12n
0878
(K12n
0878
)
A knot diagram
1
Linearized knot diagam
4 9 7 10 12 2 12 3 6 1 7 5
Solving Sequence
5,10 1,4
2 12 6 7 3 9 8 11
c
4
c
1
c
12
c
5
c
6
c
3
c
9
c
8
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.21141 × 10
651
u
110
− 1.08774 × 10
651
u
109
+ ··· + 1.65962 × 10
652
b − 7.59921 × 10
651
,
− 1.93122 × 10
651
u
110
+ 2.08824 × 10
651
u
109
+ ··· + 1.65962 × 10
652
a + 1.24469 × 10
652
,
u
111
− u
110
+ ··· − 7u + 3i
I
u
2
= h1.42494 × 10
88
u
41
− 3.45989 × 10
87
u
40
+ ··· + 6.00691 × 10
88
b + 5.71024 × 10
88
,
3.70120 × 10
88
u
41
− 6.96687 × 10
87
u
40
+ ··· + 6.00691 × 10
88
a + 1.88942 × 10
89
, u
42
+ 7u
40
+ ··· + 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 153 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
= h1.21 × 10
651
u
110
− 1.09 × 10
651
u
109
+ · · · + 1.66 × 10
652
b − 7.60 ×
10
651
, −1.93 × 10
651
u
110
+ 2.09 × 10
651
u
109
+ · · · + 1.66 × 10
652
a + 1.24 ×
10
652
, u
111
− u
110
+ · · · − 7u + 3i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
1
=
0.116365u
110
− 0.125826u
109
+ ··· + 7.34809u − 0.749986
−0.0729930u
110
+ 0.0655417u
109
+ ··· − 3.44083u + 0.457888
a
4
=
1
−u
2
a
2
=
0.164158u
110
− 0.170164u
109
+ ··· + 11.2042u − 1.23626
−0.0749935u
110
+ 0.0663564u
109
+ ··· − 3.32164u + 0.468253
a
12
=
0.189358u
110
− 0.191368u
109
+ ··· + 10.7889u − 1.20787
−0.0729930u
110
+ 0.0655417u
109
+ ··· − 3.44083u + 0.457888
a
6
=
0.196495u
110
− 0.170592u
109
+ ··· + 12.6499u − 2.20306
−0.0181036u
110
+ 0.0334053u
109
+ ··· + 0.189929u + 1.44411
a
7
=
0.191393u
110
− 0.254658u
109
+ ··· + 5.51405u + 1.37521
0.0475149u
110
− 0.0191522u
109
+ ··· + 1.31742u + 0.635649
a
3
=
−0.123405u
110
+ 0.0992140u
109
+ ··· − 9.75407u − 0.425829
−0.0883196u
110
+ 0.0385761u
109
+ ··· − 1.39081u − 1.31338
a
9
=
0.170652u
110
− 0.222197u
109
+ ··· + 6.00991u − 2.90751
0.0971444u
110
− 0.133840u
109
+ ··· + 4.19812u − 1.62097
a
8
=
−0.0974642u
110
+ 0.0834086u
109
+ ··· − 13.4622u + 0.976720
−0.0664275u
110
+ 0.0302539u
109
+ ··· − 1.59786u − 1.68074
a
11
=
0.0599303u
110
− 0.179163u
109
+ ··· + 24.5544u − 4.98031
0.0412055u
110
− 0.0537590u
109
+ ··· + 0.489793u − 0.535176
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.271714u
110
− 0.155209u
109
+ ··· + 1.22849u − 8.03638
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
111
− 4u
110
+ ··· + 1801u + 243
c
2
, c
8
u
111
− u
110
+ ··· + 6220u + 16317
c
3
u
111
+ 7u
110
+ ··· − 1407403921u + 153714813
c
4
u
111
− u
110
+ ··· − 7u + 3
c
5
, c
12
u
111
+ 48u
109
+ ··· + 261816u + 23711
c
6
u
111
+ 21u
109
+ ··· + 53u + 3
c
7
, c
11
u
111
− u
110
+ ··· + 453319u + 98619
c
9
u
111
+ 5u
110
+ ··· − 9375844u + 2723079
c
10
u
111
− 4u
110
+ ··· + 83737u − 91683
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
111
+ 2y
110
+ ··· + 3473479y −59049
c
2
, c
8
y
111
+ 59y
110
+ ··· − 9207502820y −266244489
c
3
y
111
− 11y
110
+ ··· + 591943606661337133y −23628243735624969
c
4
y
111
+ 9y
110
+ ··· − 107y −9
c
5
, c
12
y
111
+ 96y
110
+ ··· − 18841975698y −562211521
c
6
y
111
+ 42y
110
+ ··· − 103925y −9
c
7
, c
11
y
111
+ 79y
110
+ ··· + 20799127135y −9725707161
c
9
y
111
− 9y
110
+ ··· + 119784414656788y −7415159240241
c
10
y
111
− 44y
110
+ ··· + 779023452421y −8405772489
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.714374 + 0.714520I
a = −1.360370 + 0.237368I
b = −1.051980 + 0.230780I
−2.66126 − 5.69184I 0
u = 0.714374 − 0.714520I
a = −1.360370 − 0.237368I
b = −1.051980 − 0.230780I
−2.66126 + 5.69184I 0
u = 0.865449 + 0.471904I
a = −1.78076 − 0.38273I
b = −0.292204 + 0.809679I
−3.08295 − 4.55181I 0
u = 0.865449 − 0.471904I
a = −1.78076 + 0.38273I
b = −0.292204 − 0.809679I
−3.08295 + 4.55181I 0
u = −0.744405 + 0.625978I
a = 0.354718 + 0.088370I
b = 0.26601 + 1.47529I
0.90056 + 4.21838I 0
u = −0.744405 − 0.625978I
a = 0.354718 − 0.088370I
b = 0.26601 − 1.47529I
0.90056 − 4.21838I 0
u = −1.018670 + 0.221906I
a = 0.700092 + 1.209710I
b = −0.442687 − 0.142458I
−1.19315 − 6.76877I 0
u = −1.018670 − 0.221906I
a = 0.700092 − 1.209710I
b = −0.442687 + 0.142458I
−1.19315 + 6.76877I 0
u = −0.700518 + 0.811869I
a = 1.252180 + 0.046686I
b = 1.49503 + 0.14142I
0.34719 + 11.43030I 0
u = −0.700518 − 0.811869I
a = 1.252180 − 0.046686I
b = 1.49503 − 0.14142I
0.34719 − 11.43030I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.462927 + 0.771636I
a = 1.40069 − 0.31892I
b = 1.228940 − 0.544484I
5.77937 − 4.39153I 0
u = 0.462927 − 0.771636I
a = 1.40069 + 0.31892I
b = 1.228940 + 0.544484I
5.77937 + 4.39153I 0
u = 1.070260 + 0.383207I
a = 0.805900 − 0.263619I
b = 0.71928 − 1.55137I
−5.61982 − 8.80647I 0
u = 1.070260 − 0.383207I
a = 0.805900 + 0.263619I
b = 0.71928 + 1.55137I
−5.61982 + 8.80647I 0
u = 0.788734 + 0.348001I
a = 0.623744 − 0.348987I
b = 0.016183 + 0.698832I
2.83661 − 2.30918I 0
u = 0.788734 − 0.348001I
a = 0.623744 + 0.348987I
b = 0.016183 − 0.698832I
2.83661 + 2.30918I 0
u = 0.301556 + 1.107410I
a = 0.471287 − 1.118110I
b = 0.165856 − 0.537127I
7.13821 − 5.36833I 0
u = 0.301556 − 1.107410I
a = 0.471287 + 1.118110I
b = 0.165856 + 0.537127I
7.13821 + 5.36833I 0
u = 0.442659 + 1.063300I
a = −0.723596 + 0.127029I
b = −0.681753 + 0.669259I
4.95925 − 2.55415I 0
u = 0.442659 − 1.063300I
a = −0.723596 − 0.127029I
b = −0.681753 − 0.669259I
4.95925 + 2.55415I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.810382 + 0.246739I
a = 0.627222 − 0.007177I
b = 0.472691 + 0.442982I
2.68502 − 2.34907I 0. + 4.62590I
u = 0.810382 − 0.246739I
a = 0.627222 + 0.007177I
b = 0.472691 − 0.442982I
2.68502 + 2.34907I 0. − 4.62590I
u = −0.830518 + 0.807934I
a = −1.64096 − 0.52688I
b = 0.004057 − 1.205310I
−5.66828 + 2.16661I 0
u = −0.830518 − 0.807934I
a = −1.64096 + 0.52688I
b = 0.004057 + 1.205310I
−5.66828 − 2.16661I 0
u = −0.270917 + 0.795648I
a = −0.70380 + 1.98629I
b = −0.723663 + 0.638508I
−0.47949 + 3.84871I −4.00000 − 6.49874I
u = −0.270917 − 0.795648I
a = −0.70380 − 1.98629I
b = −0.723663 − 0.638508I
−0.47949 − 3.84871I −4.00000 + 6.49874I
u = −0.598161 + 0.586619I
a = 0.935048 + 0.558040I
b = 0.898596 − 0.517687I
2.65645 + 0.58417I −4.00000 + 0.I
u = −0.598161 − 0.586619I
a = 0.935048 − 0.558040I
b = 0.898596 + 0.517687I
2.65645 − 0.58417I −4.00000 + 0.I
u = −0.251585 + 1.145510I
a = −0.113209 − 0.545664I
b = −0.203945 + 0.129546I
2.50436 + 2.13405I 0
u = −0.251585 − 1.145510I
a = −0.113209 + 0.545664I
b = −0.203945 − 0.129546I
2.50436 − 2.13405I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.691497 + 0.440489I
a = 1.350100 − 0.134371I
b = 1.39227 + 0.55383I
−1.89770 − 0.44510I −6.46310 − 2.28603I
u = −0.691497 − 0.440489I
a = 1.350100 + 0.134371I
b = 1.39227 − 0.55383I
−1.89770 + 0.44510I −6.46310 + 2.28603I
u = −1.073510 + 0.556165I
a = 0.991162 − 0.506808I
b = 0.477139 + 1.167370I
0.31996 + 6.65134I 0
u = −1.073510 − 0.556165I
a = 0.991162 + 0.506808I
b = 0.477139 − 1.167370I
0.31996 − 6.65134I 0
u = −0.841097 + 0.878400I
a = −0.413392 − 0.695994I
b = 0.141549 − 1.300200I
−6.53060 − 3.65843I 0
u = −0.841097 − 0.878400I
a = −0.413392 + 0.695994I
b = 0.141549 + 1.300200I
−6.53060 + 3.65843I 0
u = −0.597370 + 1.069170I
a = 0.877314 + 0.812741I
b = −0.157504 + 0.969451I
2.11240 + 1.20009I 0
u = −0.597370 − 1.069170I
a = 0.877314 − 0.812741I
b = −0.157504 − 0.969451I
2.11240 − 1.20009I 0
u = 0.648234 + 1.041010I
a = 0.652552 + 0.092460I
b = 0.862050 + 0.578104I
4.14591 + 0.74234I 0
u = 0.648234 − 1.041010I
a = 0.652552 − 0.092460I
b = 0.862050 − 0.578104I
4.14591 − 0.74234I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.049130 + 0.640897I
a = −1.120320 − 0.032004I
b = −0.450276 + 1.161750I
−4.10087 − 3.88533I 0
u = 1.049130 − 0.640897I
a = −1.120320 + 0.032004I
b = −0.450276 − 1.161750I
−4.10087 + 3.88533I 0
u = 1.028590 + 0.705324I
a = 1.56592 + 0.21211I
b = 0.02758 − 1.51655I
−7.17972 − 5.77916I 0
u = 1.028590 − 0.705324I
a = 1.56592 − 0.21211I
b = 0.02758 + 1.51655I
−7.17972 + 5.77916I 0
u = 0.108806 + 0.738364I
a = 1.65018 + 1.06385I
b = 0.660881 + 0.421823I
−1.00746 + 1.43239I −0.712963 − 1.182765I
u = 0.108806 − 0.738364I
a = 1.65018 − 1.06385I
b = 0.660881 − 0.421823I
−1.00746 − 1.43239I −0.712963 + 1.182765I
u = 0.088345 + 1.255210I
a = 0.02028 − 1.56698I
b = −0.127970 − 1.122830I
−1.43444 + 3.95549I 0
u = 0.088345 − 1.255210I
a = 0.02028 + 1.56698I
b = −0.127970 + 1.122830I
−1.43444 − 3.95549I 0
u = −1.320290 + 0.165660I
a = −0.615887 − 0.224422I
b = −0.53967 − 1.34969I
−7.67870 + 0.79225I 0
u = −1.320290 − 0.165660I
a = −0.615887 + 0.224422I
b = −0.53967 + 1.34969I
−7.67870 − 0.79225I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591662 + 0.308130I
a = −1.48419 − 0.29327I
b = −1.278240 − 0.387702I
−2.88004 − 3.80174I −10.3585 + 11.7266I
u = 0.591662 − 0.308130I
a = −1.48419 + 0.29327I
b = −1.278240 + 0.387702I
−2.88004 + 3.80174I −10.3585 − 11.7266I
u = 0.646735 + 0.090961I
a = −1.82779 + 1.33379I
b = 0.023820 + 0.466302I
−3.24397 + 2.32203I −7.74916 + 1.18552I
u = 0.646735 − 0.090961I
a = −1.82779 − 1.33379I
b = 0.023820 − 0.466302I
−3.24397 − 2.32203I −7.74916 − 1.18552I
u = −0.957591 + 0.970816I
a = −1.255070 − 0.290968I
b = −0.61604 − 1.36478I
−6.51470 + 10.40070I 0
u = −0.957591 − 0.970816I
a = −1.255070 + 0.290968I
b = −0.61604 + 1.36478I
−6.51470 − 10.40070I 0
u = −0.765550 + 1.134320I
a = −0.477207 + 0.222027I
b = −0.843446 + 0.501365I
4.00430 + 2.46081I 0
u = −0.765550 − 1.134320I
a = −0.477207 − 0.222027I
b = −0.843446 − 0.501365I
4.00430 − 2.46081I 0
u = 0.993431 + 0.948966I
a = 1.204650 − 0.306662I
b = 0.35446 − 1.53621I
−8.80402 − 5.19154I 0
u = 0.993431 − 0.948966I
a = 1.204650 + 0.306662I
b = 0.35446 + 1.53621I
−8.80402 + 5.19154I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617717
a = −0.643374
b = −0.546644
−1.19358 −8.04680
u = −0.152825 + 0.596063I
a = −2.69132 − 1.36528I
b = −0.808836 − 0.871007I
5.01256 + 3.02445I 3.93926 + 13.39364I
u = −0.152825 − 0.596063I
a = −2.69132 + 1.36528I
b = −0.808836 + 0.871007I
5.01256 − 3.02445I 3.93926 − 13.39364I
u = 1.388250 + 0.158097I
a = −0.871222 − 0.449625I
b = −0.401550 + 0.780015I
−5.16105 − 3.41124I 0
u = 1.388250 − 0.158097I
a = −0.871222 + 0.449625I
b = −0.401550 − 0.780015I
−5.16105 + 3.41124I 0
u = 0.878004 + 1.094590I
a = 0.551431 − 0.531799I
b = −0.01753 − 1.53239I
−8.36283 − 1.86599I 0
u = 0.878004 − 1.094590I
a = 0.551431 + 0.531799I
b = −0.01753 + 1.53239I
−8.36283 + 1.86599I 0
u = −0.171107 + 0.561744I
a = 3.18410 + 0.05775I
b = 0.440311 + 0.971236I
−2.55806 + 2.86376I −2.12152 − 2.95420I
u = −0.171107 − 0.561744I
a = 3.18410 − 0.05775I
b = 0.440311 − 0.971236I
−2.55806 − 2.86376I −2.12152 + 2.95420I
u = −0.333362 + 0.475392I
a = 1.365580 + 0.265437I
b = 0.355020 + 0.629497I
−0.235630 + 1.236950I −3.14529 − 5.36463I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.333362 − 0.475392I
a = 1.365580 − 0.265437I
b = 0.355020 − 0.629497I
−0.235630 − 1.236950I −3.14529 + 5.36463I
u = −0.438474 + 0.334578I
a = −0.783807 − 0.859439I
b = −0.86580 − 1.88441I
−5.27914 + 2.07032I −6.0815 − 15.0598I
u = −0.438474 − 0.334578I
a = −0.783807 + 0.859439I
b = −0.86580 + 1.88441I
−5.27914 − 2.07032I −6.0815 + 15.0598I
u = 0.64890 + 1.32449I
a = −0.350517 + 0.263804I
b = −0.002498 + 0.446892I
5.01188 − 3.25184I 0
u = 0.64890 − 1.32449I
a = −0.350517 − 0.263804I
b = −0.002498 − 0.446892I
5.01188 + 3.25184I 0
u = −1.28098 + 0.73287I
a = 0.721659 + 0.090912I
b = 0.042035 + 1.270820I
−1.99001 − 1.39769I 0
u = −1.28098 − 0.73287I
a = 0.721659 − 0.090912I
b = 0.042035 − 1.270820I
−1.99001 + 1.39769I 0
u = 0.334374 + 0.350306I
a = 0.547809 − 0.900839I
b = 0.20466 − 2.30103I
−5.33727 + 1.59995I −4.1687 + 14.5202I
u = 0.334374 − 0.350306I
a = 0.547809 + 0.900839I
b = 0.20466 + 2.30103I
−5.33727 − 1.59995I −4.1687 − 14.5202I
u = −1.18142 + 0.95426I
a = 0.929256 − 0.277886I
b = 0.728942 + 1.043040I
2.69666 + 5.09815I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.18142 − 0.95426I
a = 0.929256 + 0.277886I
b = 0.728942 − 1.043040I
2.69666 − 5.09815I 0
u = 1.28594 + 0.88309I
a = −0.826769 − 0.473327I
b = −0.607795 + 1.101090I
2.12664 − 7.82113I 0
u = 1.28594 − 0.88309I
a = −0.826769 + 0.473327I
b = −0.607795 − 1.101090I
2.12664 + 7.82113I 0
u = 0.233019 + 0.351041I
a = −4.60590 − 3.74878I
b = −0.488333 + 0.957091I
−1.39665 − 8.53108I 2.72060 + 12.79796I
u = 0.233019 − 0.351041I
a = −4.60590 + 3.74878I
b = −0.488333 − 0.957091I
−1.39665 + 8.53108I 2.72060 − 12.79796I
u = 1.14773 + 1.12517I
a = 1.079590 − 0.195597I
b = 0.62392 − 1.51047I
−4.7963 − 18.6404I 0
u = 1.14773 − 1.12517I
a = 1.079590 + 0.195597I
b = 0.62392 + 1.51047I
−4.7963 + 18.6404I 0
u = −0.341809 + 0.180413I
a = 0.37707 + 1.37681I
b = −0.16616 − 1.50808I
3.27712 + 4.80787I −4.53718 + 6.19603I
u = −0.341809 − 0.180413I
a = 0.37707 − 1.37681I
b = −0.16616 + 1.50808I
3.27712 − 4.80787I −4.53718 − 6.19603I
u = −1.07844 + 1.20422I
a = 0.842347 + 0.309744I
b = 0.39945 + 1.50564I
−0.65444 + 9.79757I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.07844 − 1.20422I
a = 0.842347 − 0.309744I
b = 0.39945 − 1.50564I
−0.65444 − 9.79757I 0
u = −1.17285 + 1.18347I
a = −0.950123 − 0.317594I
b = −0.47746 − 1.44379I
−7.87490 + 11.20670I 0
u = −1.17285 − 1.18347I
a = −0.950123 + 0.317594I
b = −0.47746 + 1.44379I
−7.87490 − 11.20670I 0
u = 0.316465 + 0.097588I
a = −2.05845 + 2.08096I
b = −0.063427 − 1.058360I
−1.33055 − 1.69320I −8.77159 + 2.56265I
u = 0.316465 − 0.097588I
a = −2.05845 − 2.08096I
b = −0.063427 + 1.058360I
−1.33055 + 1.69320I −8.77159 − 2.56265I
u = 0.078707 + 0.281604I
a = 2.67502 − 3.53779I
b = −0.04381 − 1.58925I
−6.99222 − 2.59124I −9.51161 + 3.63597I
u = 0.078707 − 0.281604I
a = 2.67502 + 3.53779I
b = −0.04381 + 1.58925I
−6.99222 + 2.59124I −9.51161 − 3.63597I
u = −0.152170 + 0.218008I
a = 1.53368 + 6.52606I
b = −0.232022 − 0.637467I
0.13226 − 2.48870I −5.76810 − 2.40873I
u = −0.152170 − 0.218008I
a = 1.53368 − 6.52606I
b = −0.232022 + 0.637467I
0.13226 + 2.48870I −5.76810 + 2.40873I
u = 1.35063 + 1.14659I
a = 0.648783 − 0.242907I
b = 0.322194 − 1.162370I
0.42207 − 4.82384I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35063 − 1.14659I
a = 0.648783 + 0.242907I
b = 0.322194 + 1.162370I
0.42207 + 4.82384I 0
u = 1.03231 + 1.45503I
a = −0.443822 + 0.374440I
b = −0.175720 + 1.305850I
−1.50323 − 3.75862I 0
u = 1.03231 − 1.45503I
a = −0.443822 − 0.374440I
b = −0.175720 − 1.305850I
−1.50323 + 3.75862I 0
u = 1.34857 + 1.21416I
a = 0.241513 − 0.398394I
b = −0.293146 − 1.273490I
−4.86772 + 9.78923I 0
u = 1.34857 − 1.21416I
a = 0.241513 + 0.398394I
b = −0.293146 + 1.273490I
−4.86772 − 9.78923I 0
u = −1.47447 + 1.11897I
a = −0.400667 − 0.360648I
b = 0.022501 − 1.276840I
−8.34445 − 1.99063I 0
u = −1.47447 − 1.11897I
a = −0.400667 + 0.360648I
b = 0.022501 + 1.276840I
−8.34445 + 1.99063I 0
u = −1.40582 + 1.21619I
a = −0.509182 + 0.025635I
b = −0.18387 − 1.50374I
−1.98216 + 5.27302I 0
u = −1.40582 − 1.21619I
a = −0.509182 − 0.025635I
b = −0.18387 + 1.50374I
−1.98216 − 5.27302I 0
u = 0.00011 + 2.73853I
a = −0.0175327 + 0.0916424I
b = 0.165211 + 0.941148I
8.61716 + 0.63430I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00011 − 2.73853I
a = −0.0175327 − 0.0916424I
b = 0.165211 − 0.941148I
8.61716 − 0.63430I 0
16
II.
I
u
2
= h1.42 × 10
88
u
41
− 3.46 × 10
87
u
40
+ · · · + 6.01 × 10
88
b + 5.71 × 10
88
, 3.70 ×
10
88
u
41
−6.97×10
87
u
40
+· · ·+6.01×10
88
a+1.89×10
89
, u
42
+7u
40
+· · ·+4u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
1
=
−0.616157u
41
+ 0.115981u
40
+ ··· − 9.83735u − 3.14541
−0.237216u
41
+ 0.0575985u
40
+ ··· − 9.02287u − 0.950613
a
4
=
1
−u
2
a
2
=
−0.370960u
41
+ 0.00347036u
40
+ ··· − 0.966712u − 2.07882
−0.222273u
41
+ 0.0568160u
40
+ ··· − 9.22772u − 1.06312
a
12
=
−0.378941u
41
+ 0.0583825u
40
+ ··· − 0.814479u − 2.19480
−0.237216u
41
+ 0.0575985u
40
+ ··· − 9.02287u − 0.950613
a
6
=
−0.549117u
41
+ 0.0931211u
40
+ ··· − 21.4276u − 0.340771
0.0443919u
41
+ 0.172057u
40
+ ··· − 10.1516u + 3.95910
a
7
=
−0.160969u
41
− 0.176131u
40
+ ··· − 8.18078u + 1.04708
0.159303u
41
+ 0.0706371u
40
+ ··· − 2.22793u + 1.71992
a
3
=
0.760864u
41
− 0.220955u
40
+ ··· + 17.6848u − 0.811985
−0.294166u
41
− 0.0345365u
40
+ ··· + 4.37866u − 3.96354
a
9
=
0.255933u
41
− 0.0319336u
40
+ ··· − 11.1840u + 3.38021
0.445600u
41
− 0.0395565u
40
+ ··· + 7.71344u + 3.96713
a
8
=
−0.660716u
41
− 0.0172246u
40
+ ··· − 23.9144u + 0.0266400
0.186389u
41
+ 0.111646u
40
+ ··· − 10.6025u + 4.69941
a
11
=
0.297796u
41
+ 0.0137552u
40
+ ··· + 2.46563u + 1.31737
0.265178u
41
− 0.0358788u
40
+ ··· + 5.63723u + 0.504725
(ii) Obstruction class = 1
(iii) Cusp Shapes = −1.10189u
41
+ 0.603477u
40
+ ··· + 3.90743u − 20.7365
17
(iv) u-Polynomials at the component
18
Crossings u-Polynomials at each crossing
c
1
u
42
− 5u
41
+ ··· + 8u + 1
c
2
u
42
+ 16u
40
+ ··· + 3u + 13
c
3
u
42
− 2u
41
+ ··· + 760u + 275
c
4
u
42
+ 7u
40
+ ··· + 4u + 1
c
5
u
42
+ u
41
+ ··· + 7u + 9
c
6
u
42
+ u
41
+ ··· − 2u + 1
c
7
u
42
+ 2u
41
+ ··· − 4u + 1
c
8
u
42
+ 16u
40
+ ··· − 3u + 13
c
9
u
42
+ 16u
39
+ ··· − 177u + 199
c
10
u
42
− 11u
41
+ ··· − 6u + 1
c
11
u
42
− 2u
41
+ ··· + 4u + 1
c
12
u
42
− u
41
+ ··· − 7u + 9
19
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
+ 15y
41
+ ··· − 20y + 1
c
2
, c
8
y
42
+ 32y
41
+ ··· + 2695y + 169
c
3
y
42
+ 30y
41
+ ··· + 230350y + 75625
c
4
y
42
+ 14y
41
+ ··· + 10y + 1
c
5
, c
12
y
42
+ 41y
41
+ ··· + 1697y + 81
c
6
y
42
+ 23y
41
+ ··· + 20y + 1
c
7
, c
11
y
42
+ 12y
41
+ ··· − 24y + 1
c
9
y
42
− 28y
40
+ ··· + 525075y + 39601
c
10
y
42
− 15y
41
+ ··· + 22y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309367 + 0.935151I
a = −1.094450 − 0.525980I
b = −0.882734 − 0.687045I
6.53719 + 3.46611I 5.66711 − 2.98458I
u = −0.309367 − 0.935151I
a = −1.094450 + 0.525980I
b = −0.882734 + 0.687045I
6.53719 − 3.46611I 5.66711 + 2.98458I
u = −0.524409 + 0.877601I
a = 0.408363 − 0.099163I
b = 0.153397 + 1.148170I
0.26151 + 2.86315I −3.24965 − 2.70797I
u = −0.524409 − 0.877601I
a = 0.408363 + 0.099163I
b = 0.153397 − 1.148170I
0.26151 − 2.86315I −3.24965 + 2.70797I
u = −0.907011 + 0.232666I
a = 0.851833 + 0.235357I
b = 0.630383 − 0.543371I
1.92705 + 1.95495I −7.50090 − 1.70539I
u = −0.907011 − 0.232666I
a = 0.851833 − 0.235357I
b = 0.630383 + 0.543371I
1.92705 − 1.95495I −7.50090 + 1.70539I
u = −0.312364 + 1.139560I
a = 0.469088 + 1.235540I
b = 0.065881 + 0.734193I
6.79483 + 5.28316I −9.14045 − 2.08154I
u = −0.312364 − 1.139560I
a = 0.469088 − 1.235540I
b = 0.065881 − 0.734193I
6.79483 − 5.28316I −9.14045 + 2.08154I
u = 0.644633 + 0.452694I
a = −2.67510 − 0.26522I
b = −0.376493 + 0.911815I
−3.43489 − 3.50942I −7.98067 + 4.90592I
u = 0.644633 − 0.452694I
a = −2.67510 + 0.26522I
b = −0.376493 − 0.911815I
−3.43489 + 3.50942I −7.98067 − 4.90592I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.965193 + 0.768930I
a = −1.57136 + 0.01293I
b = −0.10248 − 1.49914I
−7.25682 + 5.39119I −6.13707 + 3.30656I
u = −0.965193 − 0.768930I
a = −1.57136 − 0.01293I
b = −0.10248 + 1.49914I
−7.25682 − 5.39119I −6.13707 − 3.30656I
u = 0.314830 + 1.214040I
a = −0.217842 + 1.020480I
b = 0.128657 + 0.863970I
1.30215 − 1.81376I −5.77013 + 4.24567I
u = 0.314830 − 1.214040I
a = −0.217842 − 1.020480I
b = 0.128657 − 0.863970I
1.30215 + 1.81376I −5.77013 − 4.24567I
u = 0.674394 + 1.090490I
a = 0.390481 + 0.051398I
b = 0.723864 + 0.737686I
4.55606 − 0.31908I 3.05170 + 1.07121I
u = 0.674394 − 1.090490I
a = 0.390481 − 0.051398I
b = 0.723864 − 0.737686I
4.55606 + 0.31908I 3.05170 − 1.07121I
u = 0.151875 + 0.691079I
a = −0.94055 + 2.57225I
b = 0.214594 + 0.454237I
0.59463 − 2.89793I 4.03984 + 5.29599I
u = 0.151875 − 0.691079I
a = −0.94055 − 2.57225I
b = 0.214594 − 0.454237I
0.59463 + 2.89793I 4.03984 − 5.29599I
u = −1.183810 + 0.555387I
a = −0.534119 − 0.346052I
b = −0.30572 − 1.45020I
−7.74656 − 0.22815I −7.23180 + 0.98981I
u = −1.183810 − 0.555387I
a = −0.534119 + 0.346052I
b = −0.30572 + 1.45020I
−7.74656 + 0.22815I −7.23180 − 0.98981I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.669886 + 0.018374I
a = 0.64348 − 2.85122I
b = 0.488566 + 0.916027I
−1.93111 + 8.28078I −9.67878 − 7.20770I
u = −0.669886 − 0.018374I
a = 0.64348 + 2.85122I
b = 0.488566 − 0.916027I
−1.93111 − 8.28078I −9.67878 + 7.20770I
u = 0.209538 + 0.616297I
a = 2.49102 − 1.49789I
b = 0.801842 − 0.774337I
4.98179 − 3.25953I 0.1818 + 18.9527I
u = 0.209538 − 0.616297I
a = 2.49102 + 1.49789I
b = 0.801842 + 0.774337I
4.98179 + 3.25953I 0.1818 − 18.9527I
u = 1.358560 + 0.081931I
a = −0.847925 − 0.543750I
b = −0.417785 + 0.795321I
−5.16428 − 3.57820I −6.6201 + 28.0621I
u = 1.358560 − 0.081931I
a = −0.847925 + 0.543750I
b = −0.417785 − 0.795321I
−5.16428 + 3.57820I −6.6201 − 28.0621I
u = 0.453714 + 0.334935I
a = −0.405807 − 0.361318I
b = −0.30446 + 1.60792I
3.30582 − 5.14111I −2.4321 + 17.3826I
u = 0.453714 − 0.334935I
a = −0.405807 + 0.361318I
b = −0.30446 − 1.60792I
3.30582 + 5.14111I −2.4321 − 17.3826I
u = 0.527493 + 0.137007I
a = −2.14951 − 0.84072I
b = −0.609364 − 0.408921I
−2.35784 − 3.34462I −0.64187 + 2.52178I
u = 0.527493 − 0.137007I
a = −2.14951 + 0.84072I
b = −0.609364 + 0.408921I
−2.35784 + 3.34462I −0.64187 − 2.52178I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.72924 + 1.37570I
a = −0.254742 + 0.063738I
b = −0.409941 + 0.397713I
5.45829 + 2.95974I 0
u = −0.72924 − 1.37570I
a = −0.254742 − 0.063738I
b = −0.409941 − 0.397713I
5.45829 − 2.95974I 0
u = 1.28872 + 0.96290I
a = −0.804575 − 0.334824I
b = −0.564395 + 1.210070I
2.60152 − 7.27233I 0
u = 1.28872 − 0.96290I
a = −0.804575 + 0.334824I
b = −0.564395 − 1.210070I
2.60152 + 7.27233I 0
u = −1.27259 + 0.99167I
a = 0.785403 − 0.176619I
b = 0.602602 + 0.991889I
3.62383 + 5.33952I 0
u = −1.27259 − 0.99167I
a = 0.785403 + 0.176619I
b = 0.602602 − 0.991889I
3.62383 − 5.33952I 0
u = 1.42319 + 1.05633I
a = 0.532865 + 0.006288I
b = 0.20956 − 1.45255I
−2.32301 − 5.16938I 0
u = 1.42319 − 1.05633I
a = 0.532865 − 0.006288I
b = 0.20956 + 1.45255I
−2.32301 + 5.16938I 0
u = −0.107968 + 0.134204I
a = −2.52258 − 2.74196I
b = −0.34737 − 2.30229I
−5.50311 + 1.82249I −22.4830 − 3.5895I
u = −0.107968 − 0.134204I
a = −2.52258 + 2.74196I
b = −0.34737 + 2.30229I
−5.50311 − 1.82249I −22.4830 + 3.5895I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06510 + 2.75589I
a = −0.0539768 + 0.1305290I
b = −0.198607 + 0.983194I
8.57734 − 0.78624I 0
u = −0.06510 − 2.75589I
a = −0.0539768 − 0.1305290I
b = −0.198607 − 0.983194I
8.57734 + 0.78624I 0
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
42
− 5u
41
+ ··· + 8u + 1)(u
111
− 4u
110
+ ··· + 1801u + 243)
c
2
(u
42
+ 16u
40
+ ··· + 3u + 13)(u
111
− u
110
+ ··· + 6220u + 16317)
c
3
(u
42
− 2u
41
+ ··· + 760u + 275)
· (u
111
+ 7u
110
+ ··· − 1407403921u + 153714813)
c
4
(u
42
+ 7u
40
+ ··· + 4u + 1)(u
111
− u
110
+ ··· − 7u + 3)
c
5
(u
42
+ u
41
+ ··· + 7u + 9)(u
111
+ 48u
109
+ ··· + 261816u + 23711)
c
6
(u
42
+ u
41
+ ··· − 2u + 1)(u
111
+ 21u
109
+ ··· + 53u + 3)
c
7
(u
42
+ 2u
41
+ ··· − 4u + 1)(u
111
− u
110
+ ··· + 453319u + 98619)
c
8
(u
42
+ 16u
40
+ ··· − 3u + 13)(u
111
− u
110
+ ··· + 6220u + 16317)
c
9
(u
42
+ 16u
39
+ ··· − 177u + 199)
· (u
111
+ 5u
110
+ ··· − 9375844u + 2723079)
c
10
(u
42
− 11u
41
+ ··· − 6u + 1)(u
111
− 4u
110
+ ··· + 83737u − 91683)
c
11
(u
42
− 2u
41
+ ··· + 4u + 1)(u
111
− u
110
+ ··· + 453319u + 98619)
c
12
(u
42
− u
41
+ ··· − 7u + 9)(u
111
+ 48u
109
+ ··· + 261816u + 23711)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
42
+ 15y
41
+ ··· − 20y + 1)(y
111
+ 2y
110
+ ··· + 3473479y −59049)
c
2
, c
8
(y
42
+ 32y
41
+ ··· + 2695y + 169)
· (y
111
+ 59y
110
+ ··· − 9207502820y −266244489)
c
3
(y
42
+ 30y
41
+ ··· + 230350y + 75625)
· (y
111
− 11y
110
+ ··· + 591943606661337133y −23628243735624969)
c
4
(y
42
+ 14y
41
+ ··· + 10y + 1)(y
111
+ 9y
110
+ ··· − 107y −9)
c
5
, c
12
(y
42
+ 41y
41
+ ··· + 1697y + 81)
· (y
111
+ 96y
110
+ ··· − 18841975698y −562211521)
c
6
(y
42
+ 23y
41
+ ··· + 20y + 1)(y
111
+ 42y
110
+ ··· − 103925y −9)
c
7
, c
11
(y
42
+ 12y
41
+ ··· − 24y + 1)
· (y
111
+ 79y
110
+ ··· + 20799127135y −9725707161)
c
9
(y
42
− 28y
40
+ ··· + 525075y + 39601)
· (y
111
− 9y
110
+ ··· + 119784414656788y −7415159240241)
c
10
(y
42
− 15y
41
+ ··· + 22y + 1)
· (y
111
− 44y
110
+ ··· + 779023452421y −8405772489)
28
