12a
0017
(K12a
0017
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 10 11 4 1 12 8 7
Solving Sequence
7,11 4,8
9 5 12 1 10 6 3 2
c
7
c
8
c
4
c
11
c
12
c
10
c
6
c
3
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
122
+ 5u
121
+ ··· + 2b − 8, −17u
122
+ 41u
121
+ ··· + 2a − 15, u
123
− 3u
122
+ ··· + 2u − 1i
I
u
2
= h−u
2
a + b, −u
4
a − u
3
a + u
2
a − u
3
+ a
2
+ au − u
2
+ 1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 135 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
= hu
122
+ 5u
121
+ · · · + 2b − 8, −17u
122
+ 41u
121
+ · · · + 2a −
15, u
123
− 3u
122
+ · · · + 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
17
2
u
122
−
41
2
u
121
+ ··· − 11u +
15
2
−
1
2
u
122
−
5
2
u
121
+ ··· +
1
2
u + 4
a
8
=
1
u
2
a
9
=
−u
11
+ 2u
9
− 2u
7
+ u
3
−u
11
+ 3u
9
− 4u
7
+ 3u
5
− u
3
+ u
a
5
=
7
2
u
122
−
11
2
u
121
+ ··· − 3u +
1
2
1
2
u
122
+
1
2
u
121
+ ··· −
5
2
u
2
+
3
2
u
a
12
=
−u
−u
3
+ u
a
1
=
−u
3
−u
3
+ u
a
10
=
u
3
u
5
− u
3
+ u
a
6
=
u
8
− u
6
+ u
4
+ 1
u
10
− 2u
8
+ 3u
6
− 2u
4
+ u
2
a
3
=
5u
122
− 12u
121
+ ··· − 5u +
9
2
−u
122
+ 29u
120
+ ··· +
3
2
u + 2
a
2
=
−u
122
+ 2u
121
+ ··· + 3u −
3
2
1
2
u
119
−
1
2
u
118
+ ··· − 2u
2
+
3
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −13u
122
+
57
2
u
121
+ ··· +
45
2
u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
123
+ 61u
122
+ ··· − 6u − 1
c
2
, c
5
u
123
+ 7u
122
+ ··· + 8u + 1
c
3
u
123
− 7u
122
+ ··· − 128330u + 93361
c
4
, c
8
u
123
− u
122
+ ··· + 4096u + 4096
c
6
u
123
− 3u
122
+ ··· − 10870u + 2425
c
7
, c
11
u
123
+ 3u
122
+ ··· + 2u + 1
c
9
u
123
+ 13u
122
+ ··· + 429074u + 27289
c
10
u
123
+ 59u
122
+ ··· − 2u + 1
c
12
u
123
+ 9u
122
+ ··· + 4066u + 1237
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
123
+ 9y
122
+ ··· − 14y −1
c
2
, c
5
y
123
+ 61y
122
+ ··· − 6y −1
c
3
y
123
− 43y
122
+ ··· − 33652263950y −8716276321
c
4
, c
8
y
123
− 65y
122
+ ··· + 419430400y −16777216
c
6
y
123
− 19y
122
+ ··· + 113874350y −5880625
c
7
, c
11
y
123
− 59y
122
+ ··· − 2y −1
c
9
y
123
+ 41y
122
+ ··· − 732678681206y −744689521
c
10
y
123
+ 13y
122
+ ··· − 14y −1
c
12
y
123
+ 33y
122
+ ··· − 130598898y −1530169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.854485 + 0.561421I
a = 0.003316 − 0.563932I
b = −0.626981 + 0.060520I
−4.46926 − 2.02015I 0
u = 0.854485 − 0.561421I
a = 0.003316 + 0.563932I
b = −0.626981 − 0.060520I
−4.46926 + 2.02015I 0
u = 1.033990 + 0.061446I
a = 1.025610 + 0.127051I
b = 0.0245682 + 0.0714771I
−4.13307 − 3.64032I 0
u = 1.033990 − 0.061446I
a = 1.025610 − 0.127051I
b = 0.0245682 − 0.0714771I
−4.13307 + 3.64032I 0
u = 1.019840 + 0.221186I
a = −0.572632 − 0.294367I
b = 0.092325 − 0.139506I
−1.90019 − 0.28526I 0
u = 1.019840 − 0.221186I
a = −0.572632 + 0.294367I
b = 0.092325 + 0.139506I
−1.90019 + 0.28526I 0
u = 0.657781 + 0.664492I
a = −0.27330 + 1.72372I
b = −0.297545 + 0.371755I
−1.85277 − 10.74350I 0
u = 0.657781 − 0.664492I
a = −0.27330 − 1.72372I
b = −0.297545 − 0.371755I
−1.85277 + 10.74350I 0
u = 0.687369 + 0.623539I
a = −0.29318 + 1.44183I
b = −0.048159 + 0.259545I
−3.96911 − 2.64638I 0
u = 0.687369 − 0.623539I
a = −0.29318 − 1.44183I
b = −0.048159 − 0.259545I
−3.96911 + 2.64638I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917903 + 0.565000I
a = 0.082196 + 0.192568I
b = 0.905526 − 0.344687I
−0.166656 + 0.924245I 0
u = 0.917903 − 0.565000I
a = 0.082196 − 0.192568I
b = 0.905526 + 0.344687I
−0.166656 − 0.924245I 0
u = −0.962014 + 0.501805I
a = 1.14651 + 1.46118I
b = 1.71891 + 0.68501I
−0.279306 − 0.572542I 0
u = −0.962014 − 0.501805I
a = 1.14651 − 1.46118I
b = 1.71891 − 0.68501I
−0.279306 + 0.572542I 0
u = 0.648152 + 0.645593I
a = 0.38530 − 1.67689I
b = 0.281699 − 0.248240I
0.62783 − 5.66862I 0
u = 0.648152 − 0.645593I
a = 0.38530 + 1.67689I
b = 0.281699 + 0.248240I
0.62783 + 5.66862I 0
u = 0.912418 + 0.590250I
a = −0.263358 − 0.252976I
b = −1.030770 + 0.176984I
−2.60544 + 5.87088I 0
u = 0.912418 − 0.590250I
a = −0.263358 + 0.252976I
b = −1.030770 − 0.176984I
−2.60544 − 5.87088I 0
u = 1.048540 + 0.385425I
a = 0.433108 − 0.660989I
b = 0.422710 + 0.320271I
−3.06638 − 1.39605I 0
u = 1.048540 − 0.385425I
a = 0.433108 + 0.660989I
b = 0.422710 − 0.320271I
−3.06638 + 1.39605I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.985605 + 0.527401I
a = −0.412366 − 0.202768I
b = 0.696926 − 1.116170I
1.30652 − 1.06855I 0
u = 0.985605 − 0.527401I
a = −0.412366 + 0.202768I
b = 0.696926 + 1.116170I
1.30652 + 1.06855I 0
u = 1.087640 + 0.274343I
a = −0.353683 − 0.740293I
b = 0.250172 − 0.184177I
−2.47005 − 0.30272I 0
u = 1.087640 − 0.274343I
a = −0.353683 + 0.740293I
b = 0.250172 + 0.184177I
−2.47005 + 0.30272I 0
u = −0.505350 + 0.716113I
a = 0.828458 + 0.277865I
b = 0.921356 − 0.358807I
1.06865 − 4.56495I 0
u = −0.505350 − 0.716113I
a = 0.828458 − 0.277865I
b = 0.921356 + 0.358807I
1.06865 + 4.56495I 0
u = −0.995492 + 0.532233I
a = −0.97900 − 1.25049I
b = −1.45523 − 0.58880I
1.41929 + 3.95035I 0
u = −0.995492 − 0.532233I
a = −0.97900 + 1.25049I
b = −1.45523 + 0.58880I
1.41929 − 3.95035I 0
u = −1.095060 + 0.295281I
a = 3.02439 + 0.12421I
b = 2.53218 − 1.86329I
−3.16948 + 2.81128I 0
u = −1.095060 − 0.295281I
a = 3.02439 − 0.12421I
b = 2.53218 + 1.86329I
−3.16948 − 2.81128I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.102410 + 0.267908I
a = −2.77281 + 0.10154I
b = −2.15753 + 2.01225I
−2.88698 − 2.46184I 0
u = −1.102410 − 0.267908I
a = −2.77281 − 0.10154I
b = −2.15753 − 2.01225I
−2.88698 + 2.46184I 0
u = −0.448019 + 0.736719I
a = 0.745796 − 0.073275I
b = 0.594549 − 0.660727I
0.78043 + 2.03644I 0
u = −0.448019 − 0.736719I
a = 0.745796 + 0.073275I
b = 0.594549 + 0.660727I
0.78043 − 2.03644I 0
u = 0.858281
a = −0.927426
b = 0.108938
−1.50207 −5.95250
u = 1.017760 + 0.522481I
a = 0.811698 + 0.352586I
b = −0.44309 + 1.64463I
0.27133 − 5.98593I 0
u = 1.017760 − 0.522481I
a = 0.811698 − 0.352586I
b = −0.44309 − 1.64463I
0.27133 + 5.98593I 0
u = −0.621924 + 0.587387I
a = 0.727972 + 1.082340I
b = 1.223970 + 0.460141I
0.70009 + 4.93753I 0
u = −0.621924 − 0.587387I
a = 0.727972 − 1.082340I
b = 1.223970 − 0.460141I
0.70009 − 4.93753I 0
u = 0.326719 + 0.783768I
a = −0.60353 − 1.35303I
b = 2.26170 − 0.29466I
−3.54566 + 13.00910I 0. − 8.03983I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.326719 − 0.783768I
a = −0.60353 + 1.35303I
b = 2.26170 + 0.29466I
−3.54566 − 13.00910I 0. + 8.03983I
u = 1.123590 + 0.265053I
a = 0.502221 + 0.942772I
b = −0.263992 + 0.306687I
−5.04425 + 3.82260I 0
u = 1.123590 − 0.265053I
a = 0.502221 − 0.942772I
b = −0.263992 − 0.306687I
−5.04425 − 3.82260I 0
u = −0.510966 + 0.671472I
a = −0.654545 − 0.468997I
b = −0.869605 + 0.071896I
2.93696 − 0.44778I 0
u = −0.510966 − 0.671472I
a = −0.654545 + 0.468997I
b = −0.869605 − 0.071896I
2.93696 + 0.44778I 0
u = 1.119360 + 0.310725I
a = 0.185438 + 1.038430I
b = −0.432873 + 0.226764I
−5.53092 − 3.70026I 0
u = 1.119360 − 0.310725I
a = 0.185438 − 1.038430I
b = −0.432873 − 0.226764I
−5.53092 + 3.70026I 0
u = 0.324855 + 0.771366I
a = 0.72033 + 1.32461I
b = −2.21918 + 0.30802I
−0.98344 + 7.78701I 0. − 4.67811I
u = 0.324855 − 0.771366I
a = 0.72033 − 1.32461I
b = −2.21918 − 0.30802I
−0.98344 − 7.78701I 0. + 4.67811I
u = 0.581489 + 0.598075I
a = 0.89914 − 1.66803I
b = 0.309435 + 0.200315I
2.49653 − 3.41082I 0. + 7.23745I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.581489 − 0.598075I
a = 0.89914 + 1.66803I
b = 0.309435 − 0.200315I
2.49653 + 3.41082I 0. − 7.23745I
u = −1.142960 + 0.238255I
a = −2.32696 − 0.11666I
b = −1.74160 + 1.67456I
−5.56302 − 4.94470I 0
u = −1.142960 − 0.238255I
a = −2.32696 + 0.11666I
b = −1.74160 − 1.67456I
−5.56302 + 4.94470I 0
u = −1.063460 + 0.492512I
a = 1.46708 + 0.61955I
b = 1.53045 − 0.21359I
−2.35808 + 5.38729I 0
u = −1.063460 − 0.492512I
a = 1.46708 − 0.61955I
b = 1.53045 + 0.21359I
−2.35808 − 5.38729I 0
u = 0.300988 + 0.770638I
a = −0.690849 − 1.102760I
b = 2.17376 − 0.22546I
−5.84365 + 4.55880I −6.44547 − 2.49035I
u = 0.300988 − 0.770638I
a = −0.690849 + 1.102760I
b = 2.17376 + 0.22546I
−5.84365 − 4.55880I −6.44547 + 2.49035I
u = −0.563362 + 0.602679I
a = −0.615246 − 0.881766I
b = −1.040120 − 0.318191I
2.69193 + 0.55935I 3.98610 + 0.I
u = −0.563362 − 0.602679I
a = −0.615246 + 0.881766I
b = −1.040120 + 0.318191I
2.69193 − 0.55935I 3.98610 + 0.I
u = −1.152950 + 0.230458I
a = 2.24298 + 0.18923I
b = 1.66975 − 1.59343I
−8.21753 − 10.13550I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.152950 − 0.230458I
a = 2.24298 − 0.18923I
b = 1.66975 + 1.59343I
−8.21753 + 10.13550I 0
u = −0.405700 + 0.715550I
a = −0.547830 + 0.258526I
b = −0.233364 + 0.680720I
2.43695 − 1.70720I 1.69325 + 0.I
u = −0.405700 − 0.715550I
a = −0.547830 − 0.258526I
b = −0.233364 − 0.680720I
2.43695 + 1.70720I 1.69325 + 0.I
u = −1.030200 + 0.571691I
a = −0.516402 − 1.134700I
b = −0.985503 − 0.722266I
1.40801 + 5.27406I 0
u = −1.030200 − 0.571691I
a = −0.516402 + 1.134700I
b = −0.985503 + 0.722266I
1.40801 − 5.27406I 0
u = −1.153290 + 0.256833I
a = 2.45010 + 0.23769I
b = 1.88125 − 1.56566I
−10.34180 − 1.56416I 0
u = −1.153290 − 0.256833I
a = 2.45010 − 0.23769I
b = 1.88125 + 1.56566I
−10.34180 + 1.56416I 0
u = −1.141170 + 0.345577I
a = 2.74400 + 0.42807I
b = 2.32803 − 1.27018I
−6.77873 + 4.44845I 0
u = −1.141170 − 0.345577I
a = 2.74400 − 0.42807I
b = 2.32803 + 1.27018I
−6.77873 − 4.44845I 0
u = −1.039880 + 0.593668I
a = 0.269757 + 1.286620I
b = 0.839442 + 0.975017I
−0.50937 + 9.58006I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.039880 − 0.593668I
a = 0.269757 − 1.286620I
b = 0.839442 − 0.975017I
−0.50937 − 9.58006I 0
u = −0.314117 + 0.738169I
a = 0.575358 − 0.604862I
b = −0.157550 − 1.089370I
−0.72558 − 6.64128I −2.45271 + 5.62875I
u = −0.314117 − 0.738169I
a = 0.575358 + 0.604862I
b = −0.157550 + 1.089370I
−0.72558 + 6.64128I −2.45271 − 5.62875I
u = −1.154440 + 0.326977I
a = −2.73063 − 0.39678I
b = −2.24616 + 1.33762I
−11.15920 + 0.73897I 0
u = −1.154440 − 0.326977I
a = −2.73063 + 0.39678I
b = −2.24616 − 1.33762I
−11.15920 − 0.73897I 0
u = 0.329435 + 0.722217I
a = 1.26469 + 1.24360I
b = −2.06959 + 0.45452I
1.34347 + 5.13610I −0.89905 − 6.52878I
u = 0.329435 − 0.722217I
a = 1.26469 − 1.24360I
b = −2.06959 − 0.45452I
1.34347 − 5.13610I −0.89905 + 6.52878I
u = −1.153440 + 0.356078I
a = −2.72091 − 0.41587I
b = −2.27381 + 1.22883I
−9.68798 + 9.41535I 0
u = −1.153440 − 0.356078I
a = −2.72091 + 0.41587I
b = −2.27381 − 1.22883I
−9.68798 − 9.41535I 0
u = −0.337945 + 0.711241I
a = −0.514362 + 0.535580I
b = 0.117785 + 0.912749I
1.68112 − 2.28331I 2.01200 + 1.73250I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.337945 − 0.711241I
a = −0.514362 − 0.535580I
b = 0.117785 − 0.912749I
1.68112 + 2.28331I 2.01200 − 1.73250I
u = 0.531699 + 0.571261I
a = −1.31269 + 1.58049I
b = −0.189489 − 0.498823I
1.71359 + 1.58676I −0.51367 + 2.12597I
u = 0.531699 − 0.571261I
a = −1.31269 − 1.58049I
b = −0.189489 + 0.498823I
1.71359 − 1.58676I −0.51367 − 2.12597I
u = −1.074920 + 0.589470I
a = −0.231426 + 1.076660I
b = 0.305449 + 1.020630I
−1.06964 + 3.01381I 0
u = −1.074920 − 0.589470I
a = −0.231426 − 1.076660I
b = 0.305449 − 1.020630I
−1.06964 − 3.01381I 0
u = −1.089820 + 0.571745I
a = 0.566381 − 0.717391I
b = 0.140524 − 0.866907I
0.42992 + 6.63920I 0
u = −1.089820 − 0.571745I
a = 0.566381 + 0.717391I
b = 0.140524 + 0.866907I
0.42992 − 6.63920I 0
u = 1.111230 + 0.545507I
a = 2.45891 − 1.62700I
b = 3.32507 + 1.26226I
−1.45622 − 4.63554I 0
u = 1.111230 − 0.545507I
a = 2.45891 + 1.62700I
b = 3.32507 − 1.26226I
−1.45622 + 4.63554I 0
u = 0.323938 + 0.689603I
a = −1.58714 − 0.95579I
b = 1.89255 − 0.55461I
0.818092 − 0.124046I −3.14780 − 0.83223I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.323938 − 0.689603I
a = −1.58714 + 0.95579I
b = 1.89255 + 0.55461I
0.818092 + 0.124046I −3.14780 + 0.83223I
u = 1.132130 + 0.504504I
a = 1.68573 − 1.49625I
b = 2.18204 + 0.67494I
−5.70491 − 3.44197I 0
u = 1.132130 − 0.504504I
a = 1.68573 + 1.49625I
b = 2.18204 − 0.67494I
−5.70491 + 3.44197I 0
u = −1.119960 + 0.532893I
a = −1.45764 + 0.36603I
b = −1.02362 + 0.98782I
−4.02319 + 3.95622I 0
u = −1.119960 − 0.532893I
a = −1.45764 − 0.36603I
b = −1.02362 − 0.98782I
−4.02319 − 3.95622I 0
u = −1.111910 + 0.553776I
a = 1.142580 − 0.571408I
b = 0.680128 − 1.006950I
−0.57041 + 7.12600I 0
u = −1.111910 − 0.553776I
a = 1.142580 + 0.571408I
b = 0.680128 + 1.006950I
−0.57041 − 7.12600I 0
u = 0.203285 + 0.729617I
a = 0.726731 + 0.322337I
b = −1.81310 − 0.11441I
−7.16219 + 2.64076I −7.80104 − 2.59513I
u = 0.203285 − 0.729617I
a = 0.726731 − 0.322337I
b = −1.81310 + 0.11441I
−7.16219 − 2.64076I −7.80104 + 2.59513I
u = 1.142870 + 0.494166I
a = −1.51219 + 1.59682I
b = −2.05783 − 0.43237I
−8.75415 + 1.36519I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.142870 − 0.494166I
a = −1.51219 − 1.59682I
b = −2.05783 + 0.43237I
−8.75415 − 1.36519I 0
u = 1.116840 + 0.555196I
a = −2.40203 + 1.83735I
b = −3.52952 − 0.89285I
−0.94884 − 10.00770I 0
u = 1.116840 − 0.555196I
a = −2.40203 − 1.83735I
b = −3.52952 + 0.89285I
−0.94884 + 10.00770I 0
u = −1.124970 + 0.555762I
a = −1.31913 + 0.71542I
b = −0.75747 + 1.20075I
−3.08943 + 11.54780I 0
u = −1.124970 − 0.555762I
a = −1.31913 − 0.71542I
b = −0.75747 − 1.20075I
−3.08943 − 11.54780I 0
u = 1.143390 + 0.517843I
a = −1.79911 + 1.70410I
b = −2.47710 − 0.50435I
−9.86641 − 7.31652I 0
u = 1.143390 − 0.517843I
a = −1.79911 − 1.70410I
b = −2.47710 + 0.50435I
−9.86641 + 7.31652I 0
u = −0.271121 + 0.683887I
a = 0.479920 − 0.674630I
b = −0.416798 − 0.951510I
−1.60447 + 0.71899I −4.24680 − 0.96822I
u = −0.271121 − 0.683887I
a = 0.479920 + 0.674630I
b = −0.416798 + 0.951510I
−1.60447 − 0.71899I −4.24680 + 0.96822I
u = 1.131700 + 0.568256I
a = −2.25505 + 1.97886I
b = −3.48207 − 0.39438I
−3.35699 − 12.82570I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.131700 − 0.568256I
a = −2.25505 − 1.97886I
b = −3.48207 + 0.39438I
−3.35699 + 12.82570I 0
u = 1.137910 + 0.560409I
a = 2.19776 − 1.94535I
b = 3.29821 + 0.41025I
−8.30040 − 9.55743I 0
u = 1.137910 − 0.560409I
a = 2.19776 + 1.94535I
b = 3.29821 − 0.41025I
−8.30040 + 9.55743I 0
u = 1.135060 + 0.572499I
a = 2.24277 − 2.00284I
b = 3.48187 + 0.30110I
−5.9309 − 18.0955I 0
u = 1.135060 − 0.572499I
a = 2.24277 + 2.00284I
b = 3.48187 − 0.30110I
−5.9309 + 18.0955I 0
u = 0.145735 + 0.712891I
a = 0.674421 + 0.018185I
b = −1.63547 − 0.32069I
−5.91594 − 5.85172I −6.29729 + 4.24575I
u = 0.145735 − 0.712891I
a = 0.674421 − 0.018185I
b = −1.63547 + 0.32069I
−5.91594 + 5.85172I −6.29729 − 4.24575I
u = 0.176087 + 0.688838I
a = −0.843367 − 0.085955I
b = 1.59406 + 0.15723I
−3.01456 − 1.05590I −3.38153 + 0.61296I
u = 0.176087 − 0.688838I
a = −0.843367 + 0.085955I
b = 1.59406 − 0.15723I
−3.01456 + 1.05590I −3.38153 − 0.61296I
u = −0.524300 + 0.363728I
a = 0.120376 + 1.403430I
b = 0.704675 + 0.874117I
−0.46580 − 1.46675I −2.13692 + 1.59125I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.524300 − 0.363728I
a = 0.120376 − 1.403430I
b = 0.704675 − 0.874117I
−0.46580 + 1.46675I −2.13692 − 1.59125I
u = −0.127753 + 0.355275I
a = −0.80595 + 1.22969I
b = 0.539578 + 0.492331I
−0.33354 − 1.50737I −2.96396 + 4.38386I
u = −0.127753 − 0.355275I
a = −0.80595 − 1.22969I
b = 0.539578 − 0.492331I
−0.33354 + 1.50737I −2.96396 − 4.38386I
17
II. I
u
2
=
h−u
2
a+b, −u
4
a−u
3
a+u
2
a−u
3
+a
2
+au−u
2
+1, u
6
+u
5
−u
4
−2u
3
+u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
a
u
2
a
a
8
=
1
u
2
a
9
=
1
u
2
a
5
=
a
u
2
a
a
12
=
−u
−u
3
+ u
a
1
=
−u
3
−u
3
+ u
a
10
=
u
3
u
5
− u
3
+ u
a
6
=
u
3
u
3
− u
a
3
=
u
3
a
u
5
a − u
3
a + au
a
2
=
u
3
a − u
4
− u
3
+ u
2
+ u
u
5
a − u
3
a − u
3
+ au + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
5
a + u
4
a + 4u
3
a + 4u
4
− 2u
2
a + u
3
− 4au − 3u
2
− 4u − 3
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
8
u
12
c
6
, c
9
, c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
10
, c
12
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
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)
6
c
4
, c
8
y
12
c
6
, c
7
, c
9
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
10
, c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0.578212 + 1.125030I
b = −0.136196 + 1.374220I
−1.89061 + 1.10558I −7.01188 − 1.87706I
u = 1.002190 + 0.295542I
a = −1.263410 − 0.061767I
b = −1.122010 − 0.805060I
−1.89061 − 2.95419I −3.50232 + 4.35344I
u = 1.002190 − 0.295542I
a = 0.578212 − 1.125030I
b = −0.136196 − 1.374220I
−1.89061 − 1.10558I −7.01188 + 1.87706I
u = 1.002190 − 0.295542I
a = −1.263410 + 0.061767I
b = −1.122010 + 0.805060I
−1.89061 + 2.95419I −3.50232 − 4.35344I
u = −0.428243 + 0.664531I
a = 0.224551 + 0.930349I
b = 0.471538 − 0.368031I
1.89061 + 1.10558I 1.81693 − 2.49433I
u = −0.428243 + 0.664531I
a = 0.693431 − 0.659641I
b = −0.554493 − 0.224349I
1.89061 − 2.95419I −0.06995 + 4.17815I
u = −0.428243 − 0.664531I
a = 0.224551 − 0.930349I
b = 0.471538 + 0.368031I
1.89061 − 1.10558I 1.81693 + 2.49433I
u = −0.428243 − 0.664531I
a = 0.693431 + 0.659641I
b = −0.554493 + 0.224349I
1.89061 + 2.95419I −0.06995 − 4.17815I
u = −1.073950 + 0.558752I
a = −0.036219 + 0.825237I
b = 0.959936 + 0.737627I
3.66314I −1.09315 − 2.75648I
u = −1.073950 + 0.558752I
a = −0.696567 − 0.443985I
b = −1.118770 + 0.462515I
7.72290I −4.13964 − 8.90605I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = −0.036219 − 0.825237I
b = 0.959936 − 0.737627I
− 3.66314I −1.09315 + 2.75648I
u = −1.073950 − 0.558752I
a = −0.696567 + 0.443985I
b = −1.118770 − 0.462515I
− 7.72290I −4.13964 + 8.90605I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
123
+ 61u
122
+ ··· − 6u − 1)
c
2
((u
2
+ u + 1)
6
)(u
123
+ 7u
122
+ ··· + 8u + 1)
c
3
((u
2
− u + 1)
6
)(u
123
− 7u
122
+ ··· − 128330u + 93361)
c
4
, c
8
u
12
(u
123
− u
122
+ ··· + 4096u + 4096)
c
5
((u
2
− u + 1)
6
)(u
123
+ 7u
122
+ ··· + 8u + 1)
c
6
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
123
− 3u
122
+ ··· − 10870u + 2425)
c
7
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
123
+ 3u
122
+ ··· + 2u + 1)
c
9
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
123
+ 13u
122
+ ··· + 429074u + 27289)
c
10
((u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
)(u
123
+ 59u
122
+ ··· − 2u + 1)
c
11
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
123
+ 3u
122
+ ··· + 2u + 1)
c
12
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
123
+ 9u
122
+ ··· + 4066u + 1237)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
123
+ 9y
122
+ ··· − 14y −1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
123
+ 61y
122
+ ··· − 6y −1)
c
3
((y
2
+ y + 1)
6
)(y
123
− 43y
122
+ ··· − 3.36523 × 10
10
y −8.71628 × 10
9
)
c
4
, c
8
y
12
(y
123
− 65y
122
+ ··· + 4.19430 × 10
8
y −1.67772 × 10
7
)
c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
123
− 19y
122
+ ··· + 113874350y −5880625)
c
7
, c
11
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
123
− 59y
122
+ ··· − 2y −1)
c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
123
+ 41y
122
+ ··· − 732678681206y −744689521)
c
10
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
123
+ 13y
122
+ ··· − 14y −1)
c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
123
+ 33y
122
+ ··· − 130598898y −1530169)
24
