12a
0047
(K12a
0047
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 4 12 10 6 1 8 11
Solving Sequence
5,9
6
3,10
2 1 11 4 7 8 12
c
5
c
9
c
2
c
1
c
10
c
4
c
6
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.18936 × 10
246
u
110
− 2.13517 × 10
246
u
109
+ ··· + 5.64432 × 10
247
b − 4.74907 × 10
248
,
4.40979 × 10
247
u
110
+ 9.13393 × 10
247
u
109
+ ··· + 4.51546 × 10
248
a + 1.43309 × 10
250
,
u
111
+ 2u
110
+ ··· + 160u + 64i
I
u
2
= hb + 1, −u
8
+ 3u
6
+ u
5
− 4u
4
− 2u
3
+ u
2
+ a + 2u + 1, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
I
v
1
= ha, −18v
5
+ 63v
4
− 193v
3
+ 63v
2
+ 55b + 27v −12, v
6
− 2v
5
+ 7v
4
+ 8v
3
+ 7v
2
+ 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 126 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−3.19 × 10
246
u
110
− 2.14 × 10
246
u
109
+ · · · + 5.64 × 10
247
b − 4.75 ×
10
248
, 4.41 × 10
247
u
110
+ 9.13 × 10
247
u
109
+ · · · + 4.52 × 10
248
a + 1.43 ×
10
250
, u
111
+ 2u
110
+ · · · + 160u + 64i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
3
=
−0.0976599u
110
− 0.202281u
109
+ ··· − 0.854738u − 31.7375
0.0565056u
110
+ 0.0378286u
109
+ ··· + 22.9253u + 8.41389
a
10
=
−u
−u
3
+ u
a
2
=
−0.0411543u
110
− 0.164453u
109
+ ··· + 22.0706u − 23.3236
0.0565056u
110
+ 0.0378286u
109
+ ··· + 22.9253u + 8.41389
a
1
=
−0.120659u
110
− 0.241271u
109
+ ··· − 2.78514u − 16.8544
0.0541953u
110
+ 0.118379u
109
+ ··· + 2.44293u − 1.61000
a
11
=
−0.143665u
110
− 0.240646u
109
+ ··· − 1.44973u − 16.5967
0.0133269u
110
+ 0.0569514u
109
+ ··· − 18.3902u − 8.25017
a
4
=
0.0111189u
110
− 0.0832837u
109
+ ··· + 26.9485u − 9.66021
0.0701195u
110
+ 0.127567u
109
+ ··· − 6.36809u + 0.618737
a
7
=
−0.0664640u
110
− 0.122892u
109
+ ··· − 0.342210u − 18.4644
−0.0333772u
110
− 0.0802479u
109
+ ··· + 0.205002u + 0.967688
a
8
=
u
3
u
5
− u
3
+ u
a
12
=
−0.113592u
110
− 0.203964u
109
+ ··· + 0.640164u − 16.1869
−0.0252501u
110
+ 0.0114473u
109
+ ··· − 19.4565u − 11.8010
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.161186u
110
− 0.677696u
109
+ ··· + 69.5252u − 36.2776
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
111
+ 50u
110
+ ··· + 45u + 1
c
2
, c
4
u
111
− 12u
110
+ ··· + u + 1
c
3
, c
6
u
111
− 3u
110
+ ··· − 2560u + 512
c
5
, c
9
u
111
+ 2u
110
+ ··· + 160u + 64
c
7
, c
11
u
111
− 5u
110
+ ··· + 6u + 1
c
8
u
111
+ 40u
110
+ ··· + 107520u + 4096
c
10
, c
12
u
111
− 39u
110
+ ··· − 34u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
111
+ 34y
110
+ ··· − 5587y −1
c
2
, c
4
y
111
− 50y
110
+ ··· + 45y −1
c
3
, c
6
y
111
+ 63y
110
+ ··· − 3932160y −262144
c
5
, c
9
y
111
− 40y
110
+ ··· + 107520y −4096
c
7
, c
11
y
111
+ 39y
110
+ ··· − 34y −1
c
8
y
111
+ 52y
110
+ ··· − 334495744y −16777216
c
10
, c
12
y
111
+ 71y
110
+ ··· + 250y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.961261 + 0.305856I
a = 0.615473 − 0.767844I
b = 0.761803 − 0.469769I
1.51893 − 1.34502I 0
u = 0.961261 − 0.305856I
a = 0.615473 + 0.767844I
b = 0.761803 + 0.469769I
1.51893 + 1.34502I 0
u = −0.857490 + 0.495314I
a = −0.52751 − 2.40166I
b = −0.930489 + 0.464651I
−1.85472 + 3.13671I 0
u = −0.857490 − 0.495314I
a = −0.52751 + 2.40166I
b = −0.930489 − 0.464651I
−1.85472 − 3.13671I 0
u = 0.972722 + 0.028500I
a = 1.72566 + 0.16118I
b = 0.926889 + 0.540738I
0.91466 − 5.55388I 0
u = 0.972722 − 0.028500I
a = 1.72566 − 0.16118I
b = 0.926889 − 0.540738I
0.91466 + 5.55388I 0
u = 0.580825 + 0.879729I
a = 1.19720 − 1.21005I
b = −0.916016 + 0.511238I
−0.64800 + 5.40513I 0
u = 0.580825 − 0.879729I
a = 1.19720 + 1.21005I
b = −0.916016 − 0.511238I
−0.64800 − 5.40513I 0
u = −0.765501 + 0.553121I
a = −0.500470 − 1.110230I
b = 1.029320 + 0.785263I
3.64520 + 0.60285I 0
u = −0.765501 − 0.553121I
a = −0.500470 + 1.110230I
b = 1.029320 − 0.785263I
3.64520 − 0.60285I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.716525 + 0.613563I
a = −0.153728 − 1.308980I
b = 0.689023 + 0.854328I
3.48851 − 1.75426I 0
u = 0.716525 − 0.613563I
a = −0.153728 + 1.308980I
b = 0.689023 − 0.854328I
3.48851 + 1.75426I 0
u = 0.788393 + 0.725909I
a = 1.10459 − 1.09562I
b = −0.781000 + 0.575014I
3.15897 − 0.41518I 0
u = 0.788393 − 0.725909I
a = 1.10459 + 1.09562I
b = −0.781000 − 0.575014I
3.15897 + 0.41518I 0
u = −0.849847 + 0.655093I
a = −0.165620 + 1.385900I
b = 0.674325 − 0.922324I
4.71931 + 6.83549I 0
u = −0.849847 − 0.655093I
a = −0.165620 − 1.385900I
b = 0.674325 + 0.922324I
4.71931 − 6.83549I 0
u = −0.472703 + 0.795398I
a = 1.28208 + 1.21302I
b = −0.908601 − 0.434969I
−1.65724 − 0.25812I 0
u = −0.472703 − 0.795398I
a = 1.28208 − 1.21302I
b = −0.908601 + 0.434969I
−1.65724 + 0.25812I 0
u = −0.847842 + 0.674035I
a = −0.296981 − 0.910876I
b = −1.294380 − 0.050287I
1.45768 + 2.60301I 0
u = −0.847842 − 0.674035I
a = −0.296981 + 0.910876I
b = −1.294380 + 0.050287I
1.45768 − 2.60301I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500463 + 0.766009I
a = 0.15270 − 1.69929I
b = −1.219930 + 0.077295I
−1.75055 − 3.19219I 0
u = −0.500463 − 0.766009I
a = 0.15270 + 1.69929I
b = −1.219930 − 0.077295I
−1.75055 + 3.19219I 0
u = −1.077640 + 0.129946I
a = 0.361937 − 0.584101I
b = −0.084940 + 0.655027I
−4.12746 − 0.17488I 0
u = −1.077640 − 0.129946I
a = 0.361937 + 0.584101I
b = −0.084940 − 0.655027I
−4.12746 + 0.17488I 0
u = −0.074865 + 1.083460I
a = −0.251254 + 0.791988I
b = 0.912226 − 0.474868I
−1.46708 + 4.63529I 0
u = −0.074865 − 1.083460I
a = −0.251254 − 0.791988I
b = 0.912226 + 0.474868I
−1.46708 − 4.63529I 0
u = −0.690756 + 0.843068I
a = −0.535950 − 1.011050I
b = 1.080660 + 0.712649I
6.97174 − 5.31220I 0
u = −0.690756 − 0.843068I
a = −0.535950 + 1.011050I
b = 1.080660 − 0.712649I
6.97174 + 5.31220I 0
u = −0.956831 + 0.525019I
a = 0.954350 + 0.985429I
b = −0.621966 − 0.625924I
−2.27963 + 0.82457I 0
u = −0.956831 − 0.525019I
a = 0.954350 − 0.985429I
b = −0.621966 + 0.625924I
−2.27963 − 0.82457I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192505 + 1.075250I
a = −0.177114 − 0.778854I
b = 0.860535 + 0.445165I
−1.23200 + 0.90790I 0
u = 0.192505 − 1.075250I
a = −0.177114 + 0.778854I
b = 0.860535 − 0.445165I
−1.23200 − 0.90790I 0
u = −0.859755 + 0.675252I
a = −1.135270 − 0.160639I
b = 0.532972 + 0.838336I
4.68879 − 1.68552I 0
u = −0.859755 − 0.675252I
a = −1.135270 + 0.160639I
b = 0.532972 − 0.838336I
4.68879 + 1.68552I 0
u = −0.945558 + 0.570571I
a = 1.26787 + 2.01034I
b = 1.077520 − 0.661944I
3.04138 + 3.90587I 0
u = −0.945558 − 0.570571I
a = 1.26787 − 2.01034I
b = 1.077520 + 0.661944I
3.04138 − 3.90587I 0
u = 0.664358 + 0.599954I
a = −0.08780 + 2.94975I
b = −0.802872 − 0.455801I
−0.20502 + 1.39970I 0
u = 0.664358 − 0.599954I
a = −0.08780 − 2.94975I
b = −0.802872 + 0.455801I
−0.20502 − 1.39970I 0
u = 0.641635 + 0.909705I
a = 0.072845 − 1.364280I
b = 0.486017 + 0.821449I
2.97384 + 0.23222I 0
u = 0.641635 − 0.909705I
a = 0.072845 + 1.364280I
b = 0.486017 − 0.821449I
2.97384 − 0.23222I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.112920 + 0.132238I
a = 1.000340 + 0.261885I
b = 0.897392 + 0.447328I
−2.09929 − 1.79300I 0
u = −1.112920 − 0.132238I
a = 1.000340 − 0.261885I
b = 0.897392 − 0.447328I
−2.09929 + 1.79300I 0
u = 1.100350 + 0.229120I
a = 0.212933 + 0.553604I
b = 0.005517 − 0.693265I
−3.81029 − 5.38817I 0
u = 1.100350 − 0.229120I
a = 0.212933 − 0.553604I
b = 0.005517 + 0.693265I
−3.81029 + 5.38817I 0
u = −0.773381 + 0.830007I
a = −0.048570 + 1.407420I
b = 0.568998 − 0.900673I
8.52723 + 0.62332I 0
u = −0.773381 − 0.830007I
a = −0.048570 − 1.407420I
b = 0.568998 + 0.900673I
8.52723 − 0.62332I 0
u = 0.938382 + 0.649116I
a = −0.861937 + 0.269194I
b = 0.464394 − 0.835909I
2.81501 − 3.26360I 0
u = 0.938382 − 0.649116I
a = −0.861937 − 0.269194I
b = 0.464394 + 0.835909I
2.81501 + 3.26360I 0
u = 0.913223 + 0.693999I
a = −0.06671 + 2.28822I
b = −0.901738 − 0.574717I
2.77609 − 5.00482I 0
u = 0.913223 − 0.693999I
a = −0.06671 − 2.28822I
b = −0.901738 + 0.574717I
2.77609 + 5.00482I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.778898 + 0.343012I
a = −1.41652 + 0.71580I
b = −1.176390 + 0.127517I
−2.73805 − 1.01723I −10.94783 + 6.27439I
u = 0.778898 − 0.343012I
a = −1.41652 − 0.71580I
b = −1.176390 − 0.127517I
−2.73805 + 1.01723I −10.94783 − 6.27439I
u = 1.153030 + 0.000762I
a = −0.760894 + 0.885736I
b = −1.195590 − 0.353101I
−7.47764 + 1.50835I 0
u = 1.153030 − 0.000762I
a = −0.760894 − 0.885736I
b = −1.195590 + 0.353101I
−7.47764 − 1.50835I 0
u = −1.157080 + 0.095057I
a = −0.720181 − 1.109600I
b = −1.170490 + 0.388339I
−7.39457 + 4.16403I 0
u = −1.157080 − 0.095057I
a = −0.720181 + 1.109600I
b = −1.170490 − 0.388339I
−7.39457 − 4.16403I 0
u = 0.993165 + 0.613622I
a = 0.95705 − 1.05542I
b = −0.669117 + 0.666637I
−1.23032 − 6.24800I 0
u = 0.993165 − 0.613622I
a = 0.95705 + 1.05542I
b = −0.669117 − 0.666637I
−1.23032 + 6.24800I 0
u = 0.571056 + 1.026180I
a = −0.532528 + 0.924418I
b = 1.096700 − 0.642791I
1.13791 + 5.71377I 0
u = 0.571056 − 1.026180I
a = −0.532528 − 0.924418I
b = 1.096700 + 0.642791I
1.13791 − 5.71377I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688824 + 0.955138I
a = 0.07067 + 1.42628I
b = 0.464226 − 0.871917I
4.21683 − 5.60824I 0
u = −0.688824 − 0.955138I
a = 0.07067 − 1.42628I
b = 0.464226 + 0.871917I
4.21683 + 5.60824I 0
u = 0.686909 + 0.436600I
a = 0.496822 − 0.215720I
b = 0.236693 − 0.173944I
1.43635 − 1.82704I −0.84954 + 4.84948I
u = 0.686909 − 0.436600I
a = 0.496822 + 0.215720I
b = 0.236693 + 0.173944I
1.43635 + 1.82704I −0.84954 − 4.84948I
u = 1.044800 + 0.576162I
a = −0.348684 + 0.417955I
b = −1.324720 + 0.135388I
−4.45792 − 2.96094I 0
u = 1.044800 − 0.576162I
a = −0.348684 − 0.417955I
b = −1.324720 − 0.135388I
−4.45792 + 2.96094I 0
u = 1.052210 + 0.597069I
a = 0.98408 − 1.77129I
b = 1.109350 + 0.642860I
0.87796 − 8.78070I 0
u = 1.052210 − 0.597069I
a = 0.98408 + 1.77129I
b = 1.109350 − 0.642860I
0.87796 + 8.78070I 0
u = 0.362203 + 0.687116I
a = −0.405923 + 1.008540I
b = 0.977149 − 0.680548I
2.67743 + 3.92833I −5.69908 − 2.39283I
u = 0.362203 − 0.687116I
a = −0.405923 − 1.008540I
b = 0.977149 + 0.680548I
2.67743 − 3.92833I −5.69908 + 2.39283I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.969355 + 0.753597I
a = −0.991867 − 0.557856I
b = 0.475097 + 0.920853I
7.90957 + 5.29556I 0
u = −0.969355 − 0.753597I
a = −0.991867 + 0.557856I
b = 0.475097 − 0.920853I
7.90957 − 5.29556I 0
u = −0.645356 + 1.047180I
a = −0.563660 − 0.932862I
b = 1.119580 + 0.656047I
2.23809 − 11.26390I 0
u = −0.645356 − 1.047180I
a = −0.563660 + 0.932862I
b = 1.119580 − 0.656047I
2.23809 + 11.26390I 0
u = −1.059270 + 0.647902I
a = −0.207983 − 0.464083I
b = −1.349170 − 0.118043I
−3.35615 + 8.53993I 0
u = −1.059270 − 0.647902I
a = −0.207983 + 0.464083I
b = −1.349170 + 0.118043I
−3.35615 − 8.53993I 0
u = −1.066380 + 0.641788I
a = −0.12862 − 2.02884I
b = −0.986679 + 0.588452I
−3.37073 + 5.61350I 0
u = −1.066380 − 0.641788I
a = −0.12862 + 2.02884I
b = −0.986679 − 0.588452I
−3.37073 − 5.61350I 0
u = 0.267839 + 0.699470I
a = 0.68721 + 2.21087I
b = −1.129410 − 0.124638I
−2.49151 − 1.68594I −7.47036 − 1.42690I
u = 0.267839 − 0.699470I
a = 0.68721 − 2.21087I
b = −1.129410 + 0.124638I
−2.49151 + 1.68594I −7.47036 + 1.42690I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.030160 + 0.720587I
a = 0.71254 + 2.00743I
b = 1.132590 − 0.678871I
5.90690 + 11.16420I 0
u = −1.030160 − 0.720587I
a = 0.71254 − 2.00743I
b = 1.132590 + 0.678871I
5.90690 − 11.16420I 0
u = 1.077120 + 0.699464I
a = −0.04264 + 2.03440I
b = −0.977779 − 0.617324I
−2.17058 − 11.24930I 0
u = 1.077120 − 0.699464I
a = −0.04264 − 2.03440I
b = −0.977779 + 0.617324I
−2.17058 + 11.24930I 0
u = 1.066800 + 0.727963I
a = −0.777069 + 0.660416I
b = 0.404198 − 0.940500I
1.63590 − 6.26824I 0
u = 1.066800 − 0.727963I
a = −0.777069 − 0.660416I
b = 0.404198 + 0.940500I
1.63590 + 6.26824I 0
u = 0.611834 + 0.346825I
a = −0.424809 + 1.132140I
b = 0.961999 − 0.784969I
2.73478 + 4.20900I −10.00721 + 0.57642I
u = 0.611834 − 0.346825I
a = −0.424809 − 1.132140I
b = 0.961999 + 0.784969I
2.73478 − 4.20900I −10.00721 − 0.57642I
u = 0.424597 + 0.530789I
a = −0.188404 − 1.154690I
b = 0.764069 + 0.739282I
3.38545 − 1.57723I −2.69554 + 5.44980I
u = 0.424597 − 0.530789I
a = −0.188404 + 1.154690I
b = 0.764069 − 0.739282I
3.38545 + 1.57723I −2.69554 − 5.44980I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.075540 + 0.768246I
a = −0.821553 − 0.734422I
b = 0.415395 + 0.967932I
2.97459 + 11.93470I 0
u = −1.075540 − 0.768246I
a = −0.821553 + 0.734422I
b = 0.415395 − 0.967932I
2.97459 − 11.93470I 0
u = −1.265160 + 0.437949I
a = 0.471571 + 0.242610I
b = 0.848355 + 0.276852I
−5.56887 + 0.59401I 0
u = −1.265160 − 0.437949I
a = 0.471571 − 0.242610I
b = 0.848355 − 0.276852I
−5.56887 − 0.59401I 0
u = −1.333270 + 0.173414I
a = 0.837831 + 0.522328I
b = 1.063820 − 0.455497I
−6.98403 + 3.40230I 0
u = −1.333270 − 0.173414I
a = 0.837831 − 0.522328I
b = 1.063820 + 0.455497I
−6.98403 − 3.40230I 0
u = 1.325960 + 0.257152I
a = 0.835359 − 0.688269I
b = 1.087480 + 0.480695I
−6.62780 − 9.38031I 0
u = 1.325960 − 0.257152I
a = 0.835359 + 0.688269I
b = 1.087480 − 0.480695I
−6.62780 + 9.38031I 0
u = 1.246820 + 0.525991I
a = 0.407713 − 0.268068I
b = 0.821780 − 0.240489I
−4.75429 − 6.49311I 0
u = 1.246820 − 0.525991I
a = 0.407713 + 0.268068I
b = 0.821780 + 0.240489I
−4.75429 + 6.49311I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.142380 + 0.741212I
a = 0.54160 − 1.78118I
b = 1.166410 + 0.658674I
−0.68346 − 12.10710I 0
u = 1.142380 − 0.741212I
a = 0.54160 + 1.78118I
b = 1.166410 − 0.658674I
−0.68346 + 12.10710I 0
u = −1.135360 + 0.783517I
a = 0.46510 + 1.83815I
b = 1.174150 − 0.671550I
0.6511 + 17.8984I 0
u = −1.135360 − 0.783517I
a = 0.46510 − 1.83815I
b = 1.174150 + 0.671550I
0.6511 − 17.8984I 0
u = −0.597936
a = 0.991036
b = −0.266692
−0.855489 −11.6530
u = 0.078117 + 0.575284I
a = 1.54993 − 0.43215I
b = −0.0983081 + 0.0963811I
−0.46663 + 2.30779I −1.91194 − 3.67862I
u = 0.078117 − 0.575284I
a = 1.54993 + 0.43215I
b = −0.0983081 − 0.0963811I
−0.46663 − 2.30779I −1.91194 + 3.67862I
u = −0.379391 + 0.286023I
a = 1.65758 + 0.59289I
b = −0.700392 − 0.183066I
−0.947135 − 0.090988I −9.16846 − 0.70332I
u = −0.379391 − 0.286023I
a = 1.65758 − 0.59289I
b = −0.700392 + 0.183066I
−0.947135 + 0.090988I −9.16846 + 0.70332I
u = −0.464260 + 0.090617I
a = −5.72829 − 3.35406I
b = −0.913336 + 0.139185I
−1.26665 + 2.32355I −25.1036 − 5.2591I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.464260 − 0.090617I
a = −5.72829 + 3.35406I
b = −0.913336 − 0.139185I
−1.26665 − 2.32355I −25.1036 + 5.2591I
16
II. I
u
2
= hb + 1, −u
8
+ 3u
6
+ u
5
− 4u
4
− 2u
3
+ u
2
+ a + 2u + 1, u
9
+ u
8
−
2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
3
=
u
8
− 3u
6
− u
5
+ 4u
4
+ 2u
3
− u
2
− 2u − 1
−1
a
10
=
−u
−u
3
+ u
a
2
=
u
8
− 3u
6
− u
5
+ 4u
4
+ 2u
3
− u
2
− 2u − 2
−1
a
1
=
−1
0
a
11
=
−u
3
−u
3
+ u
a
4
=
u
8
− 3u
6
− u
5
+ 4u
4
+ 2u
3
− u
2
− 2u − 1
−1
a
7
=
1
u
2
a
8
=
u
3
u
5
− u
3
+ u
a
12
=
−u
6
+ u
4
− 1
−u
6
+ 2u
4
− u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
8
− 2u
7
− 2u
6
+ 3u
5
+ 6u
4
− 3u
3
− 3u
2
− 4u − 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
7
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
8
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
9
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
10
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
11
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
12
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
7
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
8
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
10
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = −0.457852 − 1.072010I
b = −1.00000
0.13850 + 2.09337I −8.93344 − 3.71284I
u = −0.772920 − 0.510351I
a = −0.457852 + 1.072010I
b = −1.00000
0.13850 − 2.09337I −8.93344 + 3.71284I
u = 0.825933
a = −1.46592
b = −1.00000
−2.84338 −14.0380
u = 1.173910 + 0.391555I
a = −0.522253 + 0.392004I
b = −1.00000
−6.01628 − 1.33617I −14.5101 + 2.5441I
u = 1.173910 − 0.391555I
a = −0.522253 − 0.392004I
b = −1.00000
−6.01628 + 1.33617I −14.5101 − 2.5441I
u = −0.141484 + 0.739668I
a = 1.63880 − 0.65075I
b = −1.00000
−2.26187 − 2.45442I −7.83172 + 1.00072I
u = −0.141484 − 0.739668I
a = 1.63880 + 0.65075I
b = −1.00000
−2.26187 + 2.45442I −7.83172 − 1.00072I
u = −1.172470 + 0.500383I
a = −0.425734 − 0.444312I
b = −1.00000
−5.24306 + 7.08493I −13.7057 − 8.1735I
u = −1.172470 − 0.500383I
a = −0.425734 + 0.444312I
b = −1.00000
−5.24306 − 7.08493I −13.7057 + 8.1735I
20
III.
I
v
1
= ha, −18v
5
+ 63v
4
+ · · · + 55b − 12, v
6
− 2v
5
+ 7v
4
+ 8v
3
+ 7v
2
+ 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
v
0
a
6
=
1
0
a
3
=
0
0.327273v
5
− 1.14545v
4
+ ··· − 0.490909v + 0.218182
a
10
=
v
0
a
2
=
0.327273v
5
− 1.14545v
4
+ ··· − 0.490909v + 0.218182
0.327273v
5
− 1.14545v
4
+ ··· − 0.490909v + 0.218182
a
1
=
0.327273v
5
− 1.14545v
4
+ ··· − 0.490909v + 0.218182
−0.254545v
5
+ 0.890909v
4
+ ··· + 0.381818v + 2.16364
a
11
=
0.490909v
5
− 1.21818v
4
+ ··· + 0.763636v + 0.327273
−1.25455v
5
+ 2.89091v
4
+ ··· − 6.61818v − 0.836364
a
4
=
−0.581818v
5
+ 2.03636v
4
+ ··· + 0.872727v + 1.94545
−0.581818v
5
+ 2.03636v
4
+ ··· + 0.872727v + 0.945455
a
7
=
−0.327273v
5
+ 1.14545v
4
+ ··· + 0.490909v − 0.218182
0.254545v
5
− 0.890909v
4
+ ··· − 0.381818v − 2.16364
a
8
=
v
0
a
12
=
0.563636v
5
− 1.47273v
4
+ ··· + 0.654545v + 0.709091
−1.25455v
5
+ 2.89091v
4
+ ··· − 6.61818v − 0.836364
(ii) Obstruction class = 1
(iii) Cusp Shapes =
321
55
v
5
−
821
55
v
4
+
2681
55
v
3
+
1214
55
v
2
+
1251
55
v −
116
55
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
8
, c
9
u
6
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
12
(u
2
− u + 1)
3
c
10
, c
11
(u
2
+ u + 1)
3
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
4
(y
3
− y
2
+ 2y − 1)
2
c
5
, c
8
, c
9
y
6
c
7
, c
10
, c
11
c
12
(y
2
+ y + 1)
3
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.428020 + 0.376187I
a = 0
b = 0.877439 + 0.744862I
3.02413 − 4.85801I −4.05323 + 9.17563I
v = −0.428020 − 0.376187I
a = 0
b = 0.877439 − 0.744862I
3.02413 + 4.85801I −4.05323 − 9.17563I
v = −0.111778 + 0.558770I
a = 0
b = 0.877439 − 0.744862I
3.02413 + 0.79824I −7.63258 + 1.54443I
v = −0.111778 − 0.558770I
a = 0
b = 0.877439 + 0.744862I
3.02413 − 0.79824I −7.63258 − 1.54443I
v = 1.53980 + 2.66701I
a = 0
b = −0.754878
−1.11345 + 2.02988I −15.8142 + 4.6579I
v = 1.53980 − 2.66701I
a = 0
b = −0.754878
−1.11345 − 2.02988I −15.8142 − 4.6579I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
3
− u
2
+ 2u − 1)
2
(u
111
+ 50u
110
+ ··· + 45u + 1)
c
2
((u − 1)
9
)(u
3
+ u
2
− 1)
2
(u
111
− 12u
110
+ ··· + u + 1)
c
3
u
9
(u
3
− u
2
+ 2u − 1)
2
(u
111
− 3u
110
+ ··· − 2560u + 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)
2
(u
111
− 12u
110
+ ··· + u + 1)
c
5
u
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
111
+ 2u
110
+ ··· + 160u + 64)
c
6
u
9
(u
3
+ u
2
+ 2u + 1)
2
(u
111
− 3u
110
+ ··· − 2560u + 512)
c
7
(u
2
− u + 1)
3
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
111
− 5u
110
+ ··· + 6u + 1)
c
8
u
6
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
111
+ 40u
110
+ ··· + 107520u + 4096)
c
9
u
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
111
+ 2u
110
+ ··· + 160u + 64)
c
10
(u
2
+ u + 1)
3
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
111
− 39u
110
+ ··· − 34u + 1)
c
11
(u
2
+ u + 1)
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
111
− 5u
110
+ ··· + 6u + 1)
c
12
(u
2
− u + 1)
3
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
111
− 39u
110
+ ··· − 34u + 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
3
+ 3y
2
+ 2y − 1)
2
(y
111
+ 34y
110
+ ··· − 5587y − 1)
c
2
, c
4
((y − 1)
9
)(y
3
− y
2
+ 2y − 1)
2
(y
111
− 50y
110
+ ··· + 45y − 1)
c
3
, c
6
y
9
(y
3
+ 3y
2
+ 2y − 1)
2
(y
111
+ 63y
110
+ ··· − 3932160y − 262144)
c
5
, c
9
y
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
111
− 40y
110
+ ··· + 107520y − 4096)
c
7
, c
11
(y
2
+ y + 1)
3
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
111
+ 39y
110
+ ··· − 34y − 1)
c
8
y
6
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
111
+ 52y
110
+ ··· − 334495744y − 16777216)
c
10
, c
12
((y
2
+ y + 1)
3
)(y
9
+ 7y
8
+ ··· + 13y − 1)
· (y
111
+ 71y
110
+ ··· + 250y − 1)
26
