12a
1071
(K12a
1071
)
A knot diagram
1
Linearized knot diagam
4 7 10 9 11 12 3 5 1 2 6 8
Solving Sequence
1,9 5,10
4 2 11 3 8 7 12 6
c
9
c
4
c
1
c
10
c
3
c
8
c
7
c
12
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.77660 × 10
1245
u
148
+ 6.71415 × 10
1245
u
147
+ ··· + 3.74457 × 10
1246
b + 4.40626 × 10
1246
,
− 8.25994 × 10
1246
u
148
− 3.27069 × 10
1247
u
147
+ ··· + 7.11469 × 10
1247
a − 7.83372 × 10
1248
,
u
149
+ 4u
148
+ ··· + 73u + 19i
I
u
2
= h3.40750 × 10
59
u
37
− 4.78008 × 10
59
u
36
+ ··· + 2.11717 × 10
60
b + 2.49956 × 10
60
,
1.11713 × 10
60
u
37
+ 5.75954 × 10
59
u
36
+ ··· + 2.11717 × 10
60
a + 3.00294 × 10
59
, u
38
+ u
37
+ ··· + u + 1i
* 2 irreducible components of dim
C
= 0, with total 187 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
= h1.78 × 10
1245
u
148
+ 6.71 × 10
1245
u
147
+ · · · + 3.74 × 10
1246
b + 4.41 ×
10
1246
, −8.26 × 10
1246
u
148
− 3.27 × 10
1247
u
147
+ · · · + 7.11 × 10
1247
a −
7.83 × 10
1248
, u
149
+ 4u
148
+ · · · + 73u + 19i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
0.116097u
148
+ 0.459709u
147
+ ··· + 40.4995u + 11.0106
−0.0474446u
148
− 0.179304u
147
+ ··· − 10.7177u − 1.17671
a
10
=
1
u
2
a
4
=
0.0686524u
148
+ 0.280405u
147
+ ··· + 29.7818u + 9.83393
−0.0474446u
148
− 0.179304u
147
+ ··· − 10.7177u − 1.17671
a
2
=
−0.186978u
148
− 0.641792u
147
+ ··· − 24.8565u + 8.19043
0.00844573u
148
− 0.0141488u
147
+ ··· − 15.8056u − 7.69389
a
11
=
0.00409401u
148
+ 0.146299u
147
+ ··· + 17.3491u + 25.6214
−0.0900120u
148
− 0.368345u
147
+ ··· − 23.8847u − 6.46783
a
3
=
0.123082u
148
+ 0.486614u
147
+ ··· + 38.7720u + 10.9005
−0.0540469u
148
− 0.202096u
147
+ ··· − 10.9116u − 0.958002
a
8
=
0.381708u
148
+ 1.49767u
147
+ ··· + 76.5844u + 9.83207
0.0232331u
148
+ 0.130543u
147
+ ··· + 8.11317u + 3.92302
a
7
=
0.492860u
148
+ 1.91718u
147
+ ··· + 107.856u + 14.4413
−0.102583u
148
− 0.381654u
147
+ ··· − 19.7050u + 1.13749
a
12
=
−0.290140u
148
− 0.970062u
147
+ ··· − 14.3930u + 25.9448
−0.106358u
148
− 0.443882u
147
+ ··· − 27.3949u − 10.0581
a
6
=
−0.0591855u
148
− 0.0201284u
147
+ ··· + 40.0677u + 41.7863
−0.194071u
148
− 0.782151u
147
+ ··· − 45.3045u − 12.0010
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.147174u
148
+ 0.542286u
147
+ ··· + 1.94409u − 6.94054
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
149
− 10u
148
+ ··· + 347212u − 23201
c
2
, c
7
u
149
+ 2u
148
+ ··· − 24326u + 7187
c
3
u
149
+ u
148
+ ··· + u + 1
c
4
, c
8
u
149
+ 4u
148
+ ··· + 163388u + 15389
c
5
, c
6
, c
11
u
149
+ u
148
+ ··· − 4044u + 667
c
9
u
149
+ 4u
148
+ ··· + 73u + 19
c
10
u
149
+ 4u
148
+ ··· − 116639488u + 34307711
c
12
u
149
+ u
148
+ ··· − 3432u + 23659
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
149
+ 34y
148
+ ··· − 32477715860y −538286401
c
2
, c
7
y
149
− 80y
148
+ ··· + 2042752080y −51652969
c
3
y
149
+ 15y
148
+ ··· − 27y −1
c
4
, c
8
y
149
+ 110y
148
+ ··· − 12741844090y −236821321
c
5
, c
6
, c
11
y
149
− 141y
148
+ ··· − 16078272y −444889
c
9
y
149
+ 28y
148
+ ··· − 10593y −361
c
10
y
149
− 12y
148
+ ··· + 25050115881431194y −1177019034059521
c
12
y
149
+ 3y
148
+ ··· + 13696191542y −559748281
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.822791 + 0.566488I
a = 0.044387 − 0.717158I
b = −0.912414 + 0.652071I
−6.14043 + 2.41887I 0
u = 0.822791 − 0.566488I
a = 0.044387 + 0.717158I
b = −0.912414 − 0.652071I
−6.14043 − 2.41887I 0
u = 0.684487 + 0.702737I
a = 0.250571 − 1.362020I
b = 0.00643 + 1.64717I
0.17185 − 1.66565I 0
u = 0.684487 − 0.702737I
a = 0.250571 + 1.362020I
b = 0.00643 − 1.64717I
0.17185 + 1.66565I 0
u = −0.641687 + 0.792516I
a = −0.232348 − 1.226240I
b = −0.33350 + 1.39920I
3.07150 + 2.81514I 0
u = −0.641687 − 0.792516I
a = −0.232348 + 1.226240I
b = −0.33350 − 1.39920I
3.07150 − 2.81514I 0
u = 0.556712 + 0.869557I
a = 1.91956 − 1.09013I
b = 0.028314 + 1.005700I
3.26290 − 3.19090I 0
u = 0.556712 − 0.869557I
a = 1.91956 + 1.09013I
b = 0.028314 − 1.005700I
3.26290 + 3.19090I 0
u = 0.712704 + 0.620664I
a = −0.529672 + 0.671924I
b = 1.191280 − 0.507002I
−7.60678 − 0.81095I 0
u = 0.712704 − 0.620664I
a = −0.529672 − 0.671924I
b = 1.191280 + 0.507002I
−7.60678 + 0.81095I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.740114 + 0.574065I
a = −0.1021720 − 0.0224356I
b = 1.370960 − 0.000930I
−7.36674 + 6.08958I 0
u = −0.740114 − 0.574065I
a = −0.1021720 + 0.0224356I
b = 1.370960 + 0.000930I
−7.36674 − 6.08958I 0
u = 0.909823 + 0.208880I
a = 0.076887 − 0.857113I
b = 0.521071 − 0.246570I
1.16655 − 3.31820I 0
u = 0.909823 − 0.208880I
a = 0.076887 + 0.857113I
b = 0.521071 + 0.246570I
1.16655 + 3.31820I 0
u = −0.784235 + 0.473889I
a = 0.380299 − 0.660353I
b = 0.663142 + 0.352778I
−1.01300 + 1.08677I 0
u = −0.784235 − 0.473889I
a = 0.380299 + 0.660353I
b = 0.663142 − 0.352778I
−1.01300 − 1.08677I 0
u = 0.555083 + 0.728859I
a = 0.055058 − 1.204150I
b = 0.66833 + 1.49831I
−2.51266 − 5.39632I 0
u = 0.555083 − 0.728859I
a = 0.055058 + 1.204150I
b = 0.66833 − 1.49831I
−2.51266 + 5.39632I 0
u = −0.914640 + 0.008017I
a = −0.250572 − 0.138236I
b = −0.602304 − 0.012616I
−1.092020 + 0.014144I 0
u = −0.914640 − 0.008017I
a = −0.250572 + 0.138236I
b = −0.602304 + 0.012616I
−1.092020 − 0.014144I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.731838 + 0.545147I
a = −0.193433 − 0.016628I
b = −1.062520 − 0.136919I
−1.84016 − 3.70908I 0
u = 0.731838 − 0.545147I
a = −0.193433 + 0.016628I
b = −1.062520 + 0.136919I
−1.84016 + 3.70908I 0
u = 0.347179 + 1.032320I
a = −0.202267 + 1.398820I
b = −0.68947 − 1.43468I
1.46037 − 10.80160I 0
u = 0.347179 − 1.032320I
a = −0.202267 − 1.398820I
b = −0.68947 + 1.43468I
1.46037 + 10.80160I 0
u = 0.404945 + 1.018820I
a = −0.959555 + 0.809393I
b = −0.028656 − 0.343001I
−5.06271 − 2.99689I 0
u = 0.404945 − 1.018820I
a = −0.959555 − 0.809393I
b = −0.028656 + 0.343001I
−5.06271 + 2.99689I 0
u = −0.852504 + 0.295008I
a = 0.234306 − 1.239890I
b = −0.559603 − 0.441689I
−3.79545 + 6.56578I 0
u = −0.852504 − 0.295008I
a = 0.234306 + 1.239890I
b = −0.559603 + 0.441689I
−3.79545 − 6.56578I 0
u = −1.002830 + 0.448400I
a = −0.530112 − 1.002450I
b = −0.181425 + 1.238740I
2.67786 + 2.86179I 0
u = −1.002830 − 0.448400I
a = −0.530112 + 1.002450I
b = −0.181425 − 1.238740I
2.67786 − 2.86179I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.827165 + 0.732877I
a = 0.065449 + 0.399351I
b = −0.954242 − 0.148969I
0.52778 + 4.02864I 0
u = −0.827165 − 0.732877I
a = 0.065449 − 0.399351I
b = −0.954242 + 0.148969I
0.52778 − 4.02864I 0
u = 0.059435 + 1.123230I
a = −0.451872 − 0.783174I
b = −0.123028 + 0.175062I
3.28868 + 4.01813I 0
u = 0.059435 − 1.123230I
a = −0.451872 + 0.783174I
b = −0.123028 − 0.175062I
3.28868 − 4.01813I 0
u = −0.136752 + 1.117670I
a = −0.004680 + 1.318210I
b = −0.659862 − 1.135610I
4.32831 − 0.18892I 0
u = −0.136752 − 1.117670I
a = −0.004680 − 1.318210I
b = −0.659862 + 1.135610I
4.32831 + 0.18892I 0
u = −0.567264 + 0.981487I
a = −1.51309 − 1.55737I
b = −0.103630 + 1.215780I
7.04562 + 5.07163I 0
u = −0.567264 − 0.981487I
a = −1.51309 + 1.55737I
b = −0.103630 − 1.215780I
7.04562 − 5.07163I 0
u = 0.856339 + 0.744503I
a = −0.0741008 + 0.0814312I
b = 1.107120 + 0.073780I
1.29255 − 9.14879I 0
u = 0.856339 − 0.744503I
a = −0.0741008 − 0.0814312I
b = 1.107120 − 0.073780I
1.29255 + 9.14879I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.193727 + 1.118850I
a = 0.146515 + 1.372280I
b = 0.62993 − 1.32351I
6.87557 + 5.98406I 0
u = −0.193727 − 1.118850I
a = 0.146515 − 1.372280I
b = 0.62993 + 1.32351I
6.87557 − 5.98406I 0
u = 1.016100 + 0.510997I
a = −1.029400 − 0.247265I
b = 0.145981 − 0.973278I
−3.94520 + 0.52520I 0
u = 1.016100 − 0.510997I
a = −1.029400 + 0.247265I
b = 0.145981 + 0.973278I
−3.94520 − 0.52520I 0
u = 1.081810 + 0.393115I
a = −0.432295 + 0.129104I
b = 0.933297 − 0.166898I
−8.43281 − 0.35878I 0
u = 1.081810 − 0.393115I
a = −0.432295 − 0.129104I
b = 0.933297 + 0.166898I
−8.43281 + 0.35878I 0
u = −0.881392 + 0.750525I
a = 0.214038 − 0.055567I
b = −1.280300 + 0.108912I
−4.84553 + 13.14190I 0
u = −0.881392 − 0.750525I
a = 0.214038 + 0.055567I
b = −1.280300 − 0.108912I
−4.84553 − 13.14190I 0
u = 0.219710 + 0.801720I
a = 0.098679 − 0.522747I
b = 0.892532 + 0.181824I
3.72750 + 0.10143I 0
u = 0.219710 − 0.801720I
a = 0.098679 + 0.522747I
b = 0.892532 − 0.181824I
3.72750 − 0.10143I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.506228 + 1.072760I
a = 1.37762 − 2.03261I
b = 0.057960 + 1.370180I
2.25040 − 7.09751I 0
u = 0.506228 − 1.072760I
a = 1.37762 + 2.03261I
b = 0.057960 − 1.370180I
2.25040 + 7.09751I 0
u = −0.591028 + 0.544821I
a = 0.482732 + 0.701730I
b = 1.054950 − 0.834211I
−4.85653 + 3.11200I 0
u = −0.591028 − 0.544821I
a = 0.482732 − 0.701730I
b = 1.054950 + 0.834211I
−4.85653 − 3.11200I 0
u = −0.776279 + 0.927653I
a = −0.777082 − 1.046550I
b = −0.603480 + 1.200590I
4.28088 + 7.59415I 0
u = −0.776279 − 0.927653I
a = −0.777082 + 1.046550I
b = −0.603480 − 1.200590I
4.28088 − 7.59415I 0
u = −1.158340 + 0.371013I
a = 0.597103 − 0.122745I
b = 0.094227 − 0.983239I
0.73864 + 2.83022I 0
u = −1.158340 − 0.371013I
a = 0.597103 + 0.122745I
b = 0.094227 + 0.983239I
0.73864 − 2.83022I 0
u = −0.319801 + 0.710569I
a = 0.132260 − 0.619108I
b = −1.232260 + 0.493503I
−1.91124 − 3.32706I 0
u = −0.319801 − 0.710569I
a = 0.132260 + 0.619108I
b = −1.232260 − 0.493503I
−1.91124 + 3.32706I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.988091 + 0.723363I
a = 0.183842 + 0.017986I
b = 0.478607 − 0.061501I
−1.08906 + 2.95891I 0
u = −0.988091 − 0.723363I
a = 0.183842 − 0.017986I
b = 0.478607 + 0.061501I
−1.08906 − 2.95891I 0
u = 1.234850 + 0.092095I
a = −0.188514 − 0.205299I
b = −0.248632 − 1.085570I
−2.98414 − 6.67124I 0
u = 1.234850 − 0.092095I
a = −0.188514 + 0.205299I
b = −0.248632 + 1.085570I
−2.98414 + 6.67124I 0
u = 0.763103 + 0.992115I
a = 0.83868 − 1.25890I
b = 0.439093 + 1.337560I
8.26844 − 4.66889I 0
u = 0.763103 − 0.992115I
a = 0.83868 + 1.25890I
b = 0.439093 − 1.337560I
8.26844 + 4.66889I 0
u = 0.690619 + 0.256098I
a = −1.134530 − 0.254755I
b = −0.601353 − 0.777995I
−0.92039 − 2.54804I 0
u = 0.690619 − 0.256098I
a = −1.134530 + 0.254755I
b = −0.601353 + 0.777995I
−0.92039 + 2.54804I 0
u = −0.735269
a = −0.0426728
b = −0.565864
−1.14530 0
u = −0.709645 + 0.024755I
a = 1.02958 − 1.25535I
b = 0.596020 − 0.915779I
−5.53049 + 0.84818I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.709645 − 0.024755I
a = 1.02958 + 1.25535I
b = 0.596020 + 0.915779I
−5.53049 − 0.84818I 0
u = −0.359244 + 1.263320I
a = 0.580321 − 1.010880I
b = −0.340106 + 0.264669I
−3.12866 − 7.48606I 0
u = −0.359244 − 1.263320I
a = 0.580321 + 1.010880I
b = −0.340106 − 0.264669I
−3.12866 + 7.48606I 0
u = −0.799300 + 1.053190I
a = −0.74196 − 1.36055I
b = −0.33684 + 1.45904I
4.47048 + 1.63148I 0
u = −0.799300 − 1.053190I
a = −0.74196 + 1.36055I
b = −0.33684 − 1.45904I
4.47048 − 1.63148I 0
u = −0.397807 + 0.532565I
a = −0.23162 − 2.56983I
b = −0.155695 + 1.056100I
2.14947 + 2.63117I −4.00000 − 3.48885I
u = −0.397807 − 0.532565I
a = −0.23162 + 2.56983I
b = −0.155695 − 1.056100I
2.14947 − 2.63117I −4.00000 + 3.48885I
u = 1.105120 + 0.877439I
a = 0.199968 + 0.016509I
b = −0.677538 + 0.208812I
−6.24761 − 4.45078I 0
u = 1.105120 − 0.877439I
a = 0.199968 − 0.016509I
b = −0.677538 − 0.208812I
−6.24761 + 4.45078I 0
u = −0.292532 + 0.505444I
a = 1.40602 − 0.60186I
b = 0.044037 − 1.048900I
3.33827 − 2.84247I −1.76881 + 3.33646I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.292532 − 0.505444I
a = 1.40602 + 0.60186I
b = 0.044037 + 1.048900I
3.33827 + 2.84247I −1.76881 − 3.33646I
u = −1.08382 + 0.91193I
a = −0.300449 − 1.201790I
b = −0.222649 + 1.256110I
2.75191 + 2.86034I 0
u = −1.08382 − 0.91193I
a = −0.300449 + 1.201790I
b = −0.222649 − 1.256110I
2.75191 − 2.86034I 0
u = 0.01051 + 1.42451I
a = 0.299533 − 1.116610I
b = 0.162653 + 0.921564I
3.33018 + 1.31474I 0
u = 0.01051 − 1.42451I
a = 0.299533 + 1.116610I
b = 0.162653 − 0.921564I
3.33018 − 1.31474I 0
u = 0.116652 + 0.558197I
a = −2.24939 − 2.20309I
b = 0.250939 + 0.785151I
−4.36914 − 1.20866I −3.88970 + 4.69115I
u = 0.116652 − 0.558197I
a = −2.24939 + 2.20309I
b = 0.250939 − 0.785151I
−4.36914 + 1.20866I −3.88970 − 4.69115I
u = 0.71489 + 1.26705I
a = 0.437939 − 1.024770I
b = 0.032561 + 1.125830I
3.47028 + 0.93146I 0
u = 0.71489 − 1.26705I
a = 0.437939 + 1.024770I
b = 0.032561 − 1.125830I
3.47028 − 0.93146I 0
u = 0.535565 + 0.081022I
a = −1.68567 − 1.93268I
b = −0.387439 + 0.352998I
−5.03890 − 4.06980I −10.98331 − 1.05875I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.535565 − 0.081022I
a = −1.68567 + 1.93268I
b = −0.387439 − 0.352998I
−5.03890 + 4.06980I −10.98331 + 1.05875I
u = 0.92278 + 1.13209I
a = −0.347640 + 0.920418I
b = −0.530799 − 0.800669I
−5.44631 − 2.90760I 0
u = 0.92278 − 1.13209I
a = −0.347640 − 0.920418I
b = −0.530799 + 0.800669I
−5.44631 + 2.90760I 0
u = −0.060516 + 0.532681I
a = −0.164411 + 0.444161I
b = −1.21016 − 1.05306I
2.54178 + 1.17821I 11.64009 − 2.24509I
u = −0.060516 − 0.532681I
a = −0.164411 − 0.444161I
b = −1.21016 + 1.05306I
2.54178 − 1.17821I 11.64009 + 2.24509I
u = 0.99166 + 1.11425I
a = −0.91295 + 1.42599I
b = −0.185960 − 1.394340I
0.56601 − 4.83848I 0
u = 0.99166 − 1.11425I
a = −0.91295 − 1.42599I
b = −0.185960 + 1.394340I
0.56601 + 4.83848I 0
u = −1.07785 + 1.05994I
a = 0.462928 + 1.232370I
b = 0.61542 − 1.40165I
−2.98411 + 12.81440I 0
u = −1.07785 − 1.05994I
a = 0.462928 − 1.232370I
b = 0.61542 + 1.40165I
−2.98411 − 12.81440I 0
u = 0.311732 + 0.358910I
a = 1.26566 − 4.52195I
b = 0.287040 + 1.083010I
3.53857 − 6.53979I −2.29573 + 10.84804I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.311732 − 0.358910I
a = 1.26566 + 4.52195I
b = 0.287040 − 1.083010I
3.53857 + 6.53979I −2.29573 − 10.84804I
u = 1.10068 + 1.07688I
a = −0.497997 + 1.166620I
b = −0.49594 − 1.35858I
2.72605 − 9.15496I 0
u = 1.10068 − 1.07688I
a = −0.497997 − 1.166620I
b = −0.49594 + 1.35858I
2.72605 + 9.15496I 0
u = −0.019041 + 0.452582I
a = 0.718133 + 1.063210I
b = 0.70293 − 1.54683I
5.29844 − 2.64181I 16.0425 + 10.8617I
u = −0.019041 − 0.452582I
a = 0.718133 − 1.063210I
b = 0.70293 + 1.54683I
5.29844 + 2.64181I 16.0425 − 10.8617I
u = −0.245392 + 0.329056I
a = −0.98087 − 6.33078I
b = −0.345189 + 1.074550I
−1.91697 + 10.16090I −7.1460 − 13.4440I
u = −0.245392 − 0.329056I
a = −0.98087 + 6.33078I
b = −0.345189 − 1.074550I
−1.91697 − 10.16090I −7.1460 + 13.4440I
u = −0.208206 + 0.352641I
a = 1.83891 + 0.32050I
b = 0.149248 + 0.354691I
−0.326714 + 1.261040I −4.47886 − 3.96166I
u = −0.208206 − 0.352641I
a = 1.83891 − 0.32050I
b = 0.149248 − 0.354691I
−0.326714 − 1.261040I −4.47886 + 3.96166I
u = −0.001597 + 0.406180I
a = −0.45088 + 1.58611I
b = −0.66102 − 1.98194I
−0.18335 + 5.12037I 13.7772 − 4.9372I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.001597 − 0.406180I
a = −0.45088 − 1.58611I
b = −0.66102 + 1.98194I
−0.18335 − 5.12037I 13.7772 + 4.9372I
u = 0.142368 + 0.376973I
a = −2.64476 + 0.71982I
b = −0.134828 − 1.375840I
6.10118 + 0.21034I 4.82953 + 0.51502I
u = 0.142368 − 0.376973I
a = −2.64476 − 0.71982I
b = −0.134828 + 1.375840I
6.10118 − 0.21034I 4.82953 − 0.51502I
u = 0.92096 + 1.31604I
a = 0.064604 − 1.199110I
b = 0.648507 + 1.063430I
−5.58238 − 7.08505I 0
u = 0.92096 − 1.31604I
a = 0.064604 + 1.199110I
b = 0.648507 − 1.063430I
−5.58238 + 7.08505I 0
u = −1.13004 + 1.14773I
a = 0.498632 + 1.050560I
b = 0.360295 − 1.201120I
1.72436 + 4.88386I 0
u = −1.13004 − 1.14773I
a = 0.498632 − 1.050560I
b = 0.360295 + 1.201120I
1.72436 − 4.88386I 0
u = −0.98295 + 1.31634I
a = −0.520381 − 0.851587I
b = 0.219731 + 1.105980I
−2.60212 − 4.67238I 0
u = −0.98295 − 1.31634I
a = −0.520381 + 0.851587I
b = 0.219731 − 1.105980I
−2.60212 + 4.67238I 0
u = −0.47592 + 1.57457I
a = −0.200625 − 1.006440I
b = −0.313934 + 0.854211I
3.46409 + 4.38803I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.47592 − 1.57457I
a = −0.200625 + 1.006440I
b = −0.313934 − 0.854211I
3.46409 − 4.38803I 0
u = −1.10913 + 1.22830I
a = −0.42349 − 1.37161I
b = −0.56727 + 1.43965I
−0.0057 + 19.5333I 0
u = −1.10913 − 1.22830I
a = −0.42349 + 1.37161I
b = −0.56727 − 1.43965I
−0.0057 − 19.5333I 0
u = −0.322870 + 0.079521I
a = 4.60389 + 1.60494I
b = 0.521329 − 0.712682I
−6.14357 + 3.72546I −15.6967 − 1.8148I
u = −0.322870 − 0.079521I
a = 4.60389 − 1.60494I
b = 0.521329 + 0.712682I
−6.14357 − 3.72546I −15.6967 + 1.8148I
u = −0.101421 + 0.314930I
a = 3.77657 + 2.32255I
b = 0.03817 − 1.46841I
1.15038 + 2.98488I −1.23989 − 2.08887I
u = −0.101421 − 0.314930I
a = 3.77657 − 2.32255I
b = 0.03817 + 1.46841I
1.15038 − 2.98488I −1.23989 + 2.08887I
u = 0.76399 + 1.51490I
a = −0.17722 + 1.73202I
b = −0.335847 − 1.204970I
−3.13095 − 8.20929I 0
u = 0.76399 − 1.51490I
a = −0.17722 − 1.73202I
b = −0.335847 + 1.204970I
−3.13095 + 8.20929I 0
u = 1.12979 + 1.26882I
a = 0.392036 − 1.293300I
b = 0.51917 + 1.38258I
5.8399 − 14.8700I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12979 − 1.26882I
a = 0.392036 + 1.293300I
b = 0.51917 − 1.38258I
5.8399 + 14.8700I 0
u = −1.34716 + 1.07030I
a = 0.485580 + 1.072570I
b = 0.111570 − 1.379870I
2.74353 + 5.90452I 0
u = −1.34716 − 1.07030I
a = 0.485580 − 1.072570I
b = 0.111570 + 1.379870I
2.74353 − 5.90452I 0
u = 1.00526 + 1.41088I
a = 0.01130 − 1.49942I
b = 0.440065 + 1.245610I
−4.97260 − 5.23974I 0
u = 1.00526 − 1.41088I
a = 0.01130 + 1.49942I
b = 0.440065 − 1.245610I
−4.97260 + 5.23974I 0
u = −1.11452 + 1.35069I
a = −0.309636 − 1.220240I
b = −0.492999 + 1.279710I
4.12884 + 9.22344I 0
u = −1.11452 − 1.35069I
a = −0.309636 + 1.220240I
b = −0.492999 − 1.279710I
4.12884 − 9.22344I 0
u = −1.11423 + 1.38028I
a = 0.43755 + 1.41159I
b = 0.210804 − 1.289680I
3.11861 + 5.61511I 0
u = −1.11423 − 1.38028I
a = 0.43755 − 1.41159I
b = 0.210804 + 1.289680I
3.11861 − 5.61511I 0
u = 0.168788 + 0.117962I
a = −4.45602 + 3.79259I
b = −0.280598 − 0.840440I
−0.55056 − 1.50329I −8.82318 + 4.22354I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.168788 − 0.117962I
a = −4.45602 − 3.79259I
b = −0.280598 + 0.840440I
−0.55056 + 1.50329I −8.82318 − 4.22354I
u = 1.93305 + 0.50959I
a = −0.142191 + 0.902871I
b = 0.066677 − 1.257350I
5.77816 − 1.65318I 0
u = 1.93305 − 0.50959I
a = −0.142191 − 0.902871I
b = 0.066677 + 1.257350I
5.77816 + 1.65318I 0
u = −1.06894 + 2.02788I
a = 0.327388 + 1.050300I
b = 0.013925 − 1.040450I
3.88914 + 1.74878I 0
u = −1.06894 − 2.02788I
a = 0.327388 − 1.050300I
b = 0.013925 + 1.040450I
3.88914 − 1.74878I 0
u = −1.66582 + 1.59423I
a = 0.348814 + 0.957220I
b = −0.230037 − 1.137420I
−0.55295 − 9.90422I 0
u = −1.66582 − 1.59423I
a = 0.348814 − 0.957220I
b = −0.230037 + 1.137420I
−0.55295 + 9.90422I 0
u = 1.40388 + 2.07476I
a = −0.297089 + 1.030670I
b = 0.090175 − 1.110300I
5.54771 + 4.59569I 0
u = 1.40388 − 2.07476I
a = −0.297089 − 1.030670I
b = 0.090175 + 1.110300I
5.54771 − 4.59569I 0
19
II.
I
u
2
= h3.41 × 10
59
u
37
− 4.78 × 10
59
u
36
+ · · · + 2.12 × 10
60
b + 2.50 × 10
60
, 1.12 ×
10
60
u
37
+5.76×10
59
u
36
+· · ·+2.12×10
60
a+3.00×10
59
, u
38
+u
37
+· · ·+u+1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−0.527654u
37
− 0.272040u
36
+ ··· + 2.69562u − 0.141838
−0.160946u
37
+ 0.225777u
36
+ ··· − 3.74177u − 1.18061
a
10
=
1
u
2
a
4
=
−0.688600u
37
− 0.0462627u
36
+ ··· − 1.04615u − 1.32245
−0.160946u
37
+ 0.225777u
36
+ ··· − 3.74177u − 1.18061
a
2
=
−2.70490u
37
− 1.58675u
36
+ ··· − 2.58789u − 2.51374
−1.06367u
37
− 0.854375u
36
+ ··· + 1.82410u − 0.789642
a
11
=
1.80241u
37
+ 0.623202u
36
+ ··· + 5.76280u + 0.911275
0.223824u
37
+ 0.0376423u
36
+ ··· − 0.954155u − 1.76154
a
3
=
−0.894677u
37
− 0.628125u
36
+ ··· + 2.74189u − 0.784175
0.281975u
37
+ 0.316543u
36
+ ··· − 3.15991u − 0.804828
a
8
=
0.0958034u
37
− 0.488043u
36
+ ··· + 1.03707u + 1.30515
0.693839u
37
+ 0.214017u
36
+ ··· − 0.197944u + 1.30859
a
7
=
−0.274532u
37
− 0.751509u
36
+ ··· − 1.60654u − 0.419018
0.416502u
37
+ 0.416592u
36
+ ··· + 2.41842u + 2.42587
a
12
=
−0.607657u
37
− 0.0389698u
36
+ ··· − 4.43061u − 1.64344
−0.737209u
37
− 0.936332u
36
+ ··· + 4.58964u + 0.759813
a
6
=
−1.69112u
37
− 1.54813u
36
+ ··· − 0.427166u − 2.14299
0.0531670u
37
+ 0.360339u
36
+ ··· − 6.98830u − 1.20508
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3.31222u
37
− 0.0478282u
36
+ ··· − 8.77444u − 13.9498
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
− 3u
37
+ ··· + 8u
2
+ 1
c
2
u
38
− u
37
+ ··· − 16u
2
+ 1
c
3
u
38
+ 4u
36
+ ··· + u + 1
c
4
u
38
+ u
37
+ ··· − 16u + 1
c
5
, c
6
u
38
− 20u
36
+ ··· + 2u + 1
c
7
u
38
+ u
37
+ ··· − 16u
2
+ 1
c
8
u
38
− u
37
+ ··· + 16u + 1
c
9
u
38
+ u
37
+ ··· + u + 1
c
10
u
38
− 5u
37
+ ··· − 4u + 53
c
11
u
38
− 20u
36
+ ··· − 2u + 1
c
12
u
38
+ 6u
36
+ ··· − 10u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 11y
37
+ ··· + 16y + 1
c
2
, c
7
y
38
− 23y
37
+ ··· − 32y + 1
c
3
y
38
+ 8y
37
+ ··· + 3y + 1
c
4
, c
8
y
38
+ 35y
37
+ ··· − 78y + 1
c
5
, c
6
, c
11
y
38
− 40y
37
+ ··· + 8y + 1
c
9
y
38
+ 17y
37
+ ··· − 3y + 1
c
10
y
38
+ 9y
37
+ ··· + 52030y + 2809
c
12
y
38
+ 12y
37
+ ··· − 78y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.581819 + 0.787198I
a = −1.90066 − 1.35846I
b = −0.233545 + 1.225910I
3.84319 + 4.71088I −0.46280 − 6.88160I
u = −0.581819 − 0.787198I
a = −1.90066 + 1.35846I
b = −0.233545 − 1.225910I
3.84319 − 4.71088I −0.46280 + 6.88160I
u = −0.809020 + 0.529699I
a = −0.574982 − 0.508391I
b = 1.062970 + 0.368148I
−7.65620 + 0.44843I −5.28310 + 6.52923I
u = −0.809020 − 0.529699I
a = −0.574982 + 0.508391I
b = 1.062970 − 0.368148I
−7.65620 − 0.44843I −5.28310 − 6.52923I
u = −0.770684 + 0.489111I
a = 1.209020 − 0.469475I
b = −0.1337560 − 0.0453600I
−4.73247 + 4.87232I −6.50156 − 6.48883I
u = −0.770684 − 0.489111I
a = 1.209020 + 0.469475I
b = −0.1337560 + 0.0453600I
−4.73247 − 4.87232I −6.50156 + 6.48883I
u = 0.952857 + 0.579267I
a = −0.267959 − 0.396124I
b = −0.391639 + 0.059254I
−0.87311 − 2.32740I −5.14628 + 1.05771I
u = 0.952857 − 0.579267I
a = −0.267959 + 0.396124I
b = −0.391639 − 0.059254I
−0.87311 + 2.32740I −5.14628 − 1.05771I
u = −0.168510 + 0.821634I
a = 0.450203 + 0.707128I
b = 0.440251 − 1.087420I
4.80718 − 2.28673I 3.50663 + 1.43338I
u = −0.168510 − 0.821634I
a = 0.450203 − 0.707128I
b = 0.440251 + 1.087420I
4.80718 + 2.28673I 3.50663 − 1.43338I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.429288 + 1.103280I
a = 0.82581 − 1.88992I
b = −0.295937 + 1.059150I
−1.49530 + 9.25404I −3.65023 − 5.86849I
u = 0.429288 − 1.103280I
a = 0.82581 + 1.88992I
b = −0.295937 − 1.059150I
−1.49530 − 9.25404I −3.65023 + 5.86849I
u = −0.652127 + 0.477531I
a = −0.116840 + 0.569044I
b = 0.346306 − 1.290060I
4.84984 − 2.43886I −0.90164 + 3.88333I
u = −0.652127 − 0.477531I
a = −0.116840 − 0.569044I
b = 0.346306 + 1.290060I
4.84984 + 2.43886I −0.90164 − 3.88333I
u = 0.719715 + 0.342472I
a = −1.044510 − 0.281028I
b = −0.547744 − 0.636800I
−0.96062 − 2.81911I −6.3302 + 15.4084I
u = 0.719715 − 0.342472I
a = −1.044510 + 0.281028I
b = −0.547744 + 0.636800I
−0.96062 + 2.81911I −6.3302 − 15.4084I
u = −0.517454 + 0.528654I
a = 1.42791 + 1.11087I
b = 0.642884 − 0.618003I
−5.71245 + 4.31152I −8.79528 − 9.81076I
u = −0.517454 − 0.528654I
a = 1.42791 − 1.11087I
b = 0.642884 + 0.618003I
−5.71245 − 4.31152I −8.79528 + 9.81076I
u = 0.677000 + 1.142220I
a = 0.94945 − 1.31823I
b = 0.208074 + 1.176800I
5.85215 − 5.01077I 0. + 4.64122I
u = 0.677000 − 1.142220I
a = 0.94945 + 1.31823I
b = 0.208074 − 1.176800I
5.85215 + 5.01077I 0. − 4.64122I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.659289 + 0.103010I
a = 0.67203 − 1.75898I
b = 0.539517 − 0.759509I
−5.47128 + 1.31809I −10.72815 − 9.07865I
u = −0.659289 − 0.103010I
a = 0.67203 + 1.75898I
b = 0.539517 + 0.759509I
−5.47128 − 1.31809I −10.72815 + 9.07865I
u = 0.063673 + 1.400840I
a = 0.004534 − 1.302700I
b = −0.351265 + 1.141000I
3.52316 − 0.22029I 0
u = 0.063673 − 1.400840I
a = 0.004534 + 1.302700I
b = −0.351265 − 1.141000I
3.52316 + 0.22029I 0
u = −1.02673 + 1.00210I
a = 0.99000 + 1.28518I
b = 0.139998 − 1.382560I
0.46013 + 5.82907I 0
u = −1.02673 − 1.00210I
a = 0.99000 − 1.28518I
b = 0.139998 + 1.382560I
0.46013 − 5.82907I 0
u = 0.004135 + 0.341085I
a = −1.75504 − 0.28767I
b = −0.799811 − 1.113400I
2.15713 + 1.21822I −9.81477 − 2.56503I
u = 0.004135 − 0.341085I
a = −1.75504 + 0.28767I
b = −0.799811 + 1.113400I
2.15713 − 1.21822I −9.81477 + 2.56503I
u = 0.324169 + 0.054741I
a = 1.70793 − 0.82297I
b = −0.34703 + 1.77367I
−0.51099 − 5.17367I −11.10308 + 8.23111I
u = 0.324169 − 0.054741I
a = 1.70793 + 0.82297I
b = −0.34703 − 1.77367I
−0.51099 + 5.17367I −11.10308 − 8.23111I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05542 + 1.68112I
a = 0.00445 − 1.48523I
b = 0.224310 + 1.109410I
4.76012 − 5.14898I 0
u = 0.05542 − 1.68112I
a = 0.00445 + 1.48523I
b = 0.224310 − 1.109410I
4.76012 + 5.14898I 0
u = 1.16532 + 1.27732I
a = −0.525453 + 1.270450I
b = −0.210300 − 1.303100I
3.18408 − 4.85642I 0
u = 1.16532 − 1.27732I
a = −0.525453 − 1.270450I
b = −0.210300 + 1.303100I
3.18408 + 4.85642I 0
u = −0.92048 + 1.54996I
a = 0.02654 + 1.43190I
b = 0.437495 − 1.189770I
−4.82260 + 5.63511I 0
u = −0.92048 − 1.54996I
a = 0.02654 − 1.43190I
b = 0.437495 + 1.189770I
−4.82260 − 5.63511I 0
u = 1.21454 + 1.70439I
a = −0.082444 + 1.057460I
b = −0.230777 − 1.114510I
3.73283 − 2.84759I 0
u = 1.21454 − 1.70439I
a = −0.082444 − 1.057460I
b = −0.230777 + 1.114510I
3.73283 + 2.84759I 0
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
38
− 3u
37
+ ··· + 8u
2
+ 1)(u
149
− 10u
148
+ ··· + 347212u − 23201)
c
2
(u
38
− u
37
+ ··· − 16u
2
+ 1)(u
149
+ 2u
148
+ ··· − 24326u + 7187)
c
3
(u
38
+ 4u
36
+ ··· + u + 1)(u
149
+ u
148
+ ··· + u + 1)
c
4
(u
38
+ u
37
+ ··· − 16u + 1)(u
149
+ 4u
148
+ ··· + 163388u + 15389)
c
5
, c
6
(u
38
− 20u
36
+ ··· + 2u + 1)(u
149
+ u
148
+ ··· − 4044u + 667)
c
7
(u
38
+ u
37
+ ··· − 16u
2
+ 1)(u
149
+ 2u
148
+ ··· − 24326u + 7187)
c
8
(u
38
− u
37
+ ··· + 16u + 1)(u
149
+ 4u
148
+ ··· + 163388u + 15389)
c
9
(u
38
+ u
37
+ ··· + u + 1)(u
149
+ 4u
148
+ ··· + 73u + 19)
c
10
(u
38
− 5u
37
+ ··· − 4u + 53)
· (u
149
+ 4u
148
+ ··· − 116639488u + 34307711)
c
11
(u
38
− 20u
36
+ ··· − 2u + 1)(u
149
+ u
148
+ ··· − 4044u + 667)
c
12
(u
38
+ 6u
36
+ ··· − 10u + 1)(u
149
+ u
148
+ ··· − 3432u + 23659)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
38
+ 11y
37
+ ··· + 16y + 1)
· (y
149
+ 34y
148
+ ··· − 32477715860y −538286401)
c
2
, c
7
(y
38
− 23y
37
+ ··· − 32y + 1)
· (y
149
− 80y
148
+ ··· + 2042752080y −51652969)
c
3
(y
38
+ 8y
37
+ ··· + 3y + 1)(y
149
+ 15y
148
+ ··· − 27y −1)
c
4
, c
8
(y
38
+ 35y
37
+ ··· − 78y + 1)
· (y
149
+ 110y
148
+ ··· − 12741844090y −236821321)
c
5
, c
6
, c
11
(y
38
− 40y
37
+ ··· + 8y + 1)
· (y
149
− 141y
148
+ ··· − 16078272y −444889)
c
9
(y
38
+ 17y
37
+ ··· − 3y + 1)(y
149
+ 28y
148
+ ··· − 10593y −361)
c
10
(y
38
+ 9y
37
+ ··· + 52030y + 2809)
· (y
149
− 12y
148
+ ··· + 25050115881431194y −1177019034059521)
c
12
(y
38
+ 12y
37
+ ··· − 78y + 1)
· (y
149
+ 3y
148
+ ··· + 13696191542y −559748281)
28
