12a
0857
(K12a
0857
)
A knot diagram
1
Linearized knot diagam
4 5 9 12 10 11 3 1 7 6 2 8
Solving Sequence
5,10
6 11
3,7
8 2 12 4 1 9
c
5
c
10
c
6
c
7
c
2
c
11
c
4
c
1
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.74319 × 10
223
u
147
+ 7.21947 × 10
223
u
146
+ ··· + 6.94482 × 10
222
b − 1.64886 × 10
223
,
− 2.55680 × 10
223
u
147
+ 1.17756 × 10
224
u
146
+ ··· + 6.94482 × 10
222
a − 4.29985 × 10
224
,
u
148
− 4u
147
+ ··· + 28u + 1i
I
u
2
= h6u
28
+ 2u
27
+ ··· + b − 9, 2u
28
− 4u
27
+ ··· + a + 1, u
29
− u
28
+ ··· + 6u + 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
= h−2.74 × 10
223
u
147
+ 7.22 × 10
223
u
146
+ · · · + 6.94 × 10
222
b − 1.65 ×
10
223
, −2.56 × 10
223
u
147
+ 1.18 × 10
224
u
146
+ · · · + 6.94 × 10
222
a − 4.30 ×
10
224
, u
148
− 4u
147
+ · · · + 28u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
11
=
u
−u
3
+ u
a
3
=
3.68159u
147
− 16.9559u
146
+ ··· + 1057.19u + 61.9145
3.94998u
147
− 10.3955u
146
+ ··· + 26.0103u + 2.37422
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
−2.56776u
147
+ 11.4550u
146
+ ··· − 390.067u − 4.59737
−2.17368u
147
+ 6.02080u
146
+ ··· + 83.1920u + 4.76360
a
2
=
−0.268390u
147
− 6.56048u
146
+ ··· + 1031.18u + 59.5402
3.94998u
147
− 10.3955u
146
+ ··· + 26.0103u + 2.37422
a
12
=
−4.71414u
147
+ 19.5299u
146
+ ··· − 986.652u − 49.6532
1.96876u
147
− 4.77246u
146
+ ··· − 106.499u − 3.82153
a
4
=
3.53479u
147
− 17.1089u
146
+ ··· + 1054.78u + 62.0307
3.40108u
147
− 8.93411u
146
+ ··· + 33.4451u + 2.43885
a
1
=
−7.50495u
147
+ 18.0052u
146
+ ··· + 157.274u − 8.86158
−0.207768u
147
+ 1.08489u
146
+ ··· − 48.3846u − 3.44396
a
9
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 23.0139u
147
− 56.6855u
146
+ ··· − 967.950u − 41.0456
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
148
+ 14u
147
+ ··· + 31659u + 1009
c
2
u
148
− 3u
147
+ ··· − 22u − 1
c
3
u
148
− u
147
+ ··· − 58242827u + 11140141
c
4
u
148
+ 2u
147
+ ··· − 56u + 1
c
5
, c
6
, c
10
u
148
− 4u
147
+ ··· + 28u + 1
c
7
u
148
− u
147
+ ··· + 629u − 841
c
8
, c
12
u
148
− 2u
147
+ ··· − 174u + 599
c
9
u
148
+ 12u
147
+ ··· + 6333548u + 186337
c
11
u
148
+ 15u
147
+ ··· + 305347u + 14947
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
148
− 34y
147
+ ··· − 405878435y + 1018081
c
2
y
148
+ 7y
147
+ ··· − 18y + 1
c
3
y
148
+ 39y
147
+ ··· + 6412545735582301y + 124102741499881
c
4
y
148
− 2y
147
+ ··· − 70y + 1
c
5
, c
6
, c
10
y
148
− 130y
147
+ ··· − 174y + 1
c
7
y
148
+ 19y
147
+ ··· + 90033725y + 707281
c
8
, c
12
y
148
− 88y
147
+ ··· − 13930670y + 358801
c
9
y
148
+ 42y
147
+ ··· − 6491280746914y + 34721477569
c
11
y
148
+ 21y
147
+ ··· + 9784629847y + 223412809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.834262 + 0.559566I
a = −0.128303 + 0.506511I
b = −0.586616 + 0.645748I
−2.88757 − 9.19665I 0
u = −0.834262 − 0.559566I
a = −0.128303 − 0.506511I
b = −0.586616 − 0.645748I
−2.88757 + 9.19665I 0
u = −0.882501 + 0.485594I
a = 0.559978 + 0.598860I
b = 0.022373 + 0.954432I
−5.23857 + 1.54918I 0
u = −0.882501 − 0.485594I
a = 0.559978 − 0.598860I
b = 0.022373 − 0.954432I
−5.23857 − 1.54918I 0
u = −0.383892 + 0.898713I
a = −0.511607 − 0.101872I
b = −0.265657 − 0.369759I
−4.40189 + 4.11846I 0
u = −0.383892 − 0.898713I
a = −0.511607 + 0.101872I
b = −0.265657 + 0.369759I
−4.40189 − 4.11846I 0
u = −0.954716 + 0.426398I
a = −0.328955 − 0.422546I
b = −0.507598 − 0.928450I
−5.61580 − 0.33311I 0
u = −0.954716 − 0.426398I
a = −0.328955 + 0.422546I
b = −0.507598 + 0.928450I
−5.61580 + 0.33311I 0
u = 0.828082 + 0.672181I
a = 0.010750 − 0.276583I
b = −0.378265 − 0.336048I
0.75076 + 2.87734I 0
u = 0.828082 − 0.672181I
a = 0.010750 + 0.276583I
b = −0.378265 + 0.336048I
0.75076 − 2.87734I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.970690 + 0.468186I
a = −0.687675 + 0.123557I
b = −0.877346 + 0.884763I
−0.01311 − 4.67709I 0
u = 0.970690 − 0.468186I
a = −0.687675 − 0.123557I
b = −0.877346 − 0.884763I
−0.01311 + 4.67709I 0
u = −0.975454 + 0.461950I
a = −0.919640 − 0.243256I
b = −0.96455 − 1.05862I
−3.57878 + 10.72080I 0
u = −0.975454 − 0.461950I
a = −0.919640 + 0.243256I
b = −0.96455 + 1.05862I
−3.57878 − 10.72080I 0
u = 1.096920 + 0.224678I
a = 1.077810 − 0.355503I
b = 0.487913 − 0.925485I
1.338960 + 0.244377I 0
u = 1.096920 − 0.224678I
a = 1.077810 + 0.355503I
b = 0.487913 + 0.925485I
1.338960 − 0.244377I 0
u = −0.256354 + 0.830185I
a = −0.25310 − 1.53553I
b = 0.283713 − 1.092650I
−7.23092 − 6.20380I 0
u = −0.256354 − 0.830185I
a = −0.25310 + 1.53553I
b = 0.283713 + 1.092650I
−7.23092 + 6.20380I 0
u = 0.136768 + 0.855356I
a = 0.706378 + 0.974069I
b = 0.679992 + 0.579479I
−2.15264 + 2.82025I 0
u = 0.136768 − 0.855356I
a = 0.706378 − 0.974069I
b = 0.679992 − 0.579479I
−2.15264 − 2.82025I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.217599 + 0.836206I
a = −0.58507 + 2.16088I
b = −1.14142 + 1.16900I
−5.9224 − 15.3515I 0
u = −0.217599 − 0.836206I
a = −0.58507 − 2.16088I
b = −1.14142 − 1.16900I
−5.9224 + 15.3515I 0
u = 0.220795 + 0.835141I
a = −0.51746 − 1.84375I
b = −1.08269 − 0.98315I
−2.33041 + 9.31709I 0
u = 0.220795 − 0.835141I
a = −0.51746 + 1.84375I
b = −1.08269 + 0.98315I
−2.33041 − 9.31709I 0
u = −0.216907 + 0.813285I
a = 0.03803 + 1.71462I
b = −0.738737 + 0.926240I
−7.91109 − 4.12621I 0
u = −0.216907 − 0.813285I
a = 0.03803 − 1.71462I
b = −0.738737 − 0.926240I
−7.91109 + 4.12621I 0
u = −1.137920 + 0.250741I
a = 1.21331 + 0.81749I
b = 0.713114 + 1.184890I
0.67957 + 2.16426I 0
u = −1.137920 − 0.250741I
a = 1.21331 − 0.81749I
b = 0.713114 − 1.184890I
0.67957 − 2.16426I 0
u = 0.036176 + 0.778768I
a = 0.946637 − 0.595588I
b = −0.038242 − 0.325947I
−5.69981 + 0.05221I 0
u = 0.036176 − 0.778768I
a = 0.946637 + 0.595588I
b = −0.038242 + 0.325947I
−5.69981 − 0.05221I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.156039 + 0.750413I
a = 0.97031 + 2.26841I
b = 1.01555 + 1.09135I
−1.39682 + 3.46757I 0
u = 0.156039 − 0.750413I
a = 0.97031 − 2.26841I
b = 1.01555 − 1.09135I
−1.39682 − 3.46757I 0
u = −1.232570 + 0.149590I
a = −1.34678 − 1.81963I
b = 0.0079557 + 0.0820720I
−0.65134 + 4.12392I 0
u = −1.232570 − 0.149590I
a = −1.34678 + 1.81963I
b = 0.0079557 − 0.0820720I
−0.65134 − 4.12392I 0
u = −0.130626 + 0.744400I
a = 0.71695 − 2.90993I
b = 0.98660 − 1.31247I
−2.29627 − 5.85849I 0
u = −0.130626 − 0.744400I
a = 0.71695 + 2.90993I
b = 0.98660 + 1.31247I
−2.29627 + 5.85849I 0
u = −0.051336 + 0.751416I
a = −1.62420 − 0.69229I
b = −1.46175 − 0.46950I
−5.98505 + 1.73587I 0
u = −0.051336 − 0.751416I
a = −1.62420 + 0.69229I
b = −1.46175 + 0.46950I
−5.98505 − 1.73587I 0
u = 1.207640 + 0.318226I
a = 0.531479 + 0.572839I
b = 0.043236 + 0.652308I
−2.10884 + 3.92903I 0
u = 1.207640 − 0.318226I
a = 0.531479 − 0.572839I
b = 0.043236 − 0.652308I
−2.10884 − 3.92903I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.216070 + 0.284676I
a = 0.22126 + 1.44672I
b = −1.57369 + 0.15677I
−2.44194 − 5.49792I 0
u = −1.216070 − 0.284676I
a = 0.22126 − 1.44672I
b = −1.57369 − 0.15677I
−2.44194 + 5.49792I 0
u = −1.239860 + 0.173187I
a = 0.773397 + 0.424869I
b = 0.68782 + 1.51185I
2.37892 + 0.78548I 0
u = −1.239860 − 0.173187I
a = 0.773397 − 0.424869I
b = 0.68782 − 1.51185I
2.37892 − 0.78548I 0
u = −1.239060 + 0.251944I
a = 1.43877 + 1.68322I
b = −1.48406 + 1.39599I
−2.54709 + 2.50318I 0
u = −1.239060 − 0.251944I
a = 1.43877 − 1.68322I
b = −1.48406 − 1.39599I
−2.54709 − 2.50318I 0
u = 1.262400 + 0.107738I
a = 1.082500 − 0.540636I
b = 0.11874 − 1.85691I
0.27094 − 4.21563I 0
u = 1.262400 − 0.107738I
a = 1.082500 + 0.540636I
b = 0.11874 + 1.85691I
0.27094 + 4.21563I 0
u = 1.249400 + 0.260612I
a = 1.06393 − 1.13172I
b = −0.997724 − 0.835587I
0.53631 + 1.68964I 0
u = 1.249400 − 0.260612I
a = 1.06393 + 1.13172I
b = −0.997724 + 0.835587I
0.53631 − 1.68964I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.249760 + 0.271941I
a = 0.35669 − 1.37962I
b = 0.428838 − 1.124020I
−2.77756 − 1.61149I 0
u = 1.249760 − 0.271941I
a = 0.35669 + 1.37962I
b = 0.428838 + 1.124020I
−2.77756 + 1.61149I 0
u = 0.243349 + 0.675764I
a = 0.30508 + 2.50199I
b = 0.96287 + 1.40677I
−2.06249 + 6.40773I 0. − 10.21181I
u = 0.243349 − 0.675764I
a = 0.30508 − 2.50199I
b = 0.96287 − 1.40677I
−2.06249 − 6.40773I 0. + 10.21181I
u = 0.027955 + 0.700281I
a = −0.57906 + 2.74231I
b = 0.476324 + 0.957322I
−6.53858 + 5.12910I −6.02888 − 5.78970I
u = 0.027955 − 0.700281I
a = −0.57906 − 2.74231I
b = 0.476324 − 0.957322I
−6.53858 − 5.12910I −6.02888 + 5.78970I
u = 0.582340 + 0.379724I
a = 1.48013 − 0.01204I
b = 0.773397 − 0.967716I
−0.74585 − 2.86716I 1.86167 + 3.66817I
u = 0.582340 − 0.379724I
a = 1.48013 + 0.01204I
b = 0.773397 + 0.967716I
−0.74585 + 2.86716I 1.86167 − 3.66817I
u = 0.029223 + 0.693114I
a = −0.53721 + 2.04383I
b = −0.722494 + 1.160630I
−3.20932 + 1.76134I −1.48052 − 3.33045I
u = 0.029223 − 0.693114I
a = −0.53721 − 2.04383I
b = −0.722494 − 1.160630I
−3.20932 − 1.76134I −1.48052 + 3.33045I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.288380 + 0.220568I
a = −0.310760 + 0.060146I
b = 1.190800 + 0.741134I
2.97962 − 0.43793I 0
u = −1.288380 − 0.220568I
a = −0.310760 − 0.060146I
b = 1.190800 − 0.741134I
2.97962 + 0.43793I 0
u = −0.055555 + 0.688167I
a = −1.47974 − 2.87222I
b = −1.20801 − 1.72162I
−6.15959 − 5.89642I −6.69542 + 6.80189I
u = −0.055555 − 0.688167I
a = −1.47974 + 2.87222I
b = −1.20801 + 1.72162I
−6.15959 + 5.89642I −6.69542 − 6.80189I
u = 1.302150 + 0.156856I
a = −0.45371 + 1.69318I
b = 0.510488 + 0.190093I
4.35576 + 0.14805I 0
u = 1.302150 − 0.156856I
a = −0.45371 − 1.69318I
b = 0.510488 − 0.190093I
4.35576 − 0.14805I 0
u = −1.273880 + 0.332660I
a = 0.936615 + 0.092078I
b = −0.1058670 + 0.0205234I
−1.63408 − 4.06332I 0
u = −1.273880 − 0.332660I
a = 0.936615 − 0.092078I
b = −0.1058670 − 0.0205234I
−1.63408 + 4.06332I 0
u = −1.289870 + 0.273878I
a = −0.767033 − 0.366375I
b = −0.55499 − 1.49583I
0.89907 − 5.25630I 0
u = −1.289870 − 0.273878I
a = −0.767033 + 0.366375I
b = −0.55499 + 1.49583I
0.89907 + 5.25630I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.389085 + 0.558326I
a = 0.618664 − 0.432662I
b = −0.570599 − 0.187701I
1.00696 + 1.85359I 7.26628 + 4.55232I
u = 0.389085 − 0.558326I
a = 0.618664 + 0.432662I
b = −0.570599 + 0.187701I
1.00696 − 1.85359I 7.26628 − 4.55232I
u = −1.302760 + 0.212861I
a = −0.29581 − 1.44270I
b = 0.555211 − 0.959453I
3.01507 − 4.85601I 0
u = −1.302760 − 0.212861I
a = −0.29581 + 1.44270I
b = 0.555211 + 0.959453I
3.01507 + 4.85601I 0
u = −0.176595 + 0.656507I
a = −0.33129 + 2.39777I
b = −0.391799 + 0.271433I
−3.54982 − 6.83567I 2.98828 + 11.18078I
u = −0.176595 − 0.656507I
a = −0.33129 − 2.39777I
b = −0.391799 − 0.271433I
−3.54982 + 6.83567I 2.98828 − 11.18078I
u = −1.290940 + 0.278705I
a = −1.95472 − 1.34403I
b = 0.565532 − 0.785691I
−2.42703 − 8.66471I 0
u = −1.290940 − 0.278705I
a = −1.95472 + 1.34403I
b = 0.565532 + 0.785691I
−2.42703 + 8.66471I 0
u = 1.290760 + 0.320068I
a = −0.428671 − 0.651956I
b = −1.37338 + 0.70873I
−1.80272 + 2.14012I 0
u = 1.290760 − 0.320068I
a = −0.428671 + 0.651956I
b = −1.37338 − 0.70873I
−1.80272 − 2.14012I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.311750 + 0.241225I
a = −1.24924 + 0.67822I
b = 1.231930 + 0.218310I
3.31278 + 5.59201I 0
u = 1.311750 − 0.241225I
a = −1.24924 − 0.67822I
b = 1.231930 − 0.218310I
3.31278 − 5.59201I 0
u = 1.307720 + 0.278543I
a = −1.380210 + 0.080713I
b = −1.06974 + 2.04051I
−1.88613 + 9.39814I 0
u = 1.307720 − 0.278543I
a = −1.380210 − 0.080713I
b = −1.06974 − 2.04051I
−1.88613 − 9.39814I 0
u = −0.150051 + 0.630587I
a = 0.46734 − 2.41428I
b = 1.10321 − 1.17284I
−0.81876 − 3.53807I 4.00000 + 1.54021I
u = −0.150051 − 0.630587I
a = 0.46734 + 2.41428I
b = 1.10321 + 1.17284I
−0.81876 + 3.53807I 4.00000 − 1.54021I
u = 1.283320 + 0.450508I
a = 0.288235 + 0.459970I
b = 0.607895 − 0.095074I
1.26288 + 1.99839I 0
u = 1.283320 − 0.450508I
a = 0.288235 − 0.459970I
b = 0.607895 + 0.095074I
1.26288 − 1.99839I 0
u = 1.363690 + 0.013125I
a = −0.868984 + 0.413583I
b = 1.29272 − 0.70915I
6.29495 − 3.07582I 0
u = 1.363690 − 0.013125I
a = −0.868984 − 0.413583I
b = 1.29272 + 0.70915I
6.29495 + 3.07582I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36457
a = 0.800300
b = −0.265614
2.39925 0
u = 0.290323 + 0.556988I
a = 0.385505 − 1.133770I
b = −0.323122 − 0.055224I
0.85288 + 1.53171I 8.92387 − 4.22600I
u = 0.290323 − 0.556988I
a = 0.385505 + 1.133770I
b = −0.323122 + 0.055224I
0.85288 − 1.53171I 8.92387 + 4.22600I
u = 1.344750 + 0.313792I
a = −1.14992 + 1.85647I
b = 1.16266 + 1.37871I
2.35286 + 9.69335I 0
u = 1.344750 − 0.313792I
a = −1.14992 − 1.85647I
b = 1.16266 − 1.37871I
2.35286 − 9.69335I 0
u = 1.356540 + 0.264667I
a = −1.17529 + 1.30491I
b = 1.41228 + 1.12611I
3.96376 + 6.83580I 0
u = 1.356540 − 0.264667I
a = −1.17529 − 1.30491I
b = 1.41228 − 1.12611I
3.96376 − 6.83580I 0
u = 0.616271 + 0.023761I
a = 0.710288 + 0.110865I
b = 0.698856 + 0.247047I
1.342650 + 0.121848I 8.91227 + 0.84671I
u = 0.616271 − 0.023761I
a = 0.710288 − 0.110865I
b = 0.698856 − 0.247047I
1.342650 − 0.121848I 8.91227 − 0.84671I
u = 1.363230 + 0.273936I
a = 0.52798 − 1.81310I
b = −0.437436 − 0.467247I
1.32504 + 10.25150I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.363230 − 0.273936I
a = 0.52798 + 1.81310I
b = −0.437436 + 0.467247I
1.32504 − 10.25150I 0
u = 1.388500 + 0.091456I
a = 1.130930 + 0.524621I
b = −0.840469 + 0.361059I
3.75546 − 2.79339I 0
u = 1.388500 − 0.091456I
a = 1.130930 − 0.524621I
b = −0.840469 − 0.361059I
3.75546 + 2.79339I 0
u = −0.035107 + 0.606267I
a = 0.184481 − 1.177490I
b = 1.147090 − 0.469602I
−0.94271 − 2.50791I 2.58911 + 4.37316I
u = −0.035107 − 0.606267I
a = 0.184481 + 1.177490I
b = 1.147090 + 0.469602I
−0.94271 + 2.50791I 2.58911 − 4.37316I
u = −1.357790 + 0.316689I
a = −0.71987 − 1.64454I
b = 1.28709 − 1.16065I
3.38172 − 7.33745I 0
u = −1.357790 − 0.316689I
a = −0.71987 + 1.64454I
b = 1.28709 + 1.16065I
3.38172 + 7.33745I 0
u = −1.404980 + 0.007560I
a = −0.537581 − 0.104324I
b = 1.378350 + 0.153884I
7.52979 + 0.05295I 0
u = −1.404980 − 0.007560I
a = −0.537581 + 0.104324I
b = 1.378350 − 0.153884I
7.52979 − 0.05295I 0
u = 1.402850 + 0.118826I
a = −0.069187 + 0.972484I
b = 1.212330 − 0.312016I
5.92030 + 0.62489I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.402850 − 0.118826I
a = −0.069187 − 0.972484I
b = 1.212330 + 0.312016I
5.92030 − 0.62489I 0
u = −1.366460 + 0.353854I
a = −0.362726 − 1.063870I
b = 0.933679 − 0.734714I
2.61058 − 7.13864I 0
u = −1.366460 − 0.353854I
a = −0.362726 + 1.063870I
b = 0.933679 + 0.734714I
2.61058 + 7.13864I 0
u = −1.39286 + 0.24973I
a = 0.642759 + 1.045830I
b = −0.481530 + 0.328023I
6.15709 − 4.60004I 0
u = −1.39286 − 0.24973I
a = 0.642759 − 1.045830I
b = −0.481530 − 0.328023I
6.15709 + 4.60004I 0
u = −1.38851 + 0.28023I
a = −1.10646 − 1.27908I
b = 1.25713 − 1.46380I
3.10758 − 9.91331I 0
u = −1.38851 − 0.28023I
a = −1.10646 + 1.27908I
b = 1.25713 + 1.46380I
3.10758 + 9.91331I 0
u = 0.046660 + 0.575990I
a = 1.39715 + 1.77350I
b = 0.420585 + 0.622670I
−1.18014 + 2.00255I 1.00660 − 4.20684I
u = 0.046660 − 0.575990I
a = 1.39715 − 1.77350I
b = 0.420585 − 0.622670I
−1.18014 − 2.00255I 1.00660 + 4.20684I
u = 1.39416 + 0.33770I
a = 1.03319 − 1.11254I
b = −0.878878 − 0.875477I
−2.80416 + 8.28099I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39416 − 0.33770I
a = 1.03319 + 1.11254I
b = −0.878878 + 0.875477I
−2.80416 − 8.28099I 0
u = 1.39805 + 0.34971I
a = 0.95239 − 1.52282I
b = −1.27989 − 1.18958I
−0.8021 + 19.6275I 0
u = 1.39805 − 0.34971I
a = 0.95239 + 1.52282I
b = −1.27989 + 1.18958I
−0.8021 − 19.6275I 0
u = −1.39897 + 0.34824I
a = 0.86866 + 1.37304I
b = −1.23276 + 0.98635I
2.80389 − 13.58350I 0
u = −1.39897 − 0.34824I
a = 0.86866 − 1.37304I
b = −1.23276 − 0.98635I
2.80389 + 13.58350I 0
u = −1.43806 + 0.21229I
a = 1.161160 + 0.419970I
b = −0.715032 + 0.140045I
6.86268 − 4.69797I 0
u = −1.43806 − 0.21229I
a = 1.161160 − 0.419970I
b = −0.715032 − 0.140045I
6.86268 + 4.69797I 0
u = 1.41553 + 0.34438I
a = −0.832851 + 0.755766I
b = 0.476708 + 1.126080I
−1.92037 + 10.45010I 0
u = 1.41553 − 0.34438I
a = −0.832851 − 0.755766I
b = 0.476708 − 1.126080I
−1.92037 − 10.45010I 0
u = −1.45751 + 0.09812I
a = 0.217631 − 0.561349I
b = 1.085990 + 0.646353I
5.76160 + 1.26695I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45751 − 0.09812I
a = 0.217631 + 0.561349I
b = 1.085990 − 0.646353I
5.76160 − 1.26695I 0
u = −0.478476 + 0.243406I
a = 0.716233 − 1.176960I
b = −0.811165 − 0.122210I
−1.98595 + 3.98277I 5.42042 − 3.64011I
u = −0.478476 − 0.243406I
a = 0.716233 + 1.176960I
b = −0.811165 + 0.122210I
−1.98595 − 3.98277I 5.42042 + 3.64011I
u = 1.46499 + 0.13521I
a = 0.446762 − 0.240495I
b = −0.303105 − 0.313629I
2.56788 − 0.11111I 0
u = 1.46499 − 0.13521I
a = 0.446762 + 0.240495I
b = −0.303105 + 0.313629I
2.56788 + 0.11111I 0
u = −0.360825 + 0.371965I
a = 1.62925 − 0.96032I
b = 0.863807 + 0.552007I
0.290683 + 1.135740I 2.76448 + 3.83447I
u = −0.360825 − 0.371965I
a = 1.62925 + 0.96032I
b = 0.863807 − 0.552007I
0.290683 − 1.135740I 2.76448 − 3.83447I
u = −1.48422 + 0.05865I
a = 0.589184 − 0.135279I
b = −0.983656 + 0.330263I
8.46365 − 4.65317I 0
u = −1.48422 − 0.05865I
a = 0.589184 + 0.135279I
b = −0.983656 − 0.330263I
8.46365 + 4.65317I 0
u = 1.48915 + 0.05284I
a = 0.490479 + 0.154722I
b = −1.091250 − 0.558767I
4.85284 + 10.67920I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48915 − 0.05284I
a = 0.490479 − 0.154722I
b = −1.091250 + 0.558767I
4.85284 − 10.67920I 0
u = −0.446482 + 0.100884I
a = −0.003936 − 0.525214I
b = 0.898860 − 0.773223I
0.77460 − 3.01645I 6.81557 + 9.13013I
u = −0.446482 − 0.100884I
a = −0.003936 + 0.525214I
b = 0.898860 + 0.773223I
0.77460 + 3.01645I 6.81557 − 9.13013I
u = 1.62688
a = 0.125898
b = 0.0922858
2.90310 0
u = −0.123097 + 0.228309I
a = 1.96706 − 2.45283I
b = 0.333029 + 0.484612I
0.14087 + 1.58090I 1.55742 − 1.87730I
u = −0.123097 − 0.228309I
a = 1.96706 + 2.45283I
b = 0.333029 − 0.484612I
0.14087 − 1.58090I 1.55742 + 1.87730I
u = −0.0822211 + 0.0320855I
a = 4.67861 + 12.51900I
b = −0.254461 + 1.080010I
−3.58644 + 4.97395I 1.74208 − 5.62080I
u = −0.0822211 − 0.0320855I
a = 4.67861 − 12.51900I
b = −0.254461 − 1.080010I
−3.58644 − 4.97395I 1.74208 + 5.62080I
19
II.
I
u
2
= h6u
28
+2u
27
+· · ·+b−9, 2u
28
−4u
27
+· · ·+a+1, u
29
−u
28
+· · ·+6u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
11
=
u
−u
3
+ u
a
3
=
−2u
28
+ 4u
27
+ ··· − 9u − 1
−6u
28
− 2u
27
+ ··· + 49u + 9
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
12u
28
+ u
27
+ ··· − 46u − 7
5u
28
+ 3u
27
+ ··· − 30u − 6
a
2
=
4u
28
+ 6u
27
+ ··· − 58u − 10
−6u
28
− 2u
27
+ ··· + 49u + 9
a
12
=
2u
28
+ 2u
27
+ ··· − 24u − 2
6u
28
− u
27
+ ··· − 13u − 1
a
4
=
−u
28
+ 4u
27
+ ··· − 21u − 3
−4u
28
− 2u
27
+ ··· + 39u + 8
a
1
=
−12u
28
− u
27
+ ··· + 45u + 8
3u
28
− 2u
27
+ ··· + 9u + 3
a
9
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 12u
28
+ u
27
− 177u
26
− 41u
25
+ 1135u
24
+ 425u
23
− 4100u
22
− 2107u
21
+ 8955u
20
+
5855u
19
−11549u
18
−9250u
17
+7327u
16
+7056u
15
−241u
14
+86u
13
−1061u
12
−3222u
11
−
1735u
10
−141u
9
+ 1038u
8
+ 1862u
7
+ 1034u
6
−41u
5
−301u
4
−365u
3
−358u
2
−160u −20
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
− 15u
28
+ ··· + 15u − 1
c
2
u
29
+ 14u
28
+ ··· + 14u + 1
c
3
u
29
− 2u
27
+ ··· + 3u + 1
c
4
u
29
− u
28
+ ··· − 2u − 1
c
5
, c
6
u
29
− u
28
+ ··· + 6u + 1
c
7
u
29
+ 6u
27
+ ··· − 3u + 1
c
8
u
29
+ u
28
+ ··· − 2u + 1
c
9
u
29
− 3u
28
+ ··· − 10u + 1
c
10
u
29
+ u
28
+ ··· + 6u − 1
c
11
u
29
+ 2u
28
+ ··· + u − 1
c
12
u
29
− u
28
+ ··· − 2u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 7y
28
+ ··· − 5y −1
c
2
y
29
+ 8y
28
+ ··· + 6y −1
c
3
y
29
− 4y
28
+ ··· − 21y −1
c
4
y
29
− 5y
28
+ ··· + 2y −1
c
5
, c
6
, c
10
y
29
− 29y
28
+ ··· + 10y −1
c
7
y
29
+ 12y
28
+ ··· + 7y −1
c
8
, c
12
y
29
− 15y
28
+ ··· + 22y −1
c
9
y
29
− 5y
28
+ ··· + 10y −1
c
11
y
29
− 2y
28
+ ··· + 5y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.999979 + 0.420202I
a = −0.0487508 + 0.1242170I
b = 0.122896 − 0.425132I
0.90884 − 2.54017I 9.49679 + 4.29966I
u = −0.999979 − 0.420202I
a = −0.0487508 − 0.1242170I
b = 0.122896 + 0.425132I
0.90884 + 2.54017I 9.49679 − 4.29966I
u = −1.172400 + 0.230229I
a = 1.221070 + 0.420178I
b = 0.72438 + 1.39938I
1.30589 + 0.94412I 3.28599 − 1.78629I
u = −1.172400 − 0.230229I
a = 1.221070 − 0.420178I
b = 0.72438 − 1.39938I
1.30589 − 0.94412I 3.28599 + 1.78629I
u = 1.203770 + 0.228092I
a = 0.161500 − 0.999679I
b = −0.650867 + 0.762859I
−1.57852 + 6.79983I 3.32887 − 7.87594I
u = 1.203770 − 0.228092I
a = 0.161500 + 0.999679I
b = −0.650867 − 0.762859I
−1.57852 − 6.79983I 3.32887 + 7.87594I
u = 0.300792 + 0.701944I
a = −0.272613 − 0.212397I
b = −0.239857 − 0.472850I
−4.35092 − 3.59283I −0.677700 − 0.091139I
u = 0.300792 − 0.701944I
a = −0.272613 + 0.212397I
b = −0.239857 + 0.472850I
−4.35092 + 3.59283I −0.677700 + 0.091139I
u = 1.229560 + 0.204644I
a = 1.42332 − 1.72996I
b = −0.287250 − 1.327080I
−1.38475 − 3.11979I 2.12057 + 3.22013I
u = 1.229560 − 0.204644I
a = 1.42332 + 1.72996I
b = −0.287250 + 1.327080I
−1.38475 + 3.11979I 2.12057 − 3.22013I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.137523 + 0.716923I
a = 0.89763 − 2.72112I
b = 1.12906 − 1.36742I
−1.71916 − 4.40492I −0.59085 + 7.06882I
u = −0.137523 − 0.716923I
a = 0.89763 + 2.72112I
b = 1.12906 + 1.36742I
−1.71916 + 4.40492I −0.59085 − 7.06882I
u = −1.315220 + 0.042141I
a = −0.686067 + 0.858758I
b = 0.876355 + 0.470562I
4.00864 + 1.86297I 9.44509 − 1.83583I
u = −1.315220 − 0.042141I
a = −0.686067 − 0.858758I
b = 0.876355 − 0.470562I
4.00864 − 1.86297I 9.44509 + 1.83583I
u = 0.149040 + 0.644191I
a = −0.89789 + 2.87024I
b = 0.033509 + 1.176040I
−4.63114 + 6.08208I −2.19730 − 7.44698I
u = 0.149040 − 0.644191I
a = −0.89789 − 2.87024I
b = 0.033509 − 1.176040I
−4.63114 − 6.08208I −2.19730 + 7.44698I
u = 1.351680 + 0.301762I
a = −1.03814 + 1.67297I
b = 1.38886 + 1.38779I
2.98847 + 8.11025I 4.16972 − 8.54040I
u = 1.351680 − 0.301762I
a = −1.03814 − 1.67297I
b = 1.38886 − 1.38779I
2.98847 − 8.11025I 4.16972 + 8.54040I
u = −1.362600 + 0.278570I
a = −1.23622 − 1.13259I
b = 0.319166 − 1.192320I
0.18783 − 9.48898I 3.31208 + 8.12840I
u = −1.362600 − 0.278570I
a = −1.23622 + 1.13259I
b = 0.319166 + 1.192320I
0.18783 + 9.48898I 3.31208 − 8.12840I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.477355 + 0.364026I
a = −0.813650 + 0.175375I
b = 0.532989 − 0.404192I
0.81757 − 2.34791I 4.57851 + 8.02025I
u = −0.477355 − 0.364026I
a = −0.813650 − 0.175375I
b = 0.532989 + 0.404192I
0.81757 + 2.34791I 4.57851 − 8.02025I
u = 1.410240 + 0.086564I
a = 0.013047 + 0.669318I
b = 1.283430 − 0.564993I
6.08966 − 0.80590I 11.35130 − 0.76639I
u = 1.410240 − 0.086564I
a = 0.013047 − 0.669318I
b = 1.283430 + 0.564993I
6.08966 + 0.80590I 11.35130 + 0.76639I
u = 1.44030 + 0.20052I
a = −1.208130 + 0.321784I
b = 0.708795 + 0.177396I
6.83348 + 4.83072I 0.8987 − 31.8055I
u = 1.44030 − 0.20052I
a = −1.208130 − 0.321784I
b = 0.708795 − 0.177396I
6.83348 − 4.83072I 0.8987 + 31.8055I
u = −1.65449
a = −0.0205555
b = 0.245784
2.97055 74.7410
u = −0.293059 + 0.174102I
a = 1.99518 − 1.27971I
b = 0.935656 + 0.689805I
0.55338 + 1.99406I 7.60801 − 2.72974I
u = −0.293059 − 0.174102I
a = 1.99518 + 1.27971I
b = 0.935656 − 0.689805I
0.55338 − 1.99406I 7.60801 + 2.72974I
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
29
− 15u
28
+ ··· + 15u − 1)(u
148
+ 14u
147
+ ··· + 31659u + 1009)
c
2
(u
29
+ 14u
28
+ ··· + 14u + 1)(u
148
− 3u
147
+ ··· − 22u − 1)
c
3
(u
29
− 2u
27
+ ··· + 3u + 1)
· (u
148
− u
147
+ ··· − 58242827u + 11140141)
c
4
(u
29
− u
28
+ ··· − 2u − 1)(u
148
+ 2u
147
+ ··· − 56u + 1)
c
5
, c
6
(u
29
− u
28
+ ··· + 6u + 1)(u
148
− 4u
147
+ ··· + 28u + 1)
c
7
(u
29
+ 6u
27
+ ··· − 3u + 1)(u
148
− u
147
+ ··· + 629u − 841)
c
8
(u
29
+ u
28
+ ··· − 2u + 1)(u
148
− 2u
147
+ ··· − 174u + 599)
c
9
(u
29
− 3u
28
+ ··· − 10u + 1)
· (u
148
+ 12u
147
+ ··· + 6333548u + 186337)
c
10
(u
29
+ u
28
+ ··· + 6u − 1)(u
148
− 4u
147
+ ··· + 28u + 1)
c
11
(u
29
+ 2u
28
+ ··· + u − 1)(u
148
+ 15u
147
+ ··· + 305347u + 14947)
c
12
(u
29
− u
28
+ ··· − 2u − 1)(u
148
− 2u
147
+ ··· − 174u + 599)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
29
+ 7y
28
+ ··· − 5y −1)
· (y
148
− 34y
147
+ ··· − 405878435y + 1018081)
c
2
(y
29
+ 8y
28
+ ··· + 6y −1)(y
148
+ 7y
147
+ ··· − 18y + 1)
c
3
(y
29
− 4y
28
+ ··· − 21y −1)
· (y
148
+ 39y
147
+ ··· + 6412545735582301y + 124102741499881)
c
4
(y
29
− 5y
28
+ ··· + 2y −1)(y
148
− 2y
147
+ ··· − 70y + 1)
c
5
, c
6
, c
10
(y
29
− 29y
28
+ ··· + 10y −1)(y
148
− 130y
147
+ ··· − 174y + 1)
c
7
(y
29
+ 12y
28
+ ··· + 7y −1)
· (y
148
+ 19y
147
+ ··· + 90033725y + 707281)
c
8
, c
12
(y
29
− 15y
28
+ ··· + 22y −1)
· (y
148
− 88y
147
+ ··· − 13930670y + 358801)
c
9
(y
29
− 5y
28
+ ··· + 10y −1)
· (y
148
+ 42y
147
+ ··· − 6491280746914y + 34721477569)
c
11
(y
29
− 2y
28
+ ··· + 5y −1)
· (y
148
+ 21y
147
+ ··· + 9784629847y + 223412809)
27
