12a
0967
(K12a
0967
)
A knot diagram
1
Linearized knot diagam
4 6 10 1 8 11 3 12 5 7 2 9
Solving Sequence
7,10 4,11
3 8 6 2 12 1 5 9
c
10
c
3
c
7
c
6
c
2
c
11
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.27600 × 10
875
u
169
+ 7.13513 × 10
875
u
168
+ ··· + 1.33107 × 10
876
b + 1.90372 × 10
875
,
1.44711 × 10
876
u
169
− 1.04949 × 10
877
u
168
+ ··· + 1.33107 × 10
876
a − 2.30300 × 10
877
,
u
170
− 5u
169
+ ··· − 29u − 1i
I
u
2
= h3.48049 × 10
36
u
43
− 2.69494 × 10
36
u
42
+ ··· + 3.27331 × 10
36
b − 1.51928 × 10
37
,
− 1.62441 × 10
37
u
43
− 4.60073 × 10
35
u
42
+ ··· + 3.27331 × 10
36
a + 6.85745 × 10
37
,
u
44
+ 12u
42
+ ··· − 6u + 1i
* 2 irreducible components of dim
C
= 0, with total 214 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−4.28 × 10
875
u
169
+ 7.14 × 10
875
u
168
+ · · · + 1.33 × 10
876
b + 1.90 ×
10
875
, 1.45 × 10
876
u
169
− 1.05 × 10
877
u
168
+ · · · + 1.33 × 10
876
a − 2.30 ×
10
877
, u
170
− 5u
169
+ · · · − 29u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
−1.08718u
169
+ 7.88454u
168
+ ··· + 517.582u + 17.3019
0.321246u
169
− 0.536045u
168
+ ··· − 14.0802u − 0.143022
a
11
=
1
−u
2
a
3
=
−1.40843u
169
+ 8.42059u
168
+ ··· + 531.663u + 17.4449
0.321246u
169
− 0.536045u
168
+ ··· − 14.0802u − 0.143022
a
8
=
−4.45236u
169
+ 19.7302u
168
+ ··· + 844.035u + 32.1285
−0.329848u
169
+ 0.912181u
168
+ ··· − 39.0468u − 1.00358
a
6
=
−u
u
3
+ u
a
2
=
−1.32991u
169
+ 9.02243u
168
+ ··· + 511.041u + 16.6683
0.397065u
169
− 0.699324u
168
+ ··· − 22.3763u − 0.360872
a
12
=
2.70091u
169
− 13.9853u
168
+ ··· + 148.112u + 18.0000
0.336931u
169
− 1.15882u
168
+ ··· − 55.9492u − 2.40158
a
1
=
3.26780u
169
− 15.9430u
168
+ ··· − 576.334u − 22.1229
−0.120267u
169
+ 1.13510u
168
+ ··· + 34.2078u + 1.35183
a
5
=
−0.764452u
169
+ 7.07131u
168
+ ··· + 110.737u − 7.10687
−0.0387726u
169
+ 1.38458u
168
+ ··· − 18.0724u + 0.468304
a
9
=
−2.39912u
169
+ 10.5574u
168
+ ··· + 460.962u + 5.96555
0.423558u
169
− 2.34133u
168
+ ··· − 4.08119u + 0.413028
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.47805u
169
+ 31.7197u
168
+ ··· + 153.364u + 10.6916
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
170
+ 8u
169
+ ··· − 9499014u + 769055
c
2
u
170
− 9u
169
+ ··· − 9312096u + 1274848
c
3
u
170
+ u
169
+ ··· − 1786148797u − 5447052019
c
5
u
170
+ 13u
169
+ ··· + 2237637u + 300169
c
6
, c
10
u
170
− 5u
169
+ ··· − 29u − 1
c
7
u
170
+ 3u
169
+ ··· − 241024421u + 11830141
c
8
, c
12
u
170
+ u
169
+ ··· + 71528u − 163159
c
9
u
170
− 3u
169
+ ··· − 10173208u − 3146921
c
11
u
170
+ 12u
169
+ ··· − 16844439u + 2548801
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
170
+ 124y
169
+ ··· − 57608321480486y + 591445593025
c
2
y
170
+ 41y
169
+ ··· + 85496782077440y + 1625237423104
c
3
y
170
+ 89y
169
+ ··· + 1.51 × 10
21
y + 2.97 × 10
19
c
5
y
170
+ 43y
169
+ ··· + 3115277640751y + 90101428561
c
6
, c
10
y
170
+ 113y
169
+ ··· + 167y + 1
c
7
y
170
+ 63y
169
+ ··· − 8243419434057653y + 139952236079881
c
8
, c
12
y
170
− 133y
169
+ ··· − 836359475222y + 26620859281
c
9
y
170
− 35y
169
+ ··· + 110086202897966y + 9903111780241
c
11
y
170
+ 56y
169
+ ··· + 3101150912137203y + 6496386537601
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358984 + 0.938128I
a = 0.87626 + 1.72346I
b = −0.608562 + 0.995414I
3.07880 − 5.00603I 0
u = −0.358984 − 0.938128I
a = 0.87626 − 1.72346I
b = −0.608562 − 0.995414I
3.07880 + 5.00603I 0
u = 0.149489 + 0.981290I
a = −0.39622 + 2.63386I
b = 0.171353 + 1.173240I
3.11257 + 2.64464I 0
u = 0.149489 − 0.981290I
a = −0.39622 − 2.63386I
b = 0.171353 − 1.173240I
3.11257 − 2.64464I 0
u = −0.894429 + 0.397266I
a = 0.155099 − 0.844007I
b = 0.935844 − 0.241800I
9.21419 − 5.10834I 0
u = −0.894429 − 0.397266I
a = 0.155099 + 0.844007I
b = 0.935844 + 0.241800I
9.21419 + 5.10834I 0
u = 0.351933 + 0.905492I
a = 1.35732 − 0.46163I
b = −0.749929 − 0.904345I
4.26036 + 9.83244I 0
u = 0.351933 − 0.905492I
a = 1.35732 + 0.46163I
b = −0.749929 + 0.904345I
4.26036 − 9.83244I 0
u = −0.959787 + 0.021614I
a = 0.356042 + 0.363318I
b = −0.041148 − 0.436442I
0.36103 + 3.02788I 0
u = −0.959787 − 0.021614I
a = 0.356042 − 0.363318I
b = −0.041148 + 0.436442I
0.36103 − 3.02788I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.905359 + 0.519808I
a = −0.211162 + 1.148670I
b = 0.345219 + 1.235090I
5.79176 − 0.63772I 0
u = 0.905359 − 0.519808I
a = −0.211162 − 1.148670I
b = 0.345219 − 1.235090I
5.79176 + 0.63772I 0
u = −1.041260 + 0.162137I
a = −0.195765 − 0.371659I
b = 0.491730 − 1.137210I
−3.39653 − 4.01857I 0
u = −1.041260 − 0.162137I
a = −0.195765 + 0.371659I
b = 0.491730 + 1.137210I
−3.39653 + 4.01857I 0
u = −0.129388 + 1.047410I
a = −0.203586 − 0.159028I
b = 0.728530 + 0.259066I
1.56798 − 2.38640I 0
u = −0.129388 − 1.047410I
a = −0.203586 + 0.159028I
b = 0.728530 − 0.259066I
1.56798 + 2.38640I 0
u = −0.086351 + 1.062530I
a = 0.86211 − 2.82247I
b = 0.423310 − 1.299350I
3.02815 + 2.97469I 0
u = −0.086351 − 1.062530I
a = 0.86211 + 2.82247I
b = 0.423310 + 1.299350I
3.02815 − 2.97469I 0
u = 0.654950 + 0.662580I
a = 0.663710 + 0.797078I
b = 0.303235 − 0.747358I
4.97571 − 5.72324I 0
u = 0.654950 − 0.662580I
a = 0.663710 − 0.797078I
b = 0.303235 + 0.747358I
4.97571 + 5.72324I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363380 + 1.025540I
a = −1.66170 + 0.71346I
b = −2.25117 + 0.25267I
4.44981 − 10.87120I 0
u = −0.363380 − 1.025540I
a = −1.66170 − 0.71346I
b = −2.25117 − 0.25267I
4.44981 + 10.87120I 0
u = −0.685164 + 0.600930I
a = 0.131451 − 0.227585I
b = 0.598615 + 0.763837I
4.07366 + 0.83692I 0
u = −0.685164 − 0.600930I
a = 0.131451 + 0.227585I
b = 0.598615 − 0.763837I
4.07366 − 0.83692I 0
u = −1.076660 + 0.171449I
a = −0.0898171 + 0.0136149I
b = 0.124258 + 1.042590I
0.73430 + 3.64814I 0
u = −1.076660 − 0.171449I
a = −0.0898171 − 0.0136149I
b = 0.124258 − 1.042590I
0.73430 − 3.64814I 0
u = 1.073740 + 0.190083I
a = 0.202327 − 0.371251I
b = −0.579160 − 0.999760I
−0.17316 + 8.52716I 0
u = 1.073740 − 0.190083I
a = 0.202327 + 0.371251I
b = −0.579160 + 0.999760I
−0.17316 − 8.52716I 0
u = 0.881440 + 0.189216I
a = −0.762298 − 0.049409I
b = −1.23696 + 1.13928I
3.58537 + 1.10845I 0
u = 0.881440 − 0.189216I
a = −0.762298 + 0.049409I
b = −1.23696 − 1.13928I
3.58537 − 1.10845I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.792880 + 0.428256I
a = −0.564492 − 0.509799I
b = −1.036170 + 0.406270I
3.41659 + 0.91213I 0
u = 0.792880 − 0.428256I
a = −0.564492 + 0.509799I
b = −1.036170 − 0.406270I
3.41659 − 0.91213I 0
u = −0.272810 + 1.076190I
a = −0.37197 − 1.70523I
b = 0.32902 − 1.56267I
−4.15359 − 1.41570I 0
u = −0.272810 − 1.076190I
a = −0.37197 + 1.70523I
b = 0.32902 + 1.56267I
−4.15359 + 1.41570I 0
u = 0.391618 + 1.039960I
a = −0.04388 + 1.53153I
b = 0.97841 + 1.03325I
1.46563 + 3.45220I 0
u = 0.391618 − 1.039960I
a = −0.04388 − 1.53153I
b = 0.97841 − 1.03325I
1.46563 − 3.45220I 0
u = 0.086089 + 1.113660I
a = −0.38989 − 2.37911I
b = −0.91963 − 1.22060I
−2.12231 + 1.70533I 0
u = 0.086089 − 1.113660I
a = −0.38989 + 2.37911I
b = −0.91963 + 1.22060I
−2.12231 − 1.70533I 0
u = 0.461621 + 1.021630I
a = −1.013880 + 0.786959I
b = −0.949096 + 0.684986I
4.10713 + 5.60266I 0
u = 0.461621 − 1.021630I
a = −1.013880 − 0.786959I
b = −0.949096 − 0.684986I
4.10713 − 5.60266I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.146778 + 1.113650I
a = −0.00568 + 2.77042I
b = −0.40913 + 2.28459I
−2.23788 − 5.07178I 0
u = −0.146778 − 1.113650I
a = −0.00568 − 2.77042I
b = −0.40913 − 2.28459I
−2.23788 + 5.07178I 0
u = 0.505522 + 1.010370I
a = 1.16249 + 1.67396I
b = 1.95237 + 1.03140I
1.26931 + 3.95660I 0
u = 0.505522 − 1.010370I
a = 1.16249 − 1.67396I
b = 1.95237 − 1.03140I
1.26931 − 3.95660I 0
u = −0.002446 + 1.130940I
a = 0.51199 − 2.17240I
b = 1.10202 − 1.91613I
−5.67349 + 0.05332I 0
u = −0.002446 − 1.130940I
a = 0.51199 + 2.17240I
b = 1.10202 + 1.91613I
−5.67349 − 0.05332I 0
u = −0.140161 + 1.132330I
a = −0.05789 + 1.46164I
b = 0.648806 + 0.874273I
−2.31461 − 3.55736I 0
u = −0.140161 − 1.132330I
a = −0.05789 − 1.46164I
b = 0.648806 − 0.874273I
−2.31461 + 3.55736I 0
u = −0.263762 + 1.115710I
a = −0.81839 − 1.32101I
b = 0.832256 − 0.841845I
−0.97904 − 6.10867I 0
u = −0.263762 − 1.115710I
a = −0.81839 + 1.32101I
b = 0.832256 + 0.841845I
−0.97904 + 6.10867I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.133321 + 1.146710I
a = 1.46605 − 2.90758I
b = 0.466582 − 0.741270I
1.34073 − 10.06810I 0
u = −0.133321 − 1.146710I
a = 1.46605 + 2.90758I
b = 0.466582 + 0.741270I
1.34073 + 10.06810I 0
u = −0.482607 + 1.049530I
a = −0.583589 + 0.577217I
b = −1.303960 + 0.237660I
7.14469 + 0.17226I 0
u = −0.482607 − 1.049530I
a = −0.583589 − 0.577217I
b = −1.303960 − 0.237660I
7.14469 − 0.17226I 0
u = −0.031379 + 1.154950I
a = −1.20303 + 2.28802I
b = 0.144926 + 0.792707I
−3.86382 − 3.91324I 0
u = −0.031379 − 1.154950I
a = −1.20303 − 2.28802I
b = 0.144926 − 0.792707I
−3.86382 + 3.91324I 0
u = −0.060169 + 1.170230I
a = 1.73726 + 2.16803I
b = −0.071987 + 0.827595I
−6.51258 − 1.32939I 0
u = −0.060169 − 1.170230I
a = 1.73726 − 2.16803I
b = −0.071987 − 0.827595I
−6.51258 + 1.32939I 0
u = −0.689189 + 0.458239I
a = 0.76961 − 1.77227I
b = 1.57785 − 0.55541I
6.16352 + 6.82205I 0
u = −0.689189 − 0.458239I
a = 0.76961 + 1.77227I
b = 1.57785 + 0.55541I
6.16352 − 6.82205I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.177070 + 0.017293I
a = −0.356734 − 0.365238I
b = −0.93177 − 1.22908I
−0.81185 + 8.17295I 0
u = −1.177070 − 0.017293I
a = −0.356734 + 0.365238I
b = −0.93177 + 1.22908I
−0.81185 − 8.17295I 0
u = 1.177000 + 0.081728I
a = 0.015198 + 0.153559I
b = −0.153265 + 0.887761I
0.10469 − 2.34643I 0
u = 1.177000 − 0.081728I
a = 0.015198 − 0.153559I
b = −0.153265 − 0.887761I
0.10469 + 2.34643I 0
u = 0.141190 + 1.172410I
a = 0.681885 + 0.688923I
b = −0.590588 + 0.473327I
−0.10416 + 4.97008I 0
u = 0.141190 − 1.172410I
a = 0.681885 − 0.688923I
b = −0.590588 − 0.473327I
−0.10416 − 4.97008I 0
u = 1.181030 + 0.017013I
a = 0.176539 + 0.377081I
b = 0.80489 + 1.21474I
3.9574 + 14.5268I 0
u = 1.181030 − 0.017013I
a = 0.176539 − 0.377081I
b = 0.80489 − 1.21474I
3.9574 − 14.5268I 0
u = −0.143324 + 0.804171I
a = 1.278900 + 0.351900I
b = 1.42970 − 0.35652I
−0.45328 − 1.51618I 0
u = −0.143324 − 0.804171I
a = 1.278900 − 0.351900I
b = 1.42970 + 0.35652I
−0.45328 + 1.51618I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.006920 + 0.809989I
a = 0.208219 − 0.071614I
b = −0.994123 − 0.986019I
4.07975 − 3.55082I 0
u = 0.006920 − 0.809989I
a = 0.208219 + 0.071614I
b = −0.994123 + 0.986019I
4.07975 + 3.55082I 0
u = −0.030537 + 1.190400I
a = 0.082000 − 1.054390I
b = −0.500202 − 0.500794I
−3.34741 + 0.91547I 0
u = −0.030537 − 1.190400I
a = 0.082000 + 1.054390I
b = −0.500202 + 0.500794I
−3.34741 − 0.91547I 0
u = 0.012089 + 1.194870I
a = −0.55756 − 1.64583I
b = −1.27632 − 1.37676I
−4.50477 + 3.57230I 0
u = 0.012089 − 1.194870I
a = −0.55756 + 1.64583I
b = −1.27632 + 1.37676I
−4.50477 − 3.57230I 0
u = 0.523557 + 0.610774I
a = −0.1145730 − 0.0252207I
b = −0.657466 + 0.712414I
3.87323 + 0.06583I 0
u = 0.523557 − 0.610774I
a = −0.1145730 + 0.0252207I
b = −0.657466 − 0.712414I
3.87323 − 0.06583I 0
u = 0.155581 + 1.185740I
a = 0.41969 + 2.44964I
b = 1.01446 + 2.11185I
0.60520 + 10.41640I 0
u = 0.155581 − 1.185740I
a = 0.41969 − 2.44964I
b = 1.01446 − 2.11185I
0.60520 − 10.41640I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.186320 + 0.231731I
a = −0.319999 + 0.082786I
b = −0.124459 + 0.600565I
0.47324 − 1.33934I 0
u = 1.186320 − 0.231731I
a = −0.319999 − 0.082786I
b = −0.124459 − 0.600565I
0.47324 + 1.33934I 0
u = 0.125959 + 1.214400I
a = −1.66229 − 2.02190I
b = −0.494152 − 0.538175I
−4.18915 + 4.21221I 0
u = 0.125959 − 1.214400I
a = −1.66229 + 2.02190I
b = −0.494152 + 0.538175I
−4.18915 − 4.21221I 0
u = 0.112463 + 1.222680I
a = −0.682429 + 0.211029I
b = −1.293920 + 0.355891I
−4.23647 + 2.40719I 0
u = 0.112463 − 1.222680I
a = −0.682429 − 0.211029I
b = −1.293920 − 0.355891I
−4.23647 − 2.40719I 0
u = 0.738707 + 0.196649I
a = 0.363855 − 0.288314I
b = −0.146217 + 0.994810I
1.87552 − 2.30328I 0
u = 0.738707 − 0.196649I
a = 0.363855 + 0.288314I
b = −0.146217 − 0.994810I
1.87552 + 2.30328I 0
u = −0.169648 + 1.232630I
a = 0.792877 + 0.682508I
b = 1.31029 + 0.74185I
−2.63492 − 6.62405I 0
u = −0.169648 − 1.232630I
a = 0.792877 − 0.682508I
b = 1.31029 − 0.74185I
−2.63492 + 6.62405I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198813 + 1.228620I
a = −0.221282 − 1.295030I
b = 1.028340 − 0.759335I
−0.67043 − 5.81168I 0
u = −0.198813 − 1.228620I
a = −0.221282 + 1.295030I
b = 1.028340 + 0.759335I
−0.67043 + 5.81168I 0
u = 0.257373 + 1.243960I
a = −1.39878 + 1.55383I
b = 0.132742 + 1.042640I
−1.43857 + 6.12757I 0
u = 0.257373 − 1.243960I
a = −1.39878 − 1.55383I
b = 0.132742 − 1.042640I
−1.43857 − 6.12757I 0
u = 0.702950 + 0.145538I
a = −0.210636 − 0.383777I
b = 0.621542 + 0.158058I
0.339928 − 0.226718I 0
u = 0.702950 − 0.145538I
a = −0.210636 + 0.383777I
b = 0.621542 − 0.158058I
0.339928 + 0.226718I 0
u = 0.257093 + 1.281870I
a = 0.337818 − 0.998986I
b = −0.905144 − 0.513805I
0.56703 + 5.58880I 0
u = 0.257093 − 1.281870I
a = 0.337818 + 0.998986I
b = −0.905144 + 0.513805I
0.56703 − 5.58880I 0
u = 0.089120 + 1.306080I
a = 0.04092 − 1.48051I
b = −0.324188 − 1.284790I
−3.31007 + 0.31222I 0
u = 0.089120 − 1.306080I
a = 0.04092 + 1.48051I
b = −0.324188 + 1.284790I
−3.31007 − 0.31222I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.437398 + 1.245460I
a = −0.927788 − 0.033295I
b = −0.162519 + 0.473485I
−2.87035 + 4.53612I 0
u = 0.437398 − 1.245460I
a = −0.927788 + 0.033295I
b = −0.162519 − 0.473485I
−2.87035 − 4.53612I 0
u = −0.124227 + 1.315620I
a = 0.24894 − 1.68309I
b = 0.059017 − 0.781041I
−2.98246 + 0.79000I 0
u = −0.124227 − 1.315620I
a = 0.24894 + 1.68309I
b = 0.059017 + 0.781041I
−2.98246 − 0.79000I 0
u = −0.670747 + 0.001839I
a = 0.507676 + 0.953054I
b = −0.696949 + 0.443077I
1.35614 + 3.70926I 0
u = −0.670747 − 0.001839I
a = 0.507676 − 0.953054I
b = −0.696949 − 0.443077I
1.35614 − 3.70926I 0
u = −0.576671 + 0.315628I
a = 0.041104 + 1.266560I
b = −0.345092 − 0.509200I
1.44984 + 2.85698I 0
u = −0.576671 − 0.315628I
a = 0.041104 − 1.266560I
b = −0.345092 + 0.509200I
1.44984 − 2.85698I 0
u = −0.393385 + 1.302880I
a = −0.30569 − 1.41517I
b = 0.35923 − 1.37450I
−4.24700 − 1.20015I 0
u = −0.393385 − 1.302880I
a = −0.30569 + 1.41517I
b = 0.35923 + 1.37450I
−4.24700 + 1.20015I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.367910 + 0.102452I
a = 0.347756 − 1.202100I
b = 0.42962 − 2.11328I
4.32919 + 0.16885I 0
u = 1.367910 − 0.102452I
a = 0.347756 + 1.202100I
b = 0.42962 + 2.11328I
4.32919 − 0.16885I 0
u = −0.590101 + 1.246510I
a = −0.190565 + 1.225250I
b = −0.700767 + 1.215870I
−3.13756 − 2.07733I 0
u = −0.590101 − 1.246510I
a = −0.190565 − 1.225250I
b = −0.700767 − 1.215870I
−3.13756 + 2.07733I 0
u = −0.608738
a = 1.17642
b = −0.588708
4.90876 0
u = −0.46986 + 1.33718I
a = −0.234856 − 0.808441I
b = 0.726013 − 0.746689I
−3.85896 − 8.23184I 0
u = −0.46986 − 1.33718I
a = −0.234856 + 0.808441I
b = 0.726013 + 0.746689I
−3.85896 + 8.23184I 0
u = 0.50295 + 1.33882I
a = 1.64814 − 1.25440I
b = 0.40678 − 1.49148I
−0.87982 + 6.10551I 0
u = 0.50295 − 1.33882I
a = 1.64814 + 1.25440I
b = 0.40678 + 1.49148I
−0.87982 − 6.10551I 0
u = 0.34904 + 1.40048I
a = −1.32223 + 1.85888I
b = −0.03816 + 1.46590I
−1.54791 + 6.03526I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.34904 − 1.40048I
a = −1.32223 − 1.85888I
b = −0.03816 − 1.46590I
−1.54791 − 6.03526I 0
u = 0.42027 + 1.38795I
a = 0.204470 − 1.059950I
b = −0.653211 − 0.882158I
−4.86374 + 3.88643I 0
u = 0.42027 − 1.38795I
a = 0.204470 + 1.059950I
b = −0.653211 + 0.882158I
−4.86374 − 3.88643I 0
u = −0.57963 + 1.33233I
a = 0.610239 + 1.191450I
b = −0.515221 + 1.231590I
−2.95446 − 9.62666I 0
u = −0.57963 − 1.33233I
a = 0.610239 − 1.191450I
b = −0.515221 − 1.231590I
−2.95446 + 9.62666I 0
u = −0.46270 + 1.37892I
a = 0.42688 + 1.73651I
b = −0.70662 + 1.39334I
−8.18833 − 9.28459I 0
u = −0.46270 − 1.37892I
a = 0.42688 − 1.73651I
b = −0.70662 − 1.39334I
−8.18833 + 9.28459I 0
u = −0.28676 + 1.43559I
a = −0.367996 − 1.151240I
b = 0.398979 − 0.621131I
0.29317 − 2.83644I 0
u = −0.28676 − 1.43559I
a = −0.367996 + 1.151240I
b = 0.398979 + 0.621131I
0.29317 + 2.83644I 0
u = 0.46761 + 1.40325I
a = −0.31390 + 1.65939I
b = 0.77049 + 1.28473I
−5.1466 + 13.9272I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.46761 − 1.40325I
a = −0.31390 − 1.65939I
b = 0.77049 − 1.28473I
−5.1466 − 13.9272I 0
u = 0.44102 + 1.41372I
a = 0.280419 − 1.209350I
b = −0.452422 − 1.080790I
−4.97968 + 3.35430I 0
u = 0.44102 − 1.41372I
a = 0.280419 + 1.209350I
b = −0.452422 + 1.080790I
−4.97968 − 3.35430I 0
u = −0.55238 + 1.38004I
a = −0.15940 − 2.01339I
b = 0.94245 − 1.66519I
−5.1358 − 14.2213I 0
u = −0.55238 − 1.38004I
a = −0.15940 + 2.01339I
b = 0.94245 + 1.66519I
−5.1358 + 14.2213I 0
u = 0.54989 + 1.38904I
a = 0.24906 − 1.90123I
b = −0.88420 − 1.57528I
−0.4771 + 20.5739I 0
u = 0.54989 − 1.38904I
a = 0.24906 + 1.90123I
b = −0.88420 + 1.57528I
−0.4771 − 20.5739I 0
u = 0.56659 + 1.38300I
a = −0.391741 + 1.214660I
b = 0.541906 + 1.174940I
−4.07185 + 8.51944I 0
u = 0.56659 − 1.38300I
a = −0.391741 − 1.214660I
b = 0.541906 − 1.174940I
−4.07185 − 8.51944I 0
u = 0.500783 + 0.044259I
a = −1.69189 − 0.95478I
b = 0.554368 + 0.323226I
4.66111 + 2.62386I 21.4268 − 7.2659I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500783 − 0.044259I
a = −1.69189 + 0.95478I
b = 0.554368 − 0.323226I
4.66111 − 2.62386I 21.4268 + 7.2659I
u = 0.59612 + 1.39953I
a = −0.055130 + 1.188340I
b = 0.595156 + 1.107120I
−3.43167 + 7.89076I 0
u = 0.59612 − 1.39953I
a = −0.055130 − 1.188340I
b = 0.595156 − 1.107120I
−3.43167 − 7.89076I 0
u = 0.58287 + 1.41710I
a = 0.64117 − 2.59862I
b = −0.57051 − 2.21846I
−0.13718 + 6.51724I 0
u = 0.58287 − 1.41710I
a = 0.64117 + 2.59862I
b = −0.57051 + 2.21846I
−0.13718 − 6.51724I 0
u = −0.62582 + 1.40356I
a = −0.716498 − 1.007940I
b = −0.077784 − 1.139690I
−7.02247 − 2.27765I 0
u = −0.62582 − 1.40356I
a = −0.716498 + 1.007940I
b = −0.077784 + 1.139690I
−7.02247 + 2.27765I 0
u = 0.459152
a = −0.421273
b = 0.402988
0.696800 13.7940
u = −0.44455 + 1.47868I
a = 1.051710 + 0.638252I
b = 0.328305 + 0.824369I
−5.82788 + 2.07583I 0
u = −0.44455 − 1.47868I
a = 1.051710 − 0.638252I
b = 0.328305 − 0.824369I
−5.82788 − 2.07583I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.56302 + 1.49417I
a = 0.04275 + 1.42617I
b = −0.602592 + 1.077620I
2.77004 − 11.01100I 0
u = −0.56302 − 1.49417I
a = 0.04275 − 1.42617I
b = −0.602592 − 1.077620I
2.77004 + 11.01100I 0
u = 0.50008 + 1.54970I
a = −0.898921 + 0.785182I
b = −0.322588 + 0.925765I
−0.89047 − 8.06915I 0
u = 0.50008 − 1.54970I
a = −0.898921 − 0.785182I
b = −0.322588 − 0.925765I
−0.89047 + 8.06915I 0
u = 0.73394 + 1.47513I
a = 0.494742 − 0.811471I
b = 0.104834 − 0.934226I
−3.60644 − 1.81302I 0
u = 0.73394 − 1.47513I
a = 0.494742 + 0.811471I
b = 0.104834 + 0.934226I
−3.60644 + 1.81302I 0
u = −0.144728 + 0.249379I
a = 3.36063 + 1.11428I
b = 0.98509 + 1.27323I
0.14037 + 3.52807I 9.96847 − 1.54788I
u = −0.144728 − 0.249379I
a = 3.36063 − 1.11428I
b = 0.98509 − 1.27323I
0.14037 − 3.52807I 9.96847 + 1.54788I
u = −0.270980 + 0.082812I
a = 0.69988 + 2.40415I
b = 0.295232 + 0.512056I
0.46937 + 1.85768I 2.23040 − 2.92876I
u = −0.270980 − 0.082812I
a = 0.69988 − 2.40415I
b = 0.295232 − 0.512056I
0.46937 − 1.85768I 2.23040 + 2.92876I
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.162543 + 0.093875I
a = −4.84800 + 1.07963I
b = −0.364873 − 1.034580I
−3.06785 − 0.45708I 3.27947 + 2.16717I
u = −0.162543 − 0.093875I
a = −4.84800 − 1.07963I
b = −0.364873 + 1.034580I
−3.06785 + 0.45708I 3.27947 − 2.16717I
u = −1.81028 + 0.22195I
a = 0.221534 + 0.493693I
b = 0.240501 + 0.710115I
8.01090 + 3.31197I 0
u = −1.81028 − 0.22195I
a = 0.221534 − 0.493693I
b = 0.240501 − 0.710115I
8.01090 − 3.31197I 0
u = −0.1114820 + 0.0598260I
a = 7.84979 − 4.38129I
b = −0.514786 + 0.481492I
3.08472 − 4.08944I 10.6833 + 13.0809I
u = −0.1114820 − 0.0598260I
a = 7.84979 + 4.38129I
b = −0.514786 − 0.481492I
3.08472 + 4.08944I 10.6833 − 13.0809I
u = 0.0518069 + 0.1009840I
a = 4.96077 + 6.67191I
b = −0.98846 − 1.02020I
4.19433 + 9.07341I 12.31225 − 4.07596I
u = 0.0518069 − 0.1009840I
a = 4.96077 − 6.67191I
b = −0.98846 + 1.02020I
4.19433 − 9.07341I 12.31225 + 4.07596I
u = −0.0381800 + 0.0723039I
a = −11.89280 + 1.73569I
b = 0.504044 + 0.760514I
−0.92999 + 3.56265I 6.92723 − 5.85262I
u = −0.0381800 − 0.0723039I
a = −11.89280 − 1.73569I
b = 0.504044 − 0.760514I
−0.92999 − 3.56265I 6.92723 + 5.85262I
21
II. I
u
2
= h3.48 × 10
36
u
43
− 2.69 × 10
36
u
42
+ · · · + 3.27 × 10
36
b − 1.52 ×
10
37
, −1.62 × 10
37
u
43
− 4.60 × 10
35
u
42
+ · · · + 3.27 × 10
36
a + 6.86 ×
10
37
, u
44
+ 12u
42
+ · · · − 6u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
4.96257u
43
+ 0.140553u
42
+ ··· + 139.967u − 20.9496
−1.06329u
43
+ 0.823306u
42
+ ··· − 30.2803u + 4.64143
a
11
=
1
−u
2
a
3
=
6.02586u
43
− 0.682754u
42
+ ··· + 170.247u − 25.5910
−1.06329u
43
+ 0.823306u
42
+ ··· − 30.2803u + 4.64143
a
8
=
−1.50437u
43
+ 0.651608u
42
+ ··· − 67.4553u + 4.82112
−0.918168u
43
− 0.599653u
42
+ ··· + 3.47640u − 1.71295
a
6
=
−u
u
3
+ u
a
2
=
6.75370u
43
+ 0.480381u
42
+ ··· + 174.790u − 25.6592
−1.13152u
43
+ 1.31953u
42
+ ··· − 41.0747u + 5.87280
a
12
=
−1.86834u
43
+ 1.11053u
42
+ ··· − 39.1351u + 5.21743
1.33266u
43
+ 0.187223u
42
+ ··· + 29.8720u − 4.99007
a
1
=
7.90214u
43
− 0.170261u
42
+ ··· + 201.034u − 23.1074
−1.73375u
43
+ 0.937930u
42
+ ··· − 54.1342u + 8.37624
a
5
=
2.80544u
43
− 0.0590863u
42
+ ··· + 34.5081u + 6.92673
−0.356787u
43
+ 0.455088u
42
+ ··· − 17.9865u + 2.74765
a
9
=
−5.64262u
43
+ 1.04730u
42
+ ··· − 154.061u + 16.2060
1.04739u
43
− 0.795115u
42
+ ··· + 52.5292u − 8.96479
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2.46673u
43
− 2.84271u
42
+ ··· − 13.2599u + 16.8473
22
(iv) u-Polynomials at the component
23
Crossings u-Polynomials at each crossing
c
1
u
44
− 13u
43
+ ··· + 11u + 1
c
2
u
44
+ 2u
43
+ ··· + 6u + 1
c
3
u
44
+ 18u
42
+ ··· − 6u + 1
c
4
u
44
+ 13u
43
+ ··· − 11u + 1
c
5
u
44
+ 6u
43
+ ··· + 6u + 1
c
6
u
44
+ 12u
42
+ ··· + 6u + 1
c
7
u
44
+ 13u
42
+ ··· + 14u + 3
c
8
u
44
− 2u
43
+ ··· + 7u + 3
c
9
u
44
+ 2u
43
+ ··· − 45u + 47
c
10
u
44
+ 12u
42
+ ··· − 6u + 1
c
11
u
44
+ 3u
43
+ ··· − 14u + 1
c
12
u
44
+ 2u
43
+ ··· − 7u + 3
24
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
44
+ 39y
43
+ ··· − 201y + 1
c
2
y
44
+ 8y
43
+ ··· + 56y + 1
c
3
y
44
+ 36y
43
+ ··· + 38y + 1
c
5
y
44
+ 6y
43
+ ··· + 8y + 1
c
6
, c
10
y
44
+ 24y
43
+ ··· + 48y + 1
c
7
y
44
+ 26y
43
+ ··· + 272y + 9
c
8
, c
12
y
44
− 46y
43
+ ··· − 157y + 9
c
9
y
44
+ 4y
43
+ ··· − 2589y + 2209
c
11
y
44
+ 11y
43
+ ··· − 32y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.168699 + 0.873698I
a = −0.175400 − 0.014927I
b = 1.15323 + 0.83683I
3.23257 + 9.55584I 5.50626 − 7.33826I
u = 0.168699 − 0.873698I
a = −0.175400 + 0.014927I
b = 1.15323 − 0.83683I
3.23257 − 9.55584I 5.50626 + 7.33826I
u = −1.110520 + 0.148620I
a = −0.0650585 − 0.0240332I
b = 0.162652 + 0.880342I
−0.38676 + 3.62987I 0.59343 − 7.43414I
u = −1.110520 − 0.148620I
a = −0.0650585 + 0.0240332I
b = 0.162652 − 0.880342I
−0.38676 − 3.62987I 0.59343 + 7.43414I
u = −0.136719 + 1.148040I
a = −0.47557 − 1.96019I
b = 0.01828 − 1.51353I
−5.01666 − 1.20404I −1.16232 + 3.27359I
u = −0.136719 − 1.148040I
a = −0.47557 + 1.96019I
b = 0.01828 + 1.51353I
−5.01666 + 1.20404I −1.16232 − 3.27359I
u = 0.109699 + 1.163300I
a = 0.31484 + 1.64858I
b = −0.322438 + 1.164590I
−2.81072 + 4.05385I 0.83525 − 5.38023I
u = 0.109699 − 1.163300I
a = 0.31484 − 1.64858I
b = −0.322438 − 1.164590I
−2.81072 − 4.05385I 0.83525 + 5.38023I
u = 0.810141 + 0.161718I
a = −0.043511 + 0.487129I
b = −0.703478 + 0.345551I
1.40429 − 1.25133I 11.94052 + 1.32130I
u = 0.810141 − 0.161718I
a = −0.043511 − 0.487129I
b = −0.703478 − 0.345551I
1.40429 + 1.25133I 11.94052 − 1.32130I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.182471 + 0.804224I
a = 0.24386 + 1.61311I
b = −0.91037 + 1.46957I
−0.69093 − 4.18597I 4.41547 + 5.11288I
u = −0.182471 − 0.804224I
a = 0.24386 − 1.61311I
b = −0.91037 − 1.46957I
−0.69093 + 4.18597I 4.41547 − 5.11288I
u = −0.139899 + 1.172790I
a = 0.026640 − 1.226660I
b = 0.765242 − 1.140680I
−4.95221 − 0.82001I −0.577687 + 0.999529I
u = −0.139899 − 1.172790I
a = 0.026640 + 1.226660I
b = 0.765242 + 1.140680I
−4.95221 + 0.82001I −0.577687 − 0.999529I
u = 0.183246 + 1.177100I
a = 0.602937 + 0.139649I
b = −0.515377 − 0.215354I
−2.76547 + 4.91173I 3.60106 − 7.49272I
u = 0.183246 − 1.177100I
a = 0.602937 − 0.139649I
b = −0.515377 + 0.215354I
−2.76547 − 4.91173I 3.60106 + 7.49272I
u = −0.222872 + 1.241630I
a = −0.633369 − 0.911203I
b = 0.811917 − 0.514166I
0.24295 − 6.01476I 9.5211 + 14.2821I
u = −0.222872 − 1.241630I
a = −0.633369 + 0.911203I
b = 0.811917 + 0.514166I
0.24295 + 6.01476I 9.5211 − 14.2821I
u = −0.074310 + 1.263830I
a = −0.74613 + 1.95769I
b = −0.584824 + 1.059630I
1.29658 − 8.73606I 6.95927 + 5.76577I
u = −0.074310 − 1.263830I
a = −0.74613 − 1.95769I
b = −0.584824 − 1.059630I
1.29658 + 8.73606I 6.95927 − 5.76577I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.726564 + 0.085897I
a = −0.329187 + 0.741675I
b = −0.059331 + 0.268645I
1.23680 − 1.73750I 13.75774 + 0.59480I
u = 0.726564 − 0.085897I
a = −0.329187 − 0.741675I
b = −0.059331 − 0.268645I
1.23680 + 1.73750I 13.75774 − 0.59480I
u = 1.301920 + 0.023880I
a = 0.322885 + 1.093370I
b = 0.56673 + 1.99578I
4.37554 − 0.52152I 15.2069 + 13.1256I
u = 1.301920 − 0.023880I
a = 0.322885 − 1.093370I
b = 0.56673 − 1.99578I
4.37554 + 0.52152I 15.2069 − 13.1256I
u = 0.387819 + 1.246420I
a = 0.906279 − 0.332513I
b = −0.050648 − 0.678007I
−2.84606 + 5.14862I 4.12821 − 8.91823I
u = 0.387819 − 1.246420I
a = 0.906279 + 0.332513I
b = −0.050648 + 0.678007I
−2.84606 − 5.14862I 4.12821 + 8.91823I
u = 0.341456 + 1.275580I
a = 0.12402 − 1.61950I
b = −0.97837 − 1.06805I
−0.32119 + 4.51831I 8.00000 + 0.I
u = 0.341456 − 1.275580I
a = 0.12402 + 1.61950I
b = −0.97837 + 1.06805I
−0.32119 − 4.51831I 8.00000 + 0.I
u = 0.332596 + 1.294270I
a = 0.574149 − 1.290590I
b = 0.211910 − 0.847264I
−2.65842 − 1.90928I 8.00000 + 0.I
u = 0.332596 − 1.294270I
a = 0.574149 + 1.290590I
b = 0.211910 + 0.847264I
−2.65842 + 1.90928I 8.00000 + 0.I
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.505394 + 1.271180I
a = −0.248051 − 1.224570I
b = 0.376483 − 1.248210I
−5.08502 − 1.32219I 0
u = −0.505394 − 1.271180I
a = −0.248051 + 1.224570I
b = 0.376483 + 1.248210I
−5.08502 + 1.32219I 0
u = −0.415111 + 0.352749I
a = −0.50418 + 2.02114I
b = −0.356227 − 0.288267I
3.30173 + 3.52015I 14.3478 − 0.4980I
u = −0.415111 − 0.352749I
a = −0.50418 − 2.02114I
b = −0.356227 + 0.288267I
3.30173 − 3.52015I 14.3478 + 0.4980I
u = −0.56582 + 1.36438I
a = 0.387067 + 1.125530I
b = −0.613052 + 1.104510I
−4.31593 − 9.68588I 0
u = −0.56582 − 1.36438I
a = 0.387067 − 1.125530I
b = −0.613052 − 1.104510I
−4.31593 + 9.68588I 0
u = 0.51324 + 1.41665I
a = −1.42069 + 2.22836I
b = −0.05609 + 2.03286I
−0.60294 + 6.75977I 0
u = 0.51324 − 1.41665I
a = −1.42069 − 2.22836I
b = −0.05609 − 2.03286I
−0.60294 − 6.75977I 0
u = 0.123691 + 0.280803I
a = −0.02246 − 3.10720I
b = 0.669605 + 0.956282I
5.01238 − 3.34345I 15.8973 + 2.5521I
u = 0.123691 − 0.280803I
a = −0.02246 + 3.10720I
b = 0.669605 − 0.956282I
5.01238 + 3.34345I 15.8973 − 2.5521I
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.71903 + 0.19842I
a = 0.230010 + 0.513494I
b = 0.263488 + 0.664205I
8.11047 + 3.27851I 0
u = −1.71903 − 0.19842I
a = 0.230010 − 0.513494I
b = 0.263488 − 0.664205I
8.11047 − 3.27851I 0
u = 0.073072 + 0.240110I
a = 0.93092 + 4.47877I
b = 0.150658 − 0.543482I
4.23898 − 1.90477I 15.0152 + 0.2418I
u = 0.073072 − 0.240110I
a = 0.93092 − 4.47877I
b = 0.150658 + 0.543482I
4.23898 + 1.90477I 15.0152 − 0.2418I
31
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
44
− 13u
43
+ ··· + 11u + 1)
· (u
170
+ 8u
169
+ ··· − 9499014u + 769055)
c
2
(u
44
+ 2u
43
+ ··· + 6u + 1)(u
170
− 9u
169
+ ··· − 9312096u + 1274848)
c
3
(u
44
+ 18u
42
+ ··· − 6u + 1)
· (u
170
+ u
169
+ ··· − 1786148797u − 5447052019)
c
4
(u
44
+ 13u
43
+ ··· − 11u + 1)
· (u
170
+ 8u
169
+ ··· − 9499014u + 769055)
c
5
(u
44
+ 6u
43
+ ··· + 6u + 1)(u
170
+ 13u
169
+ ··· + 2237637u + 300169)
c
6
(u
44
+ 12u
42
+ ··· + 6u + 1)(u
170
− 5u
169
+ ··· − 29u − 1)
c
7
(u
44
+ 13u
42
+ ··· + 14u + 3)
· (u
170
+ 3u
169
+ ··· − 241024421u + 11830141)
c
8
(u
44
− 2u
43
+ ··· + 7u + 3)(u
170
+ u
169
+ ··· + 71528u − 163159)
c
9
(u
44
+ 2u
43
+ ··· − 45u + 47)
· (u
170
− 3u
169
+ ··· − 10173208u − 3146921)
c
10
(u
44
+ 12u
42
+ ··· − 6u + 1)(u
170
− 5u
169
+ ··· − 29u − 1)
c
11
(u
44
+ 3u
43
+ ··· − 14u + 1)
· (u
170
+ 12u
169
+ ··· − 16844439u + 2548801)
c
12
(u
44
+ 2u
43
+ ··· − 7u + 3)(u
170
+ u
169
+ ··· + 71528u − 163159)
32
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
44
+ 39y
43
+ ··· − 201y + 1)
· (y
170
+ 124y
169
+ ··· − 57608321480486y + 591445593025)
c
2
(y
44
+ 8y
43
+ ··· + 56y + 1)
· (y
170
+ 41y
169
+ ··· + 85496782077440y + 1625237423104)
c
3
(y
44
+ 36y
43
+ ··· + 38y + 1)
· (y
170
+ 89y
169
+ ··· + 1.51 × 10
21
y + 2.97 × 10
19
)
c
5
(y
44
+ 6y
43
+ ··· + 8y + 1)
· (y
170
+ 43y
169
+ ··· + 3115277640751y + 90101428561)
c
6
, c
10
(y
44
+ 24y
43
+ ··· + 48y + 1)(y
170
+ 113y
169
+ ··· + 167y + 1)
c
7
(y
44
+ 26y
43
+ ··· + 272y + 9)
· (y
170
+ 63y
169
+ ··· − 8243419434057653y + 139952236079881)
c
8
, c
12
(y
44
− 46y
43
+ ··· − 157y + 9)
· (y
170
− 133y
169
+ ··· − 836359475222y + 26620859281)
c
9
(y
44
+ 4y
43
+ ··· − 2589y + 2209)
· (y
170
− 35y
169
+ ··· + 110086202897966y + 9903111780241)
c
11
(y
44
+ 11y
43
+ ··· − 32y + 1)
· (y
170
+ 56y
169
+ ··· + 3101150912137203y + 6496386537601)
33
