12a
0004
(K12a
0004
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 10 4 11 12 7 1 9
Solving Sequence
2,5
3 6
4,10
7 8 11 1 12 9
c
2
c
5
c
3
c
6
c
7
c
10
c
1
c
11
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.58623 × 10
76
u
129
− 4.47141 × 10
78
u
128
+ ··· + 1.43114 × 10
77
b − 2.84585 × 10
78
,
− 6.57135 × 10
77
u
129
+ 2.71715 × 10
77
u
128
+ ··· + 2.86227 × 10
77
a − 1.19729 × 10
78
,
u
130
− 8u
129
+ ··· + 2u + 1i
I
u
2
= ha
4
u − a
3
u − a
3
+ a
2
− 2au + b − a + u + 1, a
5
+ a
4
u − a
3
u − a
3
− 2a
2
− au − u − 1, u
2
+ u + 1i
I
u
3
= hb − a, u
4
a − u
3
a − 2u
4
+ u
2
a + 2u
3
+ a
2
− 2u
2
− a − u + 2, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 150 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−5.59 × 10
76
u
129
− 4.47 × 10
78
u
128
+ · · · + 1.43 × 10
77
b − 2.85 ×
10
78
, −6.57 × 10
77
u
129
+ 2.72 × 10
77
u
128
+ · · · + 2.86 × 10
77
a − 1.20 ×
10
78
, u
130
− 8u
129
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
2.29585u
129
− 0.949298u
128
+ ··· + 20.9609u + 4.18300
0.390335u
129
+ 31.2438u
128
+ ··· + 51.6062u + 19.8853
a
7
=
10.7738u
129
− 82.0527u
128
+ ··· − 10.7181u − 6.86334
12.5299u
129
− 88.0806u
128
+ ··· + 9.84424u + 0.206116
a
8
=
1.31653u
129
+ 0.669349u
128
+ ··· + 12.0408u + 4.48855
−1.36092u
129
+ 42.7776u
128
+ ··· + 62.9324u + 23.3661
a
11
=
−0.0358964u
129
+ 12.9188u
128
+ ··· + 19.8042u + 2.41846
−5.51164u
129
+ 63.3209u
128
+ ··· + 30.5290u + 13.4695
a
1
=
u
2
+ 1
−u
4
a
12
=
0.952102u
129
+ 14.7945u
128
+ ··· + 31.3058u + 6.90175
−6.52188u
129
+ 89.6423u
128
+ ··· + 64.6648u + 26.4860
a
9
=
−1.46905u
129
+ 24.1231u
128
+ ··· + 21.6639u + 7.81213
−3.93886u
129
+ 56.7495u
128
+ ··· + 45.0240u + 18.7049
(ii) Obstruction class = −1
(iii) Cusp Shapes = −25.8022u
129
+ 180.947u
128
+ ··· − 33.4431u − 3.06530
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
130
+ 64u
129
+ ··· − 30u + 1
c
2
, c
5
u
130
+ 8u
129
+ ··· − 2u + 1
c
3
u
130
− 8u
129
+ ··· − 10406338u + 596177
c
4
, c
7
u
130
+ 3u
129
+ ··· + 3072u + 1024
c
6
, c
10
u
130
− 3u
129
+ ··· − 3072u + 1024
c
8
u
130
+ 8u
129
+ ··· + 10406338u + 596177
c
9
, c
12
u
130
− 8u
129
+ ··· + 2u + 1
c
11
u
130
− 64u
129
+ ··· + 30u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
130
+ 12y
129
+ ··· + 686y + 1
c
2
, c
5
, c
9
c
12
y
130
+ 64y
129
+ ··· − 30y + 1
c
3
, c
8
y
130
− 40y
129
+ ··· − 17001882314902y + 355427015329
c
4
, c
6
, c
7
c
10
y
130
− 65y
129
+ ··· − 22020096y + 1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.592700 + 0.792019I
a = −0.279524 + 1.370980I
b = −0.115357 + 0.676864I
0.002551 − 0.973476I 0
u = −0.592700 − 0.792019I
a = −0.279524 − 1.370980I
b = −0.115357 − 0.676864I
0.002551 + 0.973476I 0
u = −0.744003 + 0.687533I
a = 0.020821 + 0.486800I
b = −1.091330 + 0.106265I
2.03115 − 5.05572I 0
u = −0.744003 − 0.687533I
a = 0.020821 − 0.486800I
b = −1.091330 − 0.106265I
2.03115 + 5.05572I 0
u = −0.759392 + 0.616515I
a = −0.453470 − 0.697097I
b = 0.708494 − 0.160786I
6.34959 − 1.94756I 0
u = −0.759392 − 0.616515I
a = −0.453470 + 0.697097I
b = 0.708494 + 0.160786I
6.34959 + 1.94756I 0
u = −0.542109 + 0.787886I
a = −1.69307 + 1.39703I
b = −2.24766 + 1.18744I
0.00252 − 3.66806I 0
u = −0.542109 − 0.787886I
a = −1.69307 − 1.39703I
b = −2.24766 − 1.18744I
0.00252 + 3.66806I 0
u = −0.783339 + 0.694881I
a = −0.151450 − 0.242064I
b = 1.050480 + 0.115263I
4.55149 − 9.95496I 0
u = −0.783339 − 0.694881I
a = −0.151450 + 0.242064I
b = 1.050480 − 0.115263I
4.55149 + 9.95496I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.862122 + 0.340997I
a = 0.74839 − 1.92906I
b = −0.199145 − 0.718224I
2.45608 − 13.29840I 0
u = 0.862122 − 0.340997I
a = 0.74839 + 1.92906I
b = −0.199145 + 0.718224I
2.45608 + 13.29840I 0
u = −0.431112 + 0.988134I
a = −2.89647 + 0.13589I
b = −3.43417 − 0.15726I
−0.785891 + 0.018251I 0
u = −0.431112 − 0.988134I
a = −2.89647 − 0.13589I
b = −3.43417 + 0.15726I
−0.785891 − 0.018251I 0
u = −0.505657 + 0.752572I
a = −1.48334 + 2.03829I
b = −1.97303 + 1.70778I
−0.00252 − 3.66806I 0
u = −0.505657 − 0.752572I
a = −1.48334 − 2.03829I
b = −1.97303 − 1.70778I
−0.00252 + 3.66806I 0
u = −0.637914 + 0.643957I
a = 0.26515 − 1.56494I
b = −0.252681 − 0.684601I
1.64093 − 4.70889I 0
u = −0.637914 − 0.643957I
a = 0.26515 + 1.56494I
b = −0.252681 + 0.684601I
1.64093 + 4.70889I 0
u = 0.472721 + 0.986926I
a = 0.366438 + 0.491612I
b = 0.730104 − 0.899035I
5.43061 − 1.83010I 0
u = 0.472721 − 0.986926I
a = 0.366438 − 0.491612I
b = 0.730104 + 0.899035I
5.43061 + 1.83010I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.568348 + 0.936676I
a = 1.86032 + 0.03104I
b = 2.46856 − 0.26096I
0.785891 − 0.018251I 0
u = −0.568348 − 0.936676I
a = 1.86032 − 0.03104I
b = 2.46856 + 0.26096I
0.785891 + 0.018251I 0
u = 0.837632 + 0.330901I
a = −0.63276 + 1.88171I
b = 0.321496 + 0.720320I
− 8.00471I 0
u = 0.837632 − 0.330901I
a = −0.63276 − 1.88171I
b = 0.321496 − 0.720320I
8.00471I 0
u = 0.807554 + 0.375193I
a = 0.67303 − 1.65111I
b = −0.376203 − 0.491162I
5.04203 − 4.93450I 0
u = 0.807554 − 0.375193I
a = 0.67303 + 1.65111I
b = −0.376203 + 0.491162I
5.04203 + 4.93450I 0
u = −0.202837 + 1.101200I
a = 0.702355 − 0.859861I
b = 0.61872 − 1.76397I
2.02680 − 3.40551I 0
u = −0.202837 − 1.101200I
a = 0.702355 + 0.859861I
b = 0.61872 + 1.76397I
2.02680 + 3.40551I 0
u = 0.877007 + 0.063352I
a = 1.131520 + 0.385876I
b = 0.201976 + 0.136445I
−1.86134 + 3.02789I 0
u = 0.877007 − 0.063352I
a = 1.131520 − 0.385876I
b = 0.201976 − 0.136445I
−1.86134 − 3.02789I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356637 + 1.072920I
a = −1.082510 + 0.005267I
b = −2.08828 + 0.10975I
−2.02680 + 3.40551I 0
u = 0.356637 − 1.072920I
a = −1.082510 − 0.005267I
b = −2.08828 − 0.10975I
−2.02680 − 3.40551I 0
u = 0.485761 + 1.022820I
a = −0.539985 − 0.564035I
b = −0.972768 + 0.630871I
1.86134 + 3.02789I 0
u = 0.485761 − 1.022820I
a = −0.539985 + 0.564035I
b = −0.972768 − 0.630871I
1.86134 − 3.02789I 0
u = −0.450602 + 1.045830I
a = −1.61996 + 0.23774I
b = −1.99584 + 0.89329I
−1.75761 − 1.88399I 0
u = −0.450602 − 1.045830I
a = −1.61996 − 0.23774I
b = −1.99584 − 0.89329I
−1.75761 + 1.88399I 0
u = −0.338433 + 1.092870I
a = −1.25500 + 0.66822I
b = −1.41448 + 1.48706I
−1.36077 − 0.74859I 0
u = −0.338433 − 1.092870I
a = −1.25500 − 0.66822I
b = −1.41448 − 1.48706I
−1.36077 + 0.74859I 0
u = 0.527011 + 1.018560I
a = 0.642820 + 0.338568I
b = 1.28844 − 0.85517I
5.92691 + 7.48471I 0
u = 0.527011 − 1.018560I
a = 0.642820 − 0.338568I
b = 1.28844 + 0.85517I
5.92691 − 7.48471I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.468701 + 1.047850I
a = 2.38303 + 0.29053I
b = 3.03269 + 0.70962I
−1.64093 − 4.70889I 0
u = −0.468701 − 1.047850I
a = 2.38303 − 0.29053I
b = 3.03269 − 0.70962I
−1.64093 + 4.70889I 0
u = −0.675397 + 0.928630I
a = −0.332315 + 0.520207I
b = −0.570321 − 0.396184I
1.317160 − 0.310998I 0
u = −0.675397 − 0.928630I
a = −0.332315 − 0.520207I
b = −0.570321 + 0.396184I
1.317160 + 0.310998I 0
u = 0.159588 + 1.138830I
a = 0.665887 + 0.212809I
b = 1.04567 + 1.22172I
− 2.37014I 0
u = 0.159588 − 1.138830I
a = 0.665887 − 0.212809I
b = 1.04567 − 1.22172I
2.37014I 0
u = 0.251252 + 1.140130I
a = −1.54021 + 0.19344I
b = −2.49789 + 0.53268I
−4.46877 − 3.84660I 0
u = 0.251252 − 1.140130I
a = −1.54021 − 0.19344I
b = −2.49789 − 0.53268I
−4.46877 + 3.84660I 0
u = −0.513294 + 1.050470I
a = 1.84558 − 0.12849I
b = 2.37333 − 0.75961I
− 6.20757I 0
u = −0.513294 − 1.050470I
a = 1.84558 + 0.12849I
b = 2.37333 + 0.75961I
6.20757I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.765140 + 0.316117I
a = 0.69915 + 1.34740I
b = −0.337122 + 0.331391I
0.02607 − 6.72571I 0
u = 0.765140 − 0.316117I
a = 0.69915 − 1.34740I
b = −0.337122 − 0.331391I
0.02607 + 6.72571I 0
u = 0.319775 + 1.132450I
a = 0.776712 − 0.855144I
b = 1.018630 + 0.042020I
−5.24352 + 3.43630I 0
u = 0.319775 − 1.132450I
a = 0.776712 + 0.855144I
b = 1.018630 − 0.042020I
−5.24352 − 3.43630I 0
u = 0.812896 + 0.117062I
a = −0.836162 − 0.719564I
b = −0.046145 − 0.185916I
−3.30887 − 1.04774I 0
u = 0.812896 − 0.117062I
a = −0.836162 + 0.719564I
b = −0.046145 + 0.185916I
−3.30887 + 1.04774I 0
u = −0.713520 + 0.941097I
a = 0.073348 − 0.368777I
b = 0.339239 + 0.653351I
3.82254 + 4.35831I 0
u = −0.713520 − 0.941097I
a = 0.073348 + 0.368777I
b = 0.339239 − 0.653351I
3.82254 − 4.35831I 0
u = −0.720770 + 0.382430I
a = 1.21227 + 1.61500I
b = 0.040862 + 0.626279I
6.53732 − 1.08710I 0
u = −0.720770 − 0.382430I
a = 1.21227 − 1.61500I
b = 0.040862 − 0.626279I
6.53732 + 1.08710I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.607854 + 0.541029I
a = −0.364104 + 0.970250I
b = 0.992932 − 0.142984I
7.34314 − 2.99182I 0
u = 0.607854 − 0.541029I
a = −0.364104 − 0.970250I
b = 0.992932 + 0.142984I
7.34314 + 2.99182I 0
u = 0.282116 + 1.153040I
a = −0.975944 + 0.537028I
b = −1.297810 − 0.377038I
−6.34959 − 1.94756I 0
u = 0.282116 − 1.153040I
a = −0.975944 − 0.537028I
b = −1.297810 + 0.377038I
−6.34959 + 1.94756I 0
u = −0.314207 + 1.148530I
a = 1.24218 − 0.96080I
b = 1.37827 − 1.90081I
0.82517 + 3.75302I 0
u = −0.314207 − 1.148530I
a = 1.24218 + 0.96080I
b = 1.37827 + 1.90081I
0.82517 − 3.75302I 0
u = 0.298545 + 1.153470I
a = 1.330110 − 0.305323I
b = 2.22260 − 0.60801I
−6.53732 + 1.08710I 0
u = 0.298545 − 1.153470I
a = 1.330110 + 0.305323I
b = 2.22260 + 0.60801I
−6.53732 − 1.08710I 0
u = 0.504837 + 0.629537I
a = −0.066456 + 0.842581I
b = 1.390670 − 0.236290I
6.51581 + 5.82934I 0
u = 0.504837 − 0.629537I
a = −0.066456 − 0.842581I
b = 1.390670 + 0.236290I
6.51581 − 5.82934I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666933 + 0.991022I
a = 0.517466 − 0.044732I
b = 0.928061 + 0.862163I
5.24352 − 3.43630I 0
u = −0.666933 − 0.991022I
a = 0.517466 + 0.044732I
b = 0.928061 − 0.862163I
5.24352 + 3.43630I 0
u = −0.353321 + 0.721783I
a = −0.343500 + 0.722117I
b = 0.155238 + 0.612312I
−0.21075 − 1.41586I 0
u = −0.353321 − 0.721783I
a = −0.343500 − 0.722117I
b = 0.155238 − 0.612312I
−0.21075 + 1.41586I 0
u = 0.753855 + 0.274407I
a = −0.21006 + 1.73079I
b = 0.763868 + 0.769940I
−2.03115 − 5.05572I 0
u = 0.753855 − 0.274407I
a = −0.21006 − 1.73079I
b = 0.763868 − 0.769940I
−2.03115 + 5.05572I 0
u = 0.523860 + 1.095900I
a = 0.994994 + 0.110231I
b = 1.82003 + 0.70446I
−0.82517 + 3.75302I 0
u = 0.523860 − 1.095900I
a = 0.994994 − 0.110231I
b = 1.82003 − 0.70446I
−0.82517 − 3.75302I 0
u = 0.742527 + 0.251049I
a = −0.684611 − 1.196410I
b = 0.221207 − 0.237585I
−2.34021 − 2.11255I 0
u = 0.742527 − 0.251049I
a = −0.684611 + 1.196410I
b = 0.221207 + 0.237585I
−2.34021 + 2.11255I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.207139 + 1.201600I
a = −1.163270 − 0.128589I
b = −1.58002 − 1.09985I
−5.04203 − 4.93450I 0
u = 0.207139 − 1.201600I
a = −1.163270 + 0.128589I
b = −1.58002 + 1.09985I
−5.04203 + 4.93450I 0
u = −0.726869 + 0.257675I
a = 1.47665 + 1.91063I
b = 0.240041 + 0.759395I
4.91540 + 6.93250I 0
u = −0.726869 − 0.257675I
a = 1.47665 − 1.91063I
b = 0.240041 − 0.759395I
4.91540 − 6.93250I 0
u = −0.571420 + 1.093010I
a = −1.51849 − 0.70201I
b = −2.22945 − 1.39363I
4.46877 − 3.84660I 0
u = −0.571420 − 1.093010I
a = −1.51849 + 0.70201I
b = −2.22945 + 1.39363I
4.46877 + 3.84660I 0
u = −0.527541 + 1.114890I
a = 1.90836 + 0.83253I
b = 2.69017 + 1.42427I
−0.02607 − 6.72571I 0
u = −0.527541 − 1.114890I
a = 1.90836 − 0.83253I
b = 2.69017 − 1.42427I
−0.02607 + 6.72571I 0
u = 0.189253 + 1.225290I
a = 1.246120 + 0.332373I
b = 1.68589 + 1.32332I
−2.79851 − 10.17260I 0
u = 0.189253 − 1.225290I
a = 1.246120 − 0.332373I
b = 1.68589 − 1.32332I
−2.79851 + 10.17260I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.528531 + 1.127640I
a = −1.70688 − 0.63680I
b = −2.32441 + 0.03304I
−3.82254 + 4.35831I 0
u = 0.528531 − 1.127640I
a = −1.70688 + 0.63680I
b = −2.32441 − 0.03304I
−3.82254 − 4.35831I 0
u = −0.538340 + 1.137910I
a = −1.85191 − 1.02755I
b = −2.68557 − 1.65381I
2.37294 − 11.72860I 0
u = −0.538340 − 1.137910I
a = −1.85191 + 1.02755I
b = −2.68557 + 1.65381I
2.37294 + 11.72860I 0
u = 0.503014 + 0.544291I
a = 0.152514 − 1.018220I
b = −1.252910 + 0.044275I
3.30887 + 1.04774I 0
u = 0.503014 − 0.544291I
a = 0.152514 + 1.018220I
b = −1.252910 − 0.044275I
3.30887 − 1.04774I 0
u = 0.538181 + 1.140090I
a = −0.999312 − 0.285459I
b = −1.61090 − 0.95534I
−4.91540 + 6.93250I 0
u = 0.538181 − 1.140090I
a = −0.999312 + 0.285459I
b = −1.61090 + 0.95534I
−4.91540 − 6.93250I 0
u = 0.693096 + 0.248467I
a = 0.03129 − 1.52205I
b = −1.015360 − 0.684978I
−1.317160 + 0.310998I 0
u = 0.693096 − 0.248467I
a = 0.03129 + 1.52205I
b = −1.015360 + 0.684978I
−1.317160 − 0.310998I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.548101 + 1.139230I
a = 1.88806 + 0.33278I
b = 2.60546 − 0.28806I
−4.55149 + 9.95496I 0
u = 0.548101 − 1.139230I
a = 1.88806 − 0.33278I
b = 2.60546 + 0.28806I
−4.55149 − 9.95496I 0
u = 0.563356 + 1.132890I
a = 1.124730 + 0.274811I
b = 1.78260 + 1.05938I
−2.37294 + 11.72860I 0
u = 0.563356 − 1.132890I
a = 1.124730 − 0.274811I
b = 1.78260 − 1.05938I
−2.37294 − 11.72860I 0
u = 0.375686 + 1.209700I
a = 0.867750 − 0.609516I
b = 1.50084 − 0.93497I
−7.34314 + 2.99182I 0
u = 0.375686 − 1.209700I
a = 0.867750 + 0.609516I
b = 1.50084 + 0.93497I
−7.34314 − 2.99182I 0
u = 0.593573 + 1.127630I
a = −1.63430 + 0.21749I
b = −2.54523 + 0.91215I
2.79851 + 10.17260I 0
u = 0.593573 − 1.127630I
a = −1.63430 − 0.21749I
b = −2.54523 − 0.91215I
2.79851 − 10.17260I 0
u = −0.660551 + 0.287177I
a = −1.29417 − 1.96194I
b = −0.149997 − 0.806285I
2.34021 + 2.11255I 0
u = −0.660551 − 0.287177I
a = −1.29417 + 1.96194I
b = −0.149997 + 0.806285I
2.34021 − 2.11255I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547395 + 0.450281I
a = 0.84602 − 1.66085I
b = −0.151581 − 0.839571I
1.75761 + 1.88399I 0
u = −0.547395 − 0.450281I
a = 0.84602 + 1.66085I
b = −0.151581 + 0.839571I
1.75761 − 1.88399I 0
u = 0.590046 + 1.152570I
a = 1.92960 − 0.26481I
b = 2.84177 − 0.85536I
−2.45608 + 13.29840I 0
u = 0.590046 − 1.152570I
a = 1.92960 + 0.26481I
b = 2.84177 + 0.85536I
−2.45608 − 13.29840I 0
u = 0.497713 + 1.197790I
a = −0.580901 − 0.488791I
b = −0.818281 − 0.997952I
−6.51581 + 5.82934I 0
u = 0.497713 − 1.197790I
a = −0.580901 + 0.488791I
b = −0.818281 + 0.997952I
−6.51581 − 5.82934I 0
u = 0.601488 + 1.158110I
a = −1.94185 + 0.41885I
b = −2.90478 + 0.99661I
18.7022I 0
u = 0.601488 − 1.158110I
a = −1.94185 − 0.41885I
b = −2.90478 − 0.99661I
− 18.7022I 0
u = −0.393098 + 0.573073I
a = −0.29091 − 2.72525I
b = 0.05260 − 1.85375I
−0.002551 + 0.973476I 0
u = −0.393098 − 0.573073I
a = −0.29091 + 2.72525I
b = 0.05260 + 1.85375I
−0.002551 − 0.973476I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.074106 + 0.690389I
a = −0.724325 + 0.179063I
b = 0.110669 + 0.786581I
− 1.35309I 0. + 3.62859I
u = −0.074106 − 0.690389I
a = −0.724325 − 0.179063I
b = 0.110669 − 0.786581I
1.35309I 0. − 3.62859I
u = 0.607882 + 0.332211I
a = 0.507006 + 1.269540I
b = −0.409237 + 0.014203I
1.36077 + 0.74859I 0
u = 0.607882 − 0.332211I
a = 0.507006 − 1.269540I
b = −0.409237 − 0.014203I
1.36077 − 0.74859I 0
u = 0.405740 + 1.243650I
a = −0.580417 + 0.859262I
b = −1.06530 + 1.30750I
−5.92691 + 7.48471I 0
u = 0.405740 − 1.243650I
a = −0.580417 − 0.859262I
b = −1.06530 − 1.30750I
−5.92691 − 7.48471I 0
u = 0.479194 + 1.233190I
a = 0.245390 + 0.766661I
b = 0.198925 + 1.307390I
−5.43061 + 1.83010I 0
u = 0.479194 − 1.233190I
a = 0.245390 − 0.766661I
b = 0.198925 − 1.307390I
−5.43061 − 1.83010I 0
u = −0.148774 + 0.072787I
a = −3.64744 + 2.29722I
b = −0.167314 + 0.600107I
0.21075 − 1.41586I 1.88923 + 4.84252I
u = −0.148774 − 0.072787I
a = −3.64744 − 2.29722I
b = −0.167314 − 0.600107I
0.21075 + 1.41586I 1.88923 − 4.84252I
17
II. I
u
2
= ha
4
u − a
3
u − a
3
+ a
2
− 2au + b − a + u + 1, a
5
+ a
4
u − a
3
u − a
3
−
2a
2
− au − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
4
=
0
u
a
10
=
a
−a
4
u + a
3
u + a
3
− a
2
+ 2au + a − u − 1
a
7
=
0
a
4
u − 2a
3
u − 2a
3
+ 2a
2
− au + 3u + 3
a
8
=
0
a
4
u − 2a
3
u − 2a
3
+ 2a
2
− au + 3u + 3
a
11
=
a
2a
4
u − 3a
3
u − 3a
3
+ 4a
2
− 2au + a + 3u + 3
a
1
=
−u
−u
a
12
=
2a
4
+ 3a
3
u − 4a
2
u − 4a
2
− a − 3u
2a
4
u + 2a
4
− 3a
3
− 4a
2
u − 2au − a + 3
a
9
=
−u
−2a
4
u + 3a
3
u + 3a
3
− 4a
2
+ au − 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8a
4
u − 3a
4
+ 7a
3
u + 15a
3
+ 12a
2
u − 8a
2
+ 3au − 4u − 10
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
, c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
12
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
, c
8
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
9
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
11
(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 = −0.500000 + 0.866025I
a = 0.410598 − 0.711177I
b = 1.019470 + 0.343414I
2.40108 − 2.02988I 0.15429 + 1.95361I
u = −0.500000 + 0.866025I
a = −0.252108 + 0.649344I
b = −0.771697 − 0.688941I
5.87256 − 6.43072I 0.67715 + 5.27500I
u = −0.500000 + 0.866025I
a = −0.436295 + 0.543004I
b = −1.33549 − 0.57612I
5.87256 + 2.37095I 5.14480 − 4.03066I
u = −0.500000 + 0.866025I
a = −0.80632 − 1.36366I
b = −1.127600 − 0.820312I
0.329100 − 0.499304I −2.94328 − 6.15174I
u = −0.500000 + 0.866025I
a = 1.58413 + 0.01647I
b = 2.21532 + 0.00990I
0.32910 − 3.56046I 6.96704 + 8.14994I
u = −0.500000 − 0.866025I
a = 0.410598 + 0.711177I
b = 1.019470 − 0.343414I
2.40108 + 2.02988I 0.15429 − 1.95361I
u = −0.500000 − 0.866025I
a = −0.252108 − 0.649344I
b = −0.771697 + 0.688941I
5.87256 + 6.43072I 0.67715 − 5.27500I
u = −0.500000 − 0.866025I
a = −0.436295 − 0.543004I
b = −1.33549 + 0.57612I
5.87256 − 2.37095I 5.14480 + 4.03066I
u = −0.500000 − 0.866025I
a = −0.80632 + 1.36366I
b = −1.127600 + 0.820312I
0.329100 + 0.499304I −2.94328 + 6.15174I
u = −0.500000 − 0.866025I
a = 1.58413 − 0.01647I
b = 2.21532 − 0.00990I
0.32910 + 3.56046I 6.96704 − 8.14994I
21
III. I
u
3
= hb − a, u
4
a − 2u
4
+ · · · − a + 2, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
a
a
a
7
=
u
u
a
8
=
−u
2
− 1
u
4
a
11
=
a
a
a
1
=
u
2
+ 1
−u
4
a
12
=
u
4
a − u
3
a + 2u
2
a + 3a
−2u
3
a − au + 2a
a
9
=
u
4
− u
3
+ a − 2
2u
4
− u
3
+ u
2
+ a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
a + u
3
a + u
4
− u
2
a + 5u
3
− 2au − 6u
2
− 2a + 9u − 5
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
3
, c
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
6
, c
10
u
10
c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
8
, c
11
, c
12
(u
2
+ u + 1)
5
c
9
(u
2
− u + 1)
5
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
2
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
3
, c
4
, c
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
6
, c
10
y
10
c
8
, c
9
, c
11
c
12
(y
2
+ y + 1)
5
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 1.39836 + 1.74033I
b = 1.39836 + 1.74033I
−0.329100 + 0.499304I 2.94328 + 6.15174I
u = −0.339110 + 0.822375I
a = 0.80799 − 2.08118I
b = 0.80799 − 2.08118I
−0.32910 − 3.56046I −6.96704 + 8.14994I
u = −0.339110 − 0.822375I
a = 1.39836 − 1.74033I
b = 1.39836 − 1.74033I
−0.329100 − 0.499304I 2.94328 − 6.15174I
u = −0.339110 − 0.822375I
a = 0.80799 + 2.08118I
b = 0.80799 + 2.08118I
−0.32910 + 3.56046I −6.96704 − 8.14994I
u = 0.766826
a = 0.258559 + 0.447838I
b = 0.258559 + 0.447838I
−2.40108 + 2.02988I −0.15429 − 1.95361I
u = 0.766826
a = 0.258559 − 0.447838I
b = 0.258559 − 0.447838I
−2.40108 − 2.02988I −0.15429 + 1.95361I
u = 0.455697 + 1.200150I
a = 0.556121 + 0.280562I
b = 0.556121 + 0.280562I
−5.87256 + 6.43072I −0.67715 − 5.27500I
u = 0.455697 + 1.200150I
a = −0.521035 + 0.341334I
b = −0.521035 + 0.341334I
−5.87256 + 2.37095I −5.14480 − 4.03066I
u = 0.455697 − 1.200150I
a = 0.556121 − 0.280562I
b = 0.556121 − 0.280562I
−5.87256 − 6.43072I −0.67715 + 5.27500I
u = 0.455697 − 1.200150I
a = −0.521035 − 0.341334I
b = −0.521035 − 0.341334I
−5.87256 − 2.37095I −5.14480 + 4.03066I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
5
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· (u
130
+ 64u
129
+ ··· − 30u + 1)
c
2
((u
2
+ u + 1)
5
)(u
5
− u
4
+ ··· + u − 1)
2
(u
130
+ 8u
129
+ ··· − 2u + 1)
c
3
(u
2
− u + 1)
5
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
130
− 8u
129
+ ··· − 10406338u + 596177)
c
4
u
10
(u
5
+ u
4
+ ··· + u − 1)
2
(u
130
+ 3u
129
+ ··· + 3072u + 1024)
c
5
((u
2
− u + 1)
5
)(u
5
+ u
4
+ ··· + u + 1)
2
(u
130
+ 8u
129
+ ··· − 2u + 1)
c
6
u
10
(u
5
− u
4
+ ··· + u + 1)
2
(u
130
− 3u
129
+ ··· − 3072u + 1024)
c
7
u
10
(u
5
− u
4
+ ··· + u + 1)
2
(u
130
+ 3u
129
+ ··· + 3072u + 1024)
c
8
(u
2
+ u + 1)
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
· (u
130
+ 8u
129
+ ··· + 10406338u + 596177)
c
9
((u
2
− u + 1)
5
)(u
5
+ u
4
+ ··· + u + 1)
2
(u
130
− 8u
129
+ ··· + 2u + 1)
c
10
u
10
(u
5
+ u
4
+ ··· + u − 1)
2
(u
130
− 3u
129
+ ··· − 3072u + 1024)
c
11
(u
2
+ u + 1)
5
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
· (u
130
− 64u
129
+ ··· + 30u + 1)
c
12
((u
2
+ u + 1)
5
)(u
5
− u
4
+ ··· + u − 1)
2
(u
130
− 8u
129
+ ··· + 2u + 1)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
2
+ y + 1)
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
· (y
130
+ 12y
129
+ ··· + 686y + 1)
c
2
, c
5
, c
9
c
12
(y
2
+ y + 1)
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
130
+ 64y
129
+ ··· − 30y + 1)
c
3
, c
8
(y
2
+ y + 1)
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
130
− 40y
129
+ ··· − 17001882314902y + 355427015329)
c
4
, c
6
, c
7
c
10
y
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
130
− 65y
129
+ ··· − 22020096y + 1048576)
27
