12a
0466
(K12a
0466
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 9 2 12 10 5 1 4 8
Solving Sequence
8,12
1
4,7
5 11 3 2 6 10 9
c
12
c
7
c
4
c
11
c
3
c
1
c
6
c
10
c
8
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 3747u
13
− 7659u
12
+ ··· + 14581a + 18101,
u
14
− 5u
12
+ 10u
10
+ 2u
9
− 5u
8
− 6u
7
− 4u
6
+ 4u
5
+ 4u
4
+ 7u
3
− 1i
I
u
2
= h5.39240 × 10
368
u
101
− 7.26688 × 10
368
u
100
+ ··· + 4.52702 × 10
370
b − 8.26613 × 10
371
,
− 7.29228 × 10
372
u
101
+ 2.80450 × 10
373
u
100
+ ··· + 1.94571 × 10
374
a − 1.76617 × 10
376
,
u
102
− 3u
101
+ ··· + 6720u + 1228i
I
u
3
= hb − 1, 18a
2
− 3au + 24a − 2u + 7, u
2
+ 2i
I
u
4
= h54a
3
− 27a
2
+ 58b + 153a − 25, 27a
4
− 18a
3
+ 57a
2
− 18a + 19, u + 1i
I
u
5
= hb, a
2
− a + 1, u − 1i
I
v
1
= ha, b + 1, v
2
− v + 1i
* 6 irreducible components of dim
C
= 0, with total 128 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
= hb−u, 3747u
13
−7659u
12
+· · ·+14581a+18101, u
14
−5u
12
+· · ·+7u
3
−1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
−0.256978u
13
+ 0.525273u
12
+ ··· + 1.54427u − 1.24141
u
a
7
=
−u
u
a
5
=
0.0739318u
13
+ 0.434950u
12
+ ··· + 1.80125u − 1.76668
−0.330910u
13
+ 0.0903230u
12
+ ··· + 0.743022u + 0.525273
a
11
=
0.525273u
13
− 0.330910u
12
+ ··· − 1.24141u + 0.743022
u
2
a
3
=
0.0739318u
13
+ 0.434950u
12
+ ··· + 0.801248u − 1.76668
−u
3
+ u
a
2
=
0.355737u
13
− 0.504561u
12
+ ··· − 1.69659u + 1.25252
0.149304u
13
+ 0.216035u
12
+ ··· + 0.364858u − 0.645703
a
6
=
u
2
− 1
−0.434950u
13
+ 0.467115u
12
+ ··· + 1.76668u − 0.0739318
a
10
=
0.434950u
13
− 0.467115u
12
+ ··· − 1.76668u + 1.07393
0.0202318u
13
− 0.0423839u
12
+ ··· + 0.0903230u + 0.136205
a
9
=
1.15026u
13
− 0.219875u
12
+ ··· − 1.79357u − 0.720595
−0.269392u
13
+ 0.0181058u
12
+ ··· + 1.02105u + 0.155408
(ii) Obstruction class = −1
(iii) Cusp Shapes =
6748
2083
u
13
−
6908
14581
u
12
+ ··· +
3068
2083
u +
110818
14581
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
14
+ 6u
13
+ ··· − 8u + 1
c
2
, c
5
, c
6
c
9
u
14
+ 3u
12
+ 6u
10
+ 7u
8
− 2u
7
+ 6u
6
− 4u
5
+ 6u
4
− 5u
3
+ 4u
2
− 4u + 1
c
3
, c
7
, c
11
c
12
u
14
− 5u
12
+ 10u
10
+ 2u
9
− 5u
8
− 6u
7
− 4u
6
+ 4u
5
+ 4u
4
+ 7u
3
− 1
c
4
49(49u
14
− 567u
13
+ ··· − 6400u + 512)
c
10
49(49u
14
+ 567u
13
+ ··· − 256u − 32)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
14
+ 6y
13
+ ··· − 88y + 1
c
2
, c
5
, c
6
c
9
y
14
+ 6y
13
+ ··· − 8y + 1
c
3
, c
7
, c
11
c
12
y
14
− 10y
13
+ ··· − 8y
2
+ 1
c
4
2401(2401y
14
+ 13671y
13
+ ··· − 8978432y + 262144)
c
10
2401(2401y
14
− 27489y
13
+ ··· − 15872y + 1024)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.516196 + 0.668974I
a = 1.017360 + 0.288726I
b = −0.516196 + 0.668974I
−5.02201 − 5.08838I −1.61799 + 8.05922I
u = −0.516196 − 0.668974I
a = 1.017360 − 0.288726I
b = −0.516196 − 0.668974I
−5.02201 + 5.08838I −1.61799 − 8.05922I
u = 0.049265 + 0.817919I
a = 0.729990 + 0.633371I
b = 0.049265 + 0.817919I
−0.60028 + 8.39490I 2.98961 − 7.37830I
u = 0.049265 − 0.817919I
a = 0.729990 − 0.633371I
b = 0.049265 − 0.817919I
−0.60028 − 8.39490I 2.98961 + 7.37830I
u = 1.187260 + 0.433713I
a = −1.66682 + 0.63904I
b = 1.187260 + 0.433713I
−0.83636 + 3.84412I 2.45895 − 3.50905I
u = 1.187260 − 0.433713I
a = −1.66682 − 0.63904I
b = 1.187260 − 0.433713I
−0.83636 − 3.84412I 2.45895 + 3.50905I
u = −1.33396
a = 2.15674
b = −1.33396
6.74792 14.5770
u = −0.261143 + 0.528763I
a = −1.18448 + 0.94699I
b = −0.261143 + 0.528763I
1.62602 + 1.81371I 5.85449 − 2.18660I
u = −0.261143 − 0.528763I
a = −1.18448 − 0.94699I
b = −0.261143 − 0.528763I
1.62602 − 1.81371I 5.85449 + 2.18660I
u = 0.480208
a = −0.845526
b = 0.480208
0.732652 13.8190
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45636 + 0.53970I
a = −1.66668 + 0.71755I
b = 1.45636 + 0.53970I
8.7153 + 19.0009I 9.38864 − 10.26527I
u = 1.45636 − 0.53970I
a = −1.66668 − 0.71755I
b = 1.45636 − 0.53970I
8.7153 − 19.0009I 9.38864 + 10.26527I
u = −1.48868 + 0.46189I
a = 1.61503 + 0.60076I
b = −1.48868 + 0.46189I
12.11620 − 6.67391I 13.58514 + 1.84206I
u = −1.48868 − 0.46189I
a = 1.61503 − 0.60076I
b = −1.48868 − 0.46189I
12.11620 + 6.67391I 13.58514 − 1.84206I
6
II. I
u
2
= h5.39 × 10
368
u
101
− 7.27 × 10
368
u
100
+ · · · + 4.53 × 10
370
b − 8.27 ×
10
371
, −7.29 × 10
372
u
101
+ 2.80 × 10
373
u
100
+ · · · + 1.95 × 10
374
a − 1.77 ×
10
376
, u
102
− 3u
101
+ · · · + 6720u + 1228i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
0.0374787u
101
− 0.144138u
100
+ ··· + 313.271u + 90.7725
−0.0119116u
101
+ 0.0160523u
100
+ ··· + 117.702u + 18.2596
a
7
=
−u
u
a
5
=
0.0601079u
101
− 0.156706u
100
+ ··· − 0.634123u + 27.6729
−0.0345408u
101
+ 0.0286206u
100
+ ··· + 431.607u + 81.3592
a
11
=
−0.0596673u
101
+ 0.232521u
100
+ ··· − 592.389u − 163.559
−0.0317617u
101
+ 0.0733669u
100
+ ··· + 12.4678u − 8.62955
a
3
=
−0.00617077u
101
+ 0.0554503u
100
+ ··· − 356.870u − 88.3022
−0.0245955u
101
+ 0.0557894u
100
+ ··· + 26.7586u − 5.47531
a
2
=
−0.00465371u
101
− 0.0244415u
100
+ ··· + 335.002u + 75.6856
0.0104418u
101
− 0.0279042u
100
+ ··· + 9.19679u + 7.32337
a
6
=
−0.00445873u
101
+ 0.0379717u
100
+ ··· − 220.187u − 56.7212
−0.0369380u
101
+ 0.0898244u
100
+ ··· + 46.8346u − 7.57770
a
10
=
−0.0393466u
101
+ 0.143102u
100
+ ··· − 318.483u − 89.2086
−0.0178019u
101
+ 0.0644717u
100
+ ··· − 153.806u − 43.5741
a
9
=
−0.0544767u
101
+ 0.177113u
100
+ ··· − 336.426u − 101.063
−0.0360286u
101
+ 0.136503u
100
+ ··· − 317.173u − 93.1241
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0665059u
101
− 0.191404u
100
+ ··· − 267.385u + 0.0474288
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
102
+ 42u
101
+ ··· + 107216u + 5776
c
2
, c
5
, c
6
c
9
u
102
− 2u
101
+ ··· + 172u + 76
c
3
, c
7
, c
11
c
12
u
102
− 3u
101
+ ··· + 6720u + 1228
c
4
49(7u
51
+ 68u
50
+ ··· − 1074u + 167)
2
c
10
49(7u
51
− 65u
50
+ ··· + 4991u − 373)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
102
+ 42y
101
+ ··· + 456890624y + 33362176
c
2
, c
5
, c
6
c
9
y
102
+ 42y
101
+ ··· + 107216y + 5776
c
3
, c
7
, c
11
c
12
y
102
− 71y
101
+ ··· − 636032y + 1507984
c
4
2401(49y
51
+ 738y
50
+ ··· − 123072y −27889)
2
c
10
2401(49y
51
− 2279y
50
+ ··· + 1.33762 × 10
7
y −139129)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.938800 + 0.219906I
a = −0.104097 − 0.814218I
b = 0.306890 + 1.203660I
−3.98676 + 1.42787I 0
u = −0.938800 − 0.219906I
a = −0.104097 + 0.814218I
b = 0.306890 − 1.203660I
−3.98676 − 1.42787I 0
u = −0.132342 + 0.952090I
a = 0.675049 + 0.192146I
b = −0.480609 + 0.312195I
−4.31975 + 1.46497I 0
u = −0.132342 − 0.952090I
a = 0.675049 − 0.192146I
b = −0.480609 − 0.312195I
−4.31975 − 1.46497I 0
u = 0.899835 + 0.223758I
a = 1.89347 − 0.47084I
b = 0.899835 − 0.223758I
3.64125 0
u = 0.899835 − 0.223758I
a = 1.89347 + 0.47084I
b = 0.899835 + 0.223758I
3.64125 0
u = −1.039410 + 0.270775I
a = −1.42959 + 1.12062I
b = −0.496445 + 0.034634I
2.87536 − 0.22281I 0
u = −1.039410 − 0.270775I
a = −1.42959 − 1.12062I
b = −0.496445 − 0.034634I
2.87536 + 0.22281I 0
u = 1.125680 + 0.169366I
a = 2.86751 − 0.62703I
b = −1.283310 + 0.005598I
3.75261 + 3.46176I 0
u = 1.125680 − 0.169366I
a = 2.86751 + 0.62703I
b = −1.283310 − 0.005598I
3.75261 − 3.46176I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.123400 + 0.263250I
a = −1.290530 − 0.397846I
b = −0.440373 + 0.187785I
2.83235 − 4.49472I 0
u = 1.123400 − 0.263250I
a = −1.290530 + 0.397846I
b = −0.440373 − 0.187785I
2.83235 + 4.49472I 0
u = −1.158280 + 0.038901I
a = −0.044900 − 1.082900I
b = 0.10892 + 1.76473I
−2.47417 − 2.36609I 0
u = −1.158280 − 0.038901I
a = −0.044900 + 1.082900I
b = 0.10892 − 1.76473I
−2.47417 + 2.36609I 0
u = 0.635991 + 0.544847I
a = 0.163228 + 0.980450I
b = 1.213660 + 0.118860I
4.29974 − 0.52525I 0
u = 0.635991 − 0.544847I
a = 0.163228 − 0.980450I
b = 1.213660 − 0.118860I
4.29974 + 0.52525I 0
u = 1.148780 + 0.231094I
a = −0.178896 + 0.316978I
b = 0.211521 − 0.622388I
0.95763 + 1.31939I 0
u = 1.148780 − 0.231094I
a = −0.178896 − 0.316978I
b = 0.211521 + 0.622388I
0.95763 − 1.31939I 0
u = 0.284402 + 1.150140I
a = 0.436714 − 0.359320I
b = −1.306890 − 0.351758I
5.05561 + 7.21324I 0
u = 0.284402 − 1.150140I
a = 0.436714 + 0.359320I
b = −1.306890 + 0.351758I
5.05561 − 7.21324I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180890 + 0.101925I
a = −0.329287 + 0.402844I
b = 0.070577 − 0.397364I
1.03755 + 1.42394I 0
u = 1.180890 − 0.101925I
a = −0.329287 − 0.402844I
b = 0.070577 + 0.397364I
1.03755 − 1.42394I 0
u = −0.630547 + 0.473331I
a = −0.771433 − 0.171537I
b = 0.202395 − 0.600140I
−1.85835 − 1.85518I 2.88110 + 4.86946I
u = −0.630547 − 0.473331I
a = −0.771433 + 0.171537I
b = 0.202395 + 0.600140I
−1.85835 + 1.85518I 2.88110 − 4.86946I
u = 1.213660 + 0.118860I
a = −0.294299 + 0.615882I
b = 0.635991 + 0.544847I
4.29974 − 0.52525I 0
u = 1.213660 − 0.118860I
a = −0.294299 − 0.615882I
b = 0.635991 − 0.544847I
4.29974 + 0.52525I 0
u = −1.198720 + 0.266772I
a = −0.224557 − 0.808357I
b = 0.554100 − 0.529784I
4.19644 − 4.78402I 0
u = −1.198720 − 0.266772I
a = −0.224557 + 0.808357I
b = 0.554100 + 0.529784I
4.19644 + 4.78402I 0
u = 0.042252 + 0.768572I
a = 0.259981 − 0.234911I
b = −1.243120 + 0.401275I
−0.75830 − 6.15523I 2.54266 + 5.39268I
u = 0.042252 − 0.768572I
a = 0.259981 + 0.234911I
b = −1.243120 − 0.401275I
−0.75830 + 6.15523I 2.54266 − 5.39268I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.554100 + 0.529784I
a = −0.362391 − 1.294170I
b = −1.198720 − 0.266772I
4.19644 + 4.78402I 10.46471 − 6.58648I
u = 0.554100 − 0.529784I
a = −0.362391 + 1.294170I
b = −1.198720 + 0.266772I
4.19644 − 4.78402I 10.46471 + 6.58648I
u = 0.306890 + 1.203660I
a = 0.633484 − 0.068432I
b = −0.938800 + 0.219906I
−3.98676 + 1.42787I 0
u = 0.306890 − 1.203660I
a = 0.633484 + 0.068432I
b = −0.938800 − 0.219906I
−3.98676 − 1.42787I 0
u = 0.028710 + 0.734651I
a = −0.946199 − 0.618995I
b = −0.209148 − 0.578349I
0.87132 + 3.18706I 5.01381 − 3.27800I
u = 0.028710 − 0.734651I
a = −0.946199 + 0.618995I
b = −0.209148 + 0.578349I
0.87132 − 3.18706I 5.01381 + 3.27800I
u = −0.721694 + 0.102104I
a = −0.322451 − 1.362520I
b = 0.021380 − 0.371251I
0.94758 − 2.34060I 1.25710 + 5.53583I
u = −0.721694 − 0.102104I
a = −0.322451 + 1.362520I
b = 0.021380 + 0.371251I
0.94758 + 2.34060I 1.25710 − 5.53583I
u = −0.132750 + 1.267920I
a = 0.533990 + 0.282704I
b = −1.318190 + 0.376845I
3.68801 − 12.72800I 0
u = −0.132750 − 1.267920I
a = 0.533990 − 0.282704I
b = −1.318190 − 0.376845I
3.68801 + 12.72800I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.283310 + 0.005598I
a = −2.59874 + 0.16023I
b = 1.125680 + 0.169366I
3.75261 + 3.46176I 0
u = −1.283310 − 0.005598I
a = −2.59874 − 0.16023I
b = 1.125680 − 0.169366I
3.75261 − 3.46176I 0
u = 1.255770 + 0.318257I
a = 1.98536 − 0.52012I
b = −1.56842 − 0.37132I
4.44605 + 4.92843I 0
u = 1.255770 − 0.318257I
a = 1.98536 + 0.52012I
b = −1.56842 + 0.37132I
4.44605 − 4.92843I 0
u = −1.243120 + 0.401275I
a = −0.094878 − 0.183378I
b = 0.042252 + 0.768572I
−0.75830 − 6.15523I 0
u = −1.243120 − 0.401275I
a = −0.094878 + 0.183378I
b = 0.042252 − 0.768572I
−0.75830 + 6.15523I 0
u = 0.294469 + 1.272850I
a = −0.491997 + 0.240143I
b = 1.315060 + 0.204346I
6.39603 + 0.76029I 0
u = 0.294469 − 1.272850I
a = −0.491997 − 0.240143I
b = 1.315060 − 0.204346I
6.39603 − 0.76029I 0
u = 1.279400 + 0.354549I
a = −1.92627 + 0.47196I
b = 1.57701 + 0.54463I
3.13819 + 10.25710I 0
u = 1.279400 − 0.354549I
a = −1.92627 − 0.47196I
b = 1.57701 − 0.54463I
3.13819 − 10.25710I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.315060 + 0.204346I
a = −0.398620 − 0.360491I
b = 0.294469 + 1.272850I
6.39603 + 0.76029I 0
u = 1.315060 − 0.204346I
a = −0.398620 + 0.360491I
b = 0.294469 − 1.272850I
6.39603 − 0.76029I 0
u = 1.333590 + 0.062848I
a = 1.70068 − 0.12225I
b = −1.62808 + 0.65945I
8.12140 + 5.35202I 0
u = 1.333590 − 0.062848I
a = 1.70068 + 0.12225I
b = −1.62808 − 0.65945I
8.12140 − 5.35202I 0
u = 1.335810 + 0.021201I
a = −1.52156 + 0.07833I
b = 1.48991 − 0.81435I
8.28003 − 0.08726I 0
u = 1.335810 − 0.021201I
a = −1.52156 − 0.07833I
b = 1.48991 + 0.81435I
8.28003 + 0.08726I 0
u = 1.319500 + 0.242954I
a = 0.302778 + 0.490529I
b = −0.081953 − 1.362050I
5.54688 + 6.19194I 0
u = 1.319500 − 0.242954I
a = 0.302778 − 0.490529I
b = −0.081953 + 1.362050I
5.54688 − 6.19194I 0
u = 0.211521 + 0.622388I
a = −0.601398 + 0.243507I
b = 1.148780 − 0.231094I
0.95763 − 1.31939I 5.50400 − 0.11930I
u = 0.211521 − 0.622388I
a = −0.601398 − 0.243507I
b = 1.148780 + 0.231094I
0.95763 + 1.31939I 5.50400 + 0.11930I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.306890 + 0.351758I
a = −0.460310 + 0.182244I
b = 0.284402 − 1.150140I
5.05561 − 7.21324I 0
u = −1.306890 − 0.351758I
a = −0.460310 − 0.182244I
b = 0.284402 + 1.150140I
5.05561 + 7.21324I 0
u = −0.081953 + 1.362050I
a = −0.539640 − 0.173352I
b = 1.319500 − 0.242954I
5.54688 − 6.19194I 0
u = −0.081953 − 1.362050I
a = −0.539640 + 0.173352I
b = 1.319500 + 0.242954I
5.54688 + 6.19194I 0
u = 0.202395 + 0.600140I
a = 0.670871 − 0.719561I
b = −0.630547 − 0.473331I
−1.85835 + 1.85518I 2.88110 − 4.86946I
u = 0.202395 − 0.600140I
a = 0.670871 + 0.719561I
b = −0.630547 + 0.473331I
−1.85835 − 1.85518I 2.88110 + 4.86946I
u = −1.318190 + 0.376845I
a = 0.429309 − 0.362425I
b = −0.132750 + 1.267920I
3.68801 − 12.72800I 0
u = −1.318190 − 0.376845I
a = 0.429309 + 0.362425I
b = −0.132750 − 1.267920I
3.68801 + 12.72800I 0
u = −0.209148 + 0.578349I
a = 0.853649 − 1.048020I
b = 0.028710 − 0.734651I
0.87132 − 3.18706I 5.01381 + 3.27800I
u = −0.209148 − 0.578349I
a = 0.853649 + 1.048020I
b = 0.028710 + 0.734651I
0.87132 + 3.18706I 5.01381 − 3.27800I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.389870 + 0.127948I
a = −1.64619 − 0.16333I
b = 1.53449 − 0.70295I
10.26190 − 6.79269I 0
u = −1.389870 − 0.127948I
a = −1.64619 + 0.16333I
b = 1.53449 + 0.70295I
10.26190 + 6.79269I 0
u = −1.393480 + 0.095069I
a = 1.75498 + 0.14814I
b = −1.61445 + 0.53714I
10.66800 − 1.12994I 0
u = −1.393480 − 0.095069I
a = 1.75498 − 0.14814I
b = −1.61445 − 0.53714I
10.66800 + 1.12994I 0
u = −0.480609 + 0.312195I
a = 0.985140 − 0.644437I
b = −0.132342 + 0.952090I
−4.31975 + 1.46497I −2.47124 − 1.07580I
u = −0.480609 − 0.312195I
a = 0.985140 + 0.644437I
b = −0.132342 − 0.952090I
−4.31975 − 1.46497I −2.47124 + 1.07580I
u = −0.496445 + 0.034634I
a = −2.58741 + 2.94549I
b = −1.039410 + 0.270775I
2.87536 − 0.22281I 6.45523 + 2.31553I
u = −0.496445 − 0.034634I
a = −2.58741 − 2.94549I
b = −1.039410 − 0.270775I
2.87536 + 0.22281I 6.45523 − 2.31553I
u = −0.440373 + 0.187785I
a = 1.93985 + 2.61358I
b = 1.123400 + 0.263250I
2.83235 − 4.49472I 6.56893 + 6.15189I
u = −0.440373 − 0.187785I
a = 1.93985 − 2.61358I
b = 1.123400 − 0.263250I
2.83235 + 4.49472I 6.56893 − 6.15189I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46278 + 0.45766I
a = −1.66720 − 0.61988I
b = 1.47529 − 0.56121I
10.5630 − 12.8142I 0
u = −1.46278 − 0.45766I
a = −1.66720 + 0.61988I
b = 1.47529 + 0.56121I
10.5630 + 12.8142I 0
u = 1.47529 + 0.56121I
a = 1.57971 − 0.69835I
b = −1.46278 − 0.45766I
10.5630 + 12.8142I 0
u = 1.47529 − 0.56121I
a = 1.57971 + 0.69835I
b = −1.46278 + 0.45766I
10.5630 − 12.8142I 0
u = 0.070577 + 0.397364I
a = −1.26496 + 0.85723I
b = 1.180890 − 0.101925I
1.03755 − 1.42394I 2.53124 − 0.77932I
u = 0.070577 − 0.397364I
a = −1.26496 − 0.85723I
b = 1.180890 + 0.101925I
1.03755 + 1.42394I 2.53124 + 0.77932I
u = −1.56842 + 0.37132I
a = −1.60212 − 0.39288I
b = 1.255770 − 0.318257I
4.44605 − 4.92843I 0
u = −1.56842 − 0.37132I
a = −1.60212 + 0.39288I
b = 1.255770 + 0.318257I
4.44605 + 4.92843I 0
u = 0.021380 + 0.371251I
a = −2.49403 − 1.14518I
b = −0.721694 − 0.102104I
0.94758 + 2.34060I 1.25710 − 5.53583I
u = 0.021380 − 0.371251I
a = −2.49403 + 1.14518I
b = −0.721694 + 0.102104I
0.94758 − 2.34060I 1.25710 + 5.53583I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57701 + 0.54463I
a = −1.50651 + 0.47010I
b = 1.279400 + 0.354549I
3.13819 + 10.25710I 0
u = 1.57701 − 0.54463I
a = −1.50651 − 0.47010I
b = 1.279400 − 0.354549I
3.13819 − 10.25710I 0
u = 1.53449 + 0.70295I
a = 1.239640 − 0.578553I
b = −1.389870 − 0.127948I
10.26190 + 6.79269I 0
u = 1.53449 − 0.70295I
a = 1.239640 + 0.578553I
b = −1.389870 + 0.127948I
10.26190 − 6.79269I 0
u = 1.48991 + 0.81435I
a = −1.071690 + 0.537184I
b = 1.335810 − 0.021201I
8.28003 + 0.08726I 0
u = 1.48991 − 0.81435I
a = −1.071690 − 0.537184I
b = 1.335810 + 0.021201I
8.28003 − 0.08726I 0
u = −1.61445 + 0.53714I
a = 1.36431 + 0.47844I
b = −1.393480 + 0.095069I
10.66800 − 1.12994I 0
u = −1.61445 − 0.53714I
a = 1.36431 − 0.47844I
b = −1.393480 − 0.095069I
10.66800 + 1.12994I 0
u = −1.62808 + 0.65945I
a = −1.212780 − 0.456745I
b = 1.333590 + 0.062848I
8.12140 + 5.35202I 0
u = −1.62808 − 0.65945I
a = −1.212780 + 0.456745I
b = 1.333590 − 0.062848I
8.12140 − 5.35202I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10892 + 1.76473I
a = 0.710356 − 0.009498I
b = −1.158280 + 0.038901I
−2.47417 − 2.36609I 0
u = 0.10892 − 1.76473I
a = 0.710356 + 0.009498I
b = −1.158280 − 0.038901I
−2.47417 + 2.36609I 0
20
III. I
u
3
= hb − 1, 18a
2
− 3au + 24a − 2u + 7, u
2
+ 2i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
2
a
4
=
a
1
a
7
=
−u
u
a
5
=
3a + 2
−2a − 1
a
11
=
a + 1
1
a
3
=
−1
0
a
2
=
−1
2
a
6
=
0
−u
a
10
=
3a + 2
4a + 3
a
9
=
3a −
1
2
u + 2
−au + 4a −
1
3
u +
8
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12au − 8u + 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 2)
4
c
2
, c
6
, c
7
c
12
(u
2
+ 2)
2
c
3
(u + 1)
4
c
4
27(27u
4
+ 18u
3
+ 21u
2
+ 6u + 1)
c
5
, c
8
(u
2
− u + 1)
2
c
9
(u
2
+ u + 1)
2
c
10
27(27u
4
+ 36u
3
+ 12u
2
+ 1)
c
11
(u − 1)
4
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −4)
4
c
2
, c
6
, c
7
c
12
(y + 2)
4
c
3
, c
11
(y −1)
4
c
4
729(729y
4
+ 810y
3
+ 279y
2
+ 6y + 1)
c
5
, c
8
, c
9
(y
2
+ y + 1)
2
c
10
729(729y
4
− 648y
3
+ 198y
2
+ 24y + 1)
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −0.870791 + 0.117851I
b = 1.00000
−3.28987 − 2.02988I 6.00000 + 3.46410I
u = 1.414210I
a = −0.462543 + 0.117851I
b = 1.00000
−3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.414210I
a = −0.870791 − 0.117851I
b = 1.00000
−3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.414210I
a = −0.462543 − 0.117851I
b = 1.00000
−3.28987 − 2.02988I 6.00000 + 3.46410I
24
IV.
I
u
4
= h54a
3
− 27a
2
+ 58b + 153a − 25, 27a
4
− 18a
3
+ 57a
2
− 18a + 19, u + 1i
(i) Arc colorings
a
8
=
0
−1
a
12
=
1
0
a
1
=
1
−1
a
4
=
a
−0.931034a
3
+ 0.465517a
2
− 2.63793a + 0.431034
a
7
=
1
−1
a
5
=
0.931034a
3
− 0.465517a
2
+ 2.63793a − 0.431034
−1.86207a
3
+ 0.931034a
2
− 4.27586a + 0.862069
a
11
=
−0.155172a
3
− 0.672414a
2
− 0.189655a + 1.65517
−2
a
3
=
0.931034a
3
− 0.465517a
2
+ 5.63793a − 0.431034
−2.79310a
3
+ 1.39655a
2
− 7.91379a + 1.29310
a
2
=
−0.465517a
3
+ 6.98276a
2
− 0.568966a + 6.96552
−1.39655a
3
− 6.05172a
2
− 1.70690a − 7.10345
a
6
=
−2.79310a
3
+ 1.39655a
2
− 7.91379a + 1.29310
4.65517a
3
− 2.32759a
2
+ 10.1897a − 2.15517
a
10
=
2
−0.155172a
3
− 0.672414a
2
− 0.189655a − 2.34483
a
9
=
4
−0.310345a
3
− 1.34483a
2
− 0.379310a − 5.68966
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
216
29
a
3
+
108
29
a
2
−
264
29
a +
216
29
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
2
c
3
, c
5
, c
9
c
11
(u
2
+ 2)
2
c
4
27(27u
4
+ 18u
3
+ 21u
2
+ 6u + 1)
c
6
(u
2
+ u + 1)
2
c
7
(u − 1)
4
c
8
(u − 2)
4
c
10
27(27u
4
+ 36u
3
+ 12u
2
+ 1)
c
12
(u + 1)
4
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
, c
9
c
11
(y + 2)
4
c
4
729(729y
4
+ 810y
3
+ 279y
2
+ 6y + 1)
c
7
, c
12
(y − 1)
4
c
8
(y − 4)
4
c
10
729(729y
4
− 648y
3
+ 198y
2
+ 24y + 1)
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.166667 + 1.231480I
b = − 1.414210I
−3.28987 − 2.02988I 6.00000 + 3.46410I
u = −1.00000
a = 0.166667 − 1.231480I
b = 1.414210I
−3.28987 + 2.02988I 6.00000 − 3.46410I
u = −1.00000
a = 0.166667 + 0.654134I
b = − 1.414210I
−3.28987 + 2.02988I 6.00000 − 3.46410I
u = −1.00000
a = 0.166667 − 0.654134I
b = 1.414210I
−3.28987 − 2.02988I 6.00000 + 3.46410I
28
V. I
u
5
= hb, a
2
− a + 1, u − 1i
(i) Arc colorings
a
8
=
0
1
a
12
=
1
0
a
1
=
1
−1
a
4
=
a
0
a
7
=
−1
1
a
5
=
0
a
a
11
=
1
0
a
3
=
a
0
a
2
=
a
−1
a
6
=
0
a
a
10
=
0
1
a
9
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 10
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
5
, c
8
c
9
, c
11
u
2
c
7
, c
10
(u + 1)
2
c
12
(u − 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
y
2
+ y + 1
c
3
, c
5
, c
8
c
9
, c
11
y
2
c
7
, c
10
, c
12
(y − 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000 + 0.866025I
b = 0
1.64493 − 2.02988I 12.00000 + 3.46410I
u = 1.00000
a = 0.500000 − 0.866025I
b = 0
1.64493 + 2.02988I 12.00000 − 3.46410I
32
VI. I
v
1
= ha, b + 1, v
2
− v + 1i
(i) Arc colorings
a
8
=
v
0
a
12
=
1
0
a
1
=
1
0
a
4
=
0
−1
a
7
=
v
0
a
5
=
v − 1
−1
a
11
=
1
1
a
3
=
1
0
a
2
=
1
0
a
6
=
v
0
a
10
=
0
1
a
9
=
v
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 10
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
12
u
2
c
3
(u − 1)
2
c
4
, c
8
, c
9
u
2
− u + 1
c
5
u
2
+ u + 1
c
10
, c
11
(u + 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
12
y
2
c
3
, c
10
, c
11
(y − 1)
2
c
4
, c
5
, c
8
c
9
y
2
+ y + 1
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −1.00000
1.64493 − 2.02988I 12.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −1.00000
1.64493 + 2.02988I 12.00000 − 3.46410I
36
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
2
(u − 2)
4
(u
2
− u + 1)
3
(u
14
+ 6u
13
+ ··· − 8u + 1)
· (u
102
+ 42u
101
+ ··· + 107216u + 5776)
c
2
, c
5
u
2
(u
2
+ 2)
2
(u
2
− u + 1)
2
(u
2
+ u + 1)
· (u
14
+ 3u
12
+ 6u
10
+ 7u
8
− 2u
7
+ 6u
6
− 4u
5
+ 6u
4
− 5u
3
+ 4u
2
− 4u + 1)
· (u
102
− 2u
101
+ ··· + 172u + 76)
c
3
, c
12
u
2
(u − 1)
2
(u + 1)
4
(u
2
+ 2)
2
· (u
14
− 5u
12
+ 10u
10
+ 2u
9
− 5u
8
− 6u
7
− 4u
6
+ 4u
5
+ 4u
4
+ 7u
3
− 1)
· (u
102
− 3u
101
+ ··· + 6720u + 1228)
c
4
1750329(u
2
− u + 1)
2
(27u
4
+ 18u
3
+ 21u
2
+ 6u + 1)
2
· (49u
14
− 567u
13
+ ··· − 6400u + 512)
· (7u
51
+ 68u
50
+ ··· − 1074u + 167)
2
c
6
, c
9
u
2
(u
2
+ 2)
2
(u
2
− u + 1)(u
2
+ u + 1)
2
· (u
14
+ 3u
12
+ 6u
10
+ 7u
8
− 2u
7
+ 6u
6
− 4u
5
+ 6u
4
− 5u
3
+ 4u
2
− 4u + 1)
· (u
102
− 2u
101
+ ··· + 172u + 76)
c
7
, c
11
u
2
(u − 1)
4
(u + 1)
2
(u
2
+ 2)
2
· (u
14
− 5u
12
+ 10u
10
+ 2u
9
− 5u
8
− 6u
7
− 4u
6
+ 4u
5
+ 4u
4
+ 7u
3
− 1)
· (u
102
− 3u
101
+ ··· + 6720u + 1228)
c
10
1750329(u + 1)
4
(27u
4
+ 36u
3
+ 12u
2
+ 1)
2
· (49u
14
+ 567u
13
+ ··· − 256u − 32)
· (7u
51
− 65u
50
+ ··· + 4991u − 373)
2
37
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
2
(y − 4)
4
(y
2
+ y + 1)
3
(y
14
+ 6y
13
+ ··· − 88y + 1)
· (y
102
+ 42y
101
+ ··· + 456890624y + 33362176)
c
2
, c
5
, c
6
c
9
y
2
(y + 2)
4
(y
2
+ y + 1)
3
(y
14
+ 6y
13
+ ··· − 8y + 1)
· (y
102
+ 42y
101
+ ··· + 107216y + 5776)
c
3
, c
7
, c
11
c
12
y
2
(y − 1)
6
(y + 2)
4
(y
14
− 10y
13
+ ··· − 8y
2
+ 1)
· (y
102
− 71y
101
+ ··· − 636032y + 1507984)
c
4
3063651608241(y
2
+ y + 1)
2
(729y
4
+ 810y
3
+ 279y
2
+ 6y + 1)
2
· (2401y
14
+ 13671y
13
+ ··· − 8978432y + 262144)
· (49y
51
+ 738y
50
+ ··· − 123072y − 27889)
2
c
10
3063651608241(y − 1)
4
(729y
4
− 648y
3
+ 198y
2
+ 24y + 1)
2
· (2401y
14
− 27489y
13
+ ··· − 15872y + 1024)
· (49y
51
− 2279y
50
+ ··· + 13376175y − 139129)
2
38
