12a
0543
(K12a
0543
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 12 11 2 1 6 4 9 5
Solving Sequence
2,8
7 3 4 1
9,11
12 6 5 10
c
7
c
2
c
3
c
1
c
8
c
11
c
6
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.68337 × 10
119
u
144
+ 7.16684 × 10
118
u
143
+ ··· + 5.14439 × 10
118
b + 6.42016 × 10
118
,
− 1.79261 × 10
120
u
144
− 1.95501 × 10
120
u
143
+ ··· + 3.60108 × 10
119
a − 8.71578 × 10
120
,
u
145
+ u
144
+ ··· + 10u + 7i
I
u
2
= h−u
25
− u
24
+ ··· + b + 1, u
25
− 2u
24
+ ··· + a − 4, u
26
+ 7u
24
+ ··· + 3u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 171 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
= h1.68 × 10
119
u
144
+ 7.17 × 10
118
u
143
+ · · · + 5.14 × 10
118
b + 6.42 ×
10
118
, −1.79 × 10
120
u
144
− 1.96 × 10
120
u
143
+ · · · + 3.60 × 10
119
a − 8.72 ×
10
120
, u
145
+ u
144
+ · · · + 10u + 7i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
11
=
4.97800u
144
+ 5.42896u
143
+ ··· + 56.4506u + 24.2033
−3.27224u
144
− 1.39314u
143
+ ··· − 27.5746u − 1.24799
a
12
=
5.49859u
144
+ 4.11098u
143
+ ··· + 54.4352u + 13.8676
−2.49995u
144
− 0.367127u
143
+ ··· − 19.0091u + 1.60456
a
6
=
4.80687u
144
+ 6.35204u
143
+ ··· + 65.5375u + 32.7772
−2.14463u
144
− 1.10343u
143
+ ··· − 21.2231u − 3.92713
a
5
=
2.92464u
144
+ 2.24128u
143
+ ··· + 26.1845u + 8.46431
0.305108u
144
+ 0.518469u
143
+ ··· + 3.64666u + 2.19118
a
10
=
5.60505u
144
+ 4.70435u
143
+ ··· + 57.1498u + 18.1858
−2.57136u
144
− 0.200226u
143
+ ··· − 17.8815u + 2.50357
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0931173u
144
+ 4.00522u
143
+ ··· + 31.6281u + 25.6618
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
145
+ 69u
144
+ ··· − 362u − 49
c
2
, c
7
u
145
+ u
144
+ ··· + 10u + 7
c
3
u
145
− u
144
+ ··· − 194332u + 20503
c
4
, c
10
u
145
− u
144
+ ··· − 10727u + 2347
c
5
, c
12
u
145
− 2u
144
+ ··· − 12270u + 2449
c
6
u
145
+ 16u
143
+ ··· + 3486694u + 149809
c
8
u
145
+ 5u
144
+ ··· + 35208736u + 7631659
c
9
u
145
+ 7u
144
+ ··· − 13u + 1
c
11
u
145
− 21u
144
+ ··· + 135u + 83
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
145
+ 21y
144
+ ··· − 34870y −2401
c
2
, c
7
y
145
+ 69y
144
+ ··· − 362y −49
c
3
y
145
− 21y
144
+ ··· + 39082161962y −420373009
c
4
, c
10
y
145
+ 105y
144
+ ··· − 226926923y −5508409
c
5
, c
12
y
145
+ 86y
144
+ ··· + 45603454y −5997601
c
6
y
145
+ 32y
144
+ ··· − 735797446182y −22442736481
c
8
y
145
+ 73y
144
+ ··· − 2911748666672046y −58242219092281
c
9
y
145
− 7y
144
+ ··· + 67y −1
c
11
y
145
− 17y
144
+ ··· + 528509y −6889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.184394 + 0.997690I
a = 1.205560 − 0.226744I
b = −0.467031 − 0.834593I
−1.79715 + 1.32721I 0
u = −0.184394 − 0.997690I
a = 1.205560 + 0.226744I
b = −0.467031 + 0.834593I
−1.79715 − 1.32721I 0
u = 0.787390 + 0.592137I
a = −0.489679 − 0.314649I
b = −0.149224 + 0.355817I
5.28775 − 1.33253I 0
u = 0.787390 − 0.592137I
a = −0.489679 + 0.314649I
b = −0.149224 − 0.355817I
5.28775 + 1.33253I 0
u = −0.338378 + 0.957023I
a = −3.20344 + 1.10546I
b = 1.80339 + 1.12969I
−2.55022 − 4.09982I 0
u = −0.338378 − 0.957023I
a = −3.20344 − 1.10546I
b = 1.80339 − 1.12969I
−2.55022 + 4.09982I 0
u = −0.303177 + 0.976012I
a = 1.62753 − 0.47233I
b = −1.51906 + 0.55961I
1.18528 − 1.07910I 0
u = −0.303177 − 0.976012I
a = 1.62753 + 0.47233I
b = −1.51906 − 0.55961I
1.18528 + 1.07910I 0
u = 0.396214 + 0.942465I
a = −0.051002 + 0.579643I
b = −0.247222 − 0.810358I
−0.47939 + 1.85777I 0
u = 0.396214 − 0.942465I
a = −0.051002 − 0.579643I
b = −0.247222 + 0.810358I
−0.47939 − 1.85777I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.698321 + 0.678727I
a = −0.791006 + 0.117482I
b = −0.166137 − 0.243382I
5.99895 − 2.02453I 0
u = −0.698321 − 0.678727I
a = −0.791006 − 0.117482I
b = −0.166137 + 0.243382I
5.99895 + 2.02453I 0
u = −0.097852 + 1.023050I
a = 1.63457 − 0.39899I
b = −1.42349 − 0.63315I
−0.22854 + 3.12050I 0
u = −0.097852 − 1.023050I
a = 1.63457 + 0.39899I
b = −1.42349 + 0.63315I
−0.22854 − 3.12050I 0
u = 0.741562 + 0.623321I
a = 0.532405 + 0.864548I
b = 0.073970 − 0.745696I
4.64179 + 11.18290I 0
u = 0.741562 − 0.623321I
a = 0.532405 − 0.864548I
b = 0.073970 + 0.745696I
4.64179 − 11.18290I 0
u = 0.241101 + 1.005640I
a = 1.71508 + 1.43776I
b = −2.02337 − 0.03526I
0.635555 + 0.338860I 0
u = 0.241101 − 1.005640I
a = 1.71508 − 1.43776I
b = −2.02337 + 0.03526I
0.635555 − 0.338860I 0
u = 0.251556 + 1.022450I
a = −3.24031 + 0.24100I
b = 1.41535 − 1.01544I
−3.47507 − 2.68719I 0
u = 0.251556 − 1.022450I
a = −3.24031 − 0.24100I
b = 1.41535 + 1.01544I
−3.47507 + 2.68719I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.824404 + 0.433210I
a = −0.332263 − 0.322654I
b = −1.003040 + 0.868786I
4.39588 + 2.05646I 0
u = −0.824404 − 0.433210I
a = −0.332263 + 0.322654I
b = −1.003040 − 0.868786I
4.39588 − 2.05646I 0
u = 0.490005 + 0.773992I
a = 1.004320 + 0.687450I
b = −0.825636 − 0.474558I
0.13695 + 2.07089I 0
u = 0.490005 − 0.773992I
a = 1.004320 − 0.687450I
b = −0.825636 + 0.474558I
0.13695 − 2.07089I 0
u = −0.438325 + 0.992032I
a = −1.83986 − 1.03644I
b = 0.63602 + 2.34736I
−2.15013 − 6.05393I 0
u = −0.438325 − 0.992032I
a = −1.83986 + 1.03644I
b = 0.63602 − 2.34736I
−2.15013 + 6.05393I 0
u = −0.706416 + 0.581377I
a = 0.453554 − 0.977363I
b = 0.040691 + 1.056500I
7.52331 − 5.01192I 0
u = −0.706416 − 0.581377I
a = 0.453554 + 0.977363I
b = 0.040691 − 1.056500I
7.52331 + 5.01192I 0
u = 0.335392 + 1.037830I
a = 1.24878 + 0.94604I
b = −0.753812 + 1.170660I
−4.06964 + 4.22267I 0
u = 0.335392 − 1.037830I
a = 1.24878 − 0.94604I
b = −0.753812 − 1.170660I
−4.06964 − 4.22267I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.837402 + 0.346097I
a = −0.470563 + 0.071252I
b = −0.915098 − 0.992526I
4.05564 − 4.81767I 0
u = 0.837402 − 0.346097I
a = −0.470563 − 0.071252I
b = −0.915098 + 0.992526I
4.05564 + 4.81767I 0
u = −0.606369 + 0.920094I
a = −0.615571 − 0.438638I
b = −0.118732 − 0.231346I
5.28012 − 2.99417I 0
u = −0.606369 − 0.920094I
a = −0.615571 + 0.438638I
b = −0.118732 + 0.231346I
5.28012 + 2.99417I 0
u = −0.814299 + 0.375549I
a = 0.575844 + 0.635418I
b = 1.66703 − 1.41778I
3.2718 + 14.1290I 0
u = −0.814299 − 0.375549I
a = 0.575844 − 0.635418I
b = 1.66703 + 1.41778I
3.2718 − 14.1290I 0
u = −0.338107 + 0.828564I
a = 1.170070 + 0.396851I
b = 0.545917 − 1.153990I
−2.23687 + 1.29929I 0
u = −0.338107 − 0.828564I
a = 1.170070 − 0.396851I
b = 0.545917 + 1.153990I
−2.23687 − 1.29929I 0
u = 0.732572 + 0.502840I
a = −0.702309 − 1.007620I
b = 0.097958 + 0.123214I
5.00367 + 2.20048I 0
u = 0.732572 − 0.502840I
a = −0.702309 + 1.007620I
b = 0.097958 − 0.123214I
5.00367 − 2.20048I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.208756 + 1.099840I
a = 1.153790 + 0.284530I
b = −0.764283 + 1.064860I
−5.69124 − 5.08448I 0
u = 0.208756 − 1.099840I
a = 1.153790 − 0.284530I
b = −0.764283 − 1.064860I
−5.69124 + 5.08448I 0
u = −0.754912 + 0.442722I
a = −0.894123 − 0.814790I
b = −1.40872 + 1.09063I
4.68617 + 4.86935I 0
u = −0.754912 − 0.442722I
a = −0.894123 + 0.814790I
b = −1.40872 − 1.09063I
4.68617 − 4.86935I 0
u = 0.175228 + 1.115380I
a = −1.68414 − 1.85829I
b = 1.75348 + 0.18743I
1.63161 − 5.18305I 0
u = 0.175228 − 1.115380I
a = −1.68414 + 1.85829I
b = 1.75348 − 0.18743I
1.63161 + 5.18305I 0
u = 0.777707 + 0.383999I
a = 0.600592 − 0.714495I
b = 1.71002 + 1.62586I
6.48441 − 7.60554I 0
u = 0.777707 − 0.383999I
a = 0.600592 + 0.714495I
b = 1.71002 − 1.62586I
6.48441 + 7.60554I 0
u = −0.653235 + 0.563065I
a = 0.16315 + 1.61830I
b = 0.782854 − 0.672428I
−0.13545 − 5.31806I 0
u = −0.653235 − 0.563065I
a = 0.16315 − 1.61830I
b = 0.782854 + 0.672428I
−0.13545 + 5.31806I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.430800 + 1.061450I
a = −1.93162 + 0.87528I
b = 1.66325 + 0.81510I
−3.66318 − 3.44179I 0
u = −0.430800 − 1.061450I
a = −1.93162 − 0.87528I
b = 1.66325 − 0.81510I
−3.66318 + 3.44179I 0
u = −0.555844 + 1.005450I
a = −1.097740 + 0.745118I
b = 1.90293 + 0.12033I
−1.44297 + 0.59465I 0
u = −0.555844 − 1.005450I
a = −1.097740 − 0.745118I
b = 1.90293 − 0.12033I
−1.44297 − 0.59465I 0
u = −0.286561 + 1.114860I
a = −0.31602 + 1.49740I
b = 1.069560 − 0.389689I
−5.39088 + 0.00078I 0
u = −0.286561 − 1.114860I
a = −0.31602 − 1.49740I
b = 1.069560 + 0.389689I
−5.39088 − 0.00078I 0
u = 0.749711 + 0.373069I
a = −0.246364 + 1.321170I
b = −1.40342 − 0.51244I
−1.10274 − 7.51513I 0
u = 0.749711 − 0.373069I
a = −0.246364 − 1.321170I
b = −1.40342 + 0.51244I
−1.10274 + 7.51513I 0
u = 0.437131 + 1.077290I
a = 0.26927 + 1.88271I
b = −1.36581 − 1.26139I
−0.73593 + 1.52071I 0
u = 0.437131 − 1.077290I
a = 0.26927 − 1.88271I
b = −1.36581 + 1.26139I
−0.73593 − 1.52071I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.289488 + 1.127400I
a = 0.77596 + 1.28242I
b = 0.331794 − 0.970544I
−5.42792 + 0.17662I 0
u = −0.289488 − 1.127400I
a = 0.77596 − 1.28242I
b = 0.331794 + 0.970544I
−5.42792 − 0.17662I 0
u = −0.605587 + 0.994069I
a = 1.35475 + 0.78238I
b = −0.531018 − 0.543116I
6.30112 − 0.02283I 0
u = −0.605587 − 0.994069I
a = 1.35475 − 0.78238I
b = −0.531018 + 0.543116I
6.30112 + 0.02283I 0
u = 0.679698 + 0.485792I
a = 0.237669 − 1.035950I
b = 0.376722 + 0.729948I
2.95976 + 0.92488I 0
u = 0.679698 − 0.485792I
a = 0.237669 + 1.035950I
b = 0.376722 − 0.729948I
2.95976 − 0.92488I 0
u = −0.716572 + 0.425089I
a = −0.029300 − 1.060030I
b = −1.280090 + 0.563040I
2.64102 + 3.13575I 0
u = −0.716572 − 0.425089I
a = −0.029300 + 1.060030I
b = −1.280090 − 0.563040I
2.64102 − 3.13575I 0
u = 0.511208 + 0.657131I
a = 0.741436 + 0.404517I
b = −0.771755 − 0.186005I
0.27239 + 1.87412I 0
u = 0.511208 − 0.657131I
a = 0.741436 − 0.404517I
b = −0.771755 + 0.186005I
0.27239 − 1.87412I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.647175 + 0.971864I
a = 0.967998 − 0.643040I
b = −0.380814 + 0.210677I
3.60765 − 5.91767I 0
u = 0.647175 − 0.971864I
a = 0.967998 + 0.643040I
b = −0.380814 − 0.210677I
3.60765 + 5.91767I 0
u = −0.165538 + 1.164930I
a = −1.56610 + 1.52417I
b = 1.69391 − 0.15332I
−1.83364 + 11.47010I 0
u = −0.165538 − 1.164930I
a = −1.56610 − 1.52417I
b = 1.69391 + 0.15332I
−1.83364 − 11.47010I 0
u = 0.380646 + 1.117450I
a = −2.25990 − 0.29991I
b = 1.74240 − 0.96746I
−7.41429 + 5.48824I 0
u = 0.380646 − 1.117450I
a = −2.25990 + 0.29991I
b = 1.74240 + 0.96746I
−7.41429 − 5.48824I 0
u = 0.415590 + 1.106590I
a = 1.93053 − 0.83523I
b = −0.33602 + 1.90650I
−0.85504 + 5.80986I 0
u = 0.415590 − 1.106590I
a = 1.93053 + 0.83523I
b = −0.33602 − 1.90650I
−0.85504 − 5.80986I 0
u = 0.693171 + 0.424591I
a = −1.297510 + 0.408056I
b = −1.17331 − 1.38727I
4.77635 − 1.51542I 0
u = 0.693171 − 0.424591I
a = −1.297510 − 0.408056I
b = −1.17331 + 1.38727I
4.77635 + 1.51542I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.670777 + 0.453286I
a = −1.08992 + 1.00199I
b = −0.1120640 − 0.0829036I
4.93494 + 0.50336I 0
u = −0.670777 − 0.453286I
a = −1.08992 − 1.00199I
b = −0.1120640 + 0.0829036I
4.93494 − 0.50336I 0
u = −0.658657 + 0.469439I
a = 0.155719 + 0.370369I
b = 2.14970 − 0.34783I
0.96555 − 2.70815I 0
u = −0.658657 − 0.469439I
a = 0.155719 − 0.370369I
b = 2.14970 + 0.34783I
0.96555 + 2.70815I 0
u = 0.696152 + 0.409095I
a = 0.023956 + 0.141789I
b = 1.85277 − 0.60815I
0.66094 − 4.68741I 0
u = 0.696152 − 0.409095I
a = 0.023956 − 0.141789I
b = 1.85277 + 0.60815I
0.66094 + 4.68741I 0
u = 0.569625 + 1.050860I
a = −1.096000 − 0.096015I
b = 1.187160 − 0.449559I
1.29070 + 3.91656I 0
u = 0.569625 − 1.050860I
a = −1.096000 + 0.096015I
b = 1.187160 + 0.449559I
1.29070 − 3.91656I 0
u = 0.530351 + 1.072130I
a = 2.15831 + 1.00377I
b = −2.27909 + 0.16677I
−2.70997 + 2.55761I 0
u = 0.530351 − 1.072130I
a = 2.15831 − 1.00377I
b = −2.27909 − 0.16677I
−2.70997 − 2.55761I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.560721 + 1.056780I
a = −1.99582 + 2.46246I
b = 2.59318 + 0.22613I
−0.76533 − 2.05228I 0
u = −0.560721 − 1.056780I
a = −1.99582 − 2.46246I
b = 2.59318 − 0.22613I
−0.76533 + 2.05228I 0
u = −0.072536 + 1.198540I
a = 0.843928 − 0.674907I
b = −0.859816 + 0.260701I
−1.223970 − 0.253168I 0
u = −0.072536 − 1.198540I
a = 0.843928 + 0.674907I
b = −0.859816 − 0.260701I
−1.223970 + 0.253168I 0
u = 0.665080 + 1.003710I
a = −0.527424 + 0.347058I
b = −0.0028840 + 0.0612795I
4.06228 + 6.77781I 0
u = 0.665080 − 1.003710I
a = −0.527424 − 0.347058I
b = −0.0028840 − 0.0612795I
4.06228 − 6.77781I 0
u = −0.564275 + 1.065810I
a = −0.106865 − 0.291564I
b = 0.186769 − 0.738135I
3.13220 − 5.30727I 0
u = −0.564275 − 1.065810I
a = −0.106865 + 0.291564I
b = 0.186769 + 0.738135I
3.13220 + 5.30727I 0
u = 0.602451 + 1.051580I
a = −0.297227 + 0.108546I
b = 0.495009 + 0.529668I
3.37666 + 2.89310I 0
u = 0.602451 − 1.051580I
a = −0.297227 − 0.108546I
b = 0.495009 − 0.529668I
3.37666 − 2.89310I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.786073 + 0.018603I
a = −0.134255 + 0.444436I
b = −0.648623 + 1.033690I
−1.84816 + 6.47339I −4.00000 − 7.35991I
u = −0.786073 − 0.018603I
a = −0.134255 − 0.444436I
b = −0.648623 − 1.033690I
−1.84816 − 6.47339I −4.00000 + 7.35991I
u = 0.470849 + 1.123390I
a = −1.16024 − 1.31564I
b = 1.53168 − 0.31962I
−6.80529 + 2.18799I 0
u = 0.470849 − 1.123390I
a = −1.16024 + 1.31564I
b = 1.53168 + 0.31962I
−6.80529 − 2.18799I 0
u = 0.569536 + 1.079360I
a = 2.37858 + 0.41773I
b = −1.89509 + 1.91867I
2.85729 + 6.39098I 0
u = 0.569536 − 1.079360I
a = 2.37858 − 0.41773I
b = −1.89509 − 1.91867I
2.85729 − 6.39098I 0
u = −0.720675 + 0.285629I
a = 0.532398 + 0.003468I
b = −0.300937 − 1.176800I
−1.27972 + 3.13142I −4.00000 + 1.52364I
u = −0.720675 − 0.285629I
a = 0.532398 − 0.003468I
b = −0.300937 + 1.176800I
−1.27972 − 3.13142I −4.00000 − 1.52364I
u = 0.566972 + 1.085860I
a = −0.72019 − 2.70277I
b = 1.95871 + 0.64288I
−1.31995 + 9.55890I 0
u = 0.566972 − 1.085860I
a = −0.72019 + 2.70277I
b = 1.95871 − 0.64288I
−1.31995 − 9.55890I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.577640 + 1.082700I
a = 1.71775 − 1.10252I
b = −2.09488 − 0.26553I
0.70880 − 8.09519I 0
u = −0.577640 − 1.082700I
a = 1.71775 + 1.10252I
b = −2.09488 + 0.26553I
0.70880 + 8.09519I 0
u = −0.545457 + 1.112530I
a = −2.17887 − 0.42343I
b = 1.35181 + 1.72217I
−3.64516 − 7.56566I 0
u = −0.545457 − 1.112530I
a = −2.17887 + 0.42343I
b = 1.35181 − 1.72217I
−3.64516 + 7.56566I 0
u = −0.597023 + 1.086030I
a = 2.15158 − 0.82628I
b = −2.26804 − 1.36181I
2.78055 − 9.99731I 0
u = −0.597023 − 1.086030I
a = 2.15158 + 0.82628I
b = −2.26804 + 1.36181I
2.78055 + 9.99731I 0
u = 0.193774 + 1.229020I
a = 0.752680 + 0.881514I
b = −1.067280 − 0.404511I
−1.11956 − 1.75849I 0
u = 0.193774 − 1.229020I
a = 0.752680 − 0.881514I
b = −1.067280 + 0.404511I
−1.11956 + 1.75849I 0
u = −0.687980 + 0.303581I
a = 0.814867 + 0.487323I
b = 0.62146 − 1.37978I
−1.33531 + 2.81897I −6.12249 − 2.40079I
u = −0.687980 − 0.303581I
a = 0.814867 − 0.487323I
b = 0.62146 + 1.37978I
−1.33531 − 2.81897I −6.12249 + 2.40079I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.543472 + 1.126620I
a = −1.00340 − 1.43746I
b = −0.18736 + 1.58829I
−3.71059 − 7.93725I 0
u = −0.543472 − 1.126620I
a = −1.00340 + 1.43746I
b = −0.18736 − 1.58829I
−3.71059 + 7.93725I 0
u = 0.576970 + 1.110150I
a = 1.77781 + 1.07541I
b = −2.38634 + 0.30525I
−3.26812 + 12.54560I 0
u = 0.576970 − 1.110150I
a = 1.77781 − 1.07541I
b = −2.38634 − 0.30525I
−3.26812 − 12.54560I 0
u = −0.439519 + 1.177620I
a = 1.60063 + 0.53610I
b = −0.58033 − 1.55254I
−5.28717 − 10.80720I 0
u = −0.439519 − 1.177620I
a = 1.60063 − 0.53610I
b = −0.58033 + 1.55254I
−5.28717 + 10.80720I 0
u = 0.588713 + 1.114710I
a = −3.04785 − 0.61947I
b = 2.45496 − 1.83511I
4.32194 + 12.75140I 0
u = 0.588713 − 1.114710I
a = −3.04785 + 0.61947I
b = 2.45496 + 1.83511I
4.32194 − 12.75140I 0
u = −0.409051 + 1.195690I
a = 0.245838 − 1.307360I
b = −1.061410 + 0.867196I
−5.50406 + 2.24792I 0
u = −0.409051 − 1.195690I
a = 0.245838 + 1.307360I
b = −1.061410 − 0.867196I
−5.50406 − 2.24792I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621234 + 1.107540I
a = 1.59139 − 0.60187I
b = −1.45625 − 0.90520I
2.37877 − 7.44465I 0
u = −0.621234 − 1.107540I
a = 1.59139 + 0.60187I
b = −1.45625 + 0.90520I
2.37877 + 7.44465I 0
u = −0.598688 + 1.129240I
a = −2.70720 + 0.66114I
b = 2.33879 + 1.64430I
1.0265 − 19.4036I 0
u = −0.598688 − 1.129240I
a = −2.70720 − 0.66114I
b = 2.33879 − 1.64430I
1.0265 + 19.4036I 0
u = 0.599077 + 1.144460I
a = 1.64688 + 0.30692I
b = −1.26606 + 1.23218I
1.67753 + 10.14400I 0
u = 0.599077 − 1.144460I
a = 1.64688 − 0.30692I
b = −1.26606 − 1.23218I
1.67753 − 10.14400I 0
u = 0.568890 + 0.385452I
a = 0.54032 + 1.67742I
b = −1.251310 − 0.652831I
−0.75101 + 1.90370I −4.80872 − 0.09845I
u = 0.568890 − 0.385452I
a = 0.54032 − 1.67742I
b = −1.251310 + 0.652831I
−0.75101 − 1.90370I −4.80872 + 0.09845I
u = 0.642939 + 0.120216I
a = 0.566798 + 0.181916I
b = 1.162810 − 0.332187I
−4.02495 + 2.01618I −7.90744 − 1.24994I
u = 0.642939 − 0.120216I
a = 0.566798 − 0.181916I
b = 1.162810 + 0.332187I
−4.02495 − 2.01618I −7.90744 + 1.24994I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.593300 + 0.022047I
a = −0.101191 − 1.046710I
b = −0.607461 − 1.118300I
2.10728 − 2.09321I 0.33268 + 3.77036I
u = 0.593300 − 0.022047I
a = −0.101191 + 1.046710I
b = −0.607461 + 1.118300I
2.10728 + 2.09321I 0.33268 − 3.77036I
u = −0.331001 + 0.427874I
a = 2.29469 + 0.54871I
b = −0.286337 − 1.291110I
−0.66545 + 2.55610I −0.94084 − 2.48924I
u = −0.331001 − 0.427874I
a = 2.29469 − 0.54871I
b = −0.286337 + 1.291110I
−0.66545 − 2.55610I −0.94084 + 2.48924I
u = −0.461079
a = 0.707907
b = 0.893156
−1.10691 −8.89040
19
II.
I
u
2
= h−u
25
−u
24
+· · ·+b+1, u
25
−2u
24
+· · ·+a−4, u
26
+7u
24
+· · ·+3u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
11
=
−u
25
+ 2u
24
+ ··· + 6u
2
+ 4
u
25
+ u
24
+ ··· + u − 1
a
12
=
−u
25
+ u
24
+ ··· + 4u
2
+ 3
u
25
+ u
24
+ ··· + u − 1
a
6
=
u
25
+ u
24
+ ··· + 2u + 1
u
25
− u
24
+ ··· − 2u
2
− 2
a
5
=
−2u
23
+ u
22
+ ··· − 6u
3
− 4u
−u
25
− 6u
23
+ ··· + u
4
+ u
a
10
=
−u
25
+ u
24
+ ··· + 3u
2
+ 3
u
25
+ u
24
+ ··· − u
4
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 13u
25
+ 86u
23
− 2u
22
+ 287u
21
− 12u
20
+ 605u
19
− 37u
18
+
877u
17
− 71u
16
+ 918u
15
− 80u
14
+ 740u
13
− 40u
12
+ 515u
11
+ 30u
10
+ 337u
9
+ 66u
8
+
177u
7
+ 53u
6
+ 58u
5
+ 17u
4
+ 16u
3
− 5u
2
+ 10u − 9
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
26
− 14u
25
+ ··· − 6u + 1
c
2
u
26
+ 7u
24
+ ··· + 3u
2
+ 1
c
3
u
26
− 2u
24
+ ··· − 2u + 1
c
4
u
26
+ 13u
24
+ ··· − u + 1
c
5
u
26
+ u
25
+ ··· + 13u
2
+ 1
c
6
u
26
+ u
25
+ ··· − 2u + 1
c
7
u
26
+ 7u
24
+ ··· + 3u
2
+ 1
c
8
u
26
+ 7u
24
+ ··· + 3u
2
+ 1
c
9
u
26
+ 2u
25
+ ··· − u + 1
c
10
u
26
+ 13u
24
+ ··· + u + 1
c
11
u
26
− 4u
24
+ ··· + 7u + 1
c
12
u
26
− u
25
+ ··· + 13u
2
+ 1
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 2y
25
+ ··· + 10y + 1
c
2
, c
7
y
26
+ 14y
25
+ ··· + 6y + 1
c
3
y
26
− 4y
25
+ ··· + 6y + 1
c
4
, c
10
y
26
+ 26y
25
+ ··· + 19y + 1
c
5
, c
12
y
26
+ 19y
25
+ ··· + 26y + 1
c
6
y
26
− 7y
25
+ ··· − 2y + 1
c
8
y
26
+ 14y
25
+ ··· + 6y + 1
c
9
y
26
− 2y
25
+ ··· − 7y + 1
c
11
y
26
− 8y
25
+ ··· − 5y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.359440 + 0.910887I
a = 1.77754 − 1.04325I
b = −1.84702 + 0.56243I
1.81449 − 1.47433I 2.93751 + 5.13499I
u = −0.359440 − 0.910887I
a = 1.77754 + 1.04325I
b = −1.84702 − 0.56243I
1.81449 + 1.47433I 2.93751 − 5.13499I
u = 0.402070 + 1.012970I
a = −2.58496 − 0.45894I
b = 1.39908 − 1.96159I
−3.09604 + 5.11284I −9.28335 − 9.03985I
u = 0.402070 − 1.012970I
a = −2.58496 + 0.45894I
b = 1.39908 + 1.96159I
−3.09604 − 5.11284I −9.28335 + 9.03985I
u = 0.789971 + 0.415474I
a = −0.627696 + 0.302463I
b = −1.087560 − 0.836873I
4.28502 − 3.71076I −0.33164 + 1.61195I
u = 0.789971 − 0.415474I
a = −0.627696 − 0.302463I
b = −1.087560 + 0.836873I
4.28502 + 3.71076I −0.33164 − 1.61195I
u = −0.699594 + 0.550884I
a = −0.956695 + 0.481873I
b = −0.200902 + 0.037955I
5.12297 − 1.01125I 0.66466 + 1.43973I
u = −0.699594 − 0.550884I
a = −0.956695 − 0.481873I
b = −0.200902 − 0.037955I
5.12297 + 1.01125I 0.66466 − 1.43973I
u = 0.510275 + 1.047840I
a = −1.71620 − 2.34544I
b = 2.66024 + 0.58919I
−2.28523 + 1.24764I −9.11702 + 0.85683I
u = 0.510275 − 1.047840I
a = −1.71620 + 2.34544I
b = 2.66024 − 0.58919I
−2.28523 − 1.24764I −9.11702 − 0.85683I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339378 + 1.125810I
a = −0.826794 − 0.820362I
b = −0.365525 + 0.879813I
−5.01673 + 0.90484I −7.57121 − 2.48547I
u = −0.339378 − 1.125810I
a = −0.826794 + 0.820362I
b = −0.365525 − 0.879813I
−5.01673 − 0.90484I −7.57121 + 2.48547I
u = −0.585961 + 1.027330I
a = 0.071777 − 0.307147I
b = −0.069106 − 0.778948I
3.69821 − 3.93735I −0.59875 + 3.86614I
u = −0.585961 − 1.027330I
a = 0.071777 + 0.307147I
b = −0.069106 + 0.778948I
3.69821 + 3.93735I −0.59875 − 3.86614I
u = 0.131481 + 1.188190I
a = 0.920680 + 0.548104I
b = −1.067210 − 0.129315I
−0.95720 − 1.32676I −1.98837 − 1.35287I
u = 0.131481 − 1.188190I
a = 0.920680 − 0.548104I
b = −1.067210 + 0.129315I
−0.95720 + 1.32676I −1.98837 + 1.35287I
u = 0.212681 + 0.768560I
a = 2.45204 − 0.93805I
b = −0.066082 + 1.117050I
−1.90233 − 2.26974I −5.62768 + 3.67958I
u = 0.212681 − 0.768560I
a = 2.45204 + 0.93805I
b = −0.066082 − 1.117050I
−1.90233 + 2.26974I −5.62768 − 3.67958I
u = −0.528659 + 1.117570I
a = 0.76590 + 1.70640I
b = 0.35252 − 1.71795I
−3.69239 − 8.55446I −7.1343 + 12.9586I
u = −0.528659 − 1.117570I
a = 0.76590 − 1.70640I
b = 0.35252 + 1.71795I
−3.69239 + 8.55446I −7.1343 − 12.9586I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.605745 + 1.102710I
a = 1.61342 + 0.74661I
b = −1.65229 + 1.00006I
2.25080 + 8.95210I −3.57588 − 6.47276I
u = 0.605745 − 1.102710I
a = 1.61342 − 0.74661I
b = −1.65229 − 1.00006I
2.25080 − 8.95210I −3.57588 + 6.47276I
u = −0.650503 + 0.273818I
a = −1.013090 + 0.085330I
b = 0.622801 + 1.094180I
−1.29922 + 3.95173I −4.67043 − 7.77775I
u = −0.650503 − 0.273818I
a = −1.013090 − 0.085330I
b = 0.622801 − 1.094180I
−1.29922 − 3.95173I −4.67043 + 7.77775I
u = 0.511312 + 0.470800I
a = −0.87592 − 1.44241I
b = 1.82105 + 0.04411I
−0.56729 + 2.99412I −5.20352 − 6.82351I
u = 0.511312 − 0.470800I
a = −0.87592 + 1.44241I
b = 1.82105 − 0.04411I
−0.56729 − 2.99412I −5.20352 + 6.82351I
27
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 14u
25
+ ··· − 6u + 1)(u
145
+ 69u
144
+ ··· − 362u − 49)
c
2
(u
26
+ 7u
24
+ ··· + 3u
2
+ 1)(u
145
+ u
144
+ ··· + 10u + 7)
c
3
(u
26
− 2u
24
+ ··· − 2u + 1)(u
145
− u
144
+ ··· − 194332u + 20503)
c
4
(u
26
+ 13u
24
+ ··· − u + 1)(u
145
− u
144
+ ··· − 10727u + 2347)
c
5
(u
26
+ u
25
+ ··· + 13u
2
+ 1)(u
145
− 2u
144
+ ··· − 12270u + 2449)
c
6
(u
26
+ u
25
+ ··· − 2u + 1)(u
145
+ 16u
143
+ ··· + 3486694u + 149809)
c
7
(u
26
+ 7u
24
+ ··· + 3u
2
+ 1)(u
145
+ u
144
+ ··· + 10u + 7)
c
8
(u
26
+ 7u
24
+ ··· + 3u
2
+ 1)
· (u
145
+ 5u
144
+ ··· + 35208736u + 7631659)
c
9
(u
26
+ 2u
25
+ ··· − u + 1)(u
145
+ 7u
144
+ ··· − 13u + 1)
c
10
(u
26
+ 13u
24
+ ··· + u + 1)(u
145
− u
144
+ ··· − 10727u + 2347)
c
11
(u
26
− 4u
24
+ ··· + 7u + 1)(u
145
− 21u
144
+ ··· + 135u + 83)
c
12
(u
26
− u
25
+ ··· + 13u
2
+ 1)(u
145
− 2u
144
+ ··· − 12270u + 2449)
28
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
+ 2y
25
+ ··· + 10y + 1)(y
145
+ 21y
144
+ ··· − 34870y −2401)
c
2
, c
7
(y
26
+ 14y
25
+ ··· + 6y + 1)(y
145
+ 69y
144
+ ··· − 362y −49)
c
3
(y
26
− 4y
25
+ ··· + 6y + 1)
· (y
145
− 21y
144
+ ··· + 39082161962y −420373009)
c
4
, c
10
(y
26
+ 26y
25
+ ··· + 19y + 1)
· (y
145
+ 105y
144
+ ··· − 226926923y −5508409)
c
5
, c
12
(y
26
+ 19y
25
+ ··· + 26y + 1)
· (y
145
+ 86y
144
+ ··· + 45603454y −5997601)
c
6
(y
26
− 7y
25
+ ··· − 2y + 1)
· (y
145
+ 32y
144
+ ··· − 735797446182y −22442736481)
c
8
(y
26
+ 14y
25
+ ··· + 6y + 1)
· (y
145
+ 73y
144
+ ··· − 2911748666672046y −58242219092281)
c
9
(y
26
− 2y
25
+ ··· − 7y + 1)(y
145
− 7y
144
+ ··· + 67y −1)
c
11
(y
26
− 8y
25
+ ··· − 5y + 1)(y
145
− 17y
144
+ ··· + 528509y −6889)
29
