119660 0.238814I
2.53610 6.73249I 0
20
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.28579 0.82078I
a = 1.24424 + 0.74116I
b = 1.119660 + 0.238814I
2.53610 + 6.73249I 0
u = 0.465212 + 0.080124I
a = 0.239465 + 1.309490I
b = 0.547442 + 0.630341I
1.64638 0.11395I 0
u = 0.465212 0.080124I
a = 0.239465 1.309490I
b = 0.547442 0.630341I
1.64638 + 0.11395I 0
u = 0.467809 + 0.014861I
a = 2.64609 + 2.28037I
b = 1.225890 + 0.388566I
5.80101 + 6.33996I 0. 7.06124I
u = 0.467809 0.014861I
a = 2.64609 2.28037I
b = 1.225890 0.388566I
5.80101 6.33996I 0. + 7.06124I
u = 0.286355 + 0.285771I
a = 0.560194 + 0.776428I
b = 0.529473 + 0.641270I
1.63494 0.09657I 6.80149 0.80764I
u = 0.286355 0.285771I
a = 0.560194 0.776428I
b = 0.529473 0.641270I
1.63494 + 0.09657I 6.80149 + 0.80764I
u = 0.401327 + 0.049138I
a = 1.29719 1.27421I
b = 0.480512 0.408479I
1.344880 + 0.264157I 8.50256 + 0.I
u = 0.401327 0.049138I
a = 1.29719 + 1.27421I
b = 0.480512 + 0.408479I
1.344880 0.264157I 8.50256 + 0.I
u = 1.41356 + 0.77661I
a = 1.32553 + 0.62707I
b = 1.088250 + 0.290153I
5.23114 + 11.81370I 0
21
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.41356 0.77661I
a = 1.32553 0.62707I
b = 1.088250 0.290153I
5.23114 11.81370I 0
u = 0.378581 + 0.057477I
a = 0.31956 + 3.23745I
b = 0.911086 + 0.412950I
0.19556 + 3.94521I 4.70911 6.53026I
u = 0.378581 0.057477I
a = 0.31956 3.23745I
b = 0.911086 0.412950I
0.19556 3.94521I 4.70911 + 6.53026I
u = 1.64134 + 0.05277I
a = 1.50976 0.10171I
b = 1.368300 + 0.255528I
10.61310 + 9.19329I 0
u = 1.64134 0.05277I
a = 1.50976 + 0.10171I
b = 1.368300 0.255528I
10.61310 9.19329I 0
u = 0.022460 + 0.320839I
a = 0.745021 0.773789I
b = 0.422997 0.761509I
0.90772 + 2.22862I 2.47026 2.53832I
u = 0.022460 0.320839I
a = 0.745021 + 0.773789I
b = 0.422997 + 0.761509I
0.90772 2.22862I 2.47026 + 2.53832I
u = 0.136571 + 0.243739I
a = 0.09936 1.72539I
b = 1.082450 0.598037I
1.02813 7.36128I 6.02142 + 7.21859I
u = 0.136571 0.243739I
a = 0.09936 + 1.72539I
b = 1.082450 + 0.598037I
1.02813 + 7.36128I 6.02142 7.21859I
u = 0.242147 + 0.065589I
a = 0.20140 + 2.12139I
b = 1.035070 + 0.547402I
0.12375 + 4.74338I 1.54330 + 1.67365I
22
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.242147 0.065589I
a = 0.20140 2.12139I
b = 1.035070 0.547402I
0.12375 4.74338I 1.54330 1.67365I
u = 0.54931 + 1.94748I
a = 0.810600 + 0.140370I
b = 1.001170 + 0.076704I
1.69171 + 2.23002I 0
u = 0.54931 1.94748I
a = 0.810600 0.140370I
b = 1.001170 0.076704I
1.69171 2.23002I 0
23
II. I
u
2
=
h3.85×10
38
u
44
8.38×10
37
u
43
+· · ·+2.18×10
35
b1.13×10
38
, 5.32×10
38
u
44
2.06 × 10
38
u
43
+ · · · + 2.18 × 10
35
a 1.04 × 10
38
, 4u
45
2u
44
+ · · · 3u + 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
2441.64u
44
+ 943.959u
43
+ ··· + 543.100u + 477.153
1767.82u
44
+ 384.805u
43
+ ··· 178.178u + 520.431
a
7
=
u
u
a
11
=
1665.63u
44
+ 382.251u
43
+ ··· + 1450.25u 995.347
1155.32u
44
1416.60u
43
+ ··· 3020.26u + 1360.20
a
4
=
3665.27u
44
+ 3598.82u
43
+ ··· + 4863.41u 915.493
4123.01u
44
2094.90u
43
+ ··· 2172.14u 44.1903
a
2
=
4021.21u
44
+ 1450.85u
43
+ ··· + 1206.28u + 286.883
5541.40u
44
175.743u
43
+ ··· + 1859.35u 1896.32
a
10
=
2454.37u
44
+ 1621.55u
43
+ ··· + 3975.62u 2051.78
1319.10u
44
1938.71u
43
+ ··· 4048.33u + 1768.62
a
3
=
4222.33u
44
+ 875.365u
43
+ ··· + 59.9225u + 795.684
5742.52u
44
+ 399.743u
43
+ ··· + 3005.71u 2405.12
a
9
=
2024.13u
44
+ 4096.76u
43
+ ··· + 6044.93u 1481.84
3617.61u
44
1390.93u
43
+ ··· 3657.20u + 1971.96
a
6
=
1196.35u
44
7302.57u
43
+ ··· 12310.8u + 4071.84
2107.71u
44
+ 4599.13u
43
+ ··· + 9004.27u 3727.44
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2774.23u
44
295.604u
43
+ ··· 477.821u + 128.358
24
(iv) u-Polynomials at the component
25
Crossings u-Polynomials at each crossing
c
1
16(16u
45
364u
44
+ ··· 6u + 1)
c
2
4(4u
45
+ 2u
44
+ ··· + 2u + 1)
c
3
u
45
2u
44
+ ··· 66u + 52
c
4
u
45
+ 4u
44
+ ··· 2u 1
c
5
u
45
3u
44
+ ··· 6u 4
c
6
u
45
5u
44
+ ··· + 5u 1
c
7
4(4u
45
+ 2u
44
+ ··· 3u 1)
c
8
4(4u
45
6u
44
+ ··· + 7u 1)
c
9
u
45
+ 5u
44
+ ··· + 5u + 1
c
10
u
45
+ 11u
44
+ ··· + 4u + 16
c
11
u
45
4u
44
+ ··· 2u + 1
c
12
4(4u
45
2u
44
+ ··· 3u + 1)
26
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
256(256y
45
+ 1936y
44
+ ··· 12y 1)
c
2
16(16y
45
60y
44
+ ··· 72y 1)
c
3
y
45
28y
44
+ ··· + 11116y 2704
c
4
, c
11
y
45
30y
44
+ ··· + 10y 1
c
5
y
45
13y
44
+ ··· 308y 16
c
6
, c
9
y
45
+ 25y
44
+ ··· 17y 1
c
7
, c
12
16(16y
45
364y
44
+ ··· + 39y 1)
c
8
16(16y
45
204y
44
+ ··· + 29y 1)
c
10
y
45
+ y
44
+ ··· 4560y 256
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.711310 + 0.688946I
a = 1.149990 + 0.103612I
b = 0.669282 + 0.848611I
3.05920 + 3.80335I 7.30523 7.20852I
u = 0.711310 0.688946I
a = 1.149990 0.103612I
b = 0.669282 0.848611I
3.05920 3.80335I 7.30523 + 7.20852I
u = 0.950366 + 0.413490I
a = 0.442771 + 0.862539I
b = 0.144607 0.568609I
0.26794 4.56165I 0. + 8.38189I
u = 0.950366 0.413490I
a = 0.442771 0.862539I
b = 0.144607 + 0.568609I
0.26794 + 4.56165I 0. 8.38189I
u = 0.973348 + 0.378667I
a = 0.942366 0.400940I
b = 0.257885 0.310072I
0.262542 + 1.189250I 0
u = 0.973348 0.378667I
a = 0.942366 + 0.400940I
b = 0.257885 + 0.310072I
0.262542 1.189250I 0
u = 0.232608 + 0.926219I
a = 0.481978 0.245653I
b = 1.099040 0.400151I
0.40412 5.73107I 3.37144 + 8.41233I
u = 0.232608 0.926219I
a = 0.481978 + 0.245653I
b = 1.099040 + 0.400151I
0.40412 + 5.73107I 3.37144 8.41233I
u = 0.914072 + 0.525509I
a = 0.115174 0.499245I
b = 0.799437 0.310200I
0.33962 5.61210I 0. + 10.94461I
u = 0.914072 0.525509I
a = 0.115174 + 0.499245I
b = 0.799437 + 0.310200I
0.33962 + 5.61210I 0. 10.94461I
29
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.304038 + 0.855463I
a = 0.858790 0.060024I
b = 0.541732 0.318053I
2.50039 + 2.48411I 9.20085 2.31922I
u = 0.304038 0.855463I
a = 0.858790 + 0.060024I
b = 0.541732 + 0.318053I
2.50039 2.48411I 9.20085 + 2.31922I
u = 1.053930 + 0.344581I
a = 0.506964 0.384322I
b = 0.393166 0.407855I
0.417098 + 0.993421I 0
u = 1.053930 0.344581I
a = 0.506964 + 0.384322I
b = 0.393166 + 0.407855I
0.417098 0.993421I 0
u = 1.000500 + 0.527976I
a = 0.627728 + 0.516777I
b = 1.130750 + 0.523330I
6.02418 + 4.22548I 0
u = 1.000500 0.527976I
a = 0.627728 0.516777I
b = 1.130750 0.523330I
6.02418 4.22548I 0
u = 1.038560 + 0.503593I
a = 2.27263 + 1.20143I
b = 1.34547 + 0.47013I
6.24978 8.66859I 0
u = 1.038560 0.503593I
a = 2.27263 1.20143I
b = 1.34547 0.47013I
6.24978 + 8.66859I 0
u = 0.789510 + 0.266781I
a = 0.138618 0.606101I
b = 0.432205 0.804512I
0.47501 + 1.58528I 0.77882 + 1.68530I
u = 0.789510 0.266781I
a = 0.138618 + 0.606101I
b = 0.432205 + 0.804512I
0.47501 1.58528I 0.77882 1.68530I
30
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.739295 + 0.266078I
a = 2.01161 0.43011I
b = 0.989895 0.690617I
0.05671 + 1.50309I 5.20097 4.66487I
u = 0.739295 0.266078I
a = 2.01161 + 0.43011I
b = 0.989895 + 0.690617I
0.05671 1.50309I 5.20097 + 4.66487I
u = 0.779302 + 0.059785I
a = 0.117394 + 0.208190I
b = 0.475609 + 0.821510I
0.948786 + 0.169052I 1.60678 2.11095I
u = 0.779302 0.059785I
a = 0.117394 0.208190I
b = 0.475609 0.821510I
0.948786 0.169052I 1.60678 + 2.11095I
u = 0.695270 + 0.300304I
a = 0.205785 0.068107I
b = 0.866827 0.582379I
0.11500 5.35155I 3.15219 + 9.36441I
u = 0.695270 0.300304I
a = 0.205785 + 0.068107I
b = 0.866827 + 0.582379I
0.11500 + 5.35155I 3.15219 9.36441I
u = 1.202150 + 0.360708I
a = 2.16352 0.57837I
b = 1.35966 0.51837I
4.38611 + 9.29994I 0
u = 1.202150 0.360708I
a = 2.16352 + 0.57837I
b = 1.35966 + 0.51837I
4.38611 9.29994I 0
u = 1.215640 + 0.344864I
a = 1.72027 0.39613I
b = 1.64496 + 0.05319I
6.86778 7.61456I 0
u = 1.215640 0.344864I
a = 1.72027 + 0.39613I
b = 1.64496 0.05319I
6.86778 + 7.61456I 0
31
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.147970 + 0.603357I
a = 0.64148 + 1.36529I
b = 0.915632 + 0.246511I
4.54406 + 10.18430I 0
u = 1.147970 0.603357I
a = 0.64148 1.36529I
b = 0.915632 0.246511I
4.54406 10.18430I 0
u = 0.676670 + 0.001310I
a = 3.95357 + 0.58207I
b = 1.48675 + 0.29075I
4.06027 6.02530I 0.330629 0.846429I
u = 0.676670 0.001310I
a = 3.95357 0.58207I
b = 1.48675 0.29075I
4.06027 + 6.02530I 0.330629 + 0.846429I
u = 0.196097 + 1.352380I
a = 0.371046 1.349930I
b = 0.708641 0.856981I
4.10732 + 3.44949I 0
u = 0.196097 1.352380I
a = 0.371046 + 1.349930I
b = 0.708641 + 0.856981I
4.10732 3.44949I 0
u = 0.603323 + 0.040355I
a = 0.470910 + 0.027826I
b = 1.076530 0.676865I
1.51733 7.23132I 9.77735 + 2.80982I
u = 0.603323 0.040355I
a = 0.470910 0.027826I
b = 1.076530 + 0.676865I
1.51733 + 7.23132I 9.77735 2.80982I
u = 1.32646 + 0.54089I
a = 1.35220 + 0.66417I
b = 1.64627 + 0.91105I
5.46452 + 2.01994I 0
u = 1.32646 0.54089I
a = 1.35220 0.66417I
b = 1.64627 0.91105I
5.46452 2.01994I 0
32
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.471064 + 0.081382I
a = 6.55488 + 1.59636I
b = 0.759223 + 0.101306I
0.75321 6.26996I 9.87453 + 7.73257I
u = 0.471064 0.081382I
a = 6.55488 1.59636I
b = 0.759223 0.101306I
0.75321 + 6.26996I 9.87453 7.73257I
u = 0.456992
a = 7.97352
b = 0.778866
3.31828 18.3540
u = 1.51659 + 0.78555I
a = 1.154770 + 0.303734I
b = 0.911301 0.046320I
1.89798 + 2.08554I 0
u = 1.51659 0.78555I
a = 1.154770 0.303734I
b = 0.911301 + 0.046320I
1.89798 2.08554I 0
33
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
256(16u
45
364u
44
+ ··· 6u + 1)
· (16u
183
+ 252u
182
+ ··· + 449u 17)
c
2
16(4u
45
+ 2u
44
+ ··· + 2u + 1)
· (4u
183
14u
182
+ ··· + 864065u 160229)
c
3
(u
45
2u
44
+ ··· 66u + 52)(u
183
3u
182
+ ··· + 285506u 6964)
c
4
(u
45
+ 4u
44
+ ··· 2u 1)(u
183
+ 5u
182
+ ··· + 1386431u + 62039)
c
5
(u
45
3u
44
+ ··· 6u 4)
· (u
183
4u
182
+ ··· 17118874u 3362836)
c
6
(u
45
5u
44
+ ··· + 5u 1)(u
183
8u
182
+ ··· 9204u + 773)
c
7
16(4u
45
+ 2u
44
+ ··· 3u 1)(4u
183
2u
182
+ ··· 2u 1)
c
8
16(4u
45
6u
44
+ ··· + 7u 1)
· (4u
183
2u
182
+ ··· + 4507202u 289523)
c
9
(u
45
+ 5u
44
+ ··· + 5u + 1)(u
183
8u
182
+ ··· 9204u + 773)
c
10
(u
45
+ 11u
44
+ ··· + 4u + 16)
· (u
183
+ 6u
182
+ ··· + 5277708u + 199568)
c
11
(u
45
4u
44
+ ··· 2u + 1)(u
183
+ 5u
182
+ ··· + 1386431u + 62039)
c
12
16(4u
45
2u
44
+ ··· 3u + 1)(4u
183
2u
182
+ ··· 2u 1)
34
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
65536(256y
45
+ 1936y
44
+ ··· 12y 1)
· (256y
183
2416y
182
+ ··· 5697y 289)
c
2
256(16y
45
60y
44
+ ··· 72y 1)
· (16y
183
+ 404y
182
+ ··· + 751073906455y 25673332441)
c
3
(y
45
28y
44
+ ··· + 11116y 2704)
· (y
183
55y
182
+ ··· + 3956764060y 48497296)
c
4
, c
11
(y
45
30y
44
+ ··· + 10y 1)
· (y
183
121y
182
+ ··· + 995844174085y 3848837521)
c
5
(y
45
13y
44
+ ··· 308y 16)
· (y
183
20y
182
+ ··· + 1169699756063260y 11308665962896)
c
6
, c
9
(y
45
+ 25y
44
+ ··· 17y 1)
· (y
183
+ 110y
182
+ ··· 36021254y 597529)
c
7
, c
12
256(16y
45
364y
44
+ ··· + 39y 1)
· (16y
183
1564y
182
+ ··· + 82y 1)
c
8
256(16y
45
204y
44
+ ··· + 29y 1)
· (16y
183
+ 196y
182
+ ··· + 3044733745720y 83823567529)
c
10
(y
45
+ y
44
+ ··· 4560y 256)
· (y
183
18y
182
+ ··· + 2408586039216y 39827386624)
35