12a
0083
(K12a
0083
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 4 1 7 12 6 10
Solving Sequence
6,11 4,7
8 12 3 10 1 9 5 2
c
6
c
7
c
11
c
3
c
10
c
12
c
9
c
5
c
2
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
109
+ u
108
+ ··· + b − 2u, u
109
− u
108
+ ··· + a + 1, u
111
− 2u
110
+ ··· + 2u − 1i
I
u
2
= h−u
5
− u
3
+ b − u + 1, u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ a + u, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 120 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−u
109
+u
108
+· · ·+b−2u, u
109
−u
108
+· · ·+a+1, u
111
−2u
110
+· · ·+2u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
−u
109
+ u
108
+ ··· + 4u
3
− 1
u
109
− u
108
+ ··· − 2u
2
+ 2u
a
7
=
1
u
2
a
8
=
u
17
+ 2u
15
+ 5u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
−u
17
− 3u
15
− 7u
13
− 10u
11
− 11u
9
− 8u
7
− 4u
5
+ u
a
12
=
−u
u
a
3
=
u
109
− u
108
+ ··· + u − 2
u
109
− u
108
+ ··· + 3u
3
+ u
a
10
=
−u
3
u
3
+ u
a
1
=
−u
5
− u
u
5
+ u
3
+ u
a
9
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
5
=
−u
12
− u
10
− 3u
8
− 2u
6
− 2u
4
− u
2
+ 1
−u
14
− 2u
12
− 5u
10
− 6u
8
− 6u
6
− 4u
4
− u
2
a
2
=
u
107
− u
106
+ ··· + u − 1
u
109
− u
108
+ ··· − 2u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
110
− 2u
109
+ ··· − 8u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
111
+ 52u
110
+ ··· + 26u + 1
c
2
, c
4
u
111
− 10u
110
+ ··· − 6u + 1
c
3
, c
7
u
111
+ u
110
+ ··· + 1024u + 512
c
5
u
111
+ 2u
110
+ ··· + 71974u + 7769
c
6
, c
11
u
111
+ 2u
110
+ ··· + 2u + 1
c
8
u
111
− 8u
110
+ ··· − 4116076u + 591991
c
9
u
111
− 10u
110
+ ··· − 688u + 64
c
10
, c
12
u
111
− 36u
110
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
111
+ 24y
110
+ ··· + 326y −1
c
2
, c
4
y
111
− 52y
110
+ ··· + 26y −1
c
3
, c
7
y
111
+ 57y
110
+ ··· − 6291456y −262144
c
5
y
111
− 28y
110
+ ··· + 4384850918y −60357361
c
6
, c
11
y
111
+ 36y
110
+ ··· + 6y −1
c
8
y
111
+ 32y
110
+ ··· − 6104529362122y −350453344081
c
9
y
111
+ 4y
110
+ ··· − 290688y −4096
c
10
, c
12
y
111
+ 80y
110
+ ··· + 34y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192632 + 0.990436I
a = 1.008050 − 0.604735I
b = −0.482149 + 0.126128I
0.929563 − 0.936585I 0
u = 0.192632 − 0.990436I
a = 1.008050 + 0.604735I
b = −0.482149 − 0.126128I
0.929563 + 0.936585I 0
u = 0.768909 + 0.662619I
a = −0.240296 − 0.802359I
b = 0.66998 − 1.65382I
2.38224 + 2.26869I 0
u = 0.768909 − 0.662619I
a = −0.240296 + 0.802359I
b = 0.66998 + 1.65382I
2.38224 − 2.26869I 0
u = 0.736461 + 0.649245I
a = −0.073525 + 0.729912I
b = −0.323443 + 1.257520I
1.40760 − 3.27569I 0
u = 0.736461 − 0.649245I
a = −0.073525 − 0.729912I
b = −0.323443 − 1.257520I
1.40760 + 3.27569I 0
u = 0.099843 + 1.021210I
a = −1.23478 − 0.86398I
b = 0.494409 + 0.608915I
3.03959 − 1.31482I 0
u = 0.099843 − 1.021210I
a = −1.23478 + 0.86398I
b = 0.494409 − 0.608915I
3.03959 + 1.31482I 0
u = −0.125044 + 1.022840I
a = −1.03086 − 3.37868I
b = 0.43919 + 2.85055I
1.10607 + 3.24001I 0
u = −0.125044 − 1.022840I
a = −1.03086 + 3.37868I
b = 0.43919 − 2.85055I
1.10607 − 3.24001I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.254566 + 0.926058I
a = −0.663304 + 1.129570I
b = 0.355086 − 0.268387I
0.41586 − 4.48947I 0
u = 0.254566 − 0.926058I
a = −0.663304 − 1.129570I
b = 0.355086 + 0.268387I
0.41586 + 4.48947I 0
u = 0.132035 + 1.037550I
a = 1.54187 + 0.38063I
b = −0.697523 − 0.360085I
2.17831 − 5.68318I 0
u = 0.132035 − 1.037550I
a = 1.54187 − 0.38063I
b = −0.697523 + 0.360085I
2.17831 + 5.68318I 0
u = −0.780211 + 0.699337I
a = −0.629537 + 0.324564I
b = 1.213950 + 0.649893I
−2.92578 − 1.14947I 0
u = −0.780211 − 0.699337I
a = −0.629537 − 0.324564I
b = 1.213950 − 0.649893I
−2.92578 + 1.14947I 0
u = 0.530855 + 0.908540I
a = 0.283621 + 0.961919I
b = −0.0916763 + 0.0351119I
0.0533926 − 0.0055215I 0
u = 0.530855 − 0.908540I
a = 0.283621 − 0.961919I
b = −0.0916763 − 0.0351119I
0.0533926 + 0.0055215I 0
u = −0.059280 + 1.051760I
a = −1.04895 − 2.98448I
b = 0.33302 + 2.14606I
7.04699 − 3.67038I 0
u = −0.059280 − 1.051760I
a = −1.04895 + 2.98448I
b = 0.33302 − 2.14606I
7.04699 + 3.67038I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.474575 + 0.941264I
a = 0.75085 + 1.50277I
b = 1.44748 − 0.42754I
3.04019 − 5.75313I 0
u = −0.474575 − 0.941264I
a = 0.75085 − 1.50277I
b = 1.44748 + 0.42754I
3.04019 + 5.75313I 0
u = −0.082911 + 1.051710I
a = 0.97495 + 3.16678I
b = −0.33502 − 2.34474I
8.29038 + 2.01687I 0
u = −0.082911 − 1.051710I
a = 0.97495 − 3.16678I
b = −0.33502 + 2.34474I
8.29038 − 2.01687I 0
u = 0.811413 + 0.683140I
a = −1.085650 − 0.723933I
b = 1.08660 − 2.57993I
0.67183 + 6.15549I 0
u = 0.811413 − 0.683140I
a = −1.085650 + 0.723933I
b = 1.08660 + 2.57993I
0.67183 − 6.15549I 0
u = 0.797576 + 0.700033I
a = 1.10758 + 1.37941I
b = −1.70256 + 2.35602I
−5.10535 + 3.01862I 0
u = 0.797576 − 0.700033I
a = 1.10758 − 1.37941I
b = −1.70256 − 2.35602I
−5.10535 − 3.01862I 0
u = −0.805066 + 0.693292I
a = 0.597661 − 0.490927I
b = −1.49235 − 0.31506I
−4.14766 − 5.56202I 0
u = −0.805066 − 0.693292I
a = 0.597661 + 0.490927I
b = −1.49235 + 0.31506I
−4.14766 + 5.56202I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.132451 + 1.054970I
a = 0.90434 + 3.23113I
b = −0.53870 − 2.53237I
7.07789 + 6.12746I 0
u = −0.132451 − 1.054970I
a = 0.90434 − 3.23113I
b = −0.53870 + 2.53237I
7.07789 − 6.12746I 0
u = −0.146614 + 1.057970I
a = −0.83912 − 3.15269I
b = 0.59773 + 2.48167I
4.91151 + 11.83360I 0
u = −0.146614 − 1.057970I
a = −0.83912 + 3.15269I
b = 0.59773 − 2.48167I
4.91151 − 11.83360I 0
u = 0.096016 + 0.926261I
a = −0.046350 − 1.080040I
b = −0.233565 + 0.499204I
1.90349 − 1.53560I 0
u = 0.096016 − 0.926261I
a = −0.046350 + 1.080040I
b = −0.233565 − 0.499204I
1.90349 + 1.53560I 0
u = −0.764877 + 0.747204I
a = −0.782753 − 0.110036I
b = 0.560754 + 1.224240I
−3.69681 − 0.59851I 0
u = −0.764877 − 0.747204I
a = −0.782753 + 0.110036I
b = 0.560754 − 1.224240I
−3.69681 + 0.59851I 0
u = −0.568939 + 0.906736I
a = 0.47634 + 2.73143I
b = 2.65902 − 1.01527I
−1.20931 + 2.19749I 0
u = −0.568939 − 0.906736I
a = 0.47634 − 2.73143I
b = 2.65902 + 1.01527I
−1.20931 − 2.19749I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.820991 + 0.687464I
a = 1.30100 + 0.59172I
b = −1.08489 + 2.81057I
−1.63250 + 11.81960I 0
u = 0.820991 − 0.687464I
a = 1.30100 − 0.59172I
b = −1.08489 − 2.81057I
−1.63250 − 11.81960I 0
u = −0.507517 + 0.943536I
a = −0.81181 − 1.85142I
b = −1.63254 + 0.69181I
4.96384 − 0.11752I 0
u = −0.507517 − 0.943536I
a = −0.81181 + 1.85142I
b = −1.63254 − 0.69181I
4.96384 + 0.11752I 0
u = 0.772006 + 0.772780I
a = 1.58909 − 0.90180I
b = 0.576947 + 1.122740I
−6.36063 − 0.71203I 0
u = 0.772006 − 0.772780I
a = 1.58909 + 0.90180I
b = 0.576947 − 1.122740I
−6.36063 + 0.71203I 0
u = 0.662337 + 0.870835I
a = −0.397275 + 0.149125I
b = −0.0950051 + 0.0447575I
−1.01013 − 2.56602I 0
u = 0.662337 − 0.870835I
a = −0.397275 − 0.149125I
b = −0.0950051 − 0.0447575I
−1.01013 + 2.56602I 0
u = −0.815391 + 0.729941I
a = 0.142260 − 0.616883I
b = −1.009020 + 0.511024I
−5.63875 − 0.21059I 0
u = −0.815391 − 0.729941I
a = 0.142260 + 0.616883I
b = −1.009020 − 0.511024I
−5.63875 + 0.21059I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.770455 + 0.789444I
a = 1.106370 + 0.534564I
b = −0.27456 − 1.87357I
−5.82240 + 3.12989I 0
u = −0.770455 − 0.789444I
a = 1.106370 − 0.534564I
b = −0.27456 + 1.87357I
−5.82240 − 3.12989I 0
u = 0.581600 + 0.937909I
a = −0.659104 − 0.661539I
b = 0.100577 − 0.196830I
0.34882 − 4.22670I 0
u = 0.581600 − 0.937909I
a = −0.659104 + 0.661539I
b = 0.100577 + 0.196830I
0.34882 + 4.22670I 0
u = −0.808577 + 0.760102I
a = 0.420874 + 0.731250I
b = 0.507807 − 1.307110I
−6.15982 − 3.10465I 0
u = −0.808577 − 0.760102I
a = 0.420874 − 0.731250I
b = 0.507807 + 1.307110I
−6.15982 + 3.10465I 0
u = 0.767617 + 0.814930I
a = −1.341450 + 0.226399I
b = 0.254417 − 0.631786I
−1.58344 − 3.65437I 0
u = 0.767617 − 0.814930I
a = −1.341450 − 0.226399I
b = 0.254417 + 0.631786I
−1.58344 + 3.65437I 0
u = −0.573335 + 0.970305I
a = −1.17424 − 2.43459I
b = −1.72069 + 1.50758I
5.43993 + 3.94383I 0
u = −0.573335 − 0.970305I
a = −1.17424 + 2.43459I
b = −1.72069 − 1.50758I
5.43993 − 3.94383I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789834 + 0.812667I
a = 1.64616 − 0.11664I
b = −0.543734 + 0.979094I
−3.81432 − 8.80179I 0
u = 0.789834 − 0.812667I
a = 1.64616 + 0.11664I
b = −0.543734 − 0.979094I
−3.81432 + 8.80179I 0
u = −0.592860 + 0.980993I
a = 1.24435 + 2.51142I
b = 1.64111 − 1.71076I
3.89569 + 9.64082I 0
u = −0.592860 − 0.980993I
a = 1.24435 − 2.51142I
b = 1.64111 + 1.71076I
3.89569 − 9.64082I 0
u = 0.734585 + 0.916006I
a = −0.239524 − 0.207158I
b = −0.060534 + 0.753628I
−1.26885 − 2.02626I 0
u = 0.734585 − 0.916006I
a = −0.239524 + 0.207158I
b = −0.060534 − 0.753628I
−1.26885 + 2.02626I 0
u = −0.729555 + 0.940810I
a = −1.65103 − 0.88700I
b = 0.22575 + 2.04696I
−5.35605 + 2.54553I 0
u = −0.729555 − 0.940810I
a = −1.65103 + 0.88700I
b = 0.22575 − 2.04696I
−5.35605 − 2.54553I 0
u = −0.080571 + 0.801768I
a = −0.68517 + 1.41490I
b = 1.165590 − 0.301891I
−0.875710 + 0.948469I −8.68611 + 0.I
u = −0.080571 − 0.801768I
a = −0.68517 − 1.41490I
b = 1.165590 + 0.301891I
−0.875710 − 0.948469I −8.68611 + 0.I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.754108 + 0.928714I
a = 0.020894 + 0.559672I
b = −0.170032 − 1.257680I
−3.45583 + 2.99333I 0
u = 0.754108 − 0.928714I
a = 0.020894 − 0.559672I
b = −0.170032 + 1.257680I
−3.45583 − 2.99333I 0
u = 0.726683 + 0.953612I
a = −0.404649 − 0.333661I
b = 1.15069 − 1.19096I
−5.80570 − 4.95975I 0
u = 0.726683 − 0.953612I
a = −0.404649 + 0.333661I
b = 1.15069 + 1.19096I
−5.80570 + 4.95975I 0
u = −0.716470 + 0.968399I
a = 1.009940 + 0.983135I
b = 0.24035 − 1.43149I
−3.02213 + 6.21900I 0
u = −0.716470 − 0.968399I
a = 1.009940 − 0.983135I
b = 0.24035 + 1.43149I
−3.02213 − 6.21900I 0
u = 0.682596 + 1.003720I
a = −1.72286 + 0.90870I
b = −0.69420 − 1.57701I
2.44885 − 2.15395I 0
u = 0.682596 − 1.003720I
a = −1.72286 − 0.90870I
b = −0.69420 + 1.57701I
2.44885 + 2.15395I 0
u = −0.710907 + 0.998558I
a = 0.08358 + 1.50967I
b = 1.13414 − 0.92782I
−2.02005 + 6.79446I 0
u = −0.710907 − 0.998558I
a = 0.08358 − 1.50967I
b = 1.13414 + 0.92782I
−2.02005 − 6.79446I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.696196 + 1.008940I
a = 1.91104 − 1.30509I
b = 0.92895 + 2.06413I
3.41635 − 7.82906I 0
u = 0.696196 − 1.008940I
a = 1.91104 + 1.30509I
b = 0.92895 − 2.06413I
3.41635 + 7.82906I 0
u = −0.746068 + 0.973664I
a = −1.42525 − 0.12220I
b = 0.82226 + 1.25984I
−5.50452 + 8.94364I 0
u = −0.746068 − 0.973664I
a = −1.42525 + 0.12220I
b = 0.82226 − 1.25984I
−5.50452 − 8.94364I 0
u = 0.718823 + 1.003060I
a = −2.07659 + 2.17491I
b = −1.80915 − 3.12071I
−4.18525 − 8.73612I 0
u = 0.718823 − 1.003060I
a = −2.07659 − 2.17491I
b = −1.80915 + 3.12071I
−4.18525 + 8.73612I 0
u = −0.738208 + 0.993906I
a = 0.927077 − 0.659401I
b = −1.101950 − 0.318264I
−4.83099 + 6.04293I 0
u = −0.738208 − 0.993906I
a = 0.927077 + 0.659401I
b = −1.101950 + 0.318264I
−4.83099 − 6.04293I 0
u = −0.720095 + 1.008540I
a = 0.41204 − 1.59057I
b = −1.45541 + 0.62359I
−3.19045 + 11.30350I 0
u = −0.720095 − 1.008540I
a = 0.41204 + 1.59057I
b = −1.45541 − 0.62359I
−3.19045 − 11.30350I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.719408 + 1.015160I
a = 2.36088 − 1.88696I
b = 1.04853 + 3.16425I
1.67951 − 11.91070I 0
u = 0.719408 − 1.015160I
a = 2.36088 + 1.88696I
b = 1.04853 − 3.16425I
1.67951 + 11.91070I 0
u = 0.725093 + 1.016800I
a = −2.46825 + 1.95770I
b = −0.94944 − 3.40309I
−0.6299 − 17.6207I 0
u = 0.725093 − 1.016800I
a = −2.46825 − 1.95770I
b = −0.94944 + 3.40309I
−0.6299 + 17.6207I 0
u = −0.574352 + 0.418607I
a = 0.135427 + 0.714012I
b = 0.86196 + 1.26612I
2.54612 − 5.10023I −7.16882 + 3.19715I
u = −0.574352 − 0.418607I
a = 0.135427 − 0.714012I
b = 0.86196 − 1.26612I
2.54612 + 5.10023I −7.16882 − 3.19715I
u = −0.631566 + 0.179431I
a = 1.55073 + 0.65579I
b = 0.078384 + 1.100650I
0.93401 + 9.47471I −10.17613 − 7.65520I
u = −0.631566 − 0.179431I
a = 1.55073 − 0.65579I
b = 0.078384 − 1.100650I
0.93401 − 9.47471I −10.17613 + 7.65520I
u = −0.560215 + 0.341895I
a = −0.456081 − 0.838719I
b = −0.630414 − 1.220460I
3.99504 + 0.35322I −5.03327 − 2.38344I
u = −0.560215 − 0.341895I
a = −0.456081 + 0.838719I
b = −0.630414 + 1.220460I
3.99504 − 0.35322I −5.03327 + 2.38344I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.607988 + 0.205302I
a = −1.32956 − 0.79282I
b = −0.205681 − 1.140070I
3.06262 + 3.92490I −6.94599 − 3.74176I
u = −0.607988 − 0.205302I
a = −1.32956 + 0.79282I
b = −0.205681 + 1.140070I
3.06262 − 3.92490I −6.94599 + 3.74176I
u = 0.606436 + 0.043814I
a = 0.197367 − 0.784558I
b = −0.207695 + 0.574254I
−2.33432 + 1.63935I −11.54858 − 4.00697I
u = 0.606436 − 0.043814I
a = 0.197367 + 0.784558I
b = −0.207695 − 0.574254I
−2.33432 − 1.63935I −11.54858 + 4.00697I
u = 0.570119 + 0.177210I
a = 0.626226 − 0.746167I
b = −0.639347 + 0.300541I
−1.64918 − 3.56067I −12.02219 + 5.47193I
u = 0.570119 − 0.177210I
a = 0.626226 + 0.746167I
b = −0.639347 − 0.300541I
−1.64918 + 3.56067I −12.02219 − 5.47193I
u = −0.525944 + 0.152741I
a = 1.48425 + 1.60870I
b = 0.338855 + 0.955316I
−2.56426 + 1.24826I −11.02453 − 5.32858I
u = −0.525944 − 0.152741I
a = 1.48425 − 1.60870I
b = 0.338855 − 0.955316I
−2.56426 − 1.24826I −11.02453 + 5.32858I
u = 0.413113 + 0.265236I
a = −0.828742 + 0.732041I
b = 0.558168 + 0.007894I
−0.745453 + 0.267249I −9.83522 + 0.75496I
u = 0.413113 − 0.265236I
a = −0.828742 − 0.732041I
b = 0.558168 − 0.007894I
−0.745453 − 0.267249I −9.83522 − 0.75496I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376387
a = −0.936204
b = 0.379146
−0.758702 −12.9630
16
II. I
u
2
= h−u
5
− u
3
+ b − u + 1, u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ a + u, u
9
+
u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
−u
7
− u
6
− 2u
5
− u
4
− 2u
3
− u
2
− u
u
5
+ u
3
+ u − 1
a
7
=
1
u
2
a
8
=
1
u
2
a
12
=
−u
u
a
3
=
−u
7
− u
6
− 2u
5
− u
4
− 2u
3
− u
2
− u
u
5
+ u
3
+ u − 1
a
10
=
−u
3
u
3
+ u
a
1
=
−u
5
− u
u
5
+ u
3
+ u
a
9
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
5
=
u
5
+ u
−u
5
− u
3
− u
a
2
=
−u
7
− u
6
− 3u
5
− u
4
− 2u
3
− u
2
− 2u
2u
5
+ 2u
3
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 3u
5
− 3u
4
− 6u
3
− 3u
2
+ u − 13
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
, c
8
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
6
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
9
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ 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
7
y
9
c
5
, c
8
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
c
6
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1
c
9
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 = 0.140343 + 0.966856I
a = 0.900982 − 0.594909I
b = −0.663053 + 0.788921I
0.13850 − 2.09337I −6.69021 + 3.87975I
u = 0.140343 − 0.966856I
a = 0.900982 + 0.594909I
b = −0.663053 − 0.788921I
0.13850 + 2.09337I −6.69021 − 3.87975I
u = 0.628449 + 0.875112I
a = 0.249476 + 1.304240I
b = −1.52709 − 0.20930I
−2.26187 − 2.45442I −12.49381 + 3.35442I
u = 0.628449 − 0.875112I
a = 0.249476 − 1.304240I
b = −1.52709 + 0.20930I
−2.26187 + 2.45442I −12.49381 − 3.35442I
u = −0.796005 + 0.733148I
a = −0.766570 + 0.255687I
b = 0.224752 + 0.919301I
−6.01628 − 1.33617I −13.53709 + 1.22905I
u = −0.796005 − 0.733148I
a = −0.766570 − 0.255687I
b = 0.224752 − 0.919301I
−6.01628 + 1.33617I −13.53709 − 1.22905I
u = −0.728966 + 0.986295I
a = 0.721488 + 0.307914I
b = 0.124310 − 1.173370I
−5.24306 + 7.08493I −12.02676 − 6.64241I
u = −0.728966 − 0.986295I
a = 0.721488 − 0.307914I
b = 0.124310 + 1.173370I
−5.24306 − 7.08493I −12.02676 + 6.64241I
u = 0.512358
a = −1.21075
b = −0.317835
−2.84338 −14.5040
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
111
+ 52u
110
+ ··· + 26u + 1)
c
2
((u − 1)
9
)(u
111
− 10u
110
+ ··· − 6u + 1)
c
3
, c
7
u
9
(u
111
+ u
110
+ ··· + 1024u + 512)
c
4
((u + 1)
9
)(u
111
− 10u
110
+ ··· − 6u + 1)
c
5
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
111
+ 2u
110
+ ··· + 71974u + 7769)
c
6
(u
9
+ u
8
+ ··· + u − 1)(u
111
+ 2u
110
+ ··· + 2u + 1)
c
8
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
111
− 8u
110
+ ··· − 4116076u + 591991)
c
9
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
111
− 10u
110
+ ··· − 688u + 64)
c
10
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
111
− 36u
110
+ ··· + 6u + 1)
c
11
(u
9
− u
8
+ ··· + u + 1)(u
111
+ 2u
110
+ ··· + 2u + 1)
c
12
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
111
− 36u
110
+ ··· + 6u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
111
+ 24y
110
+ ··· + 326y − 1)
c
2
, c
4
((y − 1)
9
)(y
111
− 52y
110
+ ··· + 26y − 1)
c
3
, c
7
y
9
(y
111
+ 57y
110
+ ··· − 6291456y − 262144)
c
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
111
− 28y
110
+ ··· + 4384850918y − 60357361)
c
6
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
111
+ 36y
110
+ ··· + 6y − 1)
c
8
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
111
+ 32y
110
+ ··· − 6104529362122y − 350453344081)
c
9
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
111
+ 4y
110
+ ··· − 290688y − 4096)
c
10
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
111
+ 80y
110
+ ··· + 34y − 1)
22
