12a
0558
(K12a
0558
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 2 10 12 1 5 6 4
Solving Sequence
3,9 4,7
2 1 10 6 12 8 5 11
c
3
c
2
c
1
c
9
c
6
c
12
c
8
c
4
c
11
c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.96556 × 10
1272
u
150
− 4.61903 × 10
1272
u
149
+ ··· + 1.68074 × 10
1275
b − 1.40593 × 10
1275
,
5.76019 × 10
1273
u
150
+ 2.86320 × 10
1274
u
149
+ ··· + 7.54653 × 10
1277
a − 2.77801 × 10
1278
,
u
151
− 2u
150
+ ··· + 2162u − 449i
I
u
2
= h−2.90007 × 10
40
u
31
+ 3.42238 × 10
40
u
30
+ ··· + 1.17408 × 10
41
b + 1.01177 × 10
41
,
3.04606 × 10
40
u
31
− 3.49551 × 10
40
u
30
+ ··· + 1.17408 × 10
41
a − 9.77906 × 10
40
, u
32
− u
31
+ ··· − 3u − 1i
I
u
3
= hu
2
+ b + u, −u
2
+ a − u + 1, u
3
+ 2u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 186 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
= h1.97 × 10
1272
u
150
− 4.62 × 10
1272
u
149
+ · · · + 1.68 × 10
1275
b − 1.41 ×
10
1275
, 5.76 × 10
1273
u
150
+ 2.86 × 10
1274
u
149
+ · · · + 7.55 × 10
1277
a − 2.78 ×
10
1278
, u
151
− 2u
150
+ · · · + 2162u − 449i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−0.0000763290u
150
− 0.000379406u
149
+ ··· − 31.9809u + 3.68117
−0.00116946u
150
+ 0.00274821u
149
+ ··· + 7.24694u + 0.836496
a
2
=
−0.00168220u
150
+ 0.00590328u
149
+ ··· + 65.0155u − 6.42701
−6.64115 × 10
−6
u
150
− 0.000367296u
149
+ ··· − 19.2980u + 0.0982350
a
1
=
−0.00168885u
150
+ 0.00553599u
149
+ ··· + 45.7175u − 6.32878
−6.64115 × 10
−6
u
150
− 0.000367296u
149
+ ··· − 19.2980u + 0.0982350
a
10
=
0.0117674u
150
− 0.0223322u
149
+ ··· + 43.3172u − 11.8273
−0.00133968u
150
+ 0.00299390u
149
+ ··· + 2.76487u + 0.424849
a
6
=
0.00568194u
150
− 0.0122842u
149
+ ··· + 31.1122u − 0.393206
−0.00115135u
150
+ 0.00292564u
149
+ ··· − 14.9915u − 1.56282
a
12
=
−0.00168228u
150
+ 0.00557349u
149
+ ··· + 59.5909u − 5.45794
0.0000690792u
150
− 0.000523140u
149
+ ··· − 19.4045u + 0.120968
a
8
=
0.0105884u
150
− 0.0198923u
149
+ ··· + 43.1103u − 12.0399
−0.00148726u
150
+ 0.00330437u
149
+ ··· + 4.10259u + 0.904460
a
5
=
0.00860053u
150
− 0.0223541u
149
+ ··· − 59.6672u + 9.81945
0.000393479u
150
− 0.000364436u
149
+ ··· − 2.69319u − 2.04299
a
11
=
−0.00385075u
150
+ 0.0101935u
149
+ ··· + 21.0110u − 8.58046
0.000913499u
150
− 0.00139895u
149
+ ··· + 25.8880u − 0.0780800
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0168044u
150
− 0.0359252u
149
+ ··· + 562.956u + 69.1771
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
151
+ 66u
150
+ ··· + 185503u + 3481
c
2
, c
6
u
151
− 2u
150
+ ··· + 255u − 59
c
3
u
151
− 2u
150
+ ··· + 2162u − 449
c
4
u
151
− 6u
150
+ ··· − 5051302u − 765269
c
5
, c
10
, c
11
u
151
− u
150
+ ··· + 122u + 11
c
7
u
151
+ 7u
150
+ ··· + 2354104u + 756296
c
8
u
151
+ 4u
150
+ ··· − 5327u + 391
c
9
u
151
+ 3u
150
+ ··· − u + 1
c
12
u
151
+ 14u
150
+ ··· + 45u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
151
+ 42y
150
+ ··· − 823270257y −12117361
c
2
, c
6
y
151
− 66y
150
+ ··· + 185503y −3481
c
3
y
151
+ 22y
150
+ ··· + 18108324y −201601
c
4
y
151
+ 42y
150
+ ··· − 16103090955074y −585636642361
c
5
, c
10
, c
11
y
151
− 147y
150
+ ··· + 43638y −121
c
7
y
151
− 35y
150
+ ··· + 10638457160160y −571983639616
c
8
y
151
+ 6y
150
+ ··· − 424913y −152881
c
9
y
151
+ 17y
150
+ ··· + 133y −1
c
12
y
151
+ 6y
150
+ ··· + 293y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.039981 + 1.008940I
a = −0.563623 + 1.213530I
b = 0.801162 − 0.706079I
2.47108 + 2.65288I 0
u = −0.039981 − 1.008940I
a = −0.563623 − 1.213530I
b = 0.801162 + 0.706079I
2.47108 − 2.65288I 0
u = 0.703513 + 0.695907I
a = −0.618455 + 0.040468I
b = −1.177490 + 0.116883I
−4.41545 − 2.22036I 0
u = 0.703513 − 0.695907I
a = −0.618455 − 0.040468I
b = −1.177490 − 0.116883I
−4.41545 + 2.22036I 0
u = 0.939145 + 0.409369I
a = 0.0896863 + 0.0368558I
b = 0.515699 − 0.698015I
−6.34616 − 4.01409I 0
u = 0.939145 − 0.409369I
a = 0.0896863 − 0.0368558I
b = 0.515699 + 0.698015I
−6.34616 + 4.01409I 0
u = 0.713828 + 0.650377I
a = −0.98542 + 2.10443I
b = −0.970801 − 0.659759I
−0.55710 − 6.66250I 0
u = 0.713828 − 0.650377I
a = −0.98542 − 2.10443I
b = −0.970801 + 0.659759I
−0.55710 + 6.66250I 0
u = −0.537746 + 0.891491I
a = 0.287736 + 1.187750I
b = −0.847487 − 0.680236I
−1.241290 + 0.238635I 0
u = −0.537746 − 0.891491I
a = 0.287736 − 1.187750I
b = −0.847487 + 0.680236I
−1.241290 − 0.238635I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.001240 + 0.291819I
a = 0.195006 − 1.234500I
b = 0.305382 + 0.450804I
−0.31238 + 2.57038I 0
u = 1.001240 − 0.291819I
a = 0.195006 + 1.234500I
b = 0.305382 − 0.450804I
−0.31238 − 2.57038I 0
u = 0.884487 + 0.346998I
a = −0.187209 − 0.686003I
b = 1.335700 + 0.443505I
−8.59510 + 0.02221I 0
u = 0.884487 − 0.346998I
a = −0.187209 + 0.686003I
b = 1.335700 − 0.443505I
−8.59510 − 0.02221I 0
u = 0.656850 + 0.850604I
a = 0.921131 − 0.469165I
b = 0.359459 + 0.262040I
−6.51533 − 2.97279I 0
u = 0.656850 − 0.850604I
a = 0.921131 + 0.469165I
b = 0.359459 − 0.262040I
−6.51533 + 2.97279I 0
u = 0.740056 + 0.783206I
a = 0.133832 − 0.599426I
b = −0.138405 + 0.827201I
−6.77489 − 2.11958I 0
u = 0.740056 − 0.783206I
a = 0.133832 + 0.599426I
b = −0.138405 − 0.827201I
−6.77489 + 2.11958I 0
u = 0.684530 + 0.845794I
a = 0.851637 + 0.866097I
b = −0.911724 + 0.255229I
−7.33520 − 4.69044I 0
u = 0.684530 − 0.845794I
a = 0.851637 − 0.866097I
b = −0.911724 − 0.255229I
−7.33520 + 4.69044I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.874553 + 0.236922I
a = −0.063913 + 0.716291I
b = −0.998554 − 0.380216I
−1.65732 − 0.38865I 0
u = −0.874553 − 0.236922I
a = −0.063913 − 0.716291I
b = −0.998554 + 0.380216I
−1.65732 + 0.38865I 0
u = −0.414158 + 0.803206I
a = −0.19220 − 1.61244I
b = −1.184650 + 0.708377I
−4.67562 + 11.48670I 0
u = −0.414158 − 0.803206I
a = −0.19220 + 1.61244I
b = −1.184650 − 0.708377I
−4.67562 − 11.48670I 0
u = −0.633732 + 0.638046I
a = 1.054430 + 0.057142I
b = −0.679572 − 0.679532I
0.30481 + 1.46754I 0
u = −0.633732 − 0.638046I
a = 1.054430 − 0.057142I
b = −0.679572 + 0.679532I
0.30481 − 1.46754I 0
u = −1.065660 + 0.299057I
a = 1.027770 + 0.819795I
b = 1.047810 − 0.626072I
−7.88222 + 9.14328I 0
u = −1.065660 − 0.299057I
a = 1.027770 − 0.819795I
b = 1.047810 + 0.626072I
−7.88222 − 9.14328I 0
u = −0.054378 + 0.887305I
a = 0.657565 + 0.023569I
b = −0.475200 + 0.545615I
1.95450 + 3.17739I 0
u = −0.054378 − 0.887305I
a = 0.657565 − 0.023569I
b = −0.475200 − 0.545615I
1.95450 − 3.17739I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.486191 + 1.013690I
a = −0.358459 + 0.571467I
b = 0.270776 − 0.096317I
0.87014 + 3.15700I 0
u = −0.486191 − 1.013690I
a = −0.358459 − 0.571467I
b = 0.270776 + 0.096317I
0.87014 − 3.15700I 0
u = −0.349386 + 0.779593I
a = −1.93148 + 0.79619I
b = 0.824113 + 0.461791I
0.75907 + 1.21132I 0
u = −0.349386 − 0.779593I
a = −1.93148 − 0.79619I
b = 0.824113 − 0.461791I
0.75907 − 1.21132I 0
u = 0.510108 + 0.682296I
a = 0.332547 + 1.273250I
b = −0.402137 − 0.983875I
1.43305 − 4.63133I 0
u = 0.510108 − 0.682296I
a = 0.332547 − 1.273250I
b = −0.402137 + 0.983875I
1.43305 + 4.63133I 0
u = −0.170544 + 0.821873I
a = −0.45307 + 1.94856I
b = 0.864012 − 0.660336I
2.31706 + 2.60082I 0
u = −0.170544 − 0.821873I
a = −0.45307 − 1.94856I
b = 0.864012 + 0.660336I
2.31706 − 2.60082I 0
u = 1.172680 + 0.270553I
a = 0.561705 + 1.044390I
b = 0.692677 − 0.246807I
−0.34895 − 2.72408I 0
u = 1.172680 − 0.270553I
a = 0.561705 − 1.044390I
b = 0.692677 + 0.246807I
−0.34895 + 2.72408I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20530
a = 0.119339
b = −1.28443
−2.37234 0
u = −0.035138 + 0.791480I
a = −0.688063 − 0.627838I
b = 0.434675 + 0.841979I
3.61412 + 1.43650I 0
u = −0.035138 − 0.791480I
a = −0.688063 + 0.627838I
b = 0.434675 − 0.841979I
3.61412 − 1.43650I 0
u = 0.707109 + 0.352643I
a = 1.69700 − 0.31512I
b = 0.980235 + 0.009187I
−4.60050 − 1.41999I 0
u = 0.707109 − 0.352643I
a = 1.69700 + 0.31512I
b = 0.980235 − 0.009187I
−4.60050 + 1.41999I 0
u = 0.343900 + 0.703421I
a = 0.54662 − 1.51724I
b = 1.139670 + 0.641881I
1.48391 − 6.97874I 0
u = 0.343900 − 0.703421I
a = 0.54662 + 1.51724I
b = 1.139670 − 0.641881I
1.48391 + 6.97874I 0
u = −0.684542 + 0.375884I
a = 0.565949 − 0.523686I
b = 1.273910 + 0.251148I
−11.42070 − 1.71813I 0
u = −0.684542 − 0.375884I
a = 0.565949 + 0.523686I
b = 1.273910 − 0.251148I
−11.42070 + 1.71813I 0
u = −0.774735 + 0.028512I
a = −1.39398 + 1.10712I
b = −1.115300 − 0.091313I
−11.30190 + 2.36606I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.774735 − 0.028512I
a = −1.39398 − 1.10712I
b = −1.115300 + 0.091313I
−11.30190 − 2.36606I 0
u = 0.971948 + 0.754721I
a = −0.279676 − 0.490526I
b = −0.934466 + 0.481120I
−2.16344 + 2.84576I 0
u = 0.971948 − 0.754721I
a = −0.279676 + 0.490526I
b = −0.934466 − 0.481120I
−2.16344 − 2.84576I 0
u = −0.019191 + 0.758227I
a = −1.42992 + 2.58015I
b = 0.840519 − 0.669274I
2.17960 + 2.59133I 0
u = −0.019191 − 0.758227I
a = −1.42992 − 2.58015I
b = 0.840519 + 0.669274I
2.17960 − 2.59133I 0
u = 0.799867 + 0.949650I
a = 0.14204 + 1.58333I
b = −0.925437 − 0.691493I
−1.57764 − 5.52140I 0
u = 0.799867 − 0.949650I
a = 0.14204 − 1.58333I
b = −0.925437 + 0.691493I
−1.57764 + 5.52140I 0
u = −0.927660 + 0.825764I
a = 0.300167 + 0.279865I
b = 1.231230 − 0.033904I
−4.71028 + 7.33856I 0
u = −0.927660 − 0.825764I
a = 0.300167 − 0.279865I
b = 1.231230 + 0.033904I
−4.71028 − 7.33856I 0
u = 0.116359 + 0.748309I
a = 0.625750 − 0.998270I
b = −0.425643 + 1.056950I
−2.34326 − 5.17950I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.116359 − 0.748309I
a = 0.625750 + 0.998270I
b = −0.425643 − 1.056950I
−2.34326 + 5.17950I 0
u = 0.479187 + 0.567765I
a = 2.15146 − 1.72457I
b = 0.928810 + 0.502544I
0.34784 − 5.12983I 0
u = 0.479187 − 0.567765I
a = 2.15146 + 1.72457I
b = 0.928810 − 0.502544I
0.34784 + 5.12983I 0
u = −0.973470 + 0.807792I
a = −0.650484 − 1.157520I
b = −1.129410 + 0.509755I
−9.68944 + 6.79778I 0
u = −0.973470 − 0.807792I
a = −0.650484 + 1.157520I
b = −1.129410 − 0.509755I
−9.68944 − 6.79778I 0
u = −0.588303 + 0.421762I
a = −0.38630 + 1.47599I
b = 0.444568 − 1.254430I
−4.56487 + 6.76711I 0
u = −0.588303 − 0.421762I
a = −0.38630 − 1.47599I
b = 0.444568 + 1.254430I
−4.56487 − 6.76711I 0
u = −0.548054 + 0.469018I
a = −0.272258 − 0.565473I
b = −0.321105 + 0.348772I
−0.981069 + 0.675049I 0
u = −0.548054 − 0.469018I
a = −0.272258 + 0.565473I
b = −0.321105 − 0.348772I
−0.981069 − 0.675049I 0
u = −0.699564 + 1.080760I
a = −0.684863 − 0.689021I
b = 0.463445 + 0.766465I
0.81996 + 4.40543I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699564 − 1.080760I
a = −0.684863 + 0.689021I
b = 0.463445 − 0.766465I
0.81996 − 4.40543I 0
u = 0.264880 + 1.265290I
a = 0.774566 + 1.042540I
b = −0.893724 − 0.530535I
−1.61994 − 4.80324I 0
u = 0.264880 − 1.265290I
a = 0.774566 − 1.042540I
b = −0.893724 + 0.530535I
−1.61994 + 4.80324I 0
u = 0.103422 + 0.685721I
a = 3.05287 + 0.04453I
b = −0.886886 + 0.550508I
1.47781 + 5.10675I 0
u = 0.103422 − 0.685721I
a = 3.05287 − 0.04453I
b = −0.886886 − 0.550508I
1.47781 − 5.10675I 0
u = −0.024085 + 1.310030I
a = 0.29059 − 2.09296I
b = −0.690944 + 0.464454I
−6.34572 − 1.76164I 0
u = −0.024085 − 1.310030I
a = 0.29059 + 2.09296I
b = −0.690944 − 0.464454I
−6.34572 + 1.76164I 0
u = −0.329046 + 0.599417I
a = 0.62690 + 1.89085I
b = −0.709570 − 0.545400I
−1.210210 + 0.420943I 0
u = −0.329046 − 0.599417I
a = 0.62690 − 1.89085I
b = −0.709570 + 0.545400I
−1.210210 − 0.420943I 0
u = 1.32170
a = −0.458239
b = 1.49086
−6.91048 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.089553 + 0.661013I
a = −3.10919 − 1.51787I
b = 0.976704 + 0.580862I
−5.28622 − 9.93901I 0
u = 0.089553 − 0.661013I
a = −3.10919 + 1.51787I
b = 0.976704 − 0.580862I
−5.28622 + 9.93901I 0
u = −0.841993 + 1.037930I
a = 0.246589 + 1.260550I
b = −0.276920 − 0.999554I
−0.18904 + 4.43856I 0
u = −0.841993 − 1.037930I
a = 0.246589 − 1.260550I
b = −0.276920 + 0.999554I
−0.18904 − 4.43856I 0
u = −1.234190 + 0.517934I
a = −0.32568 − 1.46809I
b = −0.204742 + 0.521959I
−5.87844 − 5.67462I 0
u = −1.234190 − 0.517934I
a = −0.32568 + 1.46809I
b = −0.204742 − 0.521959I
−5.87844 + 5.67462I 0
u = −1.336730 + 0.092485I
a = −0.88139 + 1.24930I
b = −0.520147 − 0.180317I
−5.84098 + 5.80109I 0
u = −1.336730 − 0.092485I
a = −0.88139 − 1.24930I
b = −0.520147 + 0.180317I
−5.84098 − 5.80109I 0
u = 1.110730 + 0.781094I
a = −0.022663 + 0.254977I
b = −1.350050 − 0.077479I
−11.5645 − 10.7900I 0
u = 1.110730 − 0.781094I
a = −0.022663 − 0.254977I
b = −1.350050 + 0.077479I
−11.5645 + 10.7900I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.647621 + 1.201000I
a = 0.762783 + 1.103760I
b = −0.705171 − 0.872448I
0.385022 + 0.107964I 0
u = −0.647621 − 1.201000I
a = 0.762783 − 1.103760I
b = −0.705171 + 0.872448I
0.385022 − 0.107964I 0
u = 0.769908 + 1.153220I
a = −0.472047 + 1.079770I
b = 0.509078 − 0.857408I
3.87805 − 2.26852I 0
u = 0.769908 − 1.153220I
a = −0.472047 − 1.079770I
b = 0.509078 + 0.857408I
3.87805 + 2.26852I 0
u = 0.698278 + 1.201230I
a = −0.02692 + 1.90099I
b = −0.998175 − 0.747753I
−0.52356 − 6.09369I 0
u = 0.698278 − 1.201230I
a = −0.02692 − 1.90099I
b = −0.998175 + 0.747753I
−0.52356 + 6.09369I 0
u = −0.251881 + 0.531550I
a = −0.938753 − 0.899272I
b = −1.141050 + 0.529975I
−0.120299 + 1.210570I −9.4715 − 13.8749I
u = −0.251881 − 0.531550I
a = −0.938753 + 0.899272I
b = −1.141050 − 0.529975I
−0.120299 − 1.210570I −9.4715 + 13.8749I
u = 0.87395 + 1.11199I
a = 0.39038 − 1.65013I
b = 1.086800 + 0.627696I
−1.00826 − 9.69803I 0
u = 0.87395 − 1.11199I
a = 0.39038 + 1.65013I
b = 1.086800 − 0.627696I
−1.00826 + 9.69803I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.83764 + 1.17107I
a = 0.652409 − 0.941387I
b = −0.515383 + 0.903941I
1.90280 − 9.41620I 0
u = 0.83764 − 1.17107I
a = 0.652409 + 0.941387I
b = −0.515383 − 0.903941I
1.90280 + 9.41620I 0
u = 0.26966 + 1.44054I
a = −0.37076 − 1.73682I
b = 0.882042 + 0.460269I
−2.53359 − 1.87365I 0
u = 0.26966 − 1.44054I
a = −0.37076 + 1.73682I
b = 0.882042 − 0.460269I
−2.53359 + 1.87365I 0
u = −0.233905 + 0.464300I
a = −0.58755 + 2.61761I
b = 1.099530 − 0.808893I
−5.22555 + 4.13773I −14.9345 − 2.8334I
u = −0.233905 − 0.464300I
a = −0.58755 − 2.61761I
b = 1.099530 + 0.808893I
−5.22555 − 4.13773I −14.9345 + 2.8334I
u = −0.94984 + 1.18248I
a = −0.587432 − 1.051910I
b = 0.514050 + 0.989899I
−4.18881 + 13.48630I 0
u = −0.94984 − 1.18248I
a = −0.587432 + 1.051910I
b = 0.514050 − 0.989899I
−4.18881 − 13.48630I 0
u = −0.174626 + 0.394055I
a = −3.39050 − 4.42295I
b = −0.808733 + 0.552788I
1.72562 − 0.67585I −0.1046394 + 0.0437731I
u = −0.174626 − 0.394055I
a = −3.39050 + 4.42295I
b = −0.808733 − 0.552788I
1.72562 + 0.67585I −0.1046394 − 0.0437731I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.96770 + 1.24613I
a = −0.16685 − 1.63788I
b = −1.113020 + 0.683266I
0.0733 + 15.2633I 0
u = −0.96770 − 1.24613I
a = −0.16685 + 1.63788I
b = −1.113020 − 0.683266I
0.0733 − 15.2633I 0
u = −1.08724 + 1.15973I
a = −0.071711 − 0.890398I
b = −1.069550 + 0.219502I
−3.97164 − 0.36681I 0
u = −1.08724 − 1.15973I
a = −0.071711 + 0.890398I
b = −1.069550 − 0.219502I
−3.97164 + 0.36681I 0
u = 0.180044 + 0.334675I
a = 0.29086 + 3.21994I
b = −0.960656 − 0.789140I
−0.18705 − 3.08251I −13.8819 + 5.7749I
u = 0.180044 − 0.334675I
a = 0.29086 − 3.21994I
b = −0.960656 + 0.789140I
−0.18705 + 3.08251I −13.8819 − 5.7749I
u = −0.89398 + 1.36055I
a = −0.062611 − 0.226372I
b = 0.988118 + 0.358175I
−8.31788 + 0.18076I 0
u = −0.89398 − 1.36055I
a = −0.062611 + 0.226372I
b = 0.988118 − 0.358175I
−8.31788 − 0.18076I 0
u = −0.93346 + 1.33979I
a = 0.513154 + 0.743677I
b = −0.755184 − 0.623513I
2.55701 + 1.93002I 0
u = −0.93346 − 1.33979I
a = 0.513154 − 0.743677I
b = −0.755184 + 0.623513I
2.55701 − 1.93002I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.01308 + 1.31880I
a = −0.01076 + 1.49567I
b = 1.094750 − 0.672100I
2.11697 + 7.94798I 0
u = −1.01308 − 1.31880I
a = −0.01076 − 1.49567I
b = 1.094750 + 0.672100I
2.11697 − 7.94798I 0
u = −0.100215 + 0.308742I
a = −1.38356 − 7.58911I
b = 0.664047 + 0.576213I
−4.31968 + 5.28965I −3.83909 − 5.22434I
u = −0.100215 − 0.308742I
a = −1.38356 + 7.58911I
b = 0.664047 − 0.576213I
−4.31968 − 5.28965I −3.83909 + 5.22434I
u = 1.06937 + 1.29791I
a = 0.05356 − 1.57748I
b = 1.147760 + 0.711431I
−6.1639 − 19.6674I 0
u = 1.06937 − 1.29791I
a = 0.05356 + 1.57748I
b = 1.147760 − 0.711431I
−6.1639 + 19.6674I 0
u = −1.60116 + 0.54934I
a = 0.010083 − 0.801196I
b = 1.019310 + 0.546714I
−1.94906 − 6.81814I 0
u = −1.60116 − 0.54934I
a = 0.010083 + 0.801196I
b = 1.019310 − 0.546714I
−1.94906 + 6.81814I 0
u = 1.17760 + 1.22031I
a = −0.512586 + 0.795255I
b = 0.796434 − 0.754938I
−1.75309 − 3.05946I 0
u = 1.17760 − 1.22031I
a = −0.512586 − 0.795255I
b = 0.796434 + 0.754938I
−1.75309 + 3.05946I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.26832 + 1.68540I
a = 0.59758 − 1.50479I
b = −0.979726 + 0.522355I
−7.32729 + 5.88276I 0
u = −0.26832 − 1.68540I
a = 0.59758 + 1.50479I
b = −0.979726 − 0.522355I
−7.32729 − 5.88276I 0
u = 1.20607 + 1.27559I
a = −0.31054 + 1.42032I
b = −0.931493 − 0.612346I
2.00130 − 6.79686I 0
u = 1.20607 − 1.27559I
a = −0.31054 − 1.42032I
b = −0.931493 + 0.612346I
2.00130 + 6.79686I 0
u = −0.233711
a = 2.09840
b = −0.780549
−1.28591 −7.80700
u = 0.061520 + 0.222196I
a = −2.66146 + 4.07281I
b = 0.820097 − 0.895548I
−4.36742 + 2.42677I −12.68907 − 3.84305I
u = 0.061520 − 0.222196I
a = −2.66146 − 4.07281I
b = 0.820097 + 0.895548I
−4.36742 − 2.42677I −12.68907 + 3.84305I
u = 1.11273 + 1.38219I
a = 0.152711 + 1.337940I
b = −1.191970 − 0.639568I
−2.90923 − 10.25880I 0
u = 1.11273 − 1.38219I
a = 0.152711 − 1.337940I
b = −1.191970 + 0.639568I
−2.90923 + 10.25880I 0
u = −1.10550 + 1.39834I
a = 0.442322 + 1.292840I
b = 0.882770 − 0.476322I
−2.08616 + 4.53346I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10550 − 1.39834I
a = 0.442322 − 1.292840I
b = 0.882770 + 0.476322I
−2.08616 − 4.53346I 0
u = −1.37785 + 1.15881I
a = 0.29332 + 1.46570I
b = 0.923535 − 0.710671I
−2.14974 + 8.62294I 0
u = −1.37785 − 1.15881I
a = 0.29332 − 1.46570I
b = 0.923535 + 0.710671I
−2.14974 − 8.62294I 0
u = 0.83341 + 1.60435I
a = −0.550036 + 0.641053I
b = 0.862447 − 0.474747I
−2.01601 − 0.65285I 0
u = 0.83341 − 1.60435I
a = −0.550036 − 0.641053I
b = 0.862447 + 0.474747I
−2.01601 + 0.65285I 0
u = 1.87851
a = −0.0450608
b = 1.19224
−6.65544 0
u = 0.0780179
a = −2.23309
b = 1.84685
−10.0070 168.230
u = 1.24571 + 1.68316I
a = −0.310636 − 0.866579I
b = 1.162770 + 0.301482I
−9.63485 + 2.57620I 0
u = 1.24571 − 1.68316I
a = −0.310636 + 0.866579I
b = 1.162770 − 0.301482I
−9.63485 − 2.57620I 0
u = 2.00052 + 0.77434I
a = 0.165853 − 0.784226I
b = −1.076110 + 0.544915I
−7.97604 + 10.06560I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.00052 − 0.77434I
a = 0.165853 + 0.784226I
b = −1.076110 − 0.544915I
−7.97604 − 10.06560I 0
20
II.
I
u
2
= h−2.90×10
40
u
31
+3.42×10
40
u
30
+· · ·+1.17×10
41
b+1.01×10
41
, 3.05×
10
40
u
31
−3.50×10
40
u
30
+· · ·+1.17×10
41
a−9.78×10
40
, u
32
−u
31
+· · ·−3u−1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−0.259443u
31
+ 0.297724u
30
+ ··· + 1.13377u + 0.832915
0.247008u
31
− 0.291495u
30
+ ··· + 1.96496u − 0.861759
a
2
=
−0.112993u
31
+ 0.228762u
30
+ ··· − 5.05835u + 0.652592
0.312631u
31
− 0.148818u
30
+ ··· + 5.80454u − 1.80697
a
1
=
0.199638u
31
+ 0.0799439u
30
+ ··· + 0.746197u − 1.15438
0.312631u
31
− 0.148818u
30
+ ··· + 5.80454u − 1.80697
a
10
=
0.590732u
31
− 0.437882u
30
+ ··· + 0.715423u + 0.744481
0.167742u
31
− 0.139050u
30
+ ··· − 0.349573u + 0.253437
a
6
=
0.259169u
31
− 0.175413u
30
+ ··· + 7.20063u − 1.66364
−0.849297u
31
+ 0.802593u
30
+ ··· − 7.27708u + 2.23530
a
12
=
−0.0855724u
31
+ 0.163355u
30
+ ··· − 4.01996u + 0.932174
0.188127u
31
− 0.0569394u
30
+ ··· + 4.91394u − 2.00877
a
8
=
0.0922224u
31
− 0.126322u
30
+ ··· + 2.23122u + 1.34756
0.218959u
31
− 0.322426u
30
+ ··· + 1.87298u − 0.737771
a
5
=
−0.793517u
31
+ 0.496709u
30
+ ··· − 4.79774u + 0.822991
0.200468u
31
− 0.213050u
30
+ ··· + 3.85227u − 0.945761
a
11
=
0.157447u
31
− 0.483979u
30
+ ··· + 2.42869u − 2.19665
−0.0246276u
31
+ 0.258033u
30
+ ··· − 4.45651u + 2.29913
(ii) Obstruction class = 1
(iii) Cusp Shapes = 14.3644u
31
− 17.9288u
30
+ ··· + 257.537u − 99.8147
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
− 17u
31
+ ··· − 12u + 1
c
2
u
32
+ u
31
+ ··· − 2u − 1
c
3
u
32
− u
31
+ ··· − 3u − 1
c
4
u
32
− 2u
31
+ ··· + 2u − 1
c
5
u
32
− 17u
30
+ ··· − 3u − 1
c
6
u
32
− u
31
+ ··· + 2u − 1
c
7
u
32
− 12u
31
+ ··· − 485u + 53
c
8
u
32
− 6u
31
+ ··· + 7u − 1
c
9
u
32
− u
31
+ ··· − 5u − 1
c
10
, c
11
u
32
− 17u
30
+ ··· + 3u − 1
c
12
u
32
− 4u
31
+ ··· − 3u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− y
31
+ ··· + 20y + 1
c
2
, c
6
y
32
− 17y
31
+ ··· − 12y + 1
c
3
y
32
+ 7y
31
+ ··· − 25y + 1
c
4
y
32
+ 2y
31
+ ··· + 2y + 1
c
5
, c
10
, c
11
y
32
− 34y
31
+ ··· − 27y + 1
c
7
y
32
+ 4y
31
+ ··· − 18985y + 2809
c
8
y
32
+ 10y
31
+ ··· − 27y + 1
c
9
y
32
+ 17y
31
+ ··· − 17y + 1
c
12
y
32
− 10y
31
+ ··· − y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.488763 + 0.879566I
a = 0.569405 − 1.230560I
b = 0.930711 + 0.077629I
−3.60212 − 0.35271I −11.44184 + 1.16616I
u = 0.488763 − 0.879566I
a = 0.569405 + 1.230560I
b = 0.930711 − 0.077629I
−3.60212 + 0.35271I −11.44184 − 1.16616I
u = 1.04094
a = −0.0819584
b = 1.29815
−2.52536 −34.5880
u = 1.026030 + 0.254901I
a = 1.315340 + 0.096241I
b = 0.625021 − 0.470991I
−5.29143 − 5.14954I −9.59656 + 2.58832I
u = 1.026030 − 0.254901I
a = 1.315340 − 0.096241I
b = 0.625021 + 0.470991I
−5.29143 + 5.14954I −9.59656 − 2.58832I
u = −0.339151 + 0.799174I
a = −0.96550 + 1.07724I
b = 0.574094 − 0.581329I
1.38532 + 3.77616I −4.24255 − 7.68180I
u = −0.339151 − 0.799174I
a = −0.96550 − 1.07724I
b = 0.574094 + 0.581329I
1.38532 − 3.77616I −4.24255 + 7.68180I
u = −1.140530 + 0.020355I
a = 0.316295 + 0.217050I
b = 1.053640 − 0.563098I
−6.79304 + 9.50096I −9.61208 − 8.36831I
u = −1.140530 − 0.020355I
a = 0.316295 − 0.217050I
b = 1.053640 + 0.563098I
−6.79304 − 9.50096I −9.61208 + 8.36831I
u = −0.648446 + 0.993169I
a = −1.27648 − 1.05847I
b = −0.720929 + 0.038410I
−7.43281 + 2.78981I −18.8572 − 2.8332I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.648446 − 0.993169I
a = −1.27648 + 1.05847I
b = −0.720929 − 0.038410I
−7.43281 − 2.78981I −18.8572 + 2.8332I
u = −0.427348 + 0.626009I
a = 1.14010 − 1.23422I
b = −0.720446 − 0.539462I
1.40962 + 1.58717I −0.33209 − 7.04805I
u = −0.427348 − 0.626009I
a = 1.14010 + 1.23422I
b = −0.720446 + 0.539462I
1.40962 − 1.58717I −0.33209 + 7.04805I
u = −0.490350 + 1.206540I
a = 0.330426 − 0.921161I
b = −1.127460 + 0.183458I
−9.23401 − 1.87161I −13.49061 − 0.90579I
u = −0.490350 − 1.206540I
a = 0.330426 + 0.921161I
b = −1.127460 − 0.183458I
−9.23401 + 1.87161I −13.49061 + 0.90579I
u = 0.594651 + 1.175790I
a = 0.021833 + 1.195750I
b = −0.428033 − 0.483703I
−1.63100 − 2.95883I −8.63603 + 2.17883I
u = 0.594651 − 1.175790I
a = 0.021833 − 1.195750I
b = −0.428033 + 0.483703I
−1.63100 + 2.95883I −8.63603 − 2.17883I
u = 0.512118 + 0.447145I
a = −1.88937 + 1.33666I
b = −0.998073 − 0.581544I
0.46470 − 6.10591I −6.74537 + 9.41874I
u = 0.512118 − 0.447145I
a = −1.88937 − 1.33666I
b = −0.998073 + 0.581544I
0.46470 + 6.10591I −6.74537 − 9.41874I
u = 0.592008 + 0.293624I
a = 0.61138 + 2.14540I
b = −0.500066 − 0.885993I
−4.42557 − 6.14911I −8.93876 + 4.34127I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.592008 − 0.293624I
a = 0.61138 − 2.14540I
b = −0.500066 + 0.885993I
−4.42557 + 6.14911I −8.93876 − 4.34127I
u = −0.762483 + 1.129630I
a = 0.617322 + 0.539443I
b = −0.700162 − 0.615373I
1.83552 + 2.12082I −6.99441 − 2.56747I
u = −0.762483 − 1.129630I
a = 0.617322 − 0.539443I
b = −0.700162 + 0.615373I
1.83552 − 2.12082I −6.99441 + 2.56747I
u = 0.99494 + 1.04188I
a = −0.41113 + 1.50304I
b = −0.995483 − 0.633001I
0.88609 − 7.07001I −7.06142 + 8.53212I
u = 0.99494 − 1.04188I
a = −0.41113 − 1.50304I
b = −0.995483 + 0.633001I
0.88609 + 7.07001I −7.06142 − 8.53212I
u = −0.117844 + 0.444849I
a = 1.17297 + 1.74658I
b = 1.099890 − 0.592087I
−0.007912 + 0.854010I −2.86933 + 5.57519I
u = −0.117844 − 0.444849I
a = 1.17297 − 1.74658I
b = 1.099890 + 0.592087I
−0.007912 − 0.854010I −2.86933 − 5.57519I
u = 1.06050 + 1.48292I
a = −0.366424 + 1.030470I
b = 0.680650 − 0.687783I
−0.71718 − 1.95774I 0
u = 1.06050 − 1.48292I
a = −0.366424 − 1.030470I
b = 0.680650 + 0.687783I
−0.71718 + 1.95774I 0
u = −0.174657
a = 0.677629
b = −1.84431
−10.0299 −181.300
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.27599 + 1.47429I
a = 0.01599 + 1.46880I
b = 0.999736 − 0.681086I
−1.69191 + 7.28094I 0
u = −1.27599 − 1.47429I
a = 0.01599 − 1.46880I
b = 0.999736 + 0.681086I
−1.69191 − 7.28094I 0
27
III. I
u
3
= hu
2
+ b + u, −u
2
+ a − u + 1, u
3
+ 2u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
u
2
+ u − 1
−u
2
− u
a
2
=
−u
2
− 2u + 1
u
a
1
=
−u
2
− u + 1
u
a
10
=
−u
2
− 3u − 2
u + 1
a
6
=
−u
2
− 2u − 2
1
a
12
=
−u
2
− 2u
u
2
+ 2u + 1
a
8
=
u
2
+ u − 1
−u
2
− u
a
5
=
−u
0
a
11
=
−2u − 1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
2
− 10u − 9
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− 2u
2
+ u − 1
c
2
, c
5
u
3
− u + 1
c
3
u
3
+ 2u
2
+ u + 1
c
4
u
3
+ 3u
2
+ 2u + 1
c
6
, c
10
, c
11
u
3
− u − 1
c
7
u
3
c
8
, c
12
u
3
+ u
2
− 1
c
9
u
3
+ u
2
+ 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
3
− 2y
2
− 3y −1
c
2
, c
5
, c
6
c
10
, c
11
y
3
− 2y
2
+ y −1
c
4
y
3
− 5y
2
− 2y −1
c
7
y
3
c
8
, c
12
y
3
− y
2
+ 2y −1
c
9
y
3
+ 3y
2
+ 2y −1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.122561 + 0.744862I
a = −1.66236 + 0.56228I
b = 0.662359 − 0.562280I
1.45094 + 3.77083I −6.15499 − 6.90087I
u = −0.122561 − 0.744862I
a = −1.66236 − 0.56228I
b = 0.662359 + 0.562280I
1.45094 − 3.77083I −6.15499 + 6.90087I
u = −1.75488
a = 0.324718
b = −1.32472
−6.19175 −0.690010
31
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
− 2u
2
+ u − 1)(u
32
− 17u
31
+ ··· − 12u + 1)
· (u
151
+ 66u
150
+ ··· + 185503u + 3481)
c
2
(u
3
− u + 1)(u
32
+ u
31
+ ··· − 2u − 1)(u
151
− 2u
150
+ ··· + 255u − 59)
c
3
(u
3
+ 2u
2
+ u + 1)(u
32
− u
31
+ ··· − 3u − 1)
· (u
151
− 2u
150
+ ··· + 2162u − 449)
c
4
(u
3
+ 3u
2
+ 2u + 1)(u
32
− 2u
31
+ ··· + 2u − 1)
· (u
151
− 6u
150
+ ··· − 5051302u − 765269)
c
5
(u
3
− u + 1)(u
32
− 17u
30
+ ··· − 3u − 1)(u
151
− u
150
+ ··· + 122u + 11)
c
6
(u
3
− u − 1)(u
32
− u
31
+ ··· + 2u − 1)(u
151
− 2u
150
+ ··· + 255u − 59)
c
7
u
3
(u
32
− 12u
31
+ ··· − 485u + 53)
· (u
151
+ 7u
150
+ ··· + 2354104u + 756296)
c
8
(u
3
+ u
2
− 1)(u
32
− 6u
31
+ ··· + 7u − 1)(u
151
+ 4u
150
+ ··· − 5327u + 391)
c
9
(u
3
+ u
2
+ 2u + 1)(u
32
− u
31
+ ··· − 5u − 1)(u
151
+ 3u
150
+ ··· − u + 1)
c
10
, c
11
(u
3
− u − 1)(u
32
− 17u
30
+ ··· + 3u − 1)(u
151
− u
150
+ ··· + 122u + 11)
c
12
(u
3
+ u
2
− 1)(u
32
− 4u
31
+ ··· − 3u + 1)(u
151
+ 14u
150
+ ··· + 45u + 1)
32
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 2y
2
− 3y −1)(y
32
− y
31
+ ··· + 20y + 1)
· (y
151
+ 42y
150
+ ··· − 823270257y −12117361)
c
2
, c
6
(y
3
− 2y
2
+ y −1)(y
32
− 17y
31
+ ··· − 12y + 1)
· (y
151
− 66y
150
+ ··· + 185503y −3481)
c
3
(y
3
− 2y
2
− 3y −1)(y
32
+ 7y
31
+ ··· − 25y + 1)
· (y
151
+ 22y
150
+ ··· + 18108324y −201601)
c
4
(y
3
− 5y
2
− 2y −1)(y
32
+ 2y
31
+ ··· + 2y + 1)
· (y
151
+ 42y
150
+ ··· − 16103090955074y −585636642361)
c
5
, c
10
, c
11
(y
3
− 2y
2
+ y −1)(y
32
− 34y
31
+ ··· − 27y + 1)
· (y
151
− 147y
150
+ ··· + 43638y −121)
c
7
y
3
(y
32
+ 4y
31
+ ··· − 18985y + 2809)
· (y
151
− 35y
150
+ ··· + 10638457160160y −571983639616)
c
8
(y
3
− y
2
+ 2y −1)(y
32
+ 10y
31
+ ··· − 27y + 1)
· (y
151
+ 6y
150
+ ··· − 424913y −152881)
c
9
(y
3
+ 3y
2
+ 2y −1)(y
32
+ 17y
31
+ ··· − 17y + 1)
· (y
151
+ 17y
150
+ ··· + 133y −1)
c
12
(y
3
− y
2
+ 2y −1)(y
32
− 10y
31
+ ··· − y + 1)
· (y
151
+ 6y
150
+ ··· + 293y −1)
33
