12a
0185
(K12a
0185
)
A knot diagram
1
Linearized knot diagam
3 5 9 7 2 10 12 11 6 4 1 8
Solving Sequence
6,10 2,7
5 3 1 4 11 12 9 8
c
6
c
5
c
2
c
1
c
4
c
10
c
11
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.98914 × 10
445
u
128
− 1.30336 × 10
446
u
127
+ ··· + 2.09279 × 10
445
b + 7.62318 × 10
445
,
5.11649 × 10
446
u
128
− 1.01386 × 10
447
u
127
+ ··· + 1.04639 × 10
446
a + 3.19751 × 10
446
, u
129
− 3u
128
+ ··· + 6u − 1i
I
u
2
= h2u
2
a − au + 2u
2
+ b + 2a − u + 2, 15u
2
a + 25a
2
− 5au + 13u
2
+ 60a − 6u + 42, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 135 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
= h4.99 × 10
445
u
128
− 1.30 × 10
446
u
127
+ · · · + 2.09 × 10
445
b + 7.62 ×
10
445
, 5.12 × 10
446
u
128
− 1.01 × 10
447
u
127
+ · · · + 1.05 × 10
446
a + 3.20 ×
10
446
, u
129
− 3u
128
+ · · · + 6u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
2
=
−4.88965u
128
+ 9.68913u
127
+ ··· + 21.8288u − 3.05575
−2.38397u
128
+ 6.22785u
127
+ ··· + 17.3934u − 3.64260
a
7
=
1
u
2
a
5
=
−16.2649u
128
+ 36.0614u
127
+ ··· + 94.5515u − 18.4908
4.05033u
128
− 8.11181u
127
+ ··· − 22.0327u + 3.82688
a
3
=
−12.5725u
128
+ 28.3938u
127
+ ··· + 72.9033u − 14.6140
3.00818u
128
− 5.66495u
127
+ ··· − 14.4581u + 2.25274
a
1
=
7.59367u
128
− 17.3064u
127
+ ··· − 46.4404u + 9.36540
−0.489938u
128
+ 1.20604u
127
+ ··· + 5.09923u − 1.11099
a
4
=
−2.55440u
128
+ 6.03912u
127
+ ··· + 12.3850u − 1.93084
13.0262u
128
− 28.0196u
127
+ ··· − 74.9764u + 14.9359
a
11
=
−1.11099u
128
+ 2.84302u
127
+ ··· + 7.35949u − 1.56670
5.47464u
128
− 12.7709u
127
+ ··· − 36.1966u + 7.59367
a
12
=
−2.33366u
128
+ 5.14492u
127
+ ··· + 17.3240u − 3.56421
6.20152u
128
− 15.0253u
127
+ ··· − 43.6088u + 8.95686
a
9
=
u
u
a
8
=
−3.44229u
128
+ 8.53517u
127
+ ··· + 30.9440u − 5.97392
4.25086u
128
− 8.79384u
127
+ ··· − 19.2212u + 3.91476
(ii) Obstruction class = −1
(iii) Cusp Shapes = −35.3681u
128
+ 84.1056u
127
+ ··· + 260.905u − 58.9553
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
129
+ 58u
128
+ ··· + 31691u − 625
c
2
, c
5
u
129
+ 4u
128
+ ··· − 129u − 25
c
3
25(25u
129
− 195u
128
+ ··· + 2.03112 × 10
7
u + 1405871)
c
4
25(25u
129
− 30u
128
+ ··· − 2354708u + 76193)
c
6
, c
9
u
129
+ 3u
128
+ ··· + 6u + 1
c
7
, c
12
u
129
+ 3u
128
+ ··· + 2u + 1
c
8
u
129
+ 9u
128
+ ··· + 4123464u + 328729
c
10
u
129
− 3u
128
+ ··· + 26400u + 8000
c
11
u
129
+ 63u
128
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
129
+ 30y
128
+ ··· + 1330940731y −390625
c
2
, c
5
y
129
+ 58y
128
+ ··· + 31691y −625
c
3
625
· (625y
129
+ 26325y
128
+ ··· + 27395194733737y −1976473268641)
c
4
625(625y
129
− 14300y
128
+ ··· + 3.74977 × 10
11
y −5.80537 × 10
9
)
c
6
, c
9
y
129
− 71y
128
+ ··· + 6y −1
c
7
, c
12
y
129
− 63y
128
+ ··· + 6y −1
c
8
y
129
+ 45y
128
+ ··· + 5854253992682y −108062755441
c
10
y
129
+ 35y
128
+ ··· − 255360000y −64000000
c
11
y
129
+ 9y
128
+ ··· − 14y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.983463 + 0.268681I
a = −0.62036 + 1.96394I
b = 0.682768 + 1.129540I
−0.58814 + 4.93859I 0
u = −0.983463 − 0.268681I
a = −0.62036 − 1.96394I
b = 0.682768 − 1.129540I
−0.58814 − 4.93859I 0
u = −0.175616 + 0.948969I
a = 0.687811 − 0.298549I
b = −0.739891 − 0.477913I
2.15356 − 3.17502I 0
u = −0.175616 − 0.948969I
a = 0.687811 + 0.298549I
b = −0.739891 + 0.477913I
2.15356 + 3.17502I 0
u = 0.144632 + 0.952589I
a = 0.648121 + 0.279122I
b = −0.803079 + 0.453732I
−0.32991 + 8.26485I 0
u = 0.144632 − 0.952589I
a = 0.648121 − 0.279122I
b = −0.803079 − 0.453732I
−0.32991 − 8.26485I 0
u = 0.917821 + 0.279541I
a = −0.44055 − 1.58384I
b = 0.817754 − 1.027710I
−1.80994 − 1.27988I 0
u = 0.917821 − 0.279541I
a = −0.44055 + 1.58384I
b = 0.817754 + 1.027710I
−1.80994 + 1.27988I 0
u = −0.930509 + 0.131444I
a = 3.26267 + 1.98840I
b = 0.424467 − 0.884741I
−4.38795 − 5.53131I 0
u = −0.930509 − 0.131444I
a = 3.26267 − 1.98840I
b = 0.424467 + 0.884741I
−4.38795 + 5.53131I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.330032 + 0.878496I
a = 0.689662 + 0.447288I
b = −0.241147 + 1.061570I
−6.56737 − 2.23567I 0
u = −0.330032 − 0.878496I
a = 0.689662 − 0.447288I
b = −0.241147 − 1.061570I
−6.56737 + 2.23567I 0
u = 0.934471 + 0.079932I
a = −3.48829 − 0.00956I
b = 0.541935 − 0.865418I
−1.46694 − 2.16043I 0
u = 0.934471 − 0.079932I
a = −3.48829 + 0.00956I
b = 0.541935 + 0.865418I
−1.46694 + 2.16043I 0
u = 1.059820 + 0.087490I
a = −0.94711 − 4.84175I
b = 0.453431 − 0.900657I
−1.94855 − 2.12974I 0
u = 1.059820 − 0.087490I
a = −0.94711 + 4.84175I
b = 0.453431 + 0.900657I
−1.94855 + 2.12974I 0
u = −1.037490 + 0.293142I
a = −0.49223 + 2.19831I
b = 0.591524 + 1.258510I
−1.69705 + 5.73998I 0
u = −1.037490 − 0.293142I
a = −0.49223 − 2.19831I
b = 0.591524 − 1.258510I
−1.69705 − 5.73998I 0
u = 1.045160 + 0.313586I
a = −0.43290 − 2.21195I
b = 0.59443 − 1.32359I
−4.12236 − 10.24180I 0
u = 1.045160 − 0.313586I
a = −0.43290 + 2.21195I
b = 0.59443 + 1.32359I
−4.12236 + 10.24180I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.882793 + 0.210988I
a = 2.46528 + 0.82348I
b = 0.330870 − 0.872293I
−4.70234 + 2.17047I 0
u = −0.882793 − 0.210988I
a = 2.46528 − 0.82348I
b = 0.330870 + 0.872293I
−4.70234 − 2.17047I 0
u = 0.850268 + 0.301470I
a = −0.067006 − 1.297250I
b = 0.955342 − 0.885158I
−0.99778 − 7.95172I 0
u = 0.850268 − 0.301470I
a = −0.067006 + 1.297250I
b = 0.955342 + 0.885158I
−0.99778 + 7.95172I 0
u = −0.308540 + 1.057600I
a = 0.762706 − 0.454606I
b = −0.603539 − 0.665281I
4.10160 − 0.69007I 0
u = −0.308540 − 1.057600I
a = 0.762706 + 0.454606I
b = −0.603539 + 0.665281I
4.10160 + 0.69007I 0
u = −1.101470 + 0.044053I
a = 1.65006 + 4.84565I
b = 0.435278 + 0.828060I
−4.21569 − 1.91512I 0
u = −1.101470 − 0.044053I
a = 1.65006 − 4.84565I
b = 0.435278 − 0.828060I
−4.21569 + 1.91512I 0
u = 1.080440 + 0.289628I
a = −0.45069 − 2.29917I
b = 0.472374 − 1.287950I
−5.24083 − 2.81222I 0
u = 1.080440 − 0.289628I
a = −0.45069 + 2.29917I
b = 0.472374 + 1.287950I
−5.24083 + 2.81222I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.077505 + 1.116970I
a = 0.617919 − 0.590223I
b = −0.618915 − 1.098620I
−2.26166 + 13.60010I 0
u = 0.077505 − 1.116970I
a = 0.617919 + 0.590223I
b = −0.618915 + 1.098620I
−2.26166 − 13.60010I 0
u = 0.154618 + 0.866212I
a = 0.738529 + 0.202162I
b = −0.668670 + 0.330307I
−2.46704 + 0.18761I 0
u = 0.154618 − 0.866212I
a = 0.738529 − 0.202162I
b = −0.668670 − 0.330307I
−2.46704 − 0.18761I 0
u = −0.828793 + 0.275938I
a = −0.094524 + 1.077790I
b = 0.900322 + 0.807036I
1.08834 + 3.59177I 0
u = −0.828793 − 0.275938I
a = −0.094524 − 1.077790I
b = 0.900322 − 0.807036I
1.08834 − 3.59177I 0
u = 0.137134 + 1.120300I
a = 0.627586 − 0.578090I
b = −0.546670 − 1.089010I
−4.60897 + 4.87781I 0
u = 0.137134 − 1.120300I
a = 0.627586 + 0.578090I
b = −0.546670 + 1.089010I
−4.60897 − 4.87781I 0
u = −0.088221 + 1.139010I
a = 0.617847 + 0.584258I
b = −0.602534 + 1.071670I
0.39045 − 8.29549I 0
u = −0.088221 − 1.139010I
a = 0.617847 − 0.584258I
b = −0.602534 − 1.071670I
0.39045 + 8.29549I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.846643 + 0.121811I
a = 1.76479 − 1.66806I
b = 0.404616 + 0.814035I
−1.61493 + 1.51133I 0
u = 0.846643 − 0.121811I
a = 1.76479 + 1.66806I
b = 0.404616 − 0.814035I
−1.61493 − 1.51133I 0
u = 0.388528 + 0.748464I
a = 0.705392 − 0.355453I
b = −0.124235 − 0.981885I
−2.61497 − 1.72957I 0
u = 0.388528 − 0.748464I
a = 0.705392 + 0.355453I
b = −0.124235 + 0.981885I
−2.61497 + 1.72957I 0
u = 1.120410 + 0.361375I
a = 0.391824 + 0.409775I
b = −0.424807 − 0.086576I
−2.42987 − 0.61021I 0
u = 1.120410 − 0.361375I
a = 0.391824 − 0.409775I
b = −0.424807 + 0.086576I
−2.42987 + 0.61021I 0
u = −0.761610 + 0.265352I
a = 0.194084 + 0.747520I
b = 0.878946 + 0.617003I
1.48127 + 2.53507I 0
u = −0.761610 − 0.265352I
a = 0.194084 − 0.747520I
b = 0.878946 − 0.617003I
1.48127 − 2.53507I 0
u = −0.283572 + 0.735406I
a = 0.775469 + 0.385271I
b = −0.076026 + 1.087540I
−5.67794 + 6.36186I 0
u = −0.283572 − 0.735406I
a = 0.775469 − 0.385271I
b = −0.076026 − 1.087540I
−5.67794 − 6.36186I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.214880 + 0.129383I
a = 0.46615 + 2.43126I
b = 0.158810 + 0.914329I
−4.67216 + 4.81332I 0
u = −1.214880 − 0.129383I
a = 0.46615 − 2.43126I
b = 0.158810 − 0.914329I
−4.67216 − 4.81332I 0
u = 0.715395 + 0.288428I
a = 0.481009 − 0.704654I
b = 0.930821 − 0.456529I
−0.15548 + 1.57650I 0
u = 0.715395 − 0.288428I
a = 0.481009 + 0.704654I
b = 0.930821 + 0.456529I
−0.15548 − 1.57650I 0
u = 0.763368
a = 0.816194
b = 0.131616
−1.26499 0
u = −1.227300 + 0.196563I
a = 0.09851 + 2.26617I
b = 0.110958 + 1.054910I
−4.65246 + 4.81342I 0
u = −1.227300 − 0.196563I
a = 0.09851 − 2.26617I
b = 0.110958 − 1.054910I
−4.65246 − 4.81342I 0
u = −1.210290 + 0.315524I
a = 0.409683 − 0.678849I
b = −0.472854 − 0.115902I
−5.02290 − 4.05629I 0
u = −1.210290 − 0.315524I
a = 0.409683 + 0.678849I
b = −0.472854 + 0.115902I
−5.02290 + 4.05629I 0
u = 0.449856 + 1.189000I
a = 0.798817 + 0.571328I
b = −0.528504 + 0.753911I
3.39101 − 4.69695I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.449856 − 1.189000I
a = 0.798817 − 0.571328I
b = −0.528504 − 0.753911I
3.39101 + 4.69695I 0
u = −1.198590 + 0.429633I
a = 0.105430 − 0.488278I
b = −0.659760 + 0.094863I
−6.47133 + 3.95304I 0
u = −1.198590 − 0.429633I
a = 0.105430 + 0.488278I
b = −0.659760 − 0.094863I
−6.47133 − 3.95304I 0
u = 0.587319 + 0.383139I
a = 1.291290 − 0.016709I
b = 0.083690 + 0.539120I
−1.52762 − 0.09529I 0
u = 0.587319 − 0.383139I
a = 1.291290 + 0.016709I
b = 0.083690 − 0.539120I
−1.52762 + 0.09529I 0
u = 0.626876 + 0.299965I
a = 0.838928 − 0.531539I
b = 0.905222 − 0.100755I
0.03259 − 4.68683I 0. + 7.22182I
u = 0.626876 − 0.299965I
a = 0.838928 + 0.531539I
b = 0.905222 + 0.100755I
0.03259 + 4.68683I 0. − 7.22182I
u = 1.262250 + 0.346204I
a = −0.36254 − 1.95976I
b = −0.094857 − 1.381630I
−10.1858 − 10.0625I 0
u = 1.262250 − 0.346204I
a = −0.36254 + 1.95976I
b = −0.094857 + 1.381630I
−10.1858 + 10.0625I 0
u = −1.270920 + 0.330277I
a = −0.30308 + 1.94671I
b = −0.093320 + 1.328500I
−7.38638 + 5.28336I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.270920 − 0.330277I
a = −0.30308 − 1.94671I
b = −0.093320 − 1.328500I
−7.38638 − 5.28336I 0
u = 1.197390 + 0.585875I
a = −0.1126030 − 0.0193402I
b = −0.719779 − 0.507016I
0.74811 − 1.37500I 0
u = 1.197390 − 0.585875I
a = −0.1126030 + 0.0193402I
b = −0.719779 + 0.507016I
0.74811 + 1.37500I 0
u = 1.295150 + 0.344969I
a = −0.32515 − 1.85291I
b = −0.172149 − 1.325040I
−11.48090 − 1.73695I 0
u = 1.295150 − 0.344969I
a = −0.32515 + 1.85291I
b = −0.172149 + 1.325040I
−11.48090 + 1.73695I 0
u = −0.133712 + 1.336340I
a = 0.606044 + 0.587032I
b = −0.543559 + 0.949319I
3.26341 − 5.24947I 0
u = −0.133712 − 1.336340I
a = 0.606044 − 0.587032I
b = −0.543559 − 0.949319I
3.26341 + 5.24947I 0
u = −1.226480 + 0.561154I
a = −0.234021 − 0.060837I
b = −0.815819 + 0.474313I
1.11255 + 6.37416I 0
u = −1.226480 − 0.561154I
a = −0.234021 + 0.060837I
b = −0.815819 − 0.474313I
1.11255 − 6.37416I 0
u = 1.245200 + 0.518345I
a = −0.306778 + 0.295530I
b = −0.915908 − 0.328646I
−5.81317 − 5.29985I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.245200 − 0.518345I
a = −0.306778 − 0.295530I
b = −0.915908 + 0.328646I
−5.81317 + 5.29985I 0
u = −0.588449 + 0.278132I
a = 0.913984 + 0.407455I
b = 0.786059 − 0.046206I
1.83272 + 0.45496I 5.79856 − 1.66220I
u = −0.588449 − 0.278132I
a = 0.913984 − 0.407455I
b = 0.786059 + 0.046206I
1.83272 − 0.45496I 5.79856 + 1.66220I
u = −1.251440 + 0.533176I
a = −0.366058 − 0.214061I
b = −0.938070 + 0.398504I
−1.20273 + 8.51895I 0
u = −1.251440 − 0.533176I
a = −0.366058 + 0.214061I
b = −0.938070 − 0.398504I
−1.20273 − 8.51895I 0
u = 1.258880 + 0.530564I
a = −0.413635 + 0.239128I
b = −0.976388 − 0.392520I
−3.78442 − 13.60190I 0
u = 1.258880 − 0.530564I
a = −0.413635 − 0.239128I
b = −0.976388 + 0.392520I
−3.78442 + 13.60190I 0
u = −1.186270 + 0.689583I
a = 1.26776 − 1.27280I
b = −0.390070 − 1.061840I
−7.87584 − 0.93121I 0
u = −1.186270 − 0.689583I
a = 1.26776 + 1.27280I
b = −0.390070 + 1.061840I
−7.87584 + 0.93121I 0
u = −0.519093 + 0.278453I
a = 1.056830 + 0.334162I
b = 0.768552 − 0.334931I
1.75839 − 0.65436I 5.34982 − 0.15315I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.519093 − 0.278453I
a = 1.056830 − 0.334162I
b = 0.768552 + 0.334931I
1.75839 + 0.65436I 5.34982 + 0.15315I
u = −1.26057 + 0.64615I
a = 1.17659 − 1.47167I
b = −0.470241 − 1.114900I
−9.27307 + 8.12090I 0
u = −1.26057 − 0.64615I
a = 1.17659 + 1.47167I
b = −0.470241 + 1.114900I
−9.27307 − 8.12090I 0
u = 1.41428 + 0.17099I
a = 0.23804 − 1.62846I
b = −0.206084 − 0.938637I
−3.58418 − 0.24091I 0
u = 1.41428 − 0.17099I
a = 0.23804 + 1.62846I
b = −0.206084 + 0.938637I
−3.58418 + 0.24091I 0
u = 1.24503 + 0.70593I
a = 1.14437 + 1.32385I
b = −0.446392 + 1.052500I
−4.75671 − 4.16732I 0
u = 1.24503 − 0.70593I
a = 1.14437 − 1.32385I
b = −0.446392 − 1.052500I
−4.75671 + 4.16732I 0
u = 0.478659 + 0.305566I
a = 1.132950 − 0.320045I
b = 0.859647 + 0.471653I
−0.14799 + 4.91053I 0.79655 − 4.80579I
u = 0.478659 − 0.305566I
a = 1.132950 + 0.320045I
b = 0.859647 − 0.471653I
−0.14799 − 4.91053I 0.79655 + 4.80579I
u = 1.32444 + 0.58045I
a = 0.99325 + 1.74069I
b = −0.616651 + 1.174130I
−8.36816 − 10.88600I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.32444 − 0.58045I
a = 0.99325 − 1.74069I
b = −0.616651 − 1.174130I
−8.36816 + 10.88600I 0
u = 1.33532 + 0.56738I
a = 0.93205 + 1.79575I
b = −0.659633 + 1.180350I
−6.2042 − 19.5319I 0
u = 1.33532 − 0.56738I
a = 0.93205 − 1.79575I
b = −0.659633 − 1.180350I
−6.2042 + 19.5319I 0
u = −1.33721 + 0.57445I
a = 0.93028 − 1.75949I
b = −0.649568 − 1.163770I
−3.5377 + 14.3096I 0
u = −1.33721 − 0.57445I
a = 0.93028 + 1.75949I
b = −0.649568 + 1.163770I
−3.5377 − 14.3096I 0
u = −1.41941 + 0.35338I
a = −0.17051 + 1.49437I
b = −0.359827 + 1.133960I
−9.98903 + 0.41325I 0
u = −1.41941 − 0.35338I
a = −0.17051 − 1.49437I
b = −0.359827 − 1.133960I
−9.98903 − 0.41325I 0
u = 0.33718 + 1.43221I
a = 0.566529 − 0.589590I
b = −0.491172 − 0.922652I
2.88569 − 0.57683I 0
u = 0.33718 − 1.43221I
a = 0.566529 + 0.589590I
b = −0.491172 + 0.922652I
2.88569 + 0.57683I 0
u = −1.35795 + 0.60330I
a = 0.88211 − 1.62403I
b = −0.627909 − 1.091380I
−0.74343 + 11.77170I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35795 − 0.60330I
a = 0.88211 + 1.62403I
b = −0.627909 + 1.091380I
−0.74343 − 11.77170I 0
u = 1.36563 + 0.63159I
a = 0.88688 + 1.53528I
b = −0.597528 + 1.058030I
−0.89915 − 6.42948I 0
u = 1.36563 − 0.63159I
a = 0.88688 − 1.53528I
b = −0.597528 − 1.058030I
−0.89915 + 6.42948I 0
u = 0.363717 + 0.292600I
a = 1.163910 − 0.174820I
b = 0.786445 + 0.731780I
−0.52121 − 1.56530I −0.86638 + 2.57200I
u = 0.363717 − 0.292600I
a = 1.163910 + 0.174820I
b = 0.786445 − 0.731780I
−0.52121 + 1.56530I −0.86638 − 2.57200I
u = −1.48950 + 0.41586I
a = −0.153476 + 1.272430I
b = −0.465312 + 1.067160I
−7.37499 − 7.84861I 0
u = −1.48950 − 0.41586I
a = −0.153476 − 1.272430I
b = −0.465312 − 1.067160I
−7.37499 + 7.84861I 0
u = 1.50504 + 0.36378I
a = −0.064729 − 1.333380I
b = −0.415637 − 1.041460I
−4.97818 + 2.52108I 0
u = 1.50504 − 0.36378I
a = −0.064729 + 1.333380I
b = −0.415637 + 1.041460I
−4.97818 − 2.52108I 0
u = 0.143271 + 0.386362I
a = 1.169800 + 0.073681I
b = 0.645129 + 1.054690I
−1.79385 + 7.26996I −2.23125 − 5.78172I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.143271 − 0.386362I
a = 1.169800 − 0.073681I
b = 0.645129 − 1.054690I
−1.79385 − 7.26996I −2.23125 + 5.78172I
u = 0.044126 + 0.388938I
a = 1.095960 + 0.125750I
b = 0.522478 + 1.065910I
−2.53204 + 0.02473I −2.93276 + 1.49413I
u = 0.044126 − 0.388938I
a = 1.095960 − 0.125750I
b = 0.522478 − 1.065910I
−2.53204 − 0.02473I −2.93276 − 1.49413I
u = −0.266922 + 0.261058I
a = 1.126660 + 0.080683I
b = 0.685137 − 0.840591I
1.11585 − 2.30829I 1.69883 + 2.89752I
u = −0.266922 − 0.261058I
a = 1.126660 − 0.080683I
b = 0.685137 + 0.840591I
1.11585 + 2.30829I 1.69883 − 2.89752I
u = 0.183193 + 0.325091I
a = 0.933199 − 0.109578I
b = 0.357860 − 0.927565I
−0.83327 − 2.69684I −0.17117 + 8.22409I
u = 0.183193 − 0.325091I
a = 0.933199 + 0.109578I
b = 0.357860 + 0.927565I
−0.83327 + 2.69684I −0.17117 − 8.22409I
u = −0.146229 + 0.324302I
a = 1.131360 − 0.032547I
b = 0.625831 − 0.980707I
0.54489 − 2.98296I 1.35807 + 1.48155I
u = −0.146229 − 0.324302I
a = 1.131360 + 0.032547I
b = 0.625831 + 0.980707I
0.54489 + 2.98296I 1.35807 − 1.48155I
17
II. I
u
2
= h2u
2
a − au + 2u
2
+ b + 2a − u + 2, 15u
2
a + 25a
2
− 5au + 13u
2
+
60a − 6u + 42, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
2
=
a
−2u
2
a + au − 2u
2
− 2a + u − 2
a
7
=
1
u
2
a
5
=
2u
2
a − au +
13
5
u
2
+ 3a −
6
5
u +
22
5
−2u
2
a + au − 2u
2
− 2a + u − 3
a
3
=
3
5
u
2
+ a −
1
5
u +
7
5
−2u
2
a + au − 2u
2
− 2a + u − 3
a
1
=
−1
0
a
4
=
0
−2u
2
a + au −
13
5
u
2
− 3a +
6
5
u −
22
5
a
11
=
0
u
a
12
=
−u
u
a
9
=
u
u
a
8
=
u
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
33
5
u
2
a −
34
5
au −
33
5
u
2
+
3
5
a +
11
5
u −
47
5
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
25(25u
6
− 20u
5
+ 11u
4
+ 6u
3
− 3u
2
− u + 1)
c
4
25(25u
6
− 55u
5
+ 91u
4
− 56u
3
+ 25u
2
− 6u + 1)
c
6
, c
11
(u
3
− u
2
+ 2u − 1)
2
c
7
(u
3
+ u
2
− 1)
2
c
8
(u
3
+ 3u
2
+ 2u − 1)
2
c
9
(u
3
+ u
2
+ 2u + 1)
2
c
10
u
6
c
12
(u
3
− u
2
+ 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
3
c
3
625(625y
6
+ 150y
5
+ 211y
4
− 92y
3
+ 43y
2
− 7y + 1)
c
4
625(625y
6
+ 1525y
5
+ 3371y
4
+ 804y
3
+ 135y
2
+ 14y + 1)
c
6
, c
9
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
7
, c
12
(y
3
− y
2
+ 2y −1)
2
c
8
(y
3
− 5y
2
+ 10y −1)
2
c
10
y
6
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.745550 − 0.592600I
b = 0.500000 − 0.866025I
3.02413 − 4.85801I −12.95856 + 2.56770I
u = 0.215080 + 1.307140I
a = −0.614019 + 0.516660I
b = 0.500000 + 0.866025I
3.02413 − 0.79824I 2.34733 + 12.12399I
u = 0.215080 − 1.307140I
a = −0.745550 + 0.592600I
b = 0.500000 + 0.866025I
3.02413 + 4.85801I −12.95856 − 2.56770I
u = 0.215080 − 1.307140I
a = −0.614019 − 0.516660I
b = 0.500000 − 0.866025I
3.02413 + 0.79824I 2.34733 − 12.12399I
u = 0.569840
a = −1.240430 + 0.416439I
b = 0.500000 − 0.866025I
−1.11345 − 2.02988I −3.56877 − 2.25629I
u = 0.569840
a = −1.240430 − 0.416439I
b = 0.500000 + 0.866025I
−1.11345 + 2.02988I −3.56877 + 2.25629I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
129
+ 58u
128
+ ··· + 31691u − 625)
c
2
((u
2
+ u + 1)
3
)(u
129
+ 4u
128
+ ··· − 129u − 25)
c
3
625(25u
6
− 20u
5
+ 11u
4
+ 6u
3
− 3u
2
− u + 1)
· (25u
129
− 195u
128
+ ··· + 20311179u + 1405871)
c
4
625(25u
6
− 55u
5
+ 91u
4
− 56u
3
+ 25u
2
− 6u + 1)
· (25u
129
− 30u
128
+ ··· − 2354708u + 76193)
c
5
((u
2
− u + 1)
3
)(u
129
+ 4u
128
+ ··· − 129u − 25)
c
6
((u
3
− u
2
+ 2u − 1)
2
)(u
129
+ 3u
128
+ ··· + 6u + 1)
c
7
((u
3
+ u
2
− 1)
2
)(u
129
+ 3u
128
+ ··· + 2u + 1)
c
8
((u
3
+ 3u
2
+ 2u − 1)
2
)(u
129
+ 9u
128
+ ··· + 4123464u + 328729)
c
9
((u
3
+ u
2
+ 2u + 1)
2
)(u
129
+ 3u
128
+ ··· + 6u + 1)
c
10
u
6
(u
129
− 3u
128
+ ··· + 26400u + 8000)
c
11
((u
3
− u
2
+ 2u − 1)
2
)(u
129
+ 63u
128
+ ··· + 6u + 1)
c
12
((u
3
− u
2
+ 1)
2
)(u
129
+ 3u
128
+ ··· + 2u + 1)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
129
+ 30y
128
+ ··· + 1.33094 × 10
9
y −390625)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
129
+ 58y
128
+ ··· + 31691y −625)
c
3
390625(625y
6
+ 150y
5
+ 211y
4
− 92y
3
+ 43y
2
− 7y + 1)
· (625y
129
+ 26325y
128
+ ··· + 27395194733737y −1976473268641)
c
4
390625(625y
6
+ 1525y
5
+ 3371y
4
+ 804y
3
+ 135y
2
+ 14y + 1)
· (625y
129
− 14300y
128
+ ··· + 374976658848y −5805373249)
c
6
, c
9
((y
3
+ 3y
2
+ 2y −1)
2
)(y
129
− 71y
128
+ ··· + 6y −1)
c
7
, c
12
((y
3
− y
2
+ 2y −1)
2
)(y
129
− 63y
128
+ ··· + 6y −1)
c
8
(y
3
− 5y
2
+ 10y −1)
2
· (y
129
+ 45y
128
+ ··· + 5854253992682y −108062755441)
c
10
y
6
(y
129
+ 35y
128
+ ··· − 2.55360 × 10
8
y −6.40000 × 10
7
)
c
11
((y
3
+ 3y
2
+ 2y −1)
2
)(y
129
+ 9y
128
+ ··· − 14y −1)
23
