11a
196
(K11a
196
)
A knot diagram
1
Linearized knot diagam
7 1 10 8 9 2 3 11 6 4 5
Solving Sequence
4,8 5,11
9 6 1 10 3 2 7
c
4
c
8
c
5
c
11
c
10
c
3
c
2
c
7
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.56366 × 10
21
u
26
+ 2.00582 × 10
21
u
25
+ ··· + 7.42142 × 10
21
b − 9.93961 × 10
20
,
− 1.23252 × 10
22
u
26
+ 1.13313 × 10
22
u
25
+ ··· + 7.42142 × 10
21
a − 2.69156 × 10
22
, u
27
− u
26
+ ··· + 2u − 1i
I
u
2
= h−466470675905338u
23
− 397267180404293u
22
+ ··· + 6630830886537376b − 264157828925488,
26944089879716u
23
+ 14049375398024u
22
+ ··· + 121666621771328a − 16982188896888,
u
24
+ 3u
22
+ ··· − 4u + 8i
I
u
3
= hu
14
− 3u
10
− u
9
− 2u
8
− u
7
+ 3u
6
+ 4u
5
+ 4u
4
+ u
3
− u
2
+ 2b − 3,
− 2u
14
− 3u
13
− u
12
− 5u
11
+ u
10
+ 6u
9
+ u
8
+ 13u
7
+ 6u
6
− 7u
5
+ u
4
− 7u
3
− 8u
2
+ 2a + u − 1,
u
15
+ u
13
+ u
12
− 2u
11
− 2u
9
− 4u
8
+ 2u
7
+ u
5
+ 4u
4
− 1i
I
u
4
= h5.79410 × 10
18
u
23
+ 1.97168 × 10
19
u
22
+ ··· + 1.42067 × 10
19
b − 3.77005 × 10
17
,
19264503378333u
23
+ 64217498098488u
22
+ ··· + 8090899806416a − 59730846409593,
u
24
+ 3u
23
+ ··· − 6u + 1i
I
u
5
= hb − 1, 59u
5
+ 76u
4
+ 242u
3
+ 190u
2
+ 67a + 487u + 146, u
6
+ u
5
+ 4u
4
+ 2u
3
+ 8u
2
+ 1i
I
u
6
= h−u
2
+ b, −u
2
+ a − 1, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
u
7
= hb − 1, a − 2, u + 1i
* 7 irreducible components of dim
C
= 0, with total 103 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
1
I.
I
u
1
= h−1.56×10
21
u
26
+2.01×10
21
u
25
+· · ·+7.42×10
21
b−9.94×10
20
, −1.23×
10
22
u
26
+1.13×10
22
u
25
+· · ·+7.42×10
21
a−2.69×10
22
, u
27
−u
26
+· · ·+2u−1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
1.66077u
26
− 1.52684u
25
+ ··· + 1.11901u + 3.62674
0.210696u
26
− 0.270275u
25
+ ··· + 2.39290u + 0.133931
a
9
=
0.312172u
26
+ 0.638396u
25
+ ··· − 1.77480u + 3.01621
0.581257u
26
− 0.629489u
25
+ ··· + 0.803940u + 1.08450
a
6
=
−1.18988u
26
+ 1.11302u
25
+ ··· − 4.45598u + 1.89491
−0.241743u
26
+ 0.0536668u
25
+ ··· − 0.670686u − 0.868814
a
1
=
1.66077u
26
− 1.52684u
25
+ ··· + 0.119008u + 3.62674
0.210696u
26
− 0.270275u
25
+ ··· + 2.39290u + 0.133931
a
10
=
1.45007u
26
− 1.25656u
25
+ ··· − 1.27390u + 3.49281
0.210696u
26
− 0.270275u
25
+ ··· + 2.39290u + 0.133931
a
3
=
1.19231u
26
− 0.633674u
25
+ ··· + 3.06255u + 2.18099
−0.107812u
26
+ 0.130431u
25
+ ··· − 0.365474u + 0.791952
a
2
=
1.19260u
26
− 0.799146u
25
+ ··· + 2.64209u − 0.651268
−0.0394366u
26
+ 0.164653u
25
+ ··· + 0.0481946u + 0.646177
a
7
=
−0.451600u
26
+ 0.986823u
25
+ ··· + 5.66786u − 0.00121263
0.328533u
26
− 0.284050u
25
+ ··· − 0.908870u + 0.936550
a
7
=
−0.451600u
26
+ 0.986823u
25
+ ··· + 5.66786u − 0.00121263
0.328533u
26
− 0.284050u
25
+ ··· − 0.908870u + 0.936550
(ii) Obstruction class = −1
(iii) Cusp Shapes =
24366089866600657610153
7421416129906443651586
u
26
−
13344042961471974440973
3710708064953221825793
u
25
+ ··· +
123365016888052989817509
7421416129906443651586
u +
5771013155102072120085
3710708064953221825793
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
27
+ 6u
26
+ ··· − 40u − 8
c
2
u
27
+ 14u
26
+ ··· + 32u − 64
c
3
, c
5
, c
9
c
10
u
27
− 9u
25
+ ··· − u − 1
c
4
, c
11
u
27
− u
26
+ ··· + 2u − 1
c
7
u
27
− 9u
26
+ ··· + 2296u − 232
c
8
u
27
+ 22u
26
+ ··· − 7680u − 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
27
+ 14y
26
+ ··· + 32y −64
c
2
y
27
+ 2y
26
+ ··· + 39424y −4096
c
3
, c
5
, c
9
c
10
y
27
− 18y
26
+ ··· − 7y −1
c
4
, c
11
y
27
− 5y
26
+ ··· + 16y −1
c
7
y
27
− 7y
26
+ ··· + 586144y −53824
c
8
y
27
− 4y
26
+ ··· + 1966080y −262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.898231 + 0.526385I
a = 0.209642 + 0.703154I
b = −0.122251 + 0.700628I
−1.84219 + 1.61763I −0.34752 − 1.90846I
u = −0.898231 − 0.526385I
a = 0.209642 − 0.703154I
b = −0.122251 − 0.700628I
−1.84219 − 1.61763I −0.34752 + 1.90846I
u = 1.012540 + 0.318884I
a = −0.308945 + 0.757476I
b = 0.238061 + 0.818947I
−5.36570 + 2.03204I −4.32275 − 2.13513I
u = 1.012540 − 0.318884I
a = −0.308945 − 0.757476I
b = 0.238061 − 0.818947I
−5.36570 − 2.03204I −4.32275 + 2.13513I
u = −0.276412 + 0.776716I
a = 0.023671 + 0.586360I
b = −0.037108 + 0.457608I
0.18488 + 1.81939I 2.29374 − 3.76762I
u = −0.276412 − 0.776716I
a = 0.023671 − 0.586360I
b = −0.037108 − 0.457608I
0.18488 − 1.81939I 2.29374 + 3.76762I
u = −0.795815 + 0.903407I
a = 0.26309 + 1.49507I
b = 1.305830 + 0.251781I
7.97470 + 2.85426I 8.94272 − 2.79876I
u = −0.795815 − 0.903407I
a = 0.26309 − 1.49507I
b = 1.305830 − 0.251781I
7.97470 − 2.85426I 8.94272 + 2.79876I
u = 1.074420 + 0.604846I
a = −0.257278 + 0.648739I
b = 0.028367 + 0.782017I
−4.76097 − 6.00409I −3.69772 + 5.84582I
u = 1.074420 − 0.604846I
a = −0.257278 − 0.648739I
b = 0.028367 − 0.782017I
−4.76097 + 6.00409I −3.69772 − 5.84582I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.208550 + 0.274221I
a = −1.302050 + 0.508274I
b = −0.932187 + 0.115358I
−2.56542 − 5.05729I 5.23613 + 5.90187I
u = 1.208550 − 0.274221I
a = −1.302050 − 0.508274I
b = −0.932187 − 0.115358I
−2.56542 + 5.05729I 5.23613 − 5.90187I
u = 0.878818 + 1.037850I
a = −0.167256 + 1.255180I
b = −1.359850 + 0.350164I
8.49644 − 8.55345I 9.20145 + 7.26296I
u = 0.878818 − 1.037850I
a = −0.167256 − 1.255180I
b = −1.359850 − 0.350164I
8.49644 + 8.55345I 9.20145 − 7.26296I
u = −0.421872 + 0.462971I
a = 2.45358 − 1.32260I
b = −1.027750 − 0.447368I
0.99303 + 9.06795I 3.46736 − 11.63407I
u = −0.421872 − 0.462971I
a = 2.45358 + 1.32260I
b = −1.027750 + 0.447368I
0.99303 − 9.06795I 3.46736 + 11.63407I
u = −0.591031 + 0.138214I
a = 0.54492 − 1.69705I
b = −0.688350 − 0.511205I
−2.72477 + 1.50676I −3.17250 − 4.01509I
u = −0.591031 − 0.138214I
a = 0.54492 + 1.69705I
b = −0.688350 + 0.511205I
−2.72477 − 1.50676I −3.17250 + 4.01509I
u = 0.338852 + 0.350615I
a = −3.02283 − 2.53673I
b = 0.966126 − 0.347074I
3.01066 − 3.39049I 3.02884 + 10.08685I
u = 0.338852 − 0.350615I
a = −3.02283 + 2.53673I
b = 0.966126 + 0.347074I
3.01066 + 3.39049I 3.02884 − 10.08685I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.13972 + 1.08957I
a = 0.255186 + 0.962671I
b = 1.279710 + 0.563405I
0.91508 + 8.68990I 2.54049 − 5.35859I
u = −1.13972 − 1.08957I
a = 0.255186 − 0.962671I
b = 1.279710 − 0.563405I
0.91508 − 8.68990I 2.54049 + 5.35859I
u = 1.07737 + 1.19752I
a = −0.142409 + 0.974746I
b = −1.39888 + 0.56362I
6.16613 − 11.88750I 7.81516 + 6.29925I
u = 1.07737 − 1.19752I
a = −0.142409 − 0.974746I
b = −1.39888 − 0.56362I
6.16613 + 11.88750I 7.81516 − 6.29925I
u = −1.12228 + 1.24272I
a = 0.128320 + 0.924082I
b = 1.41876 + 0.62158I
3.6775 + 17.2855I 4.85544 − 9.87335I
u = −1.12228 − 1.24272I
a = 0.128320 − 0.924082I
b = 1.41876 − 0.62158I
3.6775 − 17.2855I 4.85544 + 9.87335I
u = 0.309622
a = 3.64471
b = 0.659027
1.29009 9.31830
7
II.
I
u
2
= h−4.66×10
14
u
23
−3.97×10
14
u
22
+· · ·+6.63×10
15
b−2.64×10
14
, 2.69×
10
13
u
23
+1.40×10
13
u
22
+· · ·+1.22×10
14
a−1.70×10
13
, u
24
+3u
22
+· · ·−4u+8i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
−0.221458u
23
− 0.115474u
22
+ ··· − 5.16359u + 0.139580
0.0703488u
23
+ 0.0599121u
22
+ ··· + 3.44503u + 0.0398378
a
9
=
−0.131260u
23
− 0.121483u
22
+ ··· − 3.05755u + 2.19329
−0.0922969u
23
+ 0.000104233u
22
+ ··· − 1.11867u − 0.780159
a
6
=
−0.108244u
23
+ 0.149259u
22
+ ··· + 1.62669u + 5.33342
0.00600815u
23
+ 0.116833u
22
+ ··· − 2.41450u − 0.278416
a
1
=
−0.277967u
23
− 0.143397u
22
+ ··· − 7.29884u + 1.02354
0.0235493u
23
+ 0.106410u
22
+ ··· + 3.78541u + 0.263215
a
10
=
−0.291807u
23
− 0.175386u
22
+ ··· − 8.60861u + 0.0997419
0.0703488u
23
+ 0.0599121u
22
+ ··· + 3.44503u + 0.0398378
a
3
=
0.187834u
23
+ 0.00949931u
22
+ ··· + 7.51428u − 1.76112
−0.0903139u
23
− 0.101796u
22
+ ··· + 0.0682743u + 0.252378
a
2
=
−0.0733779u
23
+ 0.0153619u
22
+ ··· + 9.34212u + 4.09583
0.123742u
23
− 0.0875102u
22
+ ··· − 0.0211572u − 1.70617
a
7
=
−0.340801u
23
− 0.152896u
22
+ ··· − 7.31312u + 2.28466
0.170602u
23
+ 0.00657076u
22
+ ··· + 1.79380u − 0.738436
a
7
=
−0.340801u
23
− 0.152896u
22
+ ··· − 7.31312u + 2.28466
0.170602u
23
+ 0.00657076u
22
+ ··· + 1.79380u − 0.738436
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
867553217111521
1657707721634344
u
23
+
56390307623253
3315415443268688
u
22
+ ··· +
3770100918086014
207213465204293
u +
1919092137145043
207213465204293
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
4
+ u
2
+ u + 1)
6
c
2
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
6
c
3
, c
5
, c
9
c
10
u
24
− 9u
22
+ ··· + 56u + 8
c
4
, c
11
u
24
+ 3u
22
+ ··· − 4u + 8
c
7
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
6
c
8
(u
3
− u
2
+ 1)
8
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
6
c
2
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
6
c
3
, c
5
, c
9
c
10
y
24
− 18y
23
+ ··· − 864y + 64
c
4
, c
11
y
24
+ 6y
23
+ ··· + 944y + 64
c
7
(y
4
− y
3
+ 2y
2
+ 7y + 4)
6
c
8
(y
3
− y
2
+ 2y −1)
8
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.077838 + 1.001210I
a = −0.058264 + 0.749436I
b = −1.40920 + 0.84871I
3.42323 − 7.64338I 9.24932 + 6.51087I
u = 0.077838 − 1.001210I
a = −0.058264 − 0.749436I
b = −1.40920 − 0.84871I
3.42323 + 7.64338I 9.24932 − 6.51087I
u = 0.554955 + 0.881319I
a = −0.156285 − 1.094010I
b = 0.443978 − 1.026930I
2.89077 − 4.22521I 8.26043 + 6.84681I
u = 0.554955 − 0.881319I
a = −0.156285 + 1.094010I
b = 0.443978 + 1.026930I
2.89077 + 4.22521I 8.26043 − 6.84681I
u = 0.214202 + 0.934183I
a = 0.962122 − 0.718649I
b = −0.207958 + 0.155122I
2.89077 + 1.43103I 8.26043 + 0.88791I
u = 0.214202 − 0.934183I
a = 0.962122 + 0.718649I
b = −0.207958 − 0.155122I
2.89077 − 1.43103I 8.26043 − 0.88791I
u = −0.810739 + 0.684928I
a = −0.178616 − 1.069640I
b = 0.034600 − 1.374090I
−0.71436 + 10.47150I 2.72006 − 9.49032I
u = −0.810739 − 0.684928I
a = −0.178616 + 1.069640I
b = 0.034600 + 1.374090I
−0.71436 − 10.47150I 2.72006 + 9.49032I
u = −1.023630 + 0.332750I
a = −0.989201 + 0.406110I
b = −0.441767 + 0.651030I
−0.71436 + 4.81525I 2.72006 − 3.53142I
u = −1.023630 − 0.332750I
a = −0.989201 − 0.406110I
b = −0.441767 − 0.651030I
−0.71436 − 4.81525I 2.72006 + 3.53142I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.299931 + 0.824118I
a = −0.455949 − 1.230640I
b = 1.091230 − 0.434477I
2.89077 − 1.43103I 8.26043 − 0.88791I
u = 0.299931 − 0.824118I
a = −0.455949 + 1.230640I
b = 1.091230 + 0.434477I
2.89077 + 1.43103I 8.26043 + 0.88791I
u = −0.233421 + 0.551322I
a = 0.491584 + 1.161090I
b = 1.68223 + 0.39397I
7.02835 + 1.39709I 14.7897 − 3.8674I
u = −0.233421 − 0.551322I
a = 0.491584 − 1.161090I
b = 1.68223 − 0.39397I
7.02835 − 1.39709I 14.7897 + 3.8674I
u = 0.208549 + 0.403398I
a = 2.34438 − 0.96312I
b = −1.141110 + 0.176547I
−0.71436 − 4.81525I 2.72006 + 3.53142I
u = 0.208549 − 0.403398I
a = 2.34438 + 0.96312I
b = −1.141110 − 0.176547I
−0.71436 + 4.81525I 2.72006 − 3.53142I
u = −0.69942 + 1.38686I
a = 0.173806 − 0.720332I
b = −1.091770 − 0.185403I
2.89077 + 4.22521I 8.26043 − 6.84681I
u = −0.69942 − 1.38686I
a = 0.173806 + 0.720332I
b = −1.091770 + 0.185403I
2.89077 − 4.22521I 8.26043 + 6.84681I
u = 1.50603 + 0.81015I
a = −0.388743 + 0.209121I
b = −1.370290 − 0.060244I
7.02835 + 1.39709I 14.7897 − 3.8674I
u = 1.50603 − 0.81015I
a = −0.388743 − 0.209121I
b = −1.370290 + 0.060244I
7.02835 − 1.39709I 14.7897 + 3.8674I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.25615 + 1.37119I
a = 0.023380 − 0.618493I
b = 1.312800 − 0.417455I
−0.71436 − 10.47150I 2.72006 + 9.49032I
u = 1.25615 − 1.37119I
a = 0.023380 + 0.618493I
b = 1.312800 + 0.417455I
−0.71436 + 10.47150I 2.72006 − 9.49032I
u = −1.35044 + 1.60451I
a = 0.231785 + 0.275391I
b = 1.097260 − 0.209996I
3.42323 − 7.64338I 9.24932 + 6.51087I
u = −1.35044 − 1.60451I
a = 0.231785 − 0.275391I
b = 1.097260 + 0.209996I
3.42323 + 7.64338I 9.24932 − 6.51087I
13
III.
I
u
3
= hu
14
−3u
10
+· · ·+2b−3, −2u
14
−3u
13
+· · ·+2a−1, u
15
+u
13
+· · ·+4u
4
−1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
u
14
+
3
2
u
13
+ ··· −
1
2
u +
1
2
−
1
2
u
14
+
3
2
u
10
+ ··· +
1
2
u
2
+
3
2
a
9
=
u
14
+
3
2
u
13
+ ··· +
7
2
u +
1
2
u
14
+ u
12
+ u
11
− 2u
10
− 2u
8
− 4u
7
+ 2u
6
+ u
4
+ 4u
3
+ u
a
6
=
1
2
u
14
+ u
13
+ ··· + 4u +
1
2
3
2
u
14
+ 2u
12
+ ··· + 2u −
1
2
a
1
=
u
14
+
3
2
u
13
+ ··· +
1
2
u +
1
2
−
1
2
u
14
+
3
2
u
10
+ ··· +
1
2
u
2
+
3
2
a
10
=
3
2
u
14
+
3
2
u
13
+ ··· −
1
2
u − 1
−
1
2
u
14
+
3
2
u
10
+ ··· +
1
2
u
2
+
3
2
a
3
=
3
2
u
13
+
1
2
u
12
+ ··· +
3
2
u −
1
2
−
1
2
u
13
−
1
2
u
12
+ ··· −
3
2
u +
3
2
a
2
=
−u
14
+
3
2
u
13
+ ··· +
1
2
u −
3
2
−
1
2
u
14
− u
13
+ ··· − 2u +
3
2
a
7
=
−u
14
+
1
2
u
13
+ ··· +
7
2
u +
5
2
2u
14
+ 2u
12
+ ··· + u − 1
a
7
=
−u
14
+
1
2
u
13
+ ··· +
7
2
u +
5
2
2u
14
+ 2u
12
+ ··· + u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
11
2
u
14
−u
13
−2u
12
−8u
11
+
23
2
u
10
+
7
2
u
9
+6u
8
+
47
2
u
7
−
9
2
u
6
−10u
5
+4u
4
−
33
2
u
3
−
19
2
u
2
+
5
2
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 4u
13
+ 8u
11
− u
10
+ 8u
9
− 3u
8
+ 4u
7
− 5u
6
− 5u
4
− 3u
2
− 1
c
2
u
15
+ 8u
14
+ ··· − 6u − 1
c
3
, c
9
u
15
+ u
14
+ ··· − u − 1
c
4
, c
11
u
15
+ u
13
+ u
12
− 2u
11
− 2u
9
− 4u
8
+ 2u
7
+ u
5
+ 4u
4
− 1
c
5
, c
10
u
15
− u
14
+ ··· − u + 1
c
6
u
15
+ 4u
13
+ 8u
11
+ u
10
+ 8u
9
+ 3u
8
+ 4u
7
+ 5u
6
+ 5u
4
+ 3u
2
+ 1
c
7
u
15
− 4u
13
+ ··· + 2u + 1
c
8
u
15
+ 7u
14
+ ··· − 4u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
15
+ 8y
14
+ ··· − 6y −1
c
2
y
15
+ 16y
13
+ ··· − 2y −1
c
3
, c
5
, c
9
c
10
y
15
− 15y
14
+ ··· + 13y −1
c
4
, c
11
y
15
+ 2y
14
+ ··· + 8y
2
− 1
c
7
y
15
− 8y
14
+ ··· − 10y −1
c
8
y
15
− 7y
14
+ ··· + 8y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.185034 + 0.977053I
a = 0.901834 − 0.120626I
b = −0.971462 − 0.539948I
1.66412 + 7.79387I 4.71821 − 7.48440I
u = 0.185034 − 0.977053I
a = 0.901834 + 0.120626I
b = −0.971462 + 0.539948I
1.66412 − 7.79387I 4.71821 + 7.48440I
u = 1.059920 + 0.125997I
a = −0.505429 + 0.152100I
b = −1.66034 − 0.09253I
5.03009 − 3.03027I −0.29865 + 6.15454I
u = 1.059920 − 0.125997I
a = −0.505429 − 0.152100I
b = −1.66034 + 0.09253I
5.03009 + 3.03027I −0.29865 − 6.15454I
u = −1.017990 + 0.343618I
a = −1.24822 − 0.67823I
b = −0.602647 − 0.093142I
−3.33930 + 4.72492I −3.76065 − 3.56168I
u = −1.017990 − 0.343618I
a = −1.24822 + 0.67823I
b = −0.602647 + 0.093142I
−3.33930 − 4.72492I −3.76065 + 3.56168I
u = −0.877006 + 0.163803I
a = 0.740351 + 0.352474I
b = 1.52784 − 0.11487I
6.32524 − 0.81175I 6.18881 − 3.33873I
u = −0.877006 − 0.163803I
a = 0.740351 − 0.352474I
b = 1.52784 + 0.11487I
6.32524 + 0.81175I 6.18881 + 3.33873I
u = −0.034209 + 0.765835I
a = −1.59402 − 0.49939I
b = 0.941073 − 0.390006I
3.58065 − 2.83345I 10.68843 + 2.87579I
u = −0.034209 − 0.765835I
a = −1.59402 + 0.49939I
b = 0.941073 + 0.390006I
3.58065 + 2.83345I 10.68843 − 2.87579I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.162111 + 1.223850I
a = 0.441400 − 0.577132I
b = −0.716431 − 0.549731I
−0.031900 + 0.989940I 0.43333 − 2.78857I
u = −0.162111 − 1.223850I
a = 0.441400 + 0.577132I
b = −0.716431 + 0.549731I
−0.031900 − 0.989940I 0.43333 + 2.78857I
u = 0.493147 + 1.132940I
a = −0.152438 − 0.861689I
b = 0.628299 − 0.406815I
1.26100 − 3.34950I 3.87772 + 4.04913I
u = 0.493147 − 1.132940I
a = −0.152438 + 0.861689I
b = 0.628299 + 0.406815I
1.26100 + 3.34950I 3.87772 − 4.04913I
u = 0.706418
a = 2.83303
b = 0.707336
0.629027 −6.69440
18
IV.
I
u
4
= h5.79 × 10
18
u
23
+ 1.97 × 10
19
u
22
+ · · · + 1.42 × 10
19
b − 3.77 × 10
17
, 1.93 ×
10
13
u
23
+6.42×10
13
u
22
+· · ·+8.09×10
12
a−5.97×10
13
, u
24
+3u
23
+· · ·−6u+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
−2.38101u
23
− 7.93700u
22
+ ··· − 16.0638u + 7.38247
−0.407843u
23
− 1.38785u
22
+ ··· − 3.78446u + 0.0265372
a
9
=
−3.15250u
23
− 10.3010u
22
+ ··· − 32.7601u + 11.4367
0.503685u
23
+ 1.63902u
22
+ ··· + 4.73930u − 0.983119
a
6
=
−1.98429u
23
− 6.73679u
22
+ ··· − 12.6550u + 5.30508
0.0494630u
23
+ 0.168935u
22
+ ··· + 0.574708u − 1.77150
a
1
=
−2.20112u
23
− 7.24702u
22
+ ··· − 14.6622u + 8.14991
−0.371131u
23
− 1.31484u
22
+ ··· − 3.06241u − 0.123786
a
10
=
−1.97317u
23
− 6.54915u
22
+ ··· − 12.2793u + 7.35594
−0.407843u
23
− 1.38785u
22
+ ··· − 3.78446u + 0.0265372
a
3
=
0.146254u
23
+ 0.641487u
22
+ ··· − 7.52556u − 0.845528
0.836864u
23
+ 2.81155u
22
+ ··· + 6.03475u − 0.313883
a
2
=
−u
23
− 3u
22
+ ··· − 15u + 6
0.375295u
23
+ 1.14401u
22
+ ··· + 6.69523u − 0.288437
a
7
=
−1.35971u
23
− 4.26371u
22
+ ··· − 17.1675u + 3.44827
−0.195361u
23
− 0.483364u
22
+ ··· − 8.48872u + 3.10314
a
7
=
−1.35971u
23
− 4.26371u
22
+ ··· − 17.1675u + 3.44827
−0.195361u
23
− 0.483364u
22
+ ··· − 8.48872u + 3.10314
(ii) Obstruction class = −1
(iii) Cusp Shapes =
7079914424451449855
1775837212186070572
u
23
+
23544509299143752001
1775837212186070572
u
22
+ ··· +
49265834911585654277
1775837212186070572
u −
1824252325882161130
443959303046517643
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
4
c
2
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
4
c
3
, c
5
, c
9
c
10
u
24
+ 4u
23
+ ··· + 106u + 59
c
4
, c
11
u
24
+ 3u
23
+ ··· − 6u + 1
c
7
, c
8
(u
3
− u
2
+ 1)
8
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
4
c
2
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
4
c
3
, c
5
, c
9
c
10
y
24
− 20y
23
+ ··· − 32240y + 3481
c
4
, c
11
y
24
− y
23
+ ··· − 6y + 1
c
7
, c
8
(y
3
− y
2
+ 2y −1)
8
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.723079 + 0.704365I
a = 0.107758 − 1.135100I
b = 0.041447 − 1.243490I
1.64493 − 5.65624I 6.00000 + 5.95889I
u = 0.723079 − 0.704365I
a = 0.107758 + 1.135100I
b = 0.041447 + 1.243490I
1.64493 + 5.65624I 6.00000 − 5.95889I
u = −0.315281 + 0.984494I
a = 0.427343 − 1.028110I
b = −1.107680 − 0.653656I
1.64493 + 5.65624I 6.00000 − 5.95889I
u = −0.315281 − 0.984494I
a = 0.427343 + 1.028110I
b = −1.107680 + 0.653656I
1.64493 − 5.65624I 6.00000 + 5.95889I
u = −1.013310 + 0.252112I
a = −0.643211 − 0.895112I
b = −0.786818 − 0.569360I
−2.49265 + 2.82812I −0.52927 − 2.97945I
u = −1.013310 − 0.252112I
a = −0.643211 + 0.895112I
b = −0.786818 + 0.569360I
−2.49265 − 2.82812I −0.52927 + 2.97945I
u = −0.159442 + 0.926668I
a = 0.136132 + 0.791192I
b = 1.43944 + 0.70156I
5.78252 + 2.82812I 12.52927 − 2.97945I
u = −0.159442 − 0.926668I
a = 0.136132 − 0.791192I
b = 1.43944 − 0.70156I
5.78252 − 2.82812I 12.52927 + 2.97945I
u = −0.691733 + 0.527113I
a = −0.283373 − 1.292740I
b = 0.222973 − 1.116570I
−2.49265 + 2.82812I −0.52927 − 2.97945I
u = −0.691733 − 0.527113I
a = −0.283373 + 1.292740I
b = 0.222973 + 1.116570I
−2.49265 − 2.82812I −0.52927 + 2.97945I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.097732 + 1.282650I
a = −0.629193 − 0.636142I
b = 0.554361 + 0.213748I
1.64493 − 5.65624I 6.00000 + 5.95889I
u = −0.097732 − 1.282650I
a = −0.629193 + 0.636142I
b = 0.554361 − 0.213748I
1.64493 + 5.65624I 6.00000 − 5.95889I
u = 1.22255 + 1.06383I
a = 0.106727 − 0.702138I
b = 1.173390 − 0.504296I
−2.49265 − 2.82812I −0.52927 + 2.97945I
u = 1.22255 − 1.06383I
a = 0.106727 + 0.702138I
b = 1.173390 + 0.504296I
−2.49265 + 2.82812I −0.52927 − 2.97945I
u = 0.122779 + 0.275025I
a = −1.02171 + 2.28864I
b = −1.87511 + 0.22835I
5.78252 + 2.82812I 12.52927 − 2.97945I
u = 0.122779 − 0.275025I
a = −1.02171 − 2.28864I
b = −1.87511 − 0.22835I
5.78252 − 2.82812I 12.52927 + 2.97945I
u = 0.290085 + 0.035799I
a = 2.66725 − 2.89690I
b = −0.732109 − 0.436774I
−2.49265 − 2.82812I −0.52927 + 2.97945I
u = 0.290085 − 0.035799I
a = 2.66725 + 2.89690I
b = −0.732109 + 0.436774I
−2.49265 + 2.82812I −0.52927 − 2.97945I
u = −1.11766 + 1.32293I
a = 0.001573 − 0.664583I
b = −1.243000 − 0.376081I
1.64493 + 5.65624I 6.00000 − 5.95889I
u = −1.11766 − 1.32293I
a = 0.001573 + 0.664583I
b = −1.243000 + 0.376081I
1.64493 − 5.65624I 6.00000 + 5.95889I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.78242 + 0.43596I
a = 0.399606 + 0.097740I
b = 1.46829 − 0.05407I
5.78252 + 2.82812I 12.52927 − 2.97945I
u = −1.78242 − 0.43596I
a = 0.399606 − 0.097740I
b = 1.46829 + 0.05407I
5.78252 − 2.82812I 12.52927 + 2.97945I
u = 1.31909 + 1.40108I
a = −0.268903 + 0.285617I
b = −1.155190 − 0.130975I
5.78252 + 2.82812I 12.52927 − 2.97945I
u = 1.31909 − 1.40108I
a = −0.268903 − 0.285617I
b = −1.155190 + 0.130975I
5.78252 − 2.82812I 12.52927 + 2.97945I
24
V. I
u
5
= hb − 1, 59u
5
+ 76u
4
+ · · · + 67a + 146, u
6
+ u
5
+ 4u
4
+ 2u
3
+ 8u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
−0.880597u
5
− 1.13433u
4
+ ··· − 7.26866u − 2.17910
1
a
9
=
−0.149254u
5
− 0.582090u
4
+ ··· − 2.16418u − 3.77612
−0.253731u
5
− 0.0895522u
4
+ ··· − 1.17910u + 0.880597
a
6
=
−0.597015u
5
− 0.328358u
4
+ ··· − 3.65672u + 2.89552
0.179104u
5
+ 0.298507u
4
+ ··· + 1.59701u − 0.268657
a
1
=
−0.716418u
5
− 1.19403u
4
+ ··· − 6.38806u − 2.92537
−0.149254u
5
+ 0.417910u
4
+ ··· − 0.164179u + 1.22388
a
10
=
−0.880597u
5
− 1.13433u
4
+ ··· − 7.26866u − 3.17910
1
a
3
=
−0.880597u
5
− 1.13433u
4
+ ··· − 7.26866u − 2.17910
1
a
2
=
−u
5
− u
4
− 4u
3
− 2u
2
− 8u
−0.0746269u
5
+ 0.208955u
4
+ ··· + 1.41791u + 0.611940
a
7
=
−0.149254u
5
− 0.582090u
4
+ ··· − 2.16418u − 3.77612
−0.253731u
5
− 0.0895522u
4
+ ··· − 1.17910u + 0.880597
a
7
=
−0.149254u
5
− 0.582090u
4
+ ··· − 2.16418u − 3.77612
−0.253731u
5
− 0.0895522u
4
+ ··· − 1.17910u + 0.880597
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
11
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
2
, c
5
, c
9
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
3
, c
10
(u − 1)
6
c
4
u
6
+ u
5
+ 4u
4
+ 2u
3
+ 8u
2
+ 1
c
7
, c
8
(u
3
− u
2
+ 1)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
2
, c
5
, c
9
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
3
, c
10
(y −1)
6
c
4
y
6
+ 7y
5
+ 28y
4
+ 62y
3
+ 72y
2
+ 16y + 1
c
7
, c
8
(y
3
− y
2
+ 2y −1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.42975 + 1.50598I
a = −0.303615 − 0.669275I
b = 1.00000
1.64493 6.00000
u = 0.42975 − 1.50598I
a = −0.303615 + 0.669275I
b = 1.00000
1.64493 6.00000
u = 0.017526 + 0.363437I
a = −1.92858 − 2.50729I
b = 1.00000
1.64493 6.00000
u = 0.017526 − 0.363437I
a = −1.92858 + 2.50729I
b = 1.00000
1.64493 6.00000
u = −0.94728 + 1.47725I
a = 0.232199 + 0.362106I
b = 1.00000
1.64493 6.00000
u = −0.94728 − 1.47725I
a = 0.232199 − 0.362106I
b = 1.00000
1.64493 6.00000
28
VI. I
u
6
= h−u
2
+ b, −u
2
+ a − 1, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
u
2
+ 1
u
2
a
9
=
u
5
+ 2u
3
+ u
u
5
+ u
3
+ u
a
6
=
−u
5
− 2u
3
− u + 1
−u
5
− u
3
+ u
2
− u
a
1
=
u
4
+ u
2
+ 1
u
5
− 2u
4
+ 2u
3
− u
2
+ 2u − 1
a
10
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
2
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
u
5
− 2u
4
+ 2u
3
− 3u
2
+ 3u − 1
a
7
=
u
5
+ 2u
3
+ u
2u − 1
a
7
=
u
5
+ 2u
3
+ u
2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
2
, c
3
, c
10
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
5
, c
9
(u − 1)
6
c
7
, c
8
(u
3
− u
2
+ 1)
2
c
11
u
6
+ u
5
+ 4u
4
+ 2u
3
+ 8u
2
+ 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
2
, c
3
, c
10
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
5
, c
9
(y −1)
6
c
7
, c
8
(y
3
− y
2
+ 2y −1)
2
c
11
y
6
+ 7y
5
+ 28y
4
+ 62y
3
+ 72y
2
+ 16y + 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = 0.246226 − 0.998963I
b = −0.753774 − 0.998963I
1.64493 6.00000
u = −0.498832 − 1.001300I
a = 0.246226 + 0.998963I
b = −0.753774 + 0.998963I
1.64493 6.00000
u = 0.284920 + 1.115140I
a = −0.162359 + 0.635452I
b = −1.162360 + 0.635452I
1.64493 6.00000
u = 0.284920 − 1.115140I
a = −0.162359 − 0.635452I
b = −1.162360 − 0.635452I
1.64493 6.00000
u = 0.713912 + 0.305839I
a = 1.41613 + 0.43668I
b = 0.416133 + 0.436684I
1.64493 6.00000
u = 0.713912 − 0.305839I
a = 1.41613 − 0.43668I
b = 0.416133 − 0.436684I
1.64493 6.00000
32
VII. I
u
7
= hb − 1, a − 2, u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
−1
a
5
=
1
1
a
11
=
2
1
a
9
=
−4
−3
a
6
=
5
4
a
1
=
3
2
a
10
=
1
1
a
3
=
2
1
a
2
=
−1
−1
a
7
=
−4
−3
a
7
=
−4
−3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
11
u + 1
c
2
, c
3
, c
5
c
9
, c
10
u − 1
c
7
, c
8
u + 2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y −1
c
7
, c
8
y −4
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 2.00000
b = 1.00000
1.64493 6.00000
36
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
4
+ u
2
+ u + 1)
6
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
6
· (u
15
+ 4u
13
+ 8u
11
− u
10
+ 8u
9
− 3u
8
+ 4u
7
− 5u
6
− 5u
4
− 3u
2
− 1)
· (u
27
+ 6u
26
+ ··· − 40u − 8)
c
2
(u − 1)(u
4
+ 2u
3
+ 3u
2
+ u + 1)
6
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
6
· (u
15
+ 8u
14
+ ··· − 6u − 1)(u
27
+ 14u
26
+ ··· + 32u − 64)
c
3
, c
9
((u − 1)
7
)(u
6
+ 3u
5
+ ··· + 2u
3
+ 1)(u
15
+ u
14
+ ··· − u − 1)
· (u
24
− 9u
22
+ ··· + 56u + 8)(u
24
+ 4u
23
+ ··· + 106u + 59)
· (u
27
− 9u
25
+ ··· − u − 1)
c
4
, c
11
(u + 1)(u
6
− u
5
+ ··· − 2u + 1)(u
6
+ u
5
+ ··· + 8u
2
+ 1)
· (u
15
+ u
13
+ u
12
− 2u
11
− 2u
9
− 4u
8
+ 2u
7
+ u
5
+ 4u
4
− 1)
· (u
24
+ 3u
22
+ ··· − 4u + 8)(u
24
+ 3u
23
+ ··· − 6u + 1)
· (u
27
− u
26
+ ··· + 2u − 1)
c
5
, c
10
((u − 1)
7
)(u
6
+ 3u
5
+ ··· + 2u
3
+ 1)(u
15
− u
14
+ ··· − u + 1)
· (u
24
− 9u
22
+ ··· + 56u + 8)(u
24
+ 4u
23
+ ··· + 106u + 59)
· (u
27
− 9u
25
+ ··· − u − 1)
c
6
(u + 1)(u
4
+ u
2
+ u + 1)
6
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
6
· (u
15
+ 4u
13
+ 8u
11
+ u
10
+ 8u
9
+ 3u
8
+ 4u
7
+ 5u
6
+ 5u
4
+ 3u
2
+ 1)
· (u
27
+ 6u
26
+ ··· − 40u − 8)
c
7
(u + 2)(u
3
− u
2
+ 1)
12
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
6
· (u
15
− 4u
13
+ ··· + 2u + 1)(u
27
− 9u
26
+ ··· + 2296u − 232)
c
8
(u + 2)(u
3
− u
2
+ 1)
20
(u
15
+ 7u
14
+ ··· − 4u
2
+ 1)
· (u
27
+ 22u
26
+ ··· − 7680u − 512)
37
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y −1)(y
4
+ 2y
3
+ 3y
2
+ y + 1)
6
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
6
· (y
15
+ 8y
14
+ ··· − 6y −1)(y
27
+ 14y
26
+ ··· + 32y −64)
c
2
(y −1)(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
6
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
6
· (y
15
+ 16y
13
+ ··· − 2y −1)(y
27
+ 2y
26
+ ··· + 39424y −4096)
c
3
, c
5
, c
9
c
10
((y −1)
7
)(y
6
− y
5
+ ··· + 8y
2
+ 1)(y
15
− 15y
14
+ ··· + 13y −1)
· (y
24
− 20y
23
+ ··· − 32240y + 3481)(y
24
− 18y
23
+ ··· − 864y + 64)
· (y
27
− 18y
26
+ ··· − 7y −1)
c
4
, c
11
(y −1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
6
+ 7y
5
+ ··· + 16y + 1)(y
15
+ 2y
14
+ ··· + 8y
2
− 1)
· (y
24
− y
23
+ ··· − 6y + 1)(y
24
+ 6y
23
+ ··· + 944y + 64)
· (y
27
− 5y
26
+ ··· + 16y −1)
c
7
(y −4)(y
3
− y
2
+ 2y −1)
12
(y
4
− y
3
+ 2y
2
+ 7y + 4)
6
· (y
15
− 8y
14
+ ··· − 10y −1)(y
27
− 7y
26
+ ··· + 586144y −53824)
c
8
(y −4)(y
3
− y
2
+ 2y −1)
20
(y
15
− 7y
14
+ ··· + 8y −1)
· (y
27
− 4y
26
+ ··· + 1966080y −262144)
38
