12n
0597
(K12n
0597
)
A knot diagram
1
Linearized knot diagam
3 7 12 8 9 2 4 11 3 7 5 10
Solving Sequence
4,8 5,12
3 7 2 1 6 11 9 10
c
4
c
3
c
7
c
2
c
1
c
6
c
11
c
8
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h6.48488 × 10
68
u
54
+ 2.22735 × 10
69
u
53
+ ··· + 3.01163 × 10
67
b − 4.54938 × 10
69
,
7.79191 × 10
69
u
54
+ 2.67697 × 10
70
u
53
+ ··· + 6.02326 × 10
67
a − 5.52191 × 10
70
, u
55
+ 4u
54
+ ··· − 32u − 4i
I
u
2
= h1742938u
19
+ 1162593u
18
+ ··· + 1826407b + 1460687,
147076u
19
+ 1158u
18
+ ··· + 166037a − 623712, u
20
+ u
19
+ ··· − 4u + 1i
I
u
3
= h−a
3
+ b + 2a + 1, a
4
− a
3
− 4a
2
+ 2a + 5, u − 1i
I
u
4
= hb − 1, a − 1, u − 1i
I
u
5
= hb − u + 1, u
2
+ a − 2u + 1, u
3
− u
2
+ 1i
* 5 irreducible components of dim
C
= 0, with total 83 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
=
h6.48×10
68
u
54
+2.23×10
69
u
53
+· · ·+3.01×10
67
b−4.55×10
69
, 7.79×10
69
u
54
+
2.68 × 10
70
u
53
+ · · · + 6.02 × 10
67
a − 5.52 × 10
70
, u
55
+ 4u
54
+ · · · − 32u − 4i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
12
=
−129.364u
54
− 444.439u
53
+ ··· + 5697.58u + 916.764
−21.5328u
54
− 73.9584u
53
+ ··· + 941.610u + 151.061
a
3
=
3.94666u
54
+ 13.1180u
53
+ ··· − 136.672u − 18.8314
−20.4560u
54
− 70.0814u
53
+ ··· + 894.192u + 143.944
a
7
=
u
u
a
2
=
−4.54849u
54
− 15.8254u
53
+ ··· + 226.873u + 38.8130
−28.9511u
54
− 99.0248u
53
+ ··· + 1257.74u + 201.588
a
1
=
−172.432u
54
− 590.262u
53
+ ··· + 7505.58u + 1199.19
40.4434u
54
+ 139.041u
53
+ ··· − 1788.25u − 286.747
a
6
=
−20.9960u
54
− 71.3826u
53
+ ··· + 880.148u + 137.913
66.7999u
54
+ 229.120u
53
+ ··· − 2923.17u − 468.173
a
11
=
−109.774u
54
− 377.006u
53
+ ··· + 4820.14u + 775.762
−15.4249u
54
− 52.9241u
53
+ ··· + 670.322u + 107.355
a
9
=
190.838u
54
+ 654.783u
53
+ ··· − 8370.59u − 1338.55
−44.5724u
54
− 152.962u
53
+ ··· + 1958.63u + 314.711
a
10
=
−139.838u
54
− 480.350u
53
+ ··· + 6148.79u + 989.017
−45.4892u
54
− 156.268u
53
+ ··· + 1998.97u + 320.610
(ii) Obstruction class = −1
(iii) Cusp Shapes = −41.4839u
54
− 141.696u
53
+ ··· + 1753.72u + 276.705
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
+ 84u
54
+ ··· − 72u + 1
c
2
, c
6
u
55
− 2u
54
+ ··· + 22u − 1
c
3
u
55
− 8u
54
+ ··· − 120u + 25
c
4
, c
7
u
55
− 4u
54
+ ··· − 32u + 4
c
5
u
55
− 3u
54
+ ··· + 75901u − 173113
c
8
u
55
+ 10u
54
+ ··· − 1715u − 229
c
9
u
55
− u
54
+ ··· − 216467u + 35417
c
10
u
55
− 4u
54
+ ··· − 936251u − 118509
c
11
u
55
+ 2u
54
+ ··· + 4u − 24
c
12
u
55
− u
54
+ ··· + 3199358u − 321516
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
− 212y
54
+ ··· + 10440y −1
c
2
, c
6
y
55
− 84y
54
+ ··· − 72y −1
c
3
y
55
+ 20y
54
+ ··· − 800y −625
c
4
, c
7
y
55
− 36y
54
+ ··· − 200y −16
c
5
y
55
+ 35y
54
+ ··· + 119306470953y −29968110769
c
8
y
55
+ 20y
54
+ ··· − 2180589y −52441
c
9
y
55
+ 91y
54
+ ··· + 50901662647y −1254363889
c
10
y
55
+ 58y
54
+ ··· − 129372587591y −14044383081
c
11
y
55
− 6y
54
+ ··· − 12656y −576
c
12
y
55
+ 85y
54
+ ··· + 3623181372652y −103372538256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.228394 + 0.930097I
a = −0.355410 + 0.174211I
b = −0.216207 − 0.780987I
2.63763 − 2.19314I 0.766014 + 1.147808I
u = −0.228394 − 0.930097I
a = −0.355410 − 0.174211I
b = −0.216207 + 0.780987I
2.63763 + 2.19314I 0.766014 − 1.147808I
u = −0.061115 + 1.061790I
a = 0.121223 − 0.494313I
b = 0.396675 + 1.163810I
1.55867 − 3.48219I 0. + 3.47906I
u = −0.061115 − 1.061790I
a = 0.121223 + 0.494313I
b = 0.396675 − 1.163810I
1.55867 + 3.48219I 0. − 3.47906I
u = 1.013150 + 0.429080I
a = −2.09376 − 0.07084I
b = −1.30226 − 1.21278I
−8.91481 − 6.34317I 0
u = 1.013150 − 0.429080I
a = −2.09376 + 0.07084I
b = −1.30226 + 1.21278I
−8.91481 + 6.34317I 0
u = −1.079130 + 0.236177I
a = 1.53166 − 0.57910I
b = 0.77564 − 1.31217I
−1.46530 + 4.21934I 0
u = −1.079130 − 0.236177I
a = 1.53166 + 0.57910I
b = 0.77564 + 1.31217I
−1.46530 − 4.21934I 0
u = −1.113000 + 0.147678I
a = −1.55961 − 0.95086I
b = −0.546370 + 1.079590I
−12.12370 + 4.63839I 0
u = −1.113000 − 0.147678I
a = −1.55961 + 0.95086I
b = −0.546370 − 1.079590I
−12.12370 − 4.63839I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.398648 + 0.764365I
a = 0.490007 + 1.105910I
b = −0.751133 − 0.461027I
−10.69800 + 3.28061I −4.43813 − 2.05243I
u = −0.398648 − 0.764365I
a = 0.490007 − 1.105910I
b = −0.751133 + 0.461027I
−10.69800 − 3.28061I −4.43813 + 2.05243I
u = −0.818436 + 0.220706I
a = −0.462335 − 0.757558I
b = −0.258171 − 1.314110I
1.02370 + 2.96901I 6.22160 − 5.57360I
u = −0.818436 − 0.220706I
a = −0.462335 + 0.757558I
b = −0.258171 + 1.314110I
1.02370 − 2.96901I 6.22160 + 5.57360I
u = 0.823693
a = 2.96416
b = 1.33894
−0.453310 −12.4430
u = 0.629407 + 1.015120I
a = −0.124519 + 0.360519I
b = 0.354817 − 0.497624I
−0.865641 − 0.009239I 0
u = 0.629407 − 1.015120I
a = −0.124519 − 0.360519I
b = 0.354817 + 0.497624I
−0.865641 + 0.009239I 0
u = 0.056692 + 1.212890I
a = −0.103950 − 0.233463I
b = −0.682228 + 1.128040I
−8.74789 + 8.87696I 0
u = 0.056692 − 1.212890I
a = −0.103950 + 0.233463I
b = −0.682228 − 1.128040I
−8.74789 − 8.87696I 0
u = 0.354907 + 0.697158I
a = −0.098793 − 0.883310I
b = 0.155774 + 1.110550I
2.01009 − 2.16153I 2.20037 + 5.52786I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.354907 − 0.697158I
a = −0.098793 + 0.883310I
b = 0.155774 − 1.110550I
2.01009 + 2.16153I 2.20037 − 5.52786I
u = 0.388472 + 0.676966I
a = 0.392074 + 0.586948I
b = −0.77671 + 1.19630I
−7.10371 + 2.13418I −1.61598 − 0.45444I
u = 0.388472 − 0.676966I
a = 0.392074 − 0.586948I
b = −0.77671 − 1.19630I
−7.10371 − 2.13418I −1.61598 + 0.45444I
u = 1.169370 + 0.406827I
a = 0.160942 − 0.680261I
b = 0.558665 − 1.106950I
−2.81126 − 1.20544I 0
u = 1.169370 − 0.406827I
a = 0.160942 + 0.680261I
b = 0.558665 + 1.106950I
−2.81126 + 1.20544I 0
u = −1.256970 + 0.280156I
a = 1.366380 + 0.304132I
b = 1.164040 + 0.121414I
−6.24743 + 2.95707I 0
u = −1.256970 − 0.280156I
a = 1.366380 − 0.304132I
b = 1.164040 − 0.121414I
−6.24743 − 2.95707I 0
u = 1.247720 + 0.445260I
a = −1.217490 − 0.284802I
b = −0.241125 − 0.911262I
−1.00747 − 2.30946I 0
u = 1.247720 − 0.445260I
a = −1.217490 + 0.284802I
b = −0.241125 + 0.911262I
−1.00747 + 2.30946I 0
u = 1.283620 + 0.343428I
a = −1.33294 + 0.59936I
b = −1.55960 + 0.59836I
−15.4853 − 6.9210I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.283620 − 0.343428I
a = −1.33294 − 0.59936I
b = −1.55960 − 0.59836I
−15.4853 + 6.9210I 0
u = 1.318640 + 0.262440I
a = 1.39643 + 0.81108I
b = 0.598048 + 0.736018I
−3.05878 − 4.93696I 0
u = 1.318640 − 0.262440I
a = 1.39643 − 0.81108I
b = 0.598048 − 0.736018I
−3.05878 + 4.93696I 0
u = −1.254450 + 0.537906I
a = −1.361600 + 0.016121I
b = −0.644516 + 0.771416I
−0.61529 + 7.55097I 0
u = −1.254450 − 0.537906I
a = −1.361600 − 0.016121I
b = −0.644516 − 0.771416I
−0.61529 − 7.55097I 0
u = 0.543362 + 0.279828I
a = −0.184351 + 0.678862I
b = 0.386325 + 0.158096I
−1.238630 − 0.333157I −8.21440 + 1.77959I
u = 0.543362 − 0.279828I
a = −0.184351 − 0.678862I
b = 0.386325 − 0.158096I
−1.238630 + 0.333157I −8.21440 − 1.77959I
u = −0.532879 + 0.265595I
a = −1.87909 − 0.15769I
b = −0.496585 + 0.280323I
1.53458 − 0.08260I 8.02360 − 0.70539I
u = −0.532879 − 0.265595I
a = −1.87909 + 0.15769I
b = −0.496585 − 0.280323I
1.53458 + 0.08260I 8.02360 + 0.70539I
u = −1.211180 + 0.728080I
a = −0.875893 − 0.683728I
b = −0.631732 + 1.072700I
−12.79060 + 2.58251I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.211180 − 0.728080I
a = −0.875893 + 0.683728I
b = −0.631732 − 1.072700I
−12.79060 − 2.58251I 0
u = 1.25664 + 0.67520I
a = 1.073550 − 0.367845I
b = 0.700106 + 0.896451I
−3.21944 − 6.43186I 0
u = 1.25664 − 0.67520I
a = 1.073550 + 0.367845I
b = 0.700106 − 0.896451I
−3.21944 + 6.43186I 0
u = −0.568585 + 0.002353I
a = 2.93796 + 2.07601I
b = −0.463493 + 0.346007I
−10.21720 + 3.48231I −4.98199 + 0.62812I
u = −0.568585 − 0.002353I
a = 2.93796 − 2.07601I
b = −0.463493 − 0.346007I
−10.21720 − 3.48231I −4.98199 − 0.62812I
u = −1.34385 + 0.51761I
a = 1.43449 − 0.18164I
b = 0.60052 − 1.30971I
−2.54819 + 9.08466I 0
u = −1.34385 − 0.51761I
a = 1.43449 + 0.18164I
b = 0.60052 + 1.30971I
−2.54819 − 9.08466I 0
u = 1.37774 + 0.58999I
a = −1.49234 − 0.04356I
b = −0.87943 − 1.33400I
−12.9172 − 15.1751I 0
u = 1.37774 − 0.58999I
a = −1.49234 + 0.04356I
b = −0.87943 + 1.33400I
−12.9172 + 15.1751I 0
u = −1.50431 + 0.07352I
a = −0.364764 − 1.062760I
b = −0.507231 − 0.684175I
−13.50180 + 0.32367I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50431 − 0.07352I
a = −0.364764 + 1.062760I
b = −0.507231 + 0.684175I
−13.50180 − 0.32367I 0
u = −1.60007 + 0.48099I
a = −0.249894 − 0.427368I
b = −0.631921 − 0.689866I
−14.0455 − 2.4232I 0
u = −1.60007 − 0.48099I
a = −0.249894 + 0.427368I
b = −0.631921 + 0.689866I
−14.0455 + 2.4232I 0
u = −0.080542 + 0.193890I
a = 2.61995 − 1.69033I
b = 0.228619 − 1.091470I
1.26586 + 2.57084I −0.85088 − 2.32793I
u = −0.080542 − 0.193890I
a = 2.61995 + 1.69033I
b = 0.228619 + 1.091470I
1.26586 − 2.57084I −0.85088 + 2.32793I
10
II. I
u
2
= h1.74 × 10
6
u
19
+ 1.16 × 10
6
u
18
+ · · · + 1.83 × 10
6
b + 1.46 ×
10
6
, 147076u
19
+ 1158u
18
+ · · · + 166037a − 623712, u
20
+ u
19
+ · · · − 4u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
12
=
−0.885803u
19
− 0.00697435u
18
+ ··· − 0.332149u + 3.75646
−0.954299u
19
− 0.636547u
18
+ ··· + 2.12930u − 0.799760
a
3
=
−0.167149u
19
− 0.371082u
18
+ ··· − 4.30841u + 3.40433
−0.378146u
19
− 0.145836u
18
+ ··· − 2.54026u + 0.496680
a
7
=
u
u
a
2
=
−0.946799u
19
− 0.655425u
18
+ ··· − 2.35244u + 2.96809
−1.15780u
19
− 0.430180u
18
+ ··· − 0.584292u + 0.0604367
a
1
=
−2.36020u
19
− 0.734061u
18
+ ··· + 6.88680u − 0.210030
−1.50970u
19
− 0.927327u
18
+ ··· + 5.68923u − 1.07153
a
6
=
−0.0662196u
19
− 0.397076u
18
+ ··· + 1.44845u + 1.51392
0.193160u
19
+ 0.171997u
18
+ ··· + 1.73103u − 0.520690
a
11
=
−1.22425u
19
− 0.993563u
18
+ ··· − 2.60396u + 3.83553
−1.23184u
19
− 1.39082u
18
+ ··· − 0.124812u − 0.151619
a
9
=
−0.119859u
19
+ 0.185423u
18
+ ··· − 1.51911u + 2.97387
0.588138u
19
+ 0.846974u
18
+ ··· − 1.40998u − 0.239062
a
10
=
−0.807363u
19
− 0.0873266u
18
+ ··· − 1.05289u + 3.44587
−0.814955u
19
− 0.484584u
18
+ ··· + 1.42626u − 0.541284
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3759113
1826407
u
19
+
9918792
1826407
u
18
+ ··· +
33892975
1826407
u −
13352398
1826407
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
20
− 22u
19
+ ··· − 3u + 1
c
2
u
20
+ 2u
19
+ ··· − u + 1
c
3
u
20
+ 5u
19
+ ··· + 5u + 1
c
4
u
20
+ u
19
+ ··· − 4u + 1
c
5
u
20
− u
19
+ ··· + 5u + 1
c
6
u
20
− 2u
19
+ ··· + u + 1
c
7
u
20
− u
19
+ ··· + 4u + 1
c
8
u
20
+ 6u
19
+ ··· + u + 1
c
9
u
20
− u
19
+ ··· + 9u + 1
c
10
u
20
+ 6u
19
+ ··· + 62u + 25
c
11
u
20
+ u
19
+ ··· − 24u + 23
c
12
u
20
− u
19
+ ··· + 3u + 1
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 38y
19
+ ··· + 97y + 1
c
2
, c
6
y
20
− 22y
19
+ ··· − 3y + 1
c
3
y
20
+ 13y
19
+ ··· + 3y + 1
c
4
, c
7
y
20
− 15y
19
+ ··· − 14y + 1
c
5
y
20
+ 3y
19
+ ··· − 17y + 1
c
8
y
20
+ 8y
19
+ ··· + y + 1
c
9
y
20
+ 15y
19
+ ··· − 15y + 1
c
10
y
20
+ 20y
19
+ ··· − 794y + 625
c
11
y
20
+ y
19
+ ··· − 1220y + 529
c
12
y
20
+ 13y
19
+ ··· − 5y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.533776 + 0.839429I
a = 0.082187 + 0.976957I
b = −0.161143 − 1.107230I
1.33087 − 1.27262I −3.32667 − 0.25948I
u = 0.533776 − 0.839429I
a = 0.082187 − 0.976957I
b = −0.161143 + 1.107230I
1.33087 + 1.27262I −3.32667 + 0.25948I
u = −1.000530 + 0.259540I
a = −1.06090 − 1.21552I
b = −1.23287 − 1.38392I
−1.40774 + 1.89082I −2.02415 − 6.71944I
u = −1.000530 − 0.259540I
a = −1.06090 + 1.21552I
b = −1.23287 + 1.38392I
−1.40774 − 1.89082I −2.02415 + 6.71944I
u = −0.191181 + 0.929591I
a = −0.108015 + 0.312018I
b = −0.397250 − 1.097980I
2.87685 − 3.71581I 2.69381 + 5.50994I
u = −0.191181 − 0.929591I
a = −0.108015 − 0.312018I
b = −0.397250 + 1.097980I
2.87685 + 3.71581I 2.69381 − 5.50994I
u = 0.873633 + 0.175179I
a = −0.0423713 − 0.1227380I
b = −0.053990 − 1.361470I
0.38476 − 3.13050I −6.71544 + 6.46581I
u = 0.873633 − 0.175179I
a = −0.0423713 + 0.1227380I
b = −0.053990 + 1.361470I
0.38476 + 3.13050I −6.71544 − 6.46581I
u = −0.795716 + 0.349204I
a = 1.94782 + 1.71456I
b = 0.680999 − 0.825877I
−10.29940 + 4.53068I −4.78345 − 5.80170I
u = −0.795716 − 0.349204I
a = 1.94782 − 1.71456I
b = 0.680999 + 0.825877I
−10.29940 − 4.53068I −4.78345 + 5.80170I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.250290 + 0.249862I
a = −1.43958 − 0.31269I
b = −0.718556 − 0.811927I
−2.91355 − 2.89211I −7.67752 + 2.98084I
u = 1.250290 − 0.249862I
a = −1.43958 + 0.31269I
b = −0.718556 + 0.811927I
−2.91355 + 2.89211I −7.67752 − 2.98084I
u = −1.284370 + 0.538335I
a = −1.45575 + 0.12107I
b = −0.703474 + 1.149430I
−0.60784 + 9.10431I −1.89591 − 7.92757I
u = −1.284370 − 0.538335I
a = −1.45575 − 0.12107I
b = −0.703474 − 1.149430I
−0.60784 − 9.10431I −1.89591 + 7.92757I
u = 1.306690 + 0.489189I
a = 1.147690 + 0.402592I
b = 0.078049 + 0.861799I
−1.49698 − 3.77692I −3.66921 + 4.30140I
u = 1.306690 − 0.489189I
a = 1.147690 − 0.402592I
b = 0.078049 − 0.861799I
−1.49698 + 3.77692I −3.66921 − 4.30140I
u = −1.49584 + 0.23640I
a = −0.348081 + 0.618798I
b = 0.327314 + 0.504059I
−13.12220 − 1.74178I −3.87046 + 2.15304I
u = −1.49584 − 0.23640I
a = −0.348081 − 0.618798I
b = 0.327314 − 0.504059I
−13.12220 + 1.74178I −3.87046 − 2.15304I
u = 0.303243 + 0.180235I
a = 2.77701 − 1.28061I
b = −0.319083 + 0.192447I
0.581123 + 0.014308I −1.73100 + 0.68149I
u = 0.303243 − 0.180235I
a = 2.77701 + 1.28061I
b = −0.319083 − 0.192447I
0.581123 − 0.014308I −1.73100 − 0.68149I
17
III. I
u
3
= h−a
3
+ b + 2a + 1, a
4
− a
3
− 4a
2
+ 2a + 5, u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
1
a
5
=
1
1
a
12
=
a
a
3
− 2a − 1
a
3
=
−a
3
− 2a
2
+ 3a + 6
−a
3
− a
2
+ 3a + 4
a
7
=
1
1
a
2
=
−a
3
− a
2
+ 3a + 4
−a
3
+ 3a + 2
a
1
=
−a
−a
3
+ 2a + 1
a
6
=
a
3
− 3a − 1
−a
a
11
=
a
3
− 2a − 1
2a
3
− 5a − 2
a
9
=
a
3
+ a
2
− 3a − 4
a
3
− 3a − 2
a
10
=
a
a
3
− 2a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
9
u
4
+ u
3
+ 2u
2
+ 1
c
2
, c
5
, c
6
u
4
− u
3
+ 1
c
4
, c
7
(u + 1)
4
c
8
u
4
− u
3
+ 2u
2
+ 1
c
10
, c
11
u
4
− u
2
+ 2u + 3
c
12
u
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
8
c
9
y
4
+ 3y
3
+ 6y
2
+ 4y + 1
c
2
, c
5
, c
6
y
4
− y
3
+ 2y
2
+ 1
c
4
, c
7
(y −1)
4
c
10
, c
11
y
4
− 2y
3
+ 7y
2
− 10y + 9
c
12
y
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.246050 + 0.267489I
b = −0.175098 + 0.691825I
−1.64493 −6.00000
u = 1.00000
a = −1.246050 − 0.267489I
b = −0.175098 − 0.691825I
−1.64493 −6.00000
u = 1.00000
a = 1.74605 + 0.17255I
b = 0.675098 + 1.227920I
−1.64493 −6.00000
u = 1.00000
a = 1.74605 − 0.17255I
b = 0.675098 − 1.227920I
−1.64493 −6.00000
21
IV. I
u
4
= hb − 1, a − 1, u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
1
a
5
=
1
1
a
12
=
1
1
a
3
=
0
−1
a
7
=
1
1
a
2
=
−1
−2
a
1
=
−1
−1
a
6
=
0
−1
a
11
=
1
1
a
9
=
1
2
a
10
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
u + 1
c
8
u − 1
c
10
, c
11
, c
12
u
23
(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
7
, c
8
, c
9
y −1
c
10
, c
11
, c
12
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 1.00000
−1.64493 −6.00000
25
V. I
u
5
= hb − u + 1, u
2
+ a − 2u + 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
12
=
−u
2
+ 2u − 1
u − 1
a
3
=
−2u
2
+ 3u − 1
−u
2
+ 2u − 1
a
7
=
u
u
a
2
=
−2u
2
+ 2u − 1
−u
2
+ u − 1
a
1
=
−u
−u
a
6
=
−2u
2
+ 3u − 1
−u
2
+ 2u − 1
a
11
=
−u
2
+ 2u − 1
u − 1
a
9
=
−2u
2
+ 4u − 3
−u
2
+ 3u − 2
a
10
=
−u
2
+ 3u − 1
2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
2
− 4u + 4
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
c
12
(u − 1)
3
c
3
u
3
+ 2u
2
+ u + 1
c
4
, c
5
u
3
− u
2
+ 1
c
6
(u + 1)
3
c
7
, c
9
u
3
+ u
2
− 1
c
8
u
3
+ 3u
2
+ 2u + 1
c
11
u
3
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
10
, c
12
(y −1)
3
c
3
y
3
− 2y
2
− 3y −1
c
4
, c
5
, c
7
c
9
y
3
− y
2
+ 2y −1
c
8
y
3
− 5y
2
− 2y −1
c
11
y
3
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.539798 + 0.182582I
b = −0.122561 + 0.744862I
0 0.70532 − 1.67231I
u = 0.877439 − 0.744862I
a = 0.539798 − 0.182582I
b = −0.122561 − 0.744862I
0 0.70532 + 1.67231I
u = −0.754878
a = −3.07960
b = −1.75488
0 7.58940
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u + 1)(u
4
+ u
3
+ 2u
2
+ 1)(u
20
− 22u
19
+ ··· − 3u + 1)
· (u
55
+ 84u
54
+ ··· − 72u + 1)
c
2
((u − 1)
3
)(u + 1)(u
4
− u
3
+ 1)(u
20
+ 2u
19
+ ··· − u + 1)
· (u
55
− 2u
54
+ ··· + 22u − 1)
c
3
(u + 1)(u
3
+ 2u
2
+ u + 1)(u
4
+ u
3
+ 2u
2
+ 1)(u
20
+ 5u
19
+ ··· + 5u + 1)
· (u
55
− 8u
54
+ ··· − 120u + 25)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)(u
20
+ u
19
+ ··· − 4u + 1)
· (u
55
− 4u
54
+ ··· − 32u + 4)
c
5
(u + 1)(u
3
− u
2
+ 1)(u
4
− u
3
+ 1)(u
20
− u
19
+ ··· + 5u + 1)
· (u
55
− 3u
54
+ ··· + 75901u − 173113)
c
6
((u + 1)
4
)(u
4
− u
3
+ 1)(u
20
− 2u
19
+ ··· + u + 1)
· (u
55
− 2u
54
+ ··· + 22u − 1)
c
7
((u + 1)
5
)(u
3
+ u
2
− 1)(u
20
− u
19
+ ··· + 4u + 1)
· (u
55
− 4u
54
+ ··· − 32u + 4)
c
8
(u − 1)(u
3
+ 3u
2
+ 2u + 1)(u
4
− u
3
+ 2u
2
+ 1)(u
20
+ 6u
19
+ ··· + u + 1)
· (u
55
+ 10u
54
+ ··· − 1715u − 229)
c
9
(u + 1)(u
3
+ u
2
− 1)(u
4
+ u
3
+ 2u
2
+ 1)(u
20
− u
19
+ ··· + 9u + 1)
· (u
55
− u
54
+ ··· − 216467u + 35417)
c
10
u(u − 1)
3
(u
4
− u
2
+ 2u + 3)(u
20
+ 6u
19
+ ··· + 62u + 25)
· (u
55
− 4u
54
+ ··· − 936251u − 118509)
c
11
u
4
(u
4
− u
2
+ 2u + 3)(u
20
+ u
19
+ ··· − 24u + 23)
· (u
55
+ 2u
54
+ ··· + 4u − 24)
c
12
u
5
(u − 1)
3
(u
20
− u
19
+ ··· + 3u + 1)
· (u
55
− u
54
+ ··· + 3199358u − 321516)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
4
)(y
4
+ 3y
3
+ ··· + 4y + 1)(y
20
− 38y
19
+ ··· + 97y + 1)
· (y
55
− 212y
54
+ ··· + 10440y −1)
c
2
, c
6
((y −1)
4
)(y
4
− y
3
+ 2y
2
+ 1)(y
20
− 22y
19
+ ··· − 3y + 1)
· (y
55
− 84y
54
+ ··· − 72y −1)
c
3
(y −1)(y
3
− 2y
2
− 3y −1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· (y
20
+ 13y
19
+ ··· + 3y + 1)(y
55
+ 20y
54
+ ··· − 800y −625)
c
4
, c
7
((y −1)
5
)(y
3
− y
2
+ 2y −1)(y
20
− 15y
19
+ ··· − 14y + 1)
· (y
55
− 36y
54
+ ··· − 200y −16)
c
5
(y −1)(y
3
− y
2
+ 2y −1)(y
4
− y
3
+ 2y
2
+ 1)(y
20
+ 3y
19
+ ··· − 17y + 1)
· (y
55
+ 35y
54
+ ··· + 119306470953y −29968110769)
c
8
(y −1)(y
3
− 5y
2
− 2y −1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· (y
20
+ 8y
19
+ ··· + y + 1)(y
55
+ 20y
54
+ ··· − 2180589y −52441)
c
9
(y −1)(y
3
− y
2
+ 2y −1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· (y
20
+ 15y
19
+ ··· − 15y + 1)
· (y
55
+ 91y
54
+ ··· + 50901662647y −1254363889)
c
10
y(y −1)
3
(y
4
− 2y
3
+ ··· − 10y + 9)(y
20
+ 20y
19
+ ··· − 794y + 625)
· (y
55
+ 58y
54
+ ··· − 129372587591y −14044383081)
c
11
y
4
(y
4
− 2y
3
+ ··· − 10y + 9)(y
20
+ y
19
+ ··· − 1220y + 529)
· (y
55
− 6y
54
+ ··· − 12656y −576)
c
12
y
5
(y −1)
3
(y
20
+ 13y
19
+ ··· − 5y + 1)
· (y
55
+ 85y
54
+ ··· + 3623181372652y −103372538256)
31
