12a
0408
(K12a
0408
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 2 10 4 11 1 5 8 7
Solving Sequence
8,11
9
4,12
5 3 7 1 10 6 2
c
8
c
11
c
4
c
3
c
7
c
12
c
10
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.94883 × 10
82
u
65
+ 1.44814 × 10
84
u
64
+ ··· + 5.09401 × 10
83
b − 2.12573 × 10
85
,
− 4.92961 × 10
84
u
65
+ 1.25631 × 10
86
u
64
+ ··· + 3.31110 × 10
85
a + 5.80286 × 10
87
,
u
66
− 26u
65
+ ··· − 29690u + 1300i
I
u
2
= h817219108u
29
a
3
+ 512017417u
29
a
2
+ ··· + 807804715a + 597442347,
16u
29
a
2
− 224u
29
a + ··· − 1933a + 10413, u
30
+ 9u
29
+ ··· + 14u + 1i
I
u
3
= h2.05685 × 10
15
u
35
+ 3.17765 × 10
16
u
34
+ ··· + 1.33360 × 10
16
b + 3.92713 × 10
16
,
− 2.48733 × 10
16
u
35
− 3.52235 × 10
17
u
34
+ ··· + 9.33523 × 10
16
a − 1.32132 × 10
18
,
u
36
+ 15u
35
+ ··· + 100u + 7i
I
u
4
= h−8a
3
u − 6a
3
− 3a
2
u − 21a
2
+ 59au + 50b − 37a + 13u + 41,
a
4
− a
3
u + a
3
− 3a
2
u − 4a
2
+ 3au − a + 2u + 3, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 230 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−5.95 × 10
82
u
65
+ 1.45 × 10
84
u
64
+ · · · + 5.09 × 10
83
b − 2.13 ×
10
85
, −4.93 × 10
84
u
65
+ 1.26 × 10
86
u
64
+ · · · + 3.31 × 10
85
a + 5.80 ×
10
87
, u
66
− 26u
65
+ · · · − 29690u + 1300i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
4
=
0.148881u
65
− 3.79422u
64
+ ··· + 3912.79u − 175.254
0.116781u
65
− 2.84284u
64
+ ··· − 736.065u + 41.7300
a
12
=
u
u
a
5
=
−0.0445864u
65
+ 1.18662u
64
+ ··· + 403.833u − 23.4390
−0.0766864u
65
+ 2.13800u
64
+ ··· − 4245.02u + 193.545
a
3
=
0.121508u
65
− 3.33673u
64
+ ··· + 5260.00u − 233.217
0.407157u
65
− 10.5042u
64
+ ··· + 6775.86u − 288.744
a
7
=
−0.0389164u
65
+ 1.01371u
64
+ ··· − 1316.21u + 61.4204
−0.0414582u
65
+ 1.03834u
64
+ ··· − 132.582u + 3.30431
a
1
=
0.197987u
65
− 4.99729u
64
+ ··· + 2699.62u − 115.833
0.159022u
65
− 3.78559u
64
+ ··· − 2163.10u + 104.551
a
10
=
−0.00561786u
65
+ 0.162911u
64
+ ··· − 830.706u + 38.6946
−0.00627711u
65
+ 0.204138u
64
+ ··· − 741.092u + 32.1698
a
6
=
−0.0826048u
65
+ 2.15913u
64
+ ··· − 2200.04u + 99.6941
−0.141191u
65
+ 3.59078u
64
+ ··· − 2245.40u + 96.5869
a
2
=
−0.0628923u
65
+ 1.60318u
64
+ ··· − 1571.82u + 67.8794
0.00840374u
65
− 0.102004u
64
+ ··· − 1483.96u + 65.7618
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.953489u
65
+ 23.7173u
64
+ ··· − 15544.8u + 676.189
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 31u
65
+ ··· + 17676u + 2704
c
2
, c
5
u
66
+ 13u
65
+ ··· − 738u − 52
c
3
, c
10
u
66
+ 13u
64
+ ··· + 37u − 181
c
4
, c
7
u
66
− 15u
64
+ ··· − u − 1
c
6
, c
9
u
66
+ 2u
65
+ ··· + 5u + 2
c
8
, c
11
u
66
+ 26u
65
+ ··· + 29690u + 1300
c
12
u
66
+ 56u
65
+ ··· + 17045651456u + 536870912
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 17y
65
+ ··· − 505176688y + 7311616
c
2
, c
5
y
66
− 31y
65
+ ··· − 17676y + 2704
c
3
, c
10
y
66
+ 26y
65
+ ··· + 13111y + 32761
c
4
, c
7
y
66
− 30y
65
+ ··· − 51y + 1
c
6
, c
9
y
66
− 2y
65
+ ··· + 43y + 4
c
8
, c
11
y
66
+ 46y
65
+ ··· + 26109300y + 1690000
c
12
y
66
+ 6y
65
+ ··· − 1242993497154256896y + 288230376151711744
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.965644 + 0.116585I
a = −0.128217 + 0.077481I
b = 0.781461 + 0.909186I
0.04153 − 7.33110I 0
u = 0.965644 − 0.116585I
a = −0.128217 − 0.077481I
b = 0.781461 − 0.909186I
0.04153 + 7.33110I 0
u = 0.968871
a = 0.0216859
b = −0.674970
−4.57047 0
u = −0.107773 + 0.943078I
a = −2.13279 − 0.30507I
b = −1.152450 + 0.804909I
−1.36529 − 0.47729I 0
u = −0.107773 − 0.943078I
a = −2.13279 + 0.30507I
b = −1.152450 − 0.804909I
−1.36529 + 0.47729I 0
u = −0.191979 + 0.928389I
a = −1.20721 − 0.75473I
b = −0.883784 + 0.130347I
−1.54285 − 0.80188I 0
u = −0.191979 − 0.928389I
a = −1.20721 + 0.75473I
b = −0.883784 − 0.130347I
−1.54285 + 0.80188I 0
u = −0.212483 + 1.044600I
a = 1.297590 + 0.542475I
b = 0.904573 − 0.243533I
−2.15381 − 4.98396I 0
u = −0.212483 − 1.044600I
a = 1.297590 − 0.542475I
b = 0.904573 + 0.243533I
−2.15381 + 4.98396I 0
u = 0.064628 + 1.072060I
a = 1.87038 + 0.10819I
b = 1.06339 − 0.93238I
−2.26306 + 0.50106I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.064628 − 1.072060I
a = 1.87038 − 0.10819I
b = 1.06339 + 0.93238I
−2.26306 − 0.50106I 0
u = −0.038288 + 1.076850I
a = −2.00469 − 0.14451I
b = −1.14404 + 0.88729I
−2.15487 + 3.80132I 0
u = −0.038288 − 1.076850I
a = −2.00469 + 0.14451I
b = −1.14404 − 0.88729I
−2.15487 − 3.80132I 0
u = 1.000080 + 0.415641I
a = 0.190224 − 0.401848I
b = −0.776510 − 0.859685I
5.94107 − 4.21086I 0
u = 1.000080 − 0.415641I
a = 0.190224 + 0.401848I
b = −0.776510 + 0.859685I
5.94107 + 4.21086I 0
u = −0.068173 + 1.089420I
a = 1.312090 + 0.193562I
b = 0.800595 − 0.509315I
−3.63493 + 0.26678I 0
u = −0.068173 − 1.089420I
a = 1.312090 − 0.193562I
b = 0.800595 + 0.509315I
−3.63493 − 0.26678I 0
u = −1.059830 + 0.271315I
a = −0.146768 + 0.536946I
b = −0.042981 + 0.289942I
2.65184 − 2.70646I 0
u = −1.059830 − 0.271315I
a = −0.146768 − 0.536946I
b = −0.042981 − 0.289942I
2.65184 + 2.70646I 0
u = 0.932509 + 0.609781I
a = −0.176126 + 0.610050I
b = 0.843789 + 0.786001I
3.49079 + 2.01874I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932509 − 0.609781I
a = −0.176126 − 0.610050I
b = 0.843789 − 0.786001I
3.49079 − 2.01874I 0
u = −0.038605 + 0.865223I
a = 2.07405 + 0.46782I
b = 1.116710 − 0.780133I
−1.06238 + 3.87964I 0
u = −0.038605 − 0.865223I
a = 2.07405 − 0.46782I
b = 1.116710 + 0.780133I
−1.06238 − 3.87964I 0
u = −0.117598 + 1.165860I
a = −0.765345 − 0.241957I
b = −0.545559 + 0.203818I
−1.23236 − 1.99215I 0
u = −0.117598 − 1.165860I
a = −0.765345 + 0.241957I
b = −0.545559 − 0.203818I
−1.23236 + 1.99215I 0
u = 0.254162 + 1.169580I
a = 1.42656 + 0.33003I
b = 1.074210 − 0.664993I
−4.08137 + 1.75624I 0
u = 0.254162 − 1.169580I
a = 1.42656 − 0.33003I
b = 1.074210 + 0.664993I
−4.08137 − 1.75624I 0
u = 1.193540 + 0.156973I
a = −0.030280 − 0.244059I
b = −0.741582 − 0.928169I
6.96659 − 8.93778I 0
u = 1.193540 − 0.156973I
a = −0.030280 + 0.244059I
b = −0.741582 + 0.928169I
6.96659 + 8.93778I 0
u = 0.684171 + 0.997219I
a = −0.920037 − 0.922593I
b = −1.49530 + 0.18220I
−8.44397 + 2.73127I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.684171 − 0.997219I
a = −0.920037 + 0.922593I
b = −1.49530 − 0.18220I
−8.44397 − 2.73127I 0
u = 1.226440 + 0.090852I
a = 0.083985 + 0.223653I
b = 0.744800 + 0.946222I
5.3505 − 14.8237I 0
u = 1.226440 − 0.090852I
a = 0.083985 − 0.223653I
b = 0.744800 − 0.946222I
5.3505 + 14.8237I 0
u = 0.608248 + 1.097060I
a = 1.47037 + 0.24555I
b = 1.24440 − 1.01405I
1.78613 + 3.64779I 0
u = 0.608248 − 1.097060I
a = 1.47037 − 0.24555I
b = 1.24440 + 1.01405I
1.78613 − 3.64779I 0
u = 0.955531 + 0.867453I
a = 0.421538 + 0.428454I
b = 0.889319 − 0.081476I
1.203030 + 0.280799I 0
u = 0.955531 − 0.867453I
a = 0.421538 − 0.428454I
b = 0.889319 + 0.081476I
1.203030 − 0.280799I 0
u = 0.209561 + 1.287700I
a = −1.40191 − 0.27209I
b = −1.069990 + 0.612858I
−6.31133 − 2.87206I 0
u = 0.209561 − 1.287700I
a = −1.40191 + 0.27209I
b = −1.069990 − 0.612858I
−6.31133 + 2.87206I 0
u = 0.421956 + 1.251050I
a = −1.309050 − 0.347468I
b = −1.139520 + 0.620558I
−8.61831 + 4.70101I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.421956 − 1.251050I
a = −1.309050 + 0.347468I
b = −1.139520 − 0.620558I
−8.61831 − 4.70101I 0
u = 1.097080 + 0.747621I
a = −0.340634 − 0.290418I
b = −0.780833 + 0.108043I
0.10489 − 5.64548I 0
u = 1.097080 − 0.747621I
a = −0.340634 + 0.290418I
b = −0.780833 − 0.108043I
0.10489 + 5.64548I 0
u = 0.616875 + 1.179060I
a = −1.51838 − 0.12234I
b = −1.23374 + 1.07296I
3.47545 + 10.03930I 0
u = 0.616875 − 1.179060I
a = −1.51838 + 0.12234I
b = −1.23374 − 1.07296I
3.47545 − 10.03930I 0
u = 0.545484 + 1.277650I
a = 1.62855 + 0.02048I
b = 1.24027 − 1.11604I
−3.52822 + 12.78220I 0
u = 0.545484 − 1.277650I
a = 1.62855 − 0.02048I
b = 1.24027 + 1.11604I
−3.52822 − 12.78220I 0
u = 0.74868 + 1.21734I
a = 0.977453 + 0.416470I
b = 1.146590 − 0.421393I
−0.31629 + 6.51467I 0
u = 0.74868 − 1.21734I
a = 0.977453 − 0.416470I
b = 1.146590 + 0.421393I
−0.31629 − 6.51467I 0
u = 0.61794 + 1.32321I
a = −1.56379 + 0.03667I
b = −1.22324 + 1.12016I
3.2955 + 15.2496I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.61794 − 1.32321I
a = −1.56379 − 0.03667I
b = −1.22324 − 1.12016I
3.2955 − 15.2496I 0
u = 0.61054 + 1.35619I
a = 1.57770 − 0.06479I
b = 1.22494 − 1.12682I
1.3811 + 21.2028I 0
u = 0.61054 − 1.35619I
a = 1.57770 + 0.06479I
b = 1.22494 + 1.12682I
1.3811 − 21.2028I 0
u = 0.72941 + 1.29848I
a = −1.025890 − 0.333628I
b = −1.114340 + 0.474873I
−2.19090 + 12.78110I 0
u = 0.72941 − 1.29848I
a = −1.025890 + 0.333628I
b = −1.114340 − 0.474873I
−2.19090 − 12.78110I 0
u = 0.51432 + 1.39828I
a = 0.302087 + 0.428571I
b = 0.508626 + 0.140789I
−4.31937 − 2.33827I 0
u = 0.51432 − 1.39828I
a = 0.302087 − 0.428571I
b = 0.508626 − 0.140789I
−4.31937 + 2.33827I 0
u = −0.051370 + 0.503606I
a = −0.76050 − 1.80646I
b = −0.841572 − 0.127095I
−0.60859 − 4.25457I −11.06711 + 6.14084I
u = −0.051370 − 0.503606I
a = −0.76050 + 1.80646I
b = −0.841572 + 0.127095I
−0.60859 + 4.25457I −11.06711 − 6.14084I
u = 0.081734 + 0.272914I
a = −0.81815 + 2.41224I
b = 0.717888 + 0.241806I
−0.240752 + 0.181084I −10.49440 + 0.66551I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.081734 − 0.272914I
a = −0.81815 − 2.41224I
b = 0.717888 − 0.241806I
−0.240752 − 0.181084I −10.49440 − 0.66551I
u = 0.189346
a = −2.01839
b = 0.471438
−0.703695 −14.0890
u = −0.01449 + 1.83613I
a = −0.339222 − 0.183967I
b = −0.337779 − 0.000015I
0.32364 − 2.66479I 0
u = −0.01449 − 1.83613I
a = −0.339222 + 0.183967I
b = −0.337779 + 0.000015I
0.32364 + 2.66479I 0
u = 0.24295 + 1.97827I
a = 0.270137 + 0.224203I
b = 0.323412 + 0.067264I
−0.69045 − 7.86547I 0
u = 0.24295 − 1.97827I
a = 0.270137 − 0.224203I
b = 0.323412 − 0.067264I
−0.69045 + 7.86547I 0
11
II. I
u
2
= h8.17 × 10
8
a
3
u
29
+ 5.12 × 10
8
a
2
u
29
+ · · · + 8.08 × 10
8
a + 5.97 ×
10
8
, 16u
29
a
2
− 224u
29
a + · · · − 1933a + 10413, u
30
+ 9u
29
+ · · · + 14u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
4
=
a
−3.45633a
3
u
29
− 2.16552a
2
u
29
+ ··· − 3.41652a − 2.52681
a
12
=
u
u
a
5
=
2.74813a
3
u
29
+ 1.02874a
2
u
29
+ ··· + 1.18551a + 0.386995
−0.708207a
3
u
29
− 1.13678a
2
u
29
+ ··· − 3.23100a − 2.13982
a
3
=
−3.45633a
3
u
29
− 2.16552a
2
u
29
+ ··· − 2.41652a − 2.52681
−0.708207a
3
u
29
− 1.13678a
2
u
29
+ ··· − 3.23100a − 2.13982
a
7
=
−0.928707a
3
u
29
− 0.252178a
2
u
29
+ ··· − 2.45191a + 35.0430
0.287370a
3
u
29
+ 0.396556a
2
u
29
+ ··· + 1.25130a + 0.993518
a
1
=
−2.64161a
3
u
29
− 0.574265a
2
u
29
+ ··· − 2.03300a + 18.3367
−1.42553a
3
u
29
+ 0.0744681a
2
u
29
+ ··· + 1.67021a − 1.71277
a
10
=
1.54187a
3
u
29
+ 1.99595a
2
u
29
+ ··· + 2.55200a − 2.47821
−0.436306a
3
u
29
+ 0.954509a
2
u
29
+ ··· + 0.408271a + 0.432019
a
6
=
−1.74875a
3
u
29
− 1.02431a
2
u
29
+ ··· − 1.18803a + 18.6307
1.11854a
3
u
29
+ 0.475684a
2
u
29
+ ··· + 2.28116a + 3.63070
a
2
=
−2.86730a
3
u
29
− 1.50000a
2
u
29
+ ··· − 2.46918a + 15.0000
−1.11854a
3
u
29
− 0.475684a
2
u
29
+ ··· − 1.28116a − 3.63070
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
584865692
118220557
u
29
a
3
−
110051764
118220557
u
29
a
2
+ ··· −
581605732
118220557
a −
265571218
118220557
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
30
+ 13u
29
+ ··· + 8u + 1)
4
c
2
, c
5
(u
30
− 3u
29
+ ··· + 6u − 1)
4
c
3
, c
10
u
120
− u
119
+ ··· − 971506096u + 277703647
c
4
, c
7
u
120
+ 7u
119
+ ··· − 34u + 7
c
6
, c
9
u
120
+ 9u
119
+ ··· + 1147452u + 251797
c
8
, c
11
(u
30
− 9u
29
+ ··· − 14u + 1)
4
c
12
(u
2
− u + 1)
60
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
30
+ 11y
29
+ ··· − 52y + 1)
4
c
2
, c
5
(y
30
− 13y
29
+ ··· − 8y + 1)
4
c
3
, c
10
y
120
+ 41y
119
+ ··· + 4660341483603865276y + 77119315557100609
c
4
, c
7
y
120
+ 25y
119
+ ··· + 3884y + 49
c
6
, c
9
y
120
+ 51y
119
+ ··· + 3713334879894y + 63401729209
c
8
, c
11
(y
30
+ 19y
29
+ ··· − 76y + 1)
4
c
12
(y
2
+ y + 1)
60
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.745428 + 0.678147I
a = −0.115504 + 0.906628I
b = −0.358285 + 1.042520I
2.91288 − 3.27691I −2.14197 + 4.25187I
u = −0.745428 + 0.678147I
a = −0.870330 + 0.260038I
b = 0.088818 − 0.265941I
2.91288 − 3.27691I −2.14197 + 4.25187I
u = −0.745428 + 0.678147I
a = −0.062729 + 0.457190I
b = −0.431760 − 0.964251I
2.91288 − 7.33668I −2.14197 + 11.18007I
u = −0.745428 + 0.678147I
a = 1.56601 − 0.18677I
b = 1.23903 + 0.80932I
2.91288 − 7.33668I −2.14197 + 11.18007I
u = −0.745428 − 0.678147I
a = −0.115504 − 0.906628I
b = −0.358285 − 1.042520I
2.91288 + 3.27691I −2.14197 − 4.25187I
u = −0.745428 − 0.678147I
a = −0.870330 − 0.260038I
b = 0.088818 + 0.265941I
2.91288 + 3.27691I −2.14197 − 4.25187I
u = −0.745428 − 0.678147I
a = −0.062729 − 0.457190I
b = −0.431760 + 0.964251I
2.91288 + 7.33668I −2.14197 − 11.18007I
u = −0.745428 − 0.678147I
a = 1.56601 + 0.18677I
b = 1.23903 − 0.80932I
2.91288 + 7.33668I −2.14197 − 11.18007I
u = 0.294292 + 0.972034I
a = 0.236328 + 0.015046I
b = 0.037315 − 1.389410I
2.16449 + 7.46442I −6.77551 − 6.94723I
u = 0.294292 + 0.972034I
a = 1.10990 + 1.60858I
b = 1.28896 + 1.90166I
2.16449 + 11.52420I −6.7755 − 13.8754I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294292 + 0.972034I
a = −2.39204 + 0.93244I
b = −0.232185 + 0.260308I
2.16449 + 11.52420I −6.7755 − 13.8754I
u = 0.294292 + 0.972034I
a = 2.60533 − 0.17518I
b = 1.30661 − 0.60677I
2.16449 + 7.46442I −6.77551 − 6.94723I
u = 0.294292 − 0.972034I
a = 0.236328 − 0.015046I
b = 0.037315 + 1.389410I
2.16449 − 7.46442I −6.77551 + 6.94723I
u = 0.294292 − 0.972034I
a = 1.10990 − 1.60858I
b = 1.28896 − 1.90166I
2.16449 − 11.52420I −6.7755 + 13.8754I
u = 0.294292 − 0.972034I
a = −2.39204 − 0.93244I
b = −0.232185 − 0.260308I
2.16449 − 11.52420I −6.7755 + 13.8754I
u = 0.294292 − 0.972034I
a = 2.60533 + 0.17518I
b = 1.30661 + 0.60677I
2.16449 − 7.46442I −6.77551 + 6.94723I
u = 0.291928 + 0.912894I
a = −0.220592 − 0.354150I
b = −0.019177 + 1.253670I
4.20602 + 1.61366I −3.27196 − 2.59272I
u = 0.291928 + 0.912894I
a = −0.91060 − 1.59867I
b = −1.14023 − 1.89433I
4.20602 + 5.67342I −3.27196 − 9.52092I
u = 0.291928 + 0.912894I
a = 2.44781 − 0.82708I
b = 0.202872 − 0.295939I
4.20602 + 5.67342I −3.27196 − 9.52092I
u = 0.291928 + 0.912894I
a = −2.64877 + 0.23577I
b = −1.40897 + 0.65324I
4.20602 + 1.61366I −3.27196 − 2.59272I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.291928 − 0.912894I
a = −0.220592 + 0.354150I
b = −0.019177 − 1.253670I
4.20602 − 1.61366I −3.27196 + 2.59272I
u = 0.291928 − 0.912894I
a = −0.91060 + 1.59867I
b = −1.14023 + 1.89433I
4.20602 − 5.67342I −3.27196 + 9.52092I
u = 0.291928 − 0.912894I
a = 2.44781 + 0.82708I
b = 0.202872 + 0.295939I
4.20602 − 5.67342I −3.27196 + 9.52092I
u = 0.291928 − 0.912894I
a = −2.64877 − 0.23577I
b = −1.40897 − 0.65324I
4.20602 − 1.61366I −3.27196 + 2.59272I
u = −0.818708 + 0.441278I
a = −0.039565 − 0.832252I
b = 0.397332 − 1.073180I
3.53182 + 1.78757I −0.90509 − 1.30321I
u = −0.818708 + 0.441278I
a = 0.672165 − 0.422997I
b = −0.251374 + 0.390044I
3.53182 + 1.78757I −0.90509 − 1.30321I
u = −0.818708 + 0.441278I
a = −1.178310 + 0.360965I
b = −1.051790 − 0.751216I
3.53182 − 2.27220I −0.90509 + 5.62499I
u = −0.818708 + 0.441278I
a = −0.225066 − 0.281188I
b = 0.387199 + 0.966382I
3.53182 − 2.27220I −0.90509 + 5.62499I
u = −0.818708 − 0.441278I
a = −0.039565 + 0.832252I
b = 0.397332 + 1.073180I
3.53182 − 1.78757I −0.90509 + 1.30321I
u = −0.818708 − 0.441278I
a = 0.672165 + 0.422997I
b = −0.251374 − 0.390044I
3.53182 − 1.78757I −0.90509 + 1.30321I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.818708 − 0.441278I
a = −1.178310 − 0.360965I
b = −1.051790 + 0.751216I
3.53182 + 2.27220I −0.90509 − 5.62499I
u = −0.818708 − 0.441278I
a = −0.225066 + 0.281188I
b = 0.387199 − 0.966382I
3.53182 + 2.27220I −0.90509 − 5.62499I
u = −0.891676
a = −0.117329 + 0.410774I
b = −0.598534 − 0.671802I
2.74589 − 2.02988I −6.46536 + 3.46410I
u = −0.891676
a = −0.117329 − 0.410774I
b = −0.598534 + 0.671802I
2.74589 + 2.02988I −6.46536 − 3.46410I
u = −0.891676
a = −0.242167 + 0.211893I
b = 0.429079 + 0.965307I
2.74589 − 2.02988I −6.46536 + 3.46410I
u = −0.891676
a = −0.242167 − 0.211893I
b = 0.429079 − 0.965307I
2.74589 + 2.02988I −6.46536 − 3.46410I
u = 0.149725 + 0.869141I
a = 0.81554 + 1.25207I
b = 0.114962 − 0.915174I
−2.09915 − 1.13039I −3.50947 − 3.70955I
u = 0.149725 + 0.869141I
a = 0.46776 + 2.16783I
b = 0.73674 + 2.30931I
−2.09915 + 2.92938I −3.50947 − 10.63776I
u = 0.149725 + 0.869141I
a = 2.77923 − 0.62877I
b = 1.77875 − 0.93339I
−2.09915 − 1.13039I −3.50947 − 3.70955I
u = 0.149725 + 0.869141I
a = −2.80494 + 0.63368I
b = −0.082692 + 0.254969I
−2.09915 + 2.92938I −3.50947 − 10.63776I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.149725 − 0.869141I
a = 0.81554 − 1.25207I
b = 0.114962 + 0.915174I
−2.09915 + 1.13039I −3.50947 + 3.70955I
u = 0.149725 − 0.869141I
a = 0.46776 − 2.16783I
b = 0.73674 − 2.30931I
−2.09915 − 2.92938I −3.50947 + 10.63776I
u = 0.149725 − 0.869141I
a = 2.77923 + 0.62877I
b = 1.77875 + 0.93339I
−2.09915 + 1.13039I −3.50947 + 3.70955I
u = 0.149725 − 0.869141I
a = −2.80494 − 0.63368I
b = −0.082692 − 0.254969I
−2.09915 − 2.92938I −3.50947 + 10.63776I
u = −0.220472 + 1.164690I
a = −0.008805 + 1.119850I
b = −0.188691 − 0.182477I
−4.71423 + 0.51291I −15.7339 + 0.6888I
u = −0.220472 + 1.164690I
a = 1.67811 − 0.10742I
b = 1.55646 + 0.07761I
−4.71423 + 0.51291I −15.7339 + 0.I
u = −0.220472 + 1.164690I
a = −1.83754 − 0.95066I
b = −1.52331 − 1.65289I
−4.71423 − 3.54686I −15.7339 + 7.6170I
u = −0.220472 + 1.164690I
a = 1.87967 − 1.00121I
b = 0.748609 + 0.520804I
−4.71423 − 3.54686I −15.7339 + 7.6170I
u = −0.220472 − 1.164690I
a = −0.008805 − 1.119850I
b = −0.188691 + 0.182477I
−4.71423 − 0.51291I −15.7339 − 0.6888I
u = −0.220472 − 1.164690I
a = 1.67811 + 0.10742I
b = 1.55646 − 0.07761I
−4.71423 − 0.51291I −15.7339 + 0.I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220472 − 1.164690I
a = −1.83754 + 0.95066I
b = −1.52331 + 1.65289I
−4.71423 + 3.54686I −15.7339 − 7.6170I
u = −0.220472 − 1.164690I
a = 1.87967 + 1.00121I
b = 0.748609 − 0.520804I
−4.71423 + 3.54686I −15.7339 − 7.6170I
u = −1.190060 + 0.051071I
a = −0.471853 − 0.295670I
b = −0.694431 − 1.035650I
4.78890 − 4.41485I 3.36478 + 7.76487I
u = −1.190060 + 0.051071I
a = 0.356859 − 0.397473I
b = 0.626117 − 1.069100I
4.78890 − 0.35509I 3.36478 + 0.83667I
u = −1.190060 + 0.051071I
a = 0.277507 − 0.061145I
b = −0.286132 + 0.813028I
4.78890 − 0.35509I 3.36478 + 0.83667I
u = −1.190060 + 0.051071I
a = −0.242505 − 0.024398I
b = 0.302671 + 0.869252I
4.78890 − 4.41485I 3.36478 + 7.76487I
u = −1.190060 − 0.051071I
a = −0.471853 + 0.295670I
b = −0.694431 + 1.035650I
4.78890 + 4.41485I 3.36478 − 7.76487I
u = −1.190060 − 0.051071I
a = 0.356859 + 0.397473I
b = 0.626117 + 1.069100I
4.78890 + 0.35509I 3.36478 − 0.83667I
u = −1.190060 − 0.051071I
a = 0.277507 + 0.061145I
b = −0.286132 − 0.813028I
4.78890 + 0.35509I 3.36478 − 0.83667I
u = −1.190060 − 0.051071I
a = −0.242505 + 0.024398I
b = 0.302671 − 0.869252I
4.78890 + 4.41485I 3.36478 − 7.76487I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302753 + 0.680971I
a = −0.247478 − 1.106090I
b = −0.76389 − 1.50753I
4.86810 + 1.19187I −1.39665 − 6.55222I
u = 0.302753 + 0.680971I
a = 0.407661 − 1.153260I
b = 0.174799 + 1.043930I
4.86810 − 2.86790I −1.39665 + 0.37598I
u = 0.302753 + 0.680971I
a = 2.38187 − 0.58803I
b = 0.117023 − 0.473198I
4.86810 + 1.19187I −1.39665 − 6.55222I
u = 0.302753 + 0.680971I
a = −2.94201 + 0.15189I
b = −1.56673 + 0.50663I
4.86810 − 2.86790I −1.39665 + 0.37598I
u = 0.302753 − 0.680971I
a = −0.247478 + 1.106090I
b = −0.76389 + 1.50753I
4.86810 − 1.19187I −1.39665 + 6.55222I
u = 0.302753 − 0.680971I
a = 0.407661 + 1.153260I
b = 0.174799 − 1.043930I
4.86810 + 2.86790I −1.39665 − 0.37598I
u = 0.302753 − 0.680971I
a = 2.38187 + 0.58803I
b = 0.117023 + 0.473198I
4.86810 − 1.19187I −1.39665 + 6.55222I
u = 0.302753 − 0.680971I
a = −2.94201 − 0.15189I
b = −1.56673 − 0.50663I
4.86810 + 2.86790I −1.39665 − 0.37598I
u = −0.398348 + 1.237590I
a = −1.089300 − 0.011224I
b = −0.878929 − 0.257055I
−1.22803 − 2.46934I −8.00000 + 0.I
u = −0.398348 + 1.237590I
a = −1.50729 + 0.46745I
b = −0.861802 − 0.773540I
−1.22803 − 6.52911I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.398348 + 1.237590I
a = 0.201511 − 0.345827I
b = 0.220437 + 0.358276I
−1.22803 − 2.46934I −8.00000 + 0.I
u = −0.398348 + 1.237590I
a = 1.64197 + 0.47992I
b = 1.27871 + 1.29320I
−1.22803 − 6.52911I 0
u = −0.398348 − 1.237590I
a = −1.089300 + 0.011224I
b = −0.878929 + 0.257055I
−1.22803 + 2.46934I −8.00000 + 0.I
u = −0.398348 − 1.237590I
a = −1.50729 − 0.46745I
b = −0.861802 + 0.773540I
−1.22803 + 6.52911I 0
u = −0.398348 − 1.237590I
a = 0.201511 + 0.345827I
b = 0.220437 − 0.358276I
−1.22803 + 2.46934I −8.00000 + 0.I
u = −0.398348 − 1.237590I
a = 1.64197 − 0.47992I
b = 1.27871 − 1.29320I
−1.22803 + 6.52911I 0
u = 0.332931 + 0.577334I
a = 0.108408 + 0.696345I
b = 0.76800 + 1.28459I
3.27963 − 4.60146I −3.62959 − 1.24713I
u = 0.332931 + 0.577334I
a = −0.75982 + 1.30663I
b = −0.231941 − 1.021460I
3.27963 − 8.66122I −3.62959 + 5.68107I
u = 0.332931 + 0.577334I
a = −2.36545 + 0.61202I
b = −0.120017 + 0.576649I
3.27963 − 4.60146I −3.62959 − 1.24713I
u = 0.332931 + 0.577334I
a = 3.02142 − 0.00615I
b = 1.51983 − 0.47033I
3.27963 − 8.66122I −3.62959 + 5.68107I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.332931 − 0.577334I
a = 0.108408 − 0.696345I
b = 0.76800 − 1.28459I
3.27963 + 4.60146I −3.62959 + 1.24713I
u = 0.332931 − 0.577334I
a = −0.75982 − 1.30663I
b = −0.231941 + 1.021460I
3.27963 + 8.66122I −3.62959 − 5.68107I
u = 0.332931 − 0.577334I
a = −2.36545 − 0.61202I
b = −0.120017 − 0.576649I
3.27963 + 4.60146I −3.62959 + 1.24713I
u = 0.332931 − 0.577334I
a = 3.02142 + 0.00615I
b = 1.51983 + 0.47033I
3.27963 + 8.66122I −3.62959 − 5.68107I
u = −0.297124 + 1.357320I
a = −0.598970 + 0.626647I
b = −0.326366 − 0.255348I
−3.21957 − 6.47968I 0
u = −0.297124 + 1.357320I
a = 1.245450 + 0.363321I
b = 1.116150 + 0.632073I
−3.21957 − 6.47968I 0
u = −0.297124 + 1.357320I
a = −1.37775 − 0.67422I
b = −1.09901 − 1.49436I
−3.21957 − 10.53940I 0
u = −0.297124 + 1.357320I
a = 1.91185 − 0.38063I
b = 1.030370 + 0.622017I
−3.21957 − 10.53940I 0
u = −0.297124 − 1.357320I
a = −0.598970 − 0.626647I
b = −0.326366 + 0.255348I
−3.21957 + 6.47968I 0
u = −0.297124 − 1.357320I
a = 1.245450 − 0.363321I
b = 1.116150 − 0.632073I
−3.21957 + 6.47968I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.297124 − 1.357320I
a = −1.37775 + 0.67422I
b = −1.09901 + 1.49436I
−3.21957 + 10.53940I 0
u = −0.297124 − 1.357320I
a = 1.91185 + 0.38063I
b = 1.030370 − 0.622017I
−3.21957 + 10.53940I 0
u = −0.45484 + 1.37508I
a = −0.862383 − 0.321092I
b = −0.713383 − 0.653883I
−1.64738 − 2.69431I 0
u = −0.45484 + 1.37508I
a = 0.663793 − 0.253155I
b = 0.389845 + 0.356252I
−1.64738 − 2.69431I 0
u = −0.45484 + 1.37508I
a = 1.316960 + 0.363578I
b = 1.00604 + 1.26785I
−1.64738 − 6.75407I 0
u = −0.45484 + 1.37508I
a = −1.71498 + 0.09553I
b = −1.102030 − 0.838840I
−1.64738 − 6.75407I 0
u = −0.45484 − 1.37508I
a = −0.862383 + 0.321092I
b = −0.713383 + 0.653883I
−1.64738 + 2.69431I 0
u = −0.45484 − 1.37508I
a = 0.663793 + 0.253155I
b = 0.389845 − 0.356252I
−1.64738 + 2.69431I 0
u = −0.45484 − 1.37508I
a = 1.316960 − 0.363578I
b = 1.00604 − 1.26785I
−1.64738 + 6.75407I 0
u = −0.45484 − 1.37508I
a = −1.71498 − 0.09553I
b = −1.102030 + 0.838840I
−1.64738 + 6.75407I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.63185 + 1.30721I
a = −0.992305 − 0.020078I
b = −0.759553 − 1.110260I
0.96708 − 6.00374I 0
u = −0.63185 + 1.30721I
a = −0.858500 + 0.107627I
b = −0.435140 − 0.309198I
0.96708 − 1.94398I 0
u = −0.63185 + 1.30721I
a = 0.338686 + 0.454279I
b = 0.277377 + 0.816791I
0.96708 − 1.94398I 0
u = −0.63185 + 1.30721I
a = 1.73884 + 0.18930I
b = 1.27802 + 0.99309I
0.96708 − 6.00374I 0
u = −0.63185 − 1.30721I
a = −0.992305 + 0.020078I
b = −0.759553 + 1.110260I
0.96708 + 6.00374I 0
u = −0.63185 − 1.30721I
a = −0.858500 − 0.107627I
b = −0.435140 + 0.309198I
0.96708 + 1.94398I 0
u = −0.63185 − 1.30721I
a = 0.338686 − 0.454279I
b = 0.277377 − 0.816791I
0.96708 + 1.94398I 0
u = −0.63185 − 1.30721I
a = 1.73884 − 0.18930I
b = 1.27802 − 0.99309I
0.96708 + 6.00374I 0
u = −0.61552 + 1.38013I
a = 1.022350 + 0.159585I
b = 0.79145 + 1.18081I
0.41135 − 10.76760I 0
u = −0.61552 + 1.38013I
a = 0.852380 − 0.139543I
b = 0.437610 + 0.336679I
0.41135 − 6.70787I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.61552 + 1.38013I
a = −0.487473 − 0.510340I
b = −0.401949 − 0.865561I
0.41135 − 6.70787I 0
u = −0.61552 + 1.38013I
a = −1.76762 − 0.15066I
b = −1.26731 − 0.94725I
0.41135 − 10.76760I 0
u = −0.61552 − 1.38013I
a = 1.022350 − 0.159585I
b = 0.79145 − 1.18081I
0.41135 + 10.76760I 0
u = −0.61552 − 1.38013I
a = 0.852380 + 0.139543I
b = 0.437610 − 0.336679I
0.41135 + 6.70787I 0
u = −0.61552 − 1.38013I
a = −0.487473 + 0.510340I
b = −0.401949 + 0.865561I
0.41135 + 6.70787I 0
u = −0.61552 − 1.38013I
a = −1.76762 + 0.15066I
b = −1.26731 + 0.94725I
0.41135 + 10.76760I 0
u = −0.106889
a = 8.36050 + 2.31316I
b = −0.274582 + 0.980651I
−1.58088 + 2.02988I −7.94876 − 3.46410I
u = −0.106889
a = 8.36050 − 2.31316I
b = −0.274582 − 0.980651I
−1.58088 − 2.02988I −7.94876 + 3.46410I
u = −0.106889
a = −1.64586 + 9.31693I
b = 0.922993 + 0.142430I
−1.58088 + 2.02988I −7.94876 − 3.46410I
u = −0.106889
a = −1.64586 − 9.31693I
b = 0.922993 − 0.142430I
−1.58088 − 2.02988I −7.94876 + 3.46410I
26
III. I
u
3
= h2.06 × 10
15
u
35
+ 3.18 × 10
16
u
34
+ · · · + 1.33 × 10
16
b + 3.93 ×
10
16
, −2.49 × 10
16
u
35
− 3.52 × 10
17
u
34
+ · · · + 9.34 × 10
16
a − 1.32 ×
10
18
, u
36
+ 15u
35
+ · · · + 100u + 7i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
4
=
0.266446u
35
+ 3.77319u
34
+ ··· + 184.155u + 14.1541
−0.154233u
35
− 2.38276u
34
+ ··· − 24.9690u − 2.94475
a
12
=
u
u
a
5
=
0.197179u
35
+ 2.85858u
34
+ ··· + 196.634u + 15.2337
−0.223499u
35
− 3.29737u
34
+ ··· − 12.4905u − 1.86512
a
3
=
0.167336u
35
+ 2.43145u
34
+ ··· + 179.671u + 12.7738
−0.132564u
35
− 1.85500u
34
+ ··· − 11.1723u − 1.93041
a
7
=
0.282905u
35
+ 4.39197u
34
+ ··· + 74.1899u + 1.80195
−0.220213u
35
− 2.93459u
34
+ ··· − 45.9880u − 3.52183
a
1
=
−0.177239u
35
− 2.87128u
34
+ ··· − 136.709u − 10.2763
0.184217u
35
+ 2.73494u
34
+ ··· + 41.2970u + 4.07168
a
10
=
−0.196470u
35
− 2.98273u
34
+ ··· − 59.8797u − 0.201969
0.455045u
35
+ 6.44441u
34
+ ··· + 33.8097u + 2.14148
a
6
=
−0.184369u
35
− 2.58115u
34
+ ··· − 91.7208u − 13.6079
−0.689759u
35
− 9.66523u
34
+ ··· − 41.5981u − 1.85154
a
2
=
0.448887u
35
+ 6.26839u
34
+ ··· − 84.0461u − 13.8570
0.317953u
35
+ 4.14359u
34
+ ··· − 38.5208u − 1.96386
(ii) Obstruction class = 1
(iii) Cusp Shapes =
−
18462614986414268
13336038075042241
u
35
−
18237280252242258
1025849082695557
u
34
+···+
4166442410187511668
13336038075042241
u+
335464906964536671
13336038075042241
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
− 20u
35
+ ··· − 286u + 9
c
2
u
36
+ 8u
35
+ ··· − 2u + 3
c
3
, c
10
u
36
+ 6u
34
+ ··· − 16u + 7
c
4
, c
7
u
36
+ 2u
34
+ ··· + 2u + 1
c
5
u
36
− 8u
35
+ ··· + 2u + 3
c
6
, c
9
u
36
− 4u
35
+ ··· − 7u + 1
c
8
u
36
+ 15u
35
+ ··· + 100u + 7
c
11
u
36
− 15u
35
+ ··· − 100u + 7
c
12
u
36
− 11u
35
+ ··· − 29u + 7
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 4y
35
+ ··· − 15214y + 81
c
2
, c
5
y
36
− 20y
35
+ ··· − 286y + 9
c
3
, c
10
y
36
+ 12y
35
+ ··· + 444y + 49
c
4
, c
7
y
36
+ 4y
35
+ ··· + 18y + 1
c
6
, c
9
y
36
+ 20y
35
+ ··· + 67y + 1
c
8
, c
11
y
36
+ 29y
35
+ ··· + 2040y + 49
c
12
y
36
+ 5y
35
+ ··· + 909y + 49
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.996191 + 0.247442I
a = 0.242980 − 0.063848I
b = 0.485840 + 0.921857I
3.78449 − 0.74247I −1.56067 + 1.04603I
u = −0.996191 − 0.247442I
a = 0.242980 + 0.063848I
b = 0.485840 − 0.921857I
3.78449 + 0.74247I −1.56067 − 1.04603I
u = 0.202230 + 0.888062I
a = −2.05913 − 0.33443I
b = −0.818069 − 0.973002I
2.13905 + 10.41710I −7.77869 − 5.57290I
u = 0.202230 − 0.888062I
a = −2.05913 + 0.33443I
b = −0.818069 + 0.973002I
2.13905 − 10.41710I −7.77869 + 5.57290I
u = −0.721359 + 0.483077I
a = −0.622746 + 0.296070I
b = −0.524683 − 0.936490I
3.06329 − 5.44861I −2.75970 + 7.29994I
u = −0.721359 − 0.483077I
a = −0.622746 − 0.296070I
b = −0.524683 + 0.936490I
3.06329 + 5.44861I −2.75970 − 7.29994I
u = 0.002544 + 0.862070I
a = −1.99921 − 0.20416I
b = −0.752089 − 1.072900I
−2.41296 + 1.98163I −9.73483 − 4.24965I
u = 0.002544 − 0.862070I
a = −1.99921 + 0.20416I
b = −0.752089 + 1.072900I
−2.41296 − 1.98163I −9.73483 + 4.24965I
u = 0.173271 + 0.826969I
a = 2.09954 + 0.30039I
b = 0.783444 + 0.972000I
4.10139 + 4.56262I −5.09667 − 1.69067I
u = 0.173271 − 0.826969I
a = 2.09954 − 0.30039I
b = 0.783444 − 0.972000I
4.10139 − 4.56262I −5.09667 + 1.69067I
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.012059 + 1.195300I
a = 0.650787 + 0.463736I
b = 0.152926 + 0.596698I
−3.52475 − 2.14811I −12.69778 + 0.I
u = −0.012059 − 1.195300I
a = 0.650787 − 0.463736I
b = 0.152926 − 0.596698I
−3.52475 + 2.14811I −12.69778 + 0.I
u = −1.074470 + 0.525760I
a = 0.073188 + 0.396115I
b = −0.646081 + 0.637192I
2.85779 − 1.66915I 0
u = −1.074470 − 0.525760I
a = 0.073188 − 0.396115I
b = −0.646081 − 0.637192I
2.85779 + 1.66915I 0
u = −1.193700 + 0.152435I
a = −0.001017 − 0.185478I
b = 0.461093 − 0.779359I
3.83728 + 3.26733I 0
u = −1.193700 − 0.152435I
a = −0.001017 + 0.185478I
b = 0.461093 + 0.779359I
3.83728 − 3.26733I 0
u = −0.672566 + 0.999759I
a = 0.929796 − 0.910897I
b = 1.47756 + 0.19852I
−8.48858 − 2.70245I −70.7021 − 38.7120I
u = −0.672566 − 0.999759I
a = 0.929796 + 0.910897I
b = 1.47756 − 0.19852I
−8.48858 + 2.70245I −70.7021 + 38.7120I
u = −0.565558 + 1.258000I
a = −0.732745 + 0.020751I
b = −0.567765 − 0.504742I
−0.91986 − 3.39116I 0
u = −0.565558 − 1.258000I
a = −0.732745 − 0.020751I
b = −0.567765 + 0.504742I
−0.91986 + 3.39116I 0
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629437 + 1.227540I
a = −1.244920 + 0.043396I
b = −0.996744 − 0.895845I
0.35014 − 4.53280I 0
u = −0.629437 − 1.227540I
a = −1.244920 − 0.043396I
b = −0.996744 + 0.895845I
0.35014 + 4.53280I 0
u = −0.412167 + 1.324670I
a = −1.57926 − 0.12584I
b = −1.05789 − 1.08667I
−1.76384 − 9.52413I 0
u = −0.412167 − 1.324670I
a = −1.57926 + 0.12584I
b = −1.05789 + 1.08667I
−1.76384 + 9.52413I 0
u = −0.61022 + 1.32214I
a = 1.327960 + 0.097645I
b = 0.987584 + 1.001710I
0.14432 − 9.54443I 0
u = −0.61022 − 1.32214I
a = 1.327960 − 0.097645I
b = 0.987584 − 1.001710I
0.14432 + 9.54443I 0
u = −0.47918 + 1.37850I
a = 1.49042 + 0.16195I
b = 1.03015 + 1.06924I
−1.09440 − 5.99264I 0
u = −0.47918 − 1.37850I
a = 1.49042 − 0.16195I
b = 1.03015 − 1.06924I
−1.09440 + 5.99264I 0
u = −0.013410 + 0.529874I
a = 2.36343 − 0.26906I
b = 0.617859 + 0.941163I
4.65001 − 0.00873I −2.39720 − 0.09706I
u = −0.013410 − 0.529874I
a = 2.36343 + 0.26906I
b = 0.617859 − 0.941163I
4.65001 + 0.00873I −2.39720 + 0.09706I
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.098035 + 0.188990I
a = −3.10186 + 3.29731I
b = −0.541261 − 0.894912I
3.08017 − 5.69957I −4.85575 + 6.84399I
u = −0.098035 − 0.188990I
a = −3.10186 − 3.29731I
b = −0.541261 + 0.894912I
3.08017 + 5.69957I −4.85575 − 6.84399I
u = −0.35277 + 1.80568I
a = −0.402295 − 0.126543I
b = −0.269426 − 0.301712I
0.52226 − 2.86902I 0
u = −0.35277 − 1.80568I
a = −0.402295 + 0.126543I
b = −0.269426 + 0.301712I
0.52226 + 2.86902I 0
u = −0.04692 + 1.85264I
a = 0.350804 + 0.225457I
b = 0.177550 + 0.325681I
−0.45621 − 7.92269I 0
u = −0.04692 − 1.85264I
a = 0.350804 − 0.225457I
b = 0.177550 − 0.325681I
−0.45621 + 7.92269I 0
33
IV. I
u
4
= h−8a
3
u − 3a
2
u + · · · − 37a + 41, −a
3
u − 3a
2
u + · · · − a + 3, u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
1
a
4
=
a
0.160000a
3
u + 0.0600000a
2
u + ··· + 0.740000a − 0.820000
a
12
=
u
u
a
5
=
0.160000a
3
u + 0.0600000a
2
u + ··· + 0.740000a − 0.820000
0.320000a
3
u + 0.120000a
2
u + ··· + 0.480000a − 1.64000
a
3
=
0.160000a
3
u + 0.0600000a
2
u + ··· + 0.740000a − 0.820000
0.320000a
3
u + 0.120000a
2
u + ··· + 0.480000a − 1.64000
a
7
=
−0.0200000a
3
u + 0.180000a
2
u + ··· + 0.220000a + 1.04000
0.260000a
3
u + 0.660000a
2
u + ··· + 1.14000a + 0.480000
a
1
=
−0.120000a
3
u − 0.420000a
2
u + ··· − 1.18000a − 0.260000
−0.400000a
3
u − 0.900000a
2
u + ··· − 2.10000a + 0.300000
a
10
=
0.180000a
3
u + 0.380000a
2
u + ··· + 0.0200000a + 0.640000
0.220000a
3
u + 0.0200000a
2
u + ··· − 0.420000a + 0.560000
a
6
=
0.120000a
3
u + 0.420000a
2
u + ··· + 1.18000a + 0.260000
2
5
a
3
u +
9
10
a
2
u + ··· +
21
10
a −
3
10
a
2
=
0.0400000a
3
u − 0.360000a
2
u + ··· − 0.440000a − 1.08000
−0.0800000a
3
u − 0.780000a
2
u + ··· − 1.62000a − 1.34000
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4
25
a
3
u +
28
25
a
3
−
36
25
a
2
u +
48
25
a
2
−
92
25
au −
44
25
a +
56
25
u −
408
25
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
10
u
8
+ u
6
+ 2u
5
+ 2u
4
− 2u
3
+ 6u
2
− 2u + 1
c
4
, c
7
u
8
+ 2u
7
+ u
6
+ 2u
5
+ 6u
4
+ 4u
3
− 2u
2
− 2u + 1
c
5
(u + 1)
8
c
6
, c
9
(u
4
− u
2
+ 1)
2
c
8
, c
11
(u
2
+ 1)
4
c
12
(u
2
+ u + 1)
4
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
8
c
3
, c
10
y
8
+ 2y
7
+ 5y
6
+ 12y
5
+ 26y
4
+ 30y
3
+ 32y
2
+ 8y + 1
c
4
, c
7
y
8
− 2y
7
+ 5y
6
− 12y
5
+ 26y
4
− 30y
3
+ 32y
2
− 8y + 1
c
6
, c
9
(y
2
− y + 1)
4
c
8
, c
11
(y + 1)
8
c
12
(y
2
+ y + 1)
4
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.144860 + 0.022144I
b = 0.76652 − 1.24437I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = 1.000000I
a = −0.746378 + 0.279522I
b = −0.916440 + 0.695963I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = 1.000000I
a = 1.11240 + 1.08650I
b = 0.416440 + 0.170063I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = 1.000000I
a = −2.51089 − 0.38817I
b = −1.266520 + 0.378347I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = − 1.000000I
a = 1.144860 − 0.022144I
b = 0.76652 + 1.24437I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = − 1.000000I
a = −0.746378 − 0.279522I
b = −0.916440 − 0.695963I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = − 1.000000I
a = 1.11240 − 1.08650I
b = 0.416440 − 0.170063I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = − 1.000000I
a = −2.51089 + 0.38817I
b = −1.266520 − 0.378347I
−3.28987 − 2.02988I −14.0000 + 3.4641I
37
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
30
+ 13u
29
+ ··· + 8u + 1)
4
(u
36
− 20u
35
+ ··· − 286u + 9)
· (u
66
+ 31u
65
+ ··· + 17676u + 2704)
c
2
((u − 1)
8
)(u
30
− 3u
29
+ ··· + 6u − 1)
4
(u
36
+ 8u
35
+ ··· − 2u + 3)
· (u
66
+ 13u
65
+ ··· − 738u − 52)
c
3
, c
10
(u
8
+ u
6
+ ··· − 2u + 1)(u
36
+ 6u
34
+ ··· − 16u + 7)
· (u
66
+ 13u
64
+ ··· + 37u − 181)
· (u
120
− u
119
+ ··· − 971506096u + 277703647)
c
4
, c
7
(u
8
+ 2u
7
+ u
6
+ 2u
5
+ 6u
4
+ 4u
3
− 2u
2
− 2u + 1)
· (u
36
+ 2u
34
+ ··· + 2u + 1)(u
66
− 15u
64
+ ··· − u − 1)
· (u
120
+ 7u
119
+ ··· − 34u + 7)
c
5
((u + 1)
8
)(u
30
− 3u
29
+ ··· + 6u − 1)
4
(u
36
− 8u
35
+ ··· + 2u + 3)
· (u
66
+ 13u
65
+ ··· − 738u − 52)
c
6
, c
9
((u
4
− u
2
+ 1)
2
)(u
36
− 4u
35
+ ··· − 7u + 1)(u
66
+ 2u
65
+ ··· + 5u + 2)
· (u
120
+ 9u
119
+ ··· + 1147452u + 251797)
c
8
((u
2
+ 1)
4
)(u
30
− 9u
29
+ ··· − 14u + 1)
4
(u
36
+ 15u
35
+ ··· + 100u + 7)
· (u
66
+ 26u
65
+ ··· + 29690u + 1300)
c
11
((u
2
+ 1)
4
)(u
30
− 9u
29
+ ··· − 14u + 1)
4
(u
36
− 15u
35
+ ··· − 100u + 7)
· (u
66
+ 26u
65
+ ··· + 29690u + 1300)
c
12
((u
2
− u + 1)
60
)(u
2
+ u + 1)
4
(u
36
− 11u
35
+ ··· − 29u + 7)
· (u
66
+ 56u
65
+ ··· + 17045651456u + 536870912)
38
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
8
)(y
30
+ 11y
29
+ ··· − 52y + 1)
4
· (y
36
+ 4y
35
+ ··· − 15214y + 81)
· (y
66
+ 17y
65
+ ··· − 505176688y + 7311616)
c
2
, c
5
((y − 1)
8
)(y
30
− 13y
29
+ ··· − 8y + 1)
4
(y
36
− 20y
35
+ ··· − 286y + 9)
· (y
66
− 31y
65
+ ··· − 17676y + 2704)
c
3
, c
10
(y
8
+ 2y
7
+ 5y
6
+ 12y
5
+ 26y
4
+ 30y
3
+ 32y
2
+ 8y + 1)
· (y
36
+ 12y
35
+ ··· + 444y + 49)(y
66
+ 26y
65
+ ··· + 13111y + 32761)
· (y
120
+ 41y
119
+ ··· + 4660341483603865276y + 77119315557100609)
c
4
, c
7
(y
8
− 2y
7
+ 5y
6
− 12y
5
+ 26y
4
− 30y
3
+ 32y
2
− 8y + 1)
· (y
36
+ 4y
35
+ ··· + 18y + 1)(y
66
− 30y
65
+ ··· − 51y + 1)
· (y
120
+ 25y
119
+ ··· + 3884y + 49)
c
6
, c
9
((y
2
− y + 1)
4
)(y
36
+ 20y
35
+ ··· + 67y + 1)(y
66
− 2y
65
+ ··· + 43y + 4)
· (y
120
+ 51y
119
+ ··· + 3713334879894y + 63401729209)
c
8
, c
11
((y + 1)
8
)(y
30
+ 19y
29
+ ··· − 76y + 1)
4
· (y
36
+ 29y
35
+ ··· + 2040y + 49)
· (y
66
+ 46y
65
+ ··· + 26109300y + 1690000)
c
12
((y
2
+ y + 1)
64
)(y
36
+ 5y
35
+ ··· + 909y + 49)
· (y
66
+ 6y
65
+ ··· − 1242993497154256896y + 288230376151711744)
39
