12a
0929
(K12a
0929
)
A knot diagram
1
Linearized knot diagam
4 6 9 11 12 10 3 1 7 2 5 8
Solving Sequence
6,10 3,7
8 2 11 9 4 1 12 5
c
6
c
7
c
2
c
10
c
9
c
3
c
1
c
12
c
5
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h7.70151 × 10
505
u
138
− 3.75072 × 10
506
u
137
+ ··· + 1.06895 × 10
506
b − 8.54489 × 10
505
,
− 1.85390 × 10
506
u
138
+ 8.48171 × 10
506
u
137
+ ··· + 1.06895 × 10
506
a − 1.47936 × 10
507
,
u
139
− 5u
138
+ ··· − 5u − 1i
I
u
2
= h−74739457095708u
37
− 838683780419238u
36
+ ··· + 399763050242851b − 1278150090688057,
716983712604222u
37
+ 3614680862920783u
36
+ ··· + 399763050242851a + 442429692628259,
u
38
+ 6u
37
+ ··· + 8u + 1i
* 2 irreducible components of dim
C
= 0, with total 177 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
= h7.70 × 10
505
u
138
− 3.75 × 10
506
u
137
+ · · · + 1.07 × 10
506
b − 8.54 ×
10
505
, −1.85 × 10
506
u
138
+ 8.48 × 10
506
u
137
+ · · · + 1.07 × 10
506
a − 1.48 ×
10
507
, u
139
− 5u
138
+ · · · − 5u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
1.73432u
138
− 7.93462u
137
+ ··· + 278.883u + 13.8394
−0.720474u
138
+ 3.50880u
137
+ ··· − 10.8066u + 0.799373
a
7
=
1
−u
2
a
8
=
0.735856u
138
− 4.21108u
137
+ ··· + 235.088u − 15.1454
−0.0760587u
138
− 0.0133702u
137
+ ··· + 7.60471u + 1.60285
a
2
=
2.45479u
138
− 11.4434u
137
+ ··· + 289.689u + 13.0400
−0.720474u
138
+ 3.50880u
137
+ ··· − 10.8066u + 0.799373
a
11
=
1.23653u
138
− 6.01119u
137
+ ··· − 415.957u + 18.7604
0.0609717u
138
− 0.629528u
137
+ ··· + 14.1572u − 0.658718
a
9
=
−u
u
3
+ u
a
4
=
2.46548u
138
− 11.2941u
137
+ ··· + 280.398u + 13.8012
−0.485275u
138
+ 2.47123u
137
+ ··· − 14.5343u + 0.541178
a
1
=
2.38158u
138
− 11.6726u
137
+ ··· − 27.2525u − 18.2120
−1.21154u
138
+ 6.00159u
137
+ ··· − 19.9200u − 2.25614
a
12
=
−0.0581799u
138
− 0.510923u
137
+ ··· − 265.552u + 14.6717
−0.782724u
138
+ 3.73557u
137
+ ··· + 0.462355u − 2.95331
a
5
=
0.801704u
138
− 2.88019u
137
+ ··· − 374.674u + 30.2259
−0.0114680u
138
+ 0.203173u
137
+ ··· + 18.2793u − 0.985923
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.93883u
138
+ 13.5235u
137
+ ··· − 86.5187u − 10.5376
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
139
+ 12u
138
+ ··· − 96031942u − 12031189
c
2
u
139
+ 20u
137
+ ··· − 139979106u − 14998159
c
3
u
139
− u
138
+ ··· − 67319757u − 11261219
c
4
, c
5
, c
11
u
139
− u
138
+ ··· − 45u + 1
c
6
, c
9
u
139
+ 5u
138
+ ··· − 5u + 1
c
7
u
139
− u
138
+ ··· − 1730911u − 412087
c
8
, c
12
u
139
− u
138
+ ··· + 1535u + 59
c
10
u
139
− 6u
138
+ ··· − 7021256335u − 1610458073
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
139
− 68y
138
+ ··· − 3265430574626558y −144749508753721
c
2
y
139
+ 40y
138
+ ··· − 6420905976964404y −224944773389281
c
3
y
139
+ 51y
138
+ ··· − 3672999278065189y −126815053365961
c
4
, c
5
, c
11
y
139
− 139y
138
+ ··· + 167y −1
c
6
, c
9
y
139
+ 101y
138
+ ··· + 71y −1
c
7
y
139
+ 35y
138
+ ··· − 4614590704711y −169815695569
c
8
, c
12
y
139
− 85y
138
+ ··· + 3775647y −3481
c
10
y
139
+ 58y
138
+ ··· − 8.30 × 10
19
y −2.59 × 10
18
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.632104 + 0.764385I
a = −1.064890 − 0.857259I
b = 0.930191 + 0.078128I
−3.62053 − 2.47278I 0
u = −0.632104 − 0.764385I
a = −1.064890 + 0.857259I
b = 0.930191 − 0.078128I
−3.62053 + 2.47278I 0
u = −0.625186 + 0.814814I
a = 0.805602 + 0.418623I
b = −0.638835 + 0.193995I
0.79095 − 2.44484I 0
u = −0.625186 − 0.814814I
a = 0.805602 − 0.418623I
b = −0.638835 − 0.193995I
0.79095 + 2.44484I 0
u = −0.578146 + 0.849733I
a = −1.252290 + 0.061980I
b = 0.442621 − 0.563800I
−4.42501 − 3.02023I 0
u = −0.578146 − 0.849733I
a = −1.252290 − 0.061980I
b = 0.442621 + 0.563800I
−4.42501 + 3.02023I 0
u = −0.450126 + 0.939673I
a = −0.77915 − 1.58367I
b = 0.12832 − 1.64050I
−2.51785 − 5.09124I 0
u = −0.450126 − 0.939673I
a = −0.77915 + 1.58367I
b = 0.12832 + 1.64050I
−2.51785 + 5.09124I 0
u = 0.040562 + 0.956173I
a = 0.80061 − 1.50522I
b = 0.154062 − 1.006350I
−1.93236 − 1.50203I 0
u = 0.040562 − 0.956173I
a = 0.80061 + 1.50522I
b = 0.154062 + 1.006350I
−1.93236 + 1.50203I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.376090 + 0.975853I
a = 0.299159 + 1.227920I
b = −0.227847 + 0.359081I
0.20583 − 2.11439I 0
u = −0.376090 − 0.975853I
a = 0.299159 − 1.227920I
b = −0.227847 − 0.359081I
0.20583 + 2.11439I 0
u = −0.097694 + 0.948171I
a = −0.18979 − 1.76123I
b = −0.538958 − 0.292799I
−3.78394 − 0.07176I 0
u = −0.097694 − 0.948171I
a = −0.18979 + 1.76123I
b = −0.538958 + 0.292799I
−3.78394 + 0.07176I 0
u = 1.054900 + 0.033506I
a = −0.350782 + 0.054072I
b = 0.191210 − 1.182360I
−11.98150 − 0.43899I 0
u = 1.054900 − 0.033506I
a = −0.350782 − 0.054072I
b = 0.191210 + 1.182360I
−11.98150 + 0.43899I 0
u = 0.200437 + 1.044810I
a = −0.00787 + 1.78491I
b = 0.97940 + 1.44776I
−1.89065 + 2.87565I 0
u = 0.200437 − 1.044810I
a = −0.00787 − 1.78491I
b = 0.97940 − 1.44776I
−1.89065 − 2.87565I 0
u = 0.052430 + 1.085180I
a = 0.083079 + 0.887851I
b = 1.34567 + 0.62743I
−2.17992 + 2.23027I 0
u = 0.052430 − 1.085180I
a = 0.083079 − 0.887851I
b = 1.34567 − 0.62743I
−2.17992 − 2.23027I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.133183 + 1.078660I
a = 0.269627 + 0.788037I
b = −1.041810 + 0.142681I
−6.34074 + 5.65719I 0
u = 0.133183 − 1.078660I
a = 0.269627 − 0.788037I
b = −1.041810 − 0.142681I
−6.34074 − 5.65719I 0
u = −0.884291
a = 0.135616
b = 0.828989
1.73740 0
u = 1.122850 + 0.143683I
a = −0.0144874 − 0.0238569I
b = 0.913772 + 1.019110I
−9.3265 + 13.2419I 0
u = 1.122850 − 0.143683I
a = −0.0144874 + 0.0238569I
b = 0.913772 − 1.019110I
−9.3265 − 13.2419I 0
u = −0.030369 + 1.141630I
a = −1.13180 + 1.56529I
b = −0.827680 + 0.856148I
−7.14553 − 4.22155I 0
u = −0.030369 − 1.141630I
a = −1.13180 − 1.56529I
b = −0.827680 − 0.856148I
−7.14553 + 4.22155I 0
u = 0.574161 + 0.999656I
a = −1.038430 + 0.387110I
b = −0.742550 + 0.859820I
−4.00102 + 4.85639I 0
u = 0.574161 − 0.999656I
a = −1.038430 − 0.387110I
b = −0.742550 − 0.859820I
−4.00102 − 4.85639I 0
u = 0.376627 + 1.096920I
a = 0.08063 + 2.21291I
b = 0.732094 + 0.195650I
−9.83431 + 8.73999I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376627 − 1.096920I
a = 0.08063 − 2.21291I
b = 0.732094 − 0.195650I
−9.83431 − 8.73999I 0
u = 0.131427 + 1.154940I
a = −0.47784 + 1.44960I
b = −1.14341 + 1.07951I
−6.18385 + 5.50700I 0
u = 0.131427 − 1.154940I
a = −0.47784 − 1.44960I
b = −1.14341 − 1.07951I
−6.18385 − 5.50700I 0
u = −0.033659 + 1.162790I
a = −0.154800 − 1.358090I
b = −0.892725 − 1.067090I
−3.70268 − 1.30296I 0
u = −0.033659 − 1.162790I
a = −0.154800 + 1.358090I
b = −0.892725 + 1.067090I
−3.70268 + 1.30296I 0
u = 0.293787 + 1.128340I
a = −0.17563 − 1.98365I
b = −0.285408 − 0.485364I
−4.32303 + 6.86710I 0
u = 0.293787 − 1.128340I
a = −0.17563 + 1.98365I
b = −0.285408 + 0.485364I
−4.32303 − 6.86710I 0
u = −0.327936 + 1.120870I
a = −0.27163 + 2.31639I
b = −1.41225 + 2.17689I
−10.47560 − 9.06708I 0
u = −0.327936 − 1.120870I
a = −0.27163 − 2.31639I
b = −1.41225 − 2.17689I
−10.47560 + 9.06708I 0
u = 1.164710 + 0.145738I
a = −0.0718814 − 0.0205685I
b = −0.663783 − 0.821663I
−2.70772 + 8.73976I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.164710 − 0.145738I
a = −0.0718814 + 0.0205685I
b = −0.663783 + 0.821663I
−2.70772 − 8.73976I 0
u = 0.216339 + 1.157270I
a = −0.11963 − 1.76006I
b = −1.29983 − 1.46989I
−7.96668 + 6.49431I 0
u = 0.216339 − 1.157270I
a = −0.11963 + 1.76006I
b = −1.29983 + 1.46989I
−7.96668 − 6.49431I 0
u = −0.603808 + 0.512147I
a = 1.42525 + 0.13019I
b = 0.687606 + 1.058580I
−1.35003 + 0.84890I 0
u = −0.603808 − 0.512147I
a = 1.42525 − 0.13019I
b = 0.687606 − 1.058580I
−1.35003 − 0.84890I 0
u = 1.209830 + 0.053647I
a = 0.169389 + 0.030182I
b = 0.254752 + 0.774658I
−3.55913 + 2.84298I 0
u = 1.209830 − 0.053647I
a = 0.169389 − 0.030182I
b = 0.254752 − 0.774658I
−3.55913 − 2.84298I 0
u = −0.081245 + 1.213710I
a = 1.20424 + 2.16299I
b = −0.426972 + 1.087010I
−13.7202 − 7.3631I 0
u = −0.081245 − 1.213710I
a = 1.20424 − 2.16299I
b = −0.426972 − 1.087010I
−13.7202 + 7.3631I 0
u = −0.779454
a = 0.0601539
b = −1.60160
−2.60324 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.147100 + 0.428093I
a = 0.0746036 + 0.0133176I
b = −0.548048 + 0.264373I
1.64726 − 2.96897I 0
u = −1.147100 − 0.428093I
a = 0.0746036 − 0.0133176I
b = −0.548048 − 0.264373I
1.64726 + 2.96897I 0
u = −1.221970 + 0.106384I
a = −0.130642 + 0.070039I
b = 0.641240 − 0.899596I
−5.40420 − 6.34999I 0
u = −1.221970 − 0.106384I
a = −0.130642 − 0.070039I
b = 0.641240 + 0.899596I
−5.40420 + 6.34999I 0
u = 0.061866 + 1.229080I
a = 1.10101 − 2.22020I
b = 1.69509 − 2.45035I
−13.9888 + 7.0441I 0
u = 0.061866 − 1.229080I
a = 1.10101 + 2.22020I
b = 1.69509 + 2.45035I
−13.9888 − 7.0441I 0
u = −0.057965 + 1.240160I
a = −0.68750 − 1.69985I
b = 0.502615 − 0.896052I
−7.51703 − 4.43921I 0
u = −0.057965 − 1.240160I
a = −0.68750 + 1.69985I
b = 0.502615 + 0.896052I
−7.51703 + 4.43921I 0
u = 0.693216 + 0.294172I
a = −1.235230 − 0.606825I
b = 1.234120 − 0.277966I
−7.46136 − 4.66764I 0
u = 0.693216 − 0.294172I
a = −1.235230 + 0.606825I
b = 1.234120 + 0.277966I
−7.46136 + 4.66764I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.740925 + 0.039005I
a = 0.175208 + 0.012937I
b = 0.894801 + 0.094130I
1.79165 + 0.01807I 0
u = −0.740925 − 0.039005I
a = 0.175208 − 0.012937I
b = 0.894801 − 0.094130I
1.79165 − 0.01807I 0
u = 0.396515 + 0.626820I
a = 1.61618 + 0.64913I
b = 1.043350 − 0.351024I
−0.806683 − 0.430513I 0
u = 0.396515 − 0.626820I
a = 1.61618 − 0.64913I
b = 1.043350 + 0.351024I
−0.806683 + 0.430513I 0
u = −0.488716 + 1.188780I
a = 0.059634 − 1.120490I
b = 0.571156 − 0.740029I
−1.77558 − 4.94866I 0
u = −0.488716 − 1.188780I
a = 0.059634 + 1.120490I
b = 0.571156 + 0.740029I
−1.77558 + 4.94866I 0
u = −0.321103 + 1.251180I
a = −1.01316 + 1.56690I
b = −1.39219 + 0.69119I
−6.46785 − 3.98634I 0
u = −0.321103 − 1.251180I
a = −1.01316 − 1.56690I
b = −1.39219 − 0.69119I
−6.46785 + 3.98634I 0
u = −0.023033 + 1.294480I
a = 0.429469 + 1.221800I
b = 1.16918 + 1.40255I
−10.15290 − 2.95176I 0
u = −0.023033 − 1.294480I
a = 0.429469 − 1.221800I
b = 1.16918 − 1.40255I
−10.15290 + 2.95176I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663270 + 0.227218I
a = 0.517789 − 0.387904I
b = −0.698127 − 0.542906I
−2.15270 − 0.29643I 0
u = 0.663270 − 0.227218I
a = 0.517789 + 0.387904I
b = −0.698127 + 0.542906I
−2.15270 + 0.29643I 0
u = 0.269302 + 1.275940I
a = 0.23313 + 2.04139I
b = 0.85140 + 1.32317I
−3.56123 + 6.01556I 0
u = 0.269302 − 1.275940I
a = 0.23313 − 2.04139I
b = 0.85140 − 1.32317I
−3.56123 − 6.01556I 0
u = 0.231566 + 1.285870I
a = −0.15984 − 2.29698I
b = −0.84573 − 1.87240I
−8.17289 + 8.32891I 0
u = 0.231566 − 1.285870I
a = −0.15984 + 2.29698I
b = −0.84573 + 1.87240I
−8.17289 − 8.32891I 0
u = 0.081050 + 1.310830I
a = −0.697772 + 0.506852I
b = −1.39957 + 0.43759I
−6.71126 − 1.59464I 0
u = 0.081050 − 1.310830I
a = −0.697772 − 0.506852I
b = −1.39957 − 0.43759I
−6.71126 + 1.59464I 0
u = −0.640989 + 0.226911I
a = −1.19954 + 0.95018I
b = −1.02641 − 1.01692I
−7.85912 + 5.38264I 0
u = −0.640989 − 0.226911I
a = −1.19954 − 0.95018I
b = −1.02641 + 1.01692I
−7.85912 − 5.38264I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.066545 + 1.321360I
a = 0.768645 + 0.747733I
b = −0.297793 + 0.514659I
−7.17179 − 0.71597I 0
u = −0.066545 − 1.321360I
a = 0.768645 − 0.747733I
b = −0.297793 − 0.514659I
−7.17179 + 0.71597I 0
u = −0.315227 + 1.288070I
a = 0.52410 − 1.58607I
b = 1.01407 − 1.14665I
−2.20214 − 3.80235I 0
u = −0.315227 − 1.288070I
a = 0.52410 + 1.58607I
b = 1.01407 + 1.14665I
−2.20214 + 3.80235I 0
u = −0.151574 + 1.324020I
a = −1.34391 − 0.47917I
b = −0.063819 − 0.637227I
−12.81730 + 2.75952I 0
u = −0.151574 − 1.324020I
a = −1.34391 + 0.47917I
b = −0.063819 + 0.637227I
−12.81730 − 2.75952I 0
u = −0.291169 + 1.312350I
a = −0.28843 + 1.95616I
b = −0.97209 + 1.82682I
−7.62419 − 4.26111I 0
u = −0.291169 − 1.312350I
a = −0.28843 − 1.95616I
b = −0.97209 − 1.82682I
−7.62419 + 4.26111I 0
u = 0.064319 + 1.349230I
a = −0.132807 + 0.304254I
b = 0.766753 + 0.551467I
−10.16590 − 2.53861I 0
u = 0.064319 − 1.349230I
a = −0.132807 − 0.304254I
b = 0.766753 − 0.551467I
−10.16590 + 2.53861I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141759 + 1.348390I
a = 1.280460 − 0.496264I
b = 2.04695 − 0.81471I
−12.83850 − 1.98284I 0
u = 0.141759 − 1.348390I
a = 1.280460 + 0.496264I
b = 2.04695 + 0.81471I
−12.83850 + 1.98284I 0
u = 0.312822 + 1.329800I
a = −0.35508 − 1.68811I
b = −1.04846 − 0.95234I
−6.85262 + 3.32305I 0
u = 0.312822 − 1.329800I
a = −0.35508 + 1.68811I
b = −1.04846 + 0.95234I
−6.85262 − 3.32305I 0
u = 0.564982 + 0.246712I
a = 0.941868 + 0.988039I
b = −0.778969 + 0.273927I
−1.74419 − 3.51926I 0. + 6.81358I
u = 0.564982 − 0.246712I
a = 0.941868 − 0.988039I
b = −0.778969 − 0.273927I
−1.74419 + 3.51926I 0. − 6.81358I
u = −0.579514 + 0.172524I
a = −0.599116 − 0.441227I
b = −0.651970 + 0.762314I
−3.10725 − 0.93221I −1.69865 + 1.91084I
u = −0.579514 − 0.172524I
a = −0.599116 + 0.441227I
b = −0.651970 − 0.762314I
−3.10725 + 0.93221I −1.69865 − 1.91084I
u = 0.375731 + 0.430586I
a = −1.46280 − 1.70331I
b = 0.121273 + 0.381635I
−4.73205 − 3.56692I −3.56257 + 0.82297I
u = 0.375731 − 0.430586I
a = −1.46280 + 1.70331I
b = 0.121273 − 0.381635I
−4.73205 + 3.56692I −3.56257 − 0.82297I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.551351 + 0.041466I
a = −0.348797 + 0.159864I
b = 0.909573 + 0.742731I
0.49466 + 2.87994I 3.76408 − 7.17730I
u = 0.551351 − 0.041466I
a = −0.348797 − 0.159864I
b = 0.909573 − 0.742731I
0.49466 − 2.87994I 3.76408 + 7.17730I
u = 0.50487 + 1.35872I
a = 0.57340 − 1.32710I
b = −0.19555 − 1.69780I
−16.3446 + 5.0785I 0
u = 0.50487 − 1.35872I
a = 0.57340 + 1.32710I
b = −0.19555 + 1.69780I
−16.3446 − 5.0785I 0
u = 0.53916 + 1.35125I
a = −0.592181 + 1.256510I
b = 0.77271 + 1.21631I
−16.0866 + 6.1383I 0
u = 0.53916 − 1.35125I
a = −0.592181 − 1.256510I
b = 0.77271 − 1.21631I
−16.0866 − 6.1383I 0
u = 0.494920 + 0.064945I
a = −0.201421 + 0.138589I
b = −0.846145 − 1.054990I
−4.00307 + 5.55437I −0.20630 − 9.80295I
u = 0.494920 − 0.064945I
a = −0.201421 − 0.138589I
b = −0.846145 + 1.054990I
−4.00307 − 5.55437I −0.20630 + 9.80295I
u = 0.49609 + 1.41761I
a = 0.06162 + 1.67711I
b = 1.25880 + 1.44695I
−14.2338 + 18.9321I 0
u = 0.49609 − 1.41761I
a = 0.06162 − 1.67711I
b = 1.25880 − 1.44695I
−14.2338 − 18.9321I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.52629 + 1.40859I
a = −0.175667 + 1.314370I
b = 0.64333 + 1.33059I
−8.23137 + 8.85985I 0
u = 0.52629 − 1.40859I
a = −0.175667 − 1.314370I
b = 0.64333 − 1.33059I
−8.23137 − 8.85985I 0
u = 0.50533 + 1.42053I
a = −0.00810 − 1.49369I
b = −1.00508 − 1.32890I
−7.6298 + 14.5593I 0
u = 0.50533 − 1.42053I
a = −0.00810 + 1.49369I
b = −1.00508 + 1.32890I
−7.6298 − 14.5593I 0
u = −0.49851 + 1.42956I
a = −0.042542 + 1.227700I
b = −0.97671 + 1.06557I
−3.66903 − 8.81792I 0
u = −0.49851 − 1.42956I
a = −0.042542 − 1.227700I
b = −0.97671 − 1.06557I
−3.66903 + 8.81792I 0
u = −0.52229 + 1.42436I
a = −0.067096 − 1.388590I
b = 1.14001 − 1.26236I
−10.2609 − 12.3841I 0
u = −0.52229 − 1.42436I
a = −0.067096 + 1.388590I
b = 1.14001 + 1.26236I
−10.2609 + 12.3841I 0
u = 0.425096 + 0.199889I
a = −0.59446 − 1.85856I
b = −0.496624 + 0.741934I
−5.16865 − 3.96189I −8.75976 − 1.52352I
u = 0.425096 − 0.199889I
a = −0.59446 + 1.85856I
b = −0.496624 − 0.741934I
−5.16865 + 3.96189I −8.75976 + 1.52352I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.49284 + 1.45025I
a = 0.210900 − 0.948046I
b = −0.611507 − 0.865321I
−8.34973 + 3.47434I 0
u = 0.49284 − 1.45025I
a = 0.210900 + 0.948046I
b = −0.611507 + 0.865321I
−8.34973 − 3.47434I 0
u = −0.45669 + 1.46870I
a = 0.092018 − 0.950393I
b = 0.698719 − 0.926621I
−3.66154 − 4.15808I 0
u = −0.45669 − 1.46870I
a = 0.092018 + 0.950393I
b = 0.698719 + 0.926621I
−3.66154 + 4.15808I 0
u = −1.48715 + 0.40226I
a = 0.0364771 + 0.0056350I
b = −0.297858 + 0.327164I
1.67745 − 2.92146I 0
u = −1.48715 − 0.40226I
a = 0.0364771 − 0.0056350I
b = −0.297858 − 0.327164I
1.67745 + 2.92146I 0
u = 0.72226 + 1.43161I
a = 0.612530 − 0.252302I
b = 0.201225 − 0.860882I
−13.0035 − 6.6242I 0
u = 0.72226 − 1.43161I
a = 0.612530 + 0.252302I
b = 0.201225 + 0.860882I
−13.0035 + 6.6242I 0
u = 0.380334
a = 1.17264
b = −0.856573
−1.99604 −5.13480
u = −0.53570 + 1.53668I
a = 0.229727 + 0.669856I
b = −0.258142 + 1.049130I
−10.04130 − 0.47682I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.53570 − 1.53668I
a = 0.229727 − 0.669856I
b = −0.258142 − 1.049130I
−10.04130 + 0.47682I 0
u = 0.63571 + 1.55221I
a = −0.308326 + 0.460022I
b = 0.189370 + 0.699236I
−6.80659 − 1.81072I 0
u = 0.63571 − 1.55221I
a = −0.308326 − 0.460022I
b = 0.189370 − 0.699236I
−6.80659 + 1.81072I 0
u = 0.119274 + 0.183998I
a = 1.81211 + 2.71445I
b = 0.185674 − 0.485977I
−0.176249 − 1.225910I −2.45890 + 4.39822I
u = 0.119274 − 0.183998I
a = 1.81211 − 2.71445I
b = 0.185674 + 0.485977I
−0.176249 + 1.225910I −2.45890 − 4.39822I
u = 0.120753 + 0.163102I
a = −1.87698 − 5.26519I
b = −0.315069 − 0.882908I
−3.39632 − 4.21321I −4.57945 + 5.41901I
u = 0.120753 − 0.163102I
a = −1.87698 + 5.26519I
b = −0.315069 + 0.882908I
−3.39632 + 4.21321I −4.57945 − 5.41901I
u = −0.0373479 + 0.0332190I
a = 1.9496 + 27.7674I
b = 0.371405 − 1.350120I
−10.26830 + 6.64519I −5.05409 − 4.80906I
u = −0.0373479 − 0.0332190I
a = 1.9496 − 27.7674I
b = 0.371405 + 1.350120I
−10.26830 − 6.64519I −5.05409 + 4.80906I
18
II.
I
u
2
= h−7.47×10
13
u
37
−8.39×10
14
u
36
+· · ·+4.00×10
14
b−1.28×10
15
, 7.17×
10
14
u
37
+3.61×10
15
u
36
+· · ·+4.00×10
14
a+4.42×10
14
, u
38
+6u
37
+· · ·+8u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−1.79352u
37
− 9.04206u
36
+ ··· − 27.3493u − 1.10673
0.186959u
37
+ 2.09795u
36
+ ··· + 27.2435u + 3.19727
a
7
=
1
−u
2
a
8
=
−2.13819u
37
− 12.5698u
36
+ ··· − 71.6291u − 7.23204
−0.859661u
37
− 5.07197u
36
+ ··· + 4.32335u + 0.610719
a
2
=
−1.98048u
37
− 11.1400u
36
+ ··· − 54.5928u − 4.30400
0.186959u
37
+ 2.09795u
36
+ ··· + 27.2435u + 3.19727
a
11
=
0.637937u
37
+ 4.03082u
36
+ ··· + 45.7157u + 10.1968
1.53539u
37
+ 9.36935u
36
+ ··· + 4.66972u − 0.918296
a
9
=
−u
u
3
+ u
a
4
=
−2.68123u
37
− 14.5831u
36
+ ··· − 40.6733u − 2.96042
1.28610u
37
+ 8.71660u
36
+ ··· + 37.9613u + 4.83615
a
1
=
−0.00960525u
37
− 0.344384u
36
+ ··· − 59.4198u − 8.33827
0.967652u
37
+ 5.40422u
36
+ ··· + 9.54046u + 1.52625
a
12
=
0.361027u
37
+ 2.96735u
36
+ ··· − 4.73975u − 5.55696
0.446226u
37
+ 2.14513u
36
+ ··· − 2.50477u + 0.586564
a
5
=
−3.86645u
37
− 23.8815u
36
+ ··· + 16.9190u + 10.0054
−0.590981u
37
− 2.28624u
36
+ ··· + 13.5247u + 0.178064
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
2087587311673639
399763050242851
u
37
−
10535819392888632
399763050242851
u
36
+ ···+
46475107563651410
399763050242851
u +
6960004255554219
399763050242851
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
− 19u
37
+ ··· − 3u + 1
c
2
u
38
− 5u
37
+ ··· − 5u − 1
c
3
u
38
+ 2u
36
+ ··· − 16u
2
− 1
c
4
, c
5
u
38
− 19u
36
+ ··· + 2u + 1
c
6
u
38
+ 6u
37
+ ··· + 8u + 1
c
7
u
38
+ 4u
36
+ ··· − 21u
2
− 1
c
8
u
38
− 8u
36
+ ··· + 14u
2
− 1
c
9
u
38
− 6u
37
+ ··· − 8u + 1
c
10
u
38
− u
37
+ ··· − 6u
2
− 1
c
11
u
38
− 19u
36
+ ··· − 2u + 1
c
12
u
38
− 8u
36
+ ··· + 14u
2
− 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
− 7y
37
+ ··· − 55y + 1
c
2
y
38
+ 9y
37
+ ··· − y + 1
c
3
y
38
+ 4y
37
+ ··· + 32y + 1
c
4
, c
5
, c
11
y
38
− 38y
37
+ ··· − 24y + 1
c
6
, c
9
y
38
+ 26y
37
+ ··· + 28y + 1
c
7
y
38
+ 8y
37
+ ··· + 42y + 1
c
8
, c
12
y
38
− 16y
37
+ ··· − 28y + 1
c
10
y
38
+ 3y
37
+ ··· + 12y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.459651 + 0.896543I
a = 0.91267 + 1.16971I
b = −0.858713 + 0.081110I
−2.96891 − 1.85785I 0.864936 + 0.567591I
u = −0.459651 − 0.896543I
a = 0.91267 − 1.16971I
b = −0.858713 − 0.081110I
−2.96891 + 1.85785I 0.864936 − 0.567591I
u = −0.632533 + 0.725599I
a = −0.913058 − 0.292407I
b = 0.627268 − 0.246666I
0.77100 − 2.62635I −3.0604 + 23.7064I
u = −0.632533 − 0.725599I
a = −0.913058 + 0.292407I
b = 0.627268 + 0.246666I
0.77100 + 2.62635I −3.0604 − 23.7064I
u = 0.466442 + 0.804428I
a = −1.36907 + 0.54290I
b = −0.733406 + 0.580277I
−3.83815 + 5.87506I −5.26988 − 10.39206I
u = 0.466442 − 0.804428I
a = −1.36907 − 0.54290I
b = −0.733406 − 0.580277I
−3.83815 − 5.87506I −5.26988 + 10.39206I
u = 0.202685 + 1.069630I
a = 1.10022 − 2.52808I
b = −0.07535 − 1.66813I
−11.9350 + 7.6159I −9.19089 − 5.90154I
u = 0.202685 − 1.069630I
a = 1.10022 + 2.52808I
b = −0.07535 + 1.66813I
−11.9350 − 7.6159I −9.19089 + 5.90154I
u = 0.308247 + 1.109000I
a = −0.145816 + 0.022420I
b = 0.525710 + 0.914835I
−11.83070 − 5.48250I −8.28878 + 2.87322I
u = 0.308247 − 1.109000I
a = −0.145816 − 0.022420I
b = 0.525710 − 0.914835I
−11.83070 + 5.48250I −8.28878 − 2.87322I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.801220 + 0.228686I
a = −0.171628 − 0.606151I
b = 0.394548 − 0.274575I
−2.16704 − 2.43972I −1.88032 + 1.22897I
u = 0.801220 − 0.228686I
a = −0.171628 + 0.606151I
b = 0.394548 + 0.274575I
−2.16704 + 2.43972I −1.88032 − 1.22897I
u = −0.831117
a = 0.282751
b = 0.902818
1.22349 −7.63880
u = −0.430916 + 1.106430I
a = −0.27713 − 1.39247I
b = 0.215734 − 1.330590I
−2.25440 − 4.23880I −3.57235 + 1.86206I
u = −0.430916 − 1.106430I
a = −0.27713 + 1.39247I
b = 0.215734 + 1.330590I
−2.25440 + 4.23880I −3.57235 − 1.86206I
u = 0.274184 + 1.169180I
a = −0.21888 + 1.93093I
b = 0.142080 + 1.124990I
−4.95085 + 6.15707I −7.00105 − 6.50495I
u = 0.274184 − 1.169180I
a = −0.21888 − 1.93093I
b = 0.142080 − 1.124990I
−4.95085 − 6.15707I −7.00105 + 6.50495I
u = 0.191564 + 1.239710I
a = −0.62345 − 2.07606I
b = −0.466192 − 1.048500I
−7.98336 + 6.24650I −9.64109 − 6.45289I
u = 0.191564 − 1.239710I
a = −0.62345 + 2.07606I
b = −0.466192 + 1.048500I
−7.98336 − 6.24650I −9.64109 + 6.45289I
u = −0.202641 + 1.238490I
a = −0.35710 + 2.01469I
b = −1.31104 + 1.70507I
−8.72534 − 6.89692I −11.49987 + 5.96011I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.202641 − 1.238490I
a = −0.35710 − 2.01469I
b = −1.31104 − 1.70507I
−8.72534 + 6.89692I −11.49987 − 5.96011I
u = −0.314837 + 1.239870I
a = 0.36314 − 1.67057I
b = 0.93387 − 1.30771I
−2.48868 − 4.17409I −7.80230 + 8.84350I
u = −0.314837 − 1.239870I
a = 0.36314 + 1.67057I
b = 0.93387 + 1.30771I
−2.48868 + 4.17409I −7.80230 − 8.84350I
u = −0.266339 + 0.602795I
a = 2.07732 + 0.33293I
b = 1.19326 + 0.90742I
−0.340337 + 1.189810I 5.39842 − 4.79860I
u = −0.266339 − 0.602795I
a = 2.07732 − 0.33293I
b = 1.19326 − 0.90742I
−0.340337 − 1.189810I 5.39842 + 4.79860I
u = −0.278342 + 1.315920I
a = −0.89752 + 1.62148I
b = −1.32845 + 0.93588I
−5.30023 − 3.34568I 0
u = −0.278342 − 1.315920I
a = −0.89752 − 1.62148I
b = −1.32845 − 0.93588I
−5.30023 + 3.34568I 0
u = −0.645942
a = 0.171628
b = −1.35267
−1.09862 5.21690
u = 0.221722 + 1.391550I
a = −0.206253 + 0.129190I
b = −0.767445 − 0.122611I
−5.82323 − 2.29747I 0
u = 0.221722 − 1.391550I
a = −0.206253 − 0.129190I
b = −0.767445 + 0.122611I
−5.82323 + 2.29747I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.516691 + 0.228337I
a = 1.00942 − 1.18723I
b = −0.636599 + 0.726134I
−4.79778 − 4.61884I −3.10049 + 6.91308I
u = −0.516691 − 0.228337I
a = 1.00942 + 1.18723I
b = −0.636599 − 0.726134I
−4.79778 + 4.61884I −3.10049 − 6.91308I
u = −0.09314 + 1.49655I
a = −0.128522 − 0.443989I
b = 0.502075 − 0.621452I
−9.56752 + 0.97256I 0
u = −0.09314 − 1.49655I
a = −0.128522 + 0.443989I
b = 0.502075 + 0.621452I
−9.56752 − 0.97256I 0
u = −1.49962 + 0.55486I
a = −0.134365 + 0.079921I
b = 0.143495 − 0.176407I
1.66689 − 2.79605I 0
u = −1.49962 − 0.55486I
a = −0.134365 − 0.079921I
b = 0.143495 + 0.176407I
1.66689 + 2.79605I 0
u = −0.032820 + 0.296580I
a = 3.75282 − 0.47498I
b = −0.775923 + 0.592113I
−4.71032 − 4.71986I −3.12342 + 5.77728I
u = −0.032820 − 0.296580I
a = 3.75282 + 0.47498I
b = −0.775923 − 0.592113I
−4.71032 + 4.71986I −3.12342 − 5.77728I
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
38
− 19u
37
+ ··· − 3u + 1)
· (u
139
+ 12u
138
+ ··· − 96031942u − 12031189)
c
2
(u
38
− 5u
37
+ ··· − 5u − 1)
· (u
139
+ 20u
137
+ ··· − 139979106u − 14998159)
c
3
(u
38
+ 2u
36
+ ··· − 16u
2
− 1)
· (u
139
− u
138
+ ··· − 67319757u − 11261219)
c
4
, c
5
(u
38
− 19u
36
+ ··· + 2u + 1)(u
139
− u
138
+ ··· − 45u + 1)
c
6
(u
38
+ 6u
37
+ ··· + 8u + 1)(u
139
+ 5u
138
+ ··· − 5u + 1)
c
7
(u
38
+ 4u
36
+ ··· − 21u
2
− 1)(u
139
− u
138
+ ··· − 1730911u − 412087)
c
8
(u
38
− 8u
36
+ ··· + 14u
2
− 1)(u
139
− u
138
+ ··· + 1535u + 59)
c
9
(u
38
− 6u
37
+ ··· − 8u + 1)(u
139
+ 5u
138
+ ··· − 5u + 1)
c
10
(u
38
− u
37
+ ··· − 6u
2
− 1)
· (u
139
− 6u
138
+ ··· − 7021256335u − 1610458073)
c
11
(u
38
− 19u
36
+ ··· − 2u + 1)(u
139
− u
138
+ ··· − 45u + 1)
c
12
(u
38
− 8u
36
+ ··· + 14u
2
− 1)(u
139
− u
138
+ ··· + 1535u + 59)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
38
− 7y
37
+ ··· − 55y + 1)
· (y
139
− 68y
138
+ ··· − 3265430574626558y −144749508753721)
c
2
(y
38
+ 9y
37
+ ··· − y + 1)
· (y
139
+ 40y
138
+ ··· − 6420905976964404y −224944773389281)
c
3
(y
38
+ 4y
37
+ ··· + 32y + 1)
· (y
139
+ 51y
138
+ ··· − 3672999278065189y −126815053365961)
c
4
, c
5
, c
11
(y
38
− 38y
37
+ ··· − 24y + 1)(y
139
− 139y
138
+ ··· + 167y −1)
c
6
, c
9
(y
38
+ 26y
37
+ ··· + 28y + 1)(y
139
+ 101y
138
+ ··· + 71y −1)
c
7
(y
38
+ 8y
37
+ ··· + 42y + 1)
· (y
139
+ 35y
138
+ ··· − 4614590704711y −169815695569)
c
8
, c
12
(y
38
− 16y
37
+ ··· − 28y + 1)(y
139
− 85y
138
+ ··· + 3775647y −3481)
c
10
(y
38
+ 3y
37
+ ··· + 12y + 1)
· (y
139
+ 58y
138
+ ··· − 8.30 × 10
19
y −2.59 × 10
18
)
27
