12a
0126
(K12a
0126
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 10 11 4 12 1 9 7
Solving Sequence
9,11
12
4,10
8 3 7 1 6 5 2
c
11
c
9
c
8
c
3
c
7
c
12
c
6
c
4
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.19568 × 10
514
u
123
+ 1.78570 × 10
514
u
122
+ ··· + 1.37373 × 10
514
b + 9.44655 × 10
513
,
− 8.50500 × 10
513
u
123
+ 2.28055 × 10
514
u
122
+ ··· + 6.86865 × 10
513
a + 3.75076 × 10
514
,
u
124
− 3u
123
+ ··· − 17u + 1i
I
u
2
= h−u
4
b + u
3
b + 2u
4
+ u
2
b − 4u
3
+ b
2
− b + u + 2, a, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 134 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−1.20 × 10
514
u
123
+ 1.79 × 10
514
u
122
+ · · · + 1.37 × 10
514
b + 9.45 ×
10
513
, −8.51 × 10
513
u
123
+ 2.28 × 10
514
u
122
+ · · · + 6.87 × 10
513
a + 3.75 ×
10
514
, u
124
− 3u
123
+ · · · − 17u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
4
=
1.23823u
123
− 3.32023u
122
+ ··· + 92.0435u − 5.46069
0.870390u
123
− 1.29989u
122
+ ··· + 18.1293u − 0.687657
a
10
=
−u
−u
3
+ u
a
8
=
0.636769u
123
− 3.20862u
122
+ ··· + 84.3954u − 2.94586
−1.14946u
123
+ 2.37316u
122
+ ··· − 41.7539u + 2.55020
a
3
=
2.25351u
123
− 8.02311u
122
+ ··· + 332.546u − 26.9028
−0.106456u
123
+ 1.24630u
122
+ ··· − 6.66420u + 1.61535
a
7
=
−0.512693u
123
− 0.835457u
122
+ ··· + 42.6415u − 0.395659
−1.14946u
123
+ 2.37316u
122
+ ··· − 41.7539u + 2.55020
a
1
=
−0.363633u
123
+ 0.445779u
122
+ ··· + 7.87842u − 3.65412
0.170523u
123
− 0.430689u
122
+ ··· − 0.767532u + 0.281487
a
6
=
0.626018u
123
− 2.92628u
122
+ ··· + 64.5489u − 1.65616
−1.38877u
123
+ 2.78861u
122
+ ··· − 42.2698u + 2.48540
a
5
=
2.64583u
123
− 8.44868u
122
+ ··· + 327.721u − 25.5158
0.318080u
123
+ 0.453649u
122
+ ··· + 6.76485u + 0.672544
a
2
=
1.13479u
123
− 5.07219u
122
+ ··· + 147.722u − 2.40535
−0.709729u
123
+ 1.24243u
122
+ ··· − 53.4260u + 3.18946
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.43594u
123
− 17.2046u
122
+ ··· − 79.2712u + 10.6191
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
124
+ 42u
123
+ ··· + 2u + 1
c
2
, c
5
u
124
+ 6u
123
+ ··· + 2u + 1
c
3
, c
8
u
124
− u
123
+ ··· + 5120u + 1024
c
6
u
124
− 3u
123
+ ··· + 1975u + 1031
c
7
u
124
+ 3u
123
+ ··· − 376993u − 48793
c
9
, c
11
u
124
− 3u
123
+ ··· − 17u + 1
c
10
u
124
+ 21u
123
+ ··· + 3u + 1
c
12
u
124
− 9u
123
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
124
+ 86y
123
+ ··· − 1250y + 1
c
2
, c
5
y
124
+ 42y
123
+ ··· + 2y + 1
c
3
, c
8
y
124
− 55y
123
+ ··· − 26214400y + 1048576
c
6
y
124
+ 131y
123
+ ··· + 138554707y + 1062961
c
7
y
124
+ 83y
123
+ ··· − 318551403169y + 2380756849
c
9
, c
11
y
124
− 85y
123
+ ··· − 17y + 1
c
10
y
124
+ 3y
123
+ ··· − 17y + 1
c
12
y
124
− 21y
123
+ ··· − 9y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.993111 + 0.053773I
a = 0.304536 − 0.731943I
b = −3.32424 + 1.95187I
−1.07695 + 2.69734I 0
u = −0.993111 − 0.053773I
a = 0.304536 + 0.731943I
b = −3.32424 − 1.95187I
−1.07695 − 2.69734I 0
u = 0.102129 + 0.978954I
a = 0.989365 + 0.390154I
b = −0.047901 − 0.761141I
2.42925 + 1.41500I 0
u = 0.102129 − 0.978954I
a = 0.989365 − 0.390154I
b = −0.047901 + 0.761141I
2.42925 − 1.41500I 0
u = 0.960892 + 0.127416I
a = −1.02339 − 1.08127I
b = 0.001099 + 0.605351I
−0.61080 − 4.13411I 0
u = 0.960892 − 0.127416I
a = −1.02339 + 1.08127I
b = 0.001099 − 0.605351I
−0.61080 + 4.13411I 0
u = 1.023570 + 0.155026I
a = −1.305260 + 0.028917I
b = −1.114000 − 0.105881I
−2.35592 − 4.60181I 0
u = 1.023570 − 0.155026I
a = −1.305260 − 0.028917I
b = −1.114000 + 0.105881I
−2.35592 + 4.60181I 0
u = 0.103026 + 1.034420I
a = −0.420200 + 0.976552I
b = 0.04073 − 1.77407I
2.86743 + 4.32090I 0
u = 0.103026 − 1.034420I
a = −0.420200 − 0.976552I
b = 0.04073 + 1.77407I
2.86743 − 4.32090I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.565867 + 0.885433I
a = 0.551247 − 1.154640I
b = −0.07495 + 1.59124I
8.29858 − 2.50158I 0
u = 0.565867 − 0.885433I
a = 0.551247 + 1.154640I
b = −0.07495 − 1.59124I
8.29858 + 2.50158I 0
u = −0.945786 + 0.068110I
a = −0.833155 − 0.190342I
b = −1.05192 + 3.40683I
−0.377994 + 0.348299I 0
u = −0.945786 − 0.068110I
a = −0.833155 + 0.190342I
b = −1.05192 − 3.40683I
−0.377994 − 0.348299I 0
u = −0.272313 + 1.015970I
a = −0.756103 − 0.410555I
b = −0.170492 + 0.784563I
−2.52436 + 2.17800I 0
u = −0.272313 − 1.015970I
a = −0.756103 + 0.410555I
b = −0.170492 − 0.784563I
−2.52436 − 2.17800I 0
u = −1.069430 + 0.043655I
a = 0.723563 + 0.551297I
b = −1.14955 − 3.56938I
−3.73679 + 2.23882I 0
u = −1.069430 − 0.043655I
a = 0.723563 − 0.551297I
b = −1.14955 + 3.56938I
−3.73679 − 2.23882I 0
u = 0.048860 + 1.071540I
a = −0.942153 − 0.429798I
b = 0.022218 + 0.800063I
1.80176 + 6.87033I 0
u = 0.048860 − 1.071540I
a = −0.942153 + 0.429798I
b = 0.022218 − 0.800063I
1.80176 − 6.87033I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500691 + 0.951826I
a = −0.529260 + 1.127890I
b = 0.08208 − 1.62211I
8.48525 + 3.48002I 0
u = 0.500691 − 0.951826I
a = −0.529260 − 1.127890I
b = 0.08208 + 1.62211I
8.48525 − 3.48002I 0
u = −0.923100 + 0.020045I
a = −0.057279 + 0.769698I
b = 2.93503 − 0.54583I
−0.80831 − 2.19531I 0
u = −0.923100 − 0.020045I
a = −0.057279 − 0.769698I
b = 2.93503 + 0.54583I
−0.80831 + 2.19531I 0
u = 0.938192 + 0.536727I
a = 1.156670 − 0.778648I
b = 0.715665 + 1.058740I
7.06445 − 2.67846I 0
u = 0.938192 − 0.536727I
a = 1.156670 + 0.778648I
b = 0.715665 − 1.058740I
7.06445 + 2.67846I 0
u = −1.080170 + 0.152845I
a = 0.401983 + 0.218301I
b = 4.28532 − 1.02349I
−2.27737 + 2.37996I 0
u = −1.080170 − 0.152845I
a = 0.401983 − 0.218301I
b = 4.28532 + 1.02349I
−2.27737 − 2.37996I 0
u = −1.087680 + 0.156368I
a = −0.959787 − 0.541892I
b = 0.50589 + 2.83589I
2.30512 + 1.82489I 0
u = −1.087680 − 0.156368I
a = −0.959787 + 0.541892I
b = 0.50589 − 2.83589I
2.30512 − 1.82489I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.893094 + 0.091057I
a = −0.08288 − 1.62886I
b = 0.043133 + 0.471122I
0.47580 − 3.10935I 0
u = 0.893094 − 0.091057I
a = −0.08288 + 1.62886I
b = 0.043133 − 0.471122I
0.47580 + 3.10935I 0
u = 1.098910 + 0.149918I
a = −0.962113 + 0.829318I
b = −0.681615 − 1.092050I
−4.64464 − 4.28743I 0
u = 1.098910 − 0.149918I
a = −0.962113 − 0.829318I
b = −0.681615 + 1.092050I
−4.64464 + 4.28743I 0
u = −1.120530 + 0.139444I
a = 0.937700 + 0.597521I
b = −0.68811 − 2.80862I
1.44662 + 7.51048I 0
u = −1.120530 − 0.139444I
a = 0.937700 − 0.597521I
b = −0.68811 + 2.80862I
1.44662 − 7.51048I 0
u = −0.046282 + 1.136960I
a = 0.455372 − 0.888816I
b = 0.07800 + 1.76206I
−1.39443 + 6.91886I 0
u = −0.046282 − 1.136960I
a = 0.455372 + 0.888816I
b = 0.07800 − 1.76206I
−1.39443 − 6.91886I 0
u = 0.007623 + 0.853337I
a = 0.275150 − 0.956648I
b = −0.13714 + 1.95173I
0.462211 + 0.187148I 0
u = 0.007623 − 0.853337I
a = 0.275150 + 0.956648I
b = −0.13714 − 1.95173I
0.462211 − 0.187148I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.110490 + 0.325853I
a = 0.803970 − 0.959931I
b = 0.46369 + 1.37691I
2.31904 − 5.54243I 0
u = 1.110490 − 0.325853I
a = 0.803970 + 0.959931I
b = 0.46369 − 1.37691I
2.31904 + 5.54243I 0
u = 1.010790 + 0.568163I
a = −1.041410 + 0.777099I
b = −0.79240 − 1.20253I
6.82559 − 8.92441I 0
u = 1.010790 − 0.568163I
a = −1.041410 − 0.777099I
b = −0.79240 + 1.20253I
6.82559 + 8.92441I 0
u = 0.837469
a = 1.74493
b = 0.651596
1.32843 0
u = 0.834619 + 0.068459I
a = 1.11868 − 1.15771I
b = 0.122964 + 0.871724I
1.05796 − 1.60667I 0
u = 0.834619 − 0.068459I
a = 1.11868 + 1.15771I
b = 0.122964 − 0.871724I
1.05796 + 1.60667I 0
u = −0.747301 + 0.300818I
a = −1.43570 − 0.17399I
b = −0.28753 + 1.78837I
3.08312 − 0.32521I 0
u = −0.747301 − 0.300818I
a = −1.43570 + 0.17399I
b = −0.28753 − 1.78837I
3.08312 + 0.32521I 0
u = 1.171950 + 0.319156I
a = −0.769449 + 0.921693I
b = −0.53141 − 1.44621I
0.91583 − 11.46570I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.171950 − 0.319156I
a = −0.769449 − 0.921693I
b = −0.53141 + 1.44621I
0.91583 + 11.46570I 0
u = −0.676753 + 0.340805I
a = 1.57458 + 0.16811I
b = 0.22913 − 1.62356I
2.44745 − 5.97053I 0
u = −0.676753 − 0.340805I
a = 1.57458 − 0.16811I
b = 0.22913 + 1.62356I
2.44745 + 5.97053I 0
u = −1.155550 + 0.484145I
a = 0.476705 − 0.398292I
b = 0.870599 + 0.369387I
−1.89822 − 0.09517I 0
u = −1.155550 − 0.484145I
a = 0.476705 + 0.398292I
b = 0.870599 − 0.369387I
−1.89822 + 0.09517I 0
u = 0.067607 + 1.268540I
a = −0.517657 + 0.930992I
b = −0.02936 − 1.68368I
5.38445 + 7.13126I 0
u = 0.067607 − 1.268540I
a = −0.517657 − 0.930992I
b = −0.02936 + 1.68368I
5.38445 − 7.13126I 0
u = −1.271640 + 0.128056I
a = 0.298289 − 0.180579I
b = 0.544558 − 0.103827I
−2.56232 + 0.10384I 0
u = −1.271640 − 0.128056I
a = 0.298289 + 0.180579I
b = 0.544558 + 0.103827I
−2.56232 − 0.10384I 0
u = 1.275730 + 0.099499I
a = −0.261216 + 0.699980I
b = 0.022657 − 0.303271I
−7.15417 − 1.85942I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.275730 − 0.099499I
a = −0.261216 − 0.699980I
b = 0.022657 + 0.303271I
−7.15417 + 1.85942I 0
u = 1.253080 + 0.305726I
a = −0.258569 − 0.695811I
b = 0.144347 + 0.268476I
−4.19980 − 4.72472I 0
u = 1.253080 − 0.305726I
a = −0.258569 + 0.695811I
b = 0.144347 − 0.268476I
−4.19980 + 4.72472I 0
u = −0.747473 + 1.053770I
a = 0.598405 + 0.554465I
b = 0.506477 − 1.049490I
2.05301 + 3.14695I 0
u = −0.747473 − 1.053770I
a = 0.598405 − 0.554465I
b = 0.506477 + 1.049490I
2.05301 − 3.14695I 0
u = −0.645630 + 1.123760I
a = −0.641009 − 0.548285I
b = −0.393996 + 1.017120I
1.53090 − 2.31840I 0
u = −0.645630 − 1.123760I
a = −0.641009 + 0.548285I
b = −0.393996 − 1.017120I
1.53090 + 2.31840I 0
u = −1.163600 + 0.574178I
a = 0.410632 + 0.513633I
b = 1.41359 − 1.56128I
−1.69027 + 2.64124I 0
u = −1.163600 − 0.574178I
a = 0.410632 − 0.513633I
b = 1.41359 + 1.56128I
−1.69027 − 2.64124I 0
u = 0.025146 + 1.303070I
a = 0.528325 − 0.913491I
b = 0.04675 + 1.67028I
4.30507 + 12.99410I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.025146 − 1.303070I
a = 0.528325 + 0.913491I
b = 0.04675 − 1.67028I
4.30507 − 12.99410I 0
u = 1.289380 + 0.465433I
a = 0.649741 − 0.572712I
b = 1.46690 + 1.79403I
−3.47353 − 5.02118I 0
u = 1.289380 − 0.465433I
a = 0.649741 + 0.572712I
b = 1.46690 − 1.79403I
−3.47353 + 5.02118I 0
u = 1.284990 + 0.513116I
a = −0.644786 − 0.665377I
b = 0.296157 + 0.279172I
−1.27305 − 6.74434I 0
u = 1.284990 − 0.513116I
a = −0.644786 + 0.665377I
b = 0.296157 − 0.279172I
−1.27305 + 6.74434I 0
u = −1.343930 + 0.365232I
a = −0.278349 − 0.476771I
b = −1.63765 + 2.49147I
−3.12646 − 1.54964I 0
u = −1.343930 − 0.365232I
a = −0.278349 + 0.476771I
b = −1.63765 − 2.49147I
−3.12646 + 1.54964I 0
u = 1.297560 + 0.532107I
a = −0.650697 + 0.674013I
b = −1.20656 − 1.84644I
−0.88277 − 9.86930I 0
u = 1.297560 − 0.532107I
a = −0.650697 − 0.674013I
b = −1.20656 + 1.84644I
−0.88277 + 9.86930I 0
u = −1.278490 + 0.598838I
a = −0.546587 + 0.376035I
b = −0.671701 − 0.458776I
−2.69231 + 4.85276I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.278490 − 0.598838I
a = −0.546587 − 0.376035I
b = −0.671701 + 0.458776I
−2.69231 − 4.85276I 0
u = 1.32523 + 0.53448I
a = 0.683241 + 0.613107I
b = −0.319094 − 0.260395I
−2.19410 − 12.52910I 0
u = 1.32523 − 0.53448I
a = 0.683241 − 0.613107I
b = −0.319094 + 0.260395I
−2.19410 + 12.52910I 0
u = −0.139563 + 0.548703I
a = 0.772155 − 0.274422I
b = −0.118828 − 0.464969I
−0.05266 + 1.50098I 0. − 4.29764I
u = −0.139563 − 0.548703I
a = 0.772155 + 0.274422I
b = −0.118828 + 0.464969I
−0.05266 − 1.50098I 0. + 4.29764I
u = 1.38493 + 0.40377I
a = 0.512376 + 0.464165I
b = −0.251393 − 0.180457I
−7.69575 − 7.07073I 0
u = 1.38493 − 0.40377I
a = 0.512376 − 0.464165I
b = −0.251393 + 0.180457I
−7.69575 + 7.07073I 0
u = 1.37071 + 0.53049I
a = 0.551202 − 0.692060I
b = 1.17591 + 2.09806I
−5.82157 − 12.73140I 0
u = 1.37071 − 0.53049I
a = 0.551202 + 0.692060I
b = 1.17591 − 2.09806I
−5.82157 + 12.73140I 0
u = 1.47962 + 0.18220I
a = −0.393884 + 0.127316I
b = 0.163230 − 0.097710I
−5.48389 − 6.66654I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47962 − 0.18220I
a = −0.393884 − 0.127316I
b = 0.163230 + 0.097710I
−5.48389 + 6.66654I 0
u = 1.37869 + 0.60252I
a = −0.564872 + 0.782469I
b = −0.96335 − 2.05274I
1.23211 − 13.59160I 0
u = 1.37869 − 0.60252I
a = −0.564872 − 0.782469I
b = −0.96335 + 2.05274I
1.23211 + 13.59160I 0
u = 0.048491 + 0.492832I
a = −1.43730 + 2.36932I
b = 0.512932 − 0.721088I
4.15621 + 8.24899I 3.35176 − 3.91144I
u = 0.048491 − 0.492832I
a = −1.43730 − 2.36932I
b = 0.512932 + 0.721088I
4.15621 − 8.24899I 3.35176 + 3.91144I
u = 1.49041 + 0.25080I
a = 0.427983 + 0.059763I
b = −0.199490 + 0.011130I
−5.55367 − 1.98303I 0
u = 1.49041 − 0.25080I
a = 0.427983 − 0.059763I
b = −0.199490 − 0.011130I
−5.55367 + 1.98303I 0
u = 0.121490 + 0.460336I
a = 1.69615 − 2.29216I
b = −0.422681 + 0.669438I
5.08524 + 2.34478I 5.19497 + 0.97374I
u = 0.121490 − 0.460336I
a = 1.69615 + 2.29216I
b = −0.422681 − 0.669438I
5.08524 − 2.34478I 5.19497 − 0.97374I
u = 1.40485 + 0.60107I
a = 0.535007 − 0.788858I
b = 0.94234 + 2.11613I
−0.0610 − 19.5513I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40485 − 0.60107I
a = 0.535007 + 0.788858I
b = 0.94234 − 2.11613I
−0.0610 + 19.5513I 0
u = −1.41679 + 0.63944I
a = −0.344477 − 0.596096I
b = −1.00557 + 1.98778I
−5.81970 + 4.41330I 0
u = −1.41679 − 0.63944I
a = −0.344477 + 0.596096I
b = −1.00557 − 1.98778I
−5.81970 − 4.41330I 0
u = −1.51823 + 0.46024I
a = −0.579018 + 0.256271I
b = −0.476720 − 0.279194I
−6.14991 − 0.54757I 0
u = −1.51823 − 0.46024I
a = −0.579018 − 0.256271I
b = −0.476720 + 0.279194I
−6.14991 + 0.54757I 0
u = −1.36723 + 0.83790I
a = 0.408896 + 0.635332I
b = 0.80910 − 1.74193I
0.26862 + 4.52922I 0
u = −1.36723 − 0.83790I
a = 0.408896 − 0.635332I
b = 0.80910 + 1.74193I
0.26862 − 4.52922I 0
u = −0.357513 + 0.109882I
a = 2.14428 − 0.92121I
b = 0.411541 − 0.982590I
−2.39931 − 1.48408I −5.07693 + 4.49405I
u = −0.357513 − 0.109882I
a = 2.14428 + 0.92121I
b = 0.411541 + 0.982590I
−2.39931 + 1.48408I −5.07693 − 4.49405I
u = −1.43629 + 0.83574I
a = −0.391723 − 0.651726I
b = −0.76511 + 1.81712I
−0.73749 + 10.18020I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43629 − 0.83574I
a = −0.391723 + 0.651726I
b = −0.76511 − 1.81712I
−0.73749 − 10.18020I 0
u = 0.322544 + 0.075287I
a = 2.13709 + 1.54640I
b = −0.292459 − 0.797611I
1.20860 + 1.42458I 6.98331 − 3.17622I
u = 0.322544 − 0.075287I
a = 2.13709 − 1.54640I
b = −0.292459 + 0.797611I
1.20860 − 1.42458I 6.98331 + 3.17622I
u = −1.70080 + 0.27789I
a = 0.617357 − 0.138645I
b = 0.354154 + 0.150732I
−0.730807 − 0.398436I 0
u = −1.70080 − 0.27789I
a = 0.617357 + 0.138645I
b = 0.354154 − 0.150732I
−0.730807 + 0.398436I 0
u = −1.72382 + 0.35792I
a = −0.640029 + 0.169683I
b = −0.338904 − 0.198761I
−1.57172 − 5.89073I 0
u = −1.72382 − 0.35792I
a = −0.640029 − 0.169683I
b = −0.338904 + 0.198761I
−1.57172 + 5.89073I 0
u = −0.055868 + 0.219662I
a = −1.02732 + 4.31608I
b = 0.727666 − 0.348325I
−1.73197 + 2.72965I −1.78279 − 3.15925I
u = −0.055868 − 0.219662I
a = −1.02732 − 4.31608I
b = 0.727666 + 0.348325I
−1.73197 − 2.72965I −1.78279 + 3.15925I
u = −0.024246 + 0.217367I
a = 1.88720 + 2.29140I
b = 1.036280 − 0.835866I
0.00137 + 2.90749I 3.98420 − 0.02765I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.024246 − 0.217367I
a = 1.88720 − 2.29140I
b = 1.036280 + 0.835866I
0.00137 − 2.90749I 3.98420 + 0.02765I
u = 0.181935
a = 5.68101
b = −0.345979
1.67471 6.64690
u = 0.1082860 + 0.0882436I
a = 3.45481 + 5.96508I
b = 0.021195 − 0.708290I
0.94696 + 2.64839I 1.91996 − 2.43957I
u = 0.1082860 − 0.0882436I
a = 3.45481 − 5.96508I
b = 0.021195 + 0.708290I
0.94696 − 2.64839I 1.91996 + 2.43957I
17
II. I
u
2
= h−u
4
b + 2u
4
+ · · · − b + 2, a, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
4
=
0
b
a
10
=
−u
−u
3
+ u
a
8
=
0
u
a
3
=
0
b
a
7
=
u
u
a
1
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
6
=
u
4
− u
2
− 1
u
4
− 2u
2
a
5
=
−u
4
b − u
3
b + 2u
2
b + 3bu + b
bu + 2b
a
2
=
−u
4
+ u
2
+ 1
−2u
4
+ u
3
+ 3u
2
+ b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
3
b + u
4
− u
2
b + u
3
− 6bu + 2u
2
+ 2b − 7u − 7
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
8
u
10
c
6
, c
10
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
7
, c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
12
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
5
c
3
, c
8
y
10
c
6
, c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
7
, c
9
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 0
b = 1.76091 + 3.04998I
−2.40108 − 2.02988I 2.76075 − 3.67600I
u = −1.21774
a = 0
b = 1.76091 − 3.04998I
−2.40108 + 2.02988I 2.76075 + 3.67600I
u = −0.309916 + 0.549911I
a = 0
b = 0.864485 − 0.518603I
−0.32910 + 3.56046I −2.01870 − 9.75023I
u = −0.309916 + 0.549911I
a = 0
b = 0.016881 + 1.007970I
−0.329100 − 0.499304I −1.95395 + 0.91636I
u = −0.309916 − 0.549911I
a = 0
b = 0.864485 + 0.518603I
−0.32910 − 3.56046I −2.01870 + 9.75023I
u = −0.309916 − 0.549911I
a = 0
b = 0.016881 − 1.007970I
−0.329100 + 0.499304I −1.95395 − 0.91636I
u = 1.41878 + 0.21917I
a = 0
b = 0.369732 + 0.377747I
−5.87256 − 2.37095I −6.85700 + 6.98324I
u = 1.41878 + 0.21917I
a = 0
b = −0.512005 + 0.131324I
−5.87256 − 6.43072I −9.93110 + 1.72471I
u = 1.41878 − 0.21917I
a = 0
b = 0.369732 − 0.377747I
−5.87256 + 2.37095I −6.85700 − 6.98324I
u = 1.41878 − 0.21917I
a = 0
b = −0.512005 − 0.131324I
−5.87256 + 6.43072I −9.93110 − 1.72471I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
5
)(u
124
+ 42u
123
+ ··· + 2u + 1)
c
2
((u
2
+ u + 1)
5
)(u
124
+ 6u
123
+ ··· + 2u + 1)
c
3
, c
8
u
10
(u
124
− u
123
+ ··· + 5120u + 1024)
c
5
((u
2
− u + 1)
5
)(u
124
+ 6u
123
+ ··· + 2u + 1)
c
6
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
124
− 3u
123
+ ··· + 1975u + 1031)
c
7
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
124
+ 3u
123
+ ··· − 376993u − 48793)
c
9
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
124
− 3u
123
+ ··· − 17u + 1)
c
10
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
124
+ 21u
123
+ ··· + 3u + 1)
c
11
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
124
− 3u
123
+ ··· − 17u + 1)
c
12
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
)(u
124
− 9u
123
+ ··· − 3u + 1)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
5
)(y
124
+ 86y
123
+ ··· − 1250y + 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
124
+ 42y
123
+ ··· + 2y + 1)
c
3
, c
8
y
10
(y
124
− 55y
123
+ ··· − 2.62144 × 10
7
y + 1048576)
c
6
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
124
+ 131y
123
+ ··· + 138554707y + 1062961)
c
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
124
+ 83y
123
+ ··· − 318551403169y + 2380756849)
c
9
, c
11
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
124
− 85y
123
+ ··· − 17y + 1)
c
10
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
124
+ 3y
123
+ ··· − 17y + 1)
c
12
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
124
− 21y
123
+ ··· − 9y + 1)
23
