12a
1193
(K12a
1193
)
A knot diagram
1
Linearized knot diagam
4 10 11 9 12 2 3 1 6 7 8 5
Solving Sequence
5,9 1,4
2 8 12 6 7 10 11 3
c
4
c
1
c
8
c
12
c
5
c
6
c
9
c
11
c
3
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.94312 × 10
80
u
49
− 2.48619 × 10
79
u
48
+ ··· + 7.87680 × 10
79
b + 1.28241 × 10
80
, a − 1,
u
50
+ 5u
48
+ ··· + 5u + 1i
I
u
2
= h1.63014 × 10
1735
u
155
− 9.72983 × 10
1735
u
154
+ ··· + 1.03065 × 10
1738
b + 8.61106 × 10
1738
,
1.64322 × 10
1736
u
155
− 2.98949 × 10
1735
u
154
+ ··· + 4.74098 × 10
1739
a + 1.16259 × 10
1741
,
u
156
− 6u
155
+ ··· + 6790u + 1288i
I
u
3
= h−5.51879 × 10
28
u
32
+ 2.59045 × 10
28
u
31
+ ··· + 5.79727 × 10
28
b − 5.00823 × 10
27
, a + 1,
u
33
+ 5u
31
+ ··· + 4u + 1i
I
u
4
= h−484122u
11
− 2829135u
10
+ ··· + 24262754b + 7309133,
19820339u
11
+ 138389241u
10
+ ··· + 48525508a − 191613318,
u
12
+ 7u
11
+ 16u
10
+ 12u
9
+ 9u
8
+ 29u
7
+ 43u
6
+ 6u
5
+ 3u
4
+ 38u
3
+ 7u
2
− 6u + 8i
* 4 irreducible components of dim
C
= 0, with total 251 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
= h1.94 × 10
80
u
49
− 2.49 × 10
79
u
48
+ · · · + 7.88 × 10
79
b + 1.28 ×
10
80
, a − 1, u
50
+ 5u
48
+ · · · + 5u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
1
−2.46689u
49
+ 0.315634u
48
+ ··· − 30.2403u − 1.62809
a
4
=
1
u
2
a
2
=
2.46689u
49
− 0.315634u
48
+ ··· + 30.2403u + 2.62809
−2.59720u
49
+ 0.343485u
48
+ ··· − 31.1290u − 1.31245
a
8
=
−u
−0.315634u
49
− 0.130315u
48
+ ··· − 9.70634u − 2.46689
a
12
=
2.46689u
49
− 0.315634u
48
+ ··· + 30.2403u + 2.62809
−2.46689u
49
+ 0.315634u
48
+ ··· − 30.2403u − 1.62809
a
6
=
0.723740u
49
− 0.524718u
48
+ ··· + 6.95916u − 5.96362
1.74315u
49
+ 0.209084u
48
+ ··· + 23.2812u + 8.59171
a
7
=
1.29977u
49
+ 0.0121696u
48
+ ··· + 13.6811u − 0.964916
−0.327667u
49
− 0.224139u
48
+ ··· − 5.88790u + 1.64958
a
10
=
1.17574u
49
+ 0.670154u
48
+ ··· + 56.3848u + 11.9751
−1.61868u
49
+ 0.605612u
48
+ ··· − 38.8939u − 4.19712
a
11
=
2.16799u
49
− 0.221391u
48
+ ··· + 28.3405u + 2.10337
−1.19112u
49
+ 0.0824317u
48
+ ··· − 20.2477u − 1.18515
a
3
=
−1.17145u
49
− 0.615972u
48
+ ··· − 14.7992u − 4.90764
1.33864u
49
+ 0.700909u
48
+ ··· + 28.4451u + 6.40340
(ii) Obstruction class = −1
(iii) Cusp Shapes = 16.2604u
49
− 4.35079u
48
+ ··· + 259.730u + 13.6919
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
− 37u
49
+ ··· − 1343488u + 65536
c
2
, c
7
u
50
+ u
49
+ ··· + u + 1
c
3
, c
6
u
50
+ u
49
+ ··· + u + 1
c
4
, c
8
u
50
+ 5u
48
+ ··· + 5u + 1
c
5
, c
12
u
50
− 27u
49
+ ··· − 45312u + 2560
c
9
, c
11
u
50
+ 2u
49
+ ··· − 284u + 148
c
10
u
50
+ 33u
49
+ ··· + 3584u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
+ 15y
49
+ ··· + 68719476736y + 4294967296
c
2
, c
7
y
50
− 23y
49
+ ··· − 51y + 1
c
3
, c
6
y
50
+ 5y
49
+ ··· + 29y + 1
c
4
, c
8
y
50
+ 10y
49
+ ··· + 37y + 1
c
5
, c
12
y
50
+ 35y
49
+ ··· + 254345216y + 6553600
c
9
, c
11
y
50
− 12y
49
+ ··· − 46320y + 21904
c
10
y
50
+ 7y
49
+ ··· + 1769472y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.643464 + 0.769213I
a = 1.00000
b = 1.166190 + 0.558776I
4.36390 − 1.77312I 8.40093 + 4.75657I
u = −0.643464 − 0.769213I
a = 1.00000
b = 1.166190 − 0.558776I
4.36390 + 1.77312I 8.40093 − 4.75657I
u = −0.209680 + 0.984180I
a = 1.00000
b = 0.982677 − 0.823149I
−0.65225 + 5.66298I 1.39055 − 3.29167I
u = −0.209680 − 0.984180I
a = 1.00000
b = 0.982677 + 0.823149I
−0.65225 − 5.66298I 1.39055 + 3.29167I
u = 0.111854 + 0.935193I
a = 1.00000
b = 0.014940 − 0.254880I
−2.13721 + 4.98350I −0.46686 − 6.95288I
u = 0.111854 − 0.935193I
a = 1.00000
b = 0.014940 + 0.254880I
−2.13721 − 4.98350I −0.46686 + 6.95288I
u = 0.454709 + 0.811898I
a = 1.00000
b = 0.73450 + 1.36481I
0.29883 + 6.52796I 4.59641 − 9.04204I
u = 0.454709 − 0.811898I
a = 1.00000
b = 0.73450 − 1.36481I
0.29883 − 6.52796I 4.59641 + 9.04204I
u = −0.792910 + 0.423437I
a = 1.00000
b = 1.176340 + 0.218285I
5.47703 − 0.93007I 13.31306 + 3.09237I
u = −0.792910 − 0.423437I
a = 1.00000
b = 1.176340 − 0.218285I
5.47703 + 0.93007I 13.31306 − 3.09237I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.892105 + 0.668186I
a = 1.00000
b = 1.277600 + 0.060374I
6.15364 − 7.17141I 12.2491 + 7.9503I
u = −0.892105 − 0.668186I
a = 1.00000
b = 1.277600 − 0.060374I
6.15364 + 7.17141I 12.2491 − 7.9503I
u = −0.726926 + 0.378293I
a = 1.00000
b = 0.262626 − 1.136960I
−1.59993 − 2.70489I 3.40729 + 2.86854I
u = −0.726926 − 0.378293I
a = 1.00000
b = 0.262626 + 1.136960I
−1.59993 + 2.70489I 3.40729 − 2.86854I
u = 0.727284 + 0.360560I
a = 1.00000
b = 0.620921 + 0.171349I
1.246370 + 0.482488I 7.31465 − 2.33574I
u = 0.727284 − 0.360560I
a = 1.00000
b = 0.620921 − 0.171349I
1.246370 − 0.482488I 7.31465 + 2.33574I
u = 0.909966 + 0.776093I
a = 1.00000
b = 1.241250 − 0.156499I
4.5544 + 15.8113I 0
u = 0.909966 − 0.776093I
a = 1.00000
b = 1.241250 + 0.156499I
4.5544 − 15.8113I 0
u = −0.324125 + 1.157810I
a = 1.00000
b = 0.79105 − 1.25368I
−2.24034 − 12.75630I 0
u = −0.324125 − 1.157810I
a = 1.00000
b = 0.79105 + 1.25368I
−2.24034 + 12.75630I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.952387 + 0.735226I
a = 1.00000
b = 0.892872 − 0.485258I
5.37270 − 1.91715I 0
u = 0.952387 − 0.735226I
a = 1.00000
b = 0.892872 + 0.485258I
5.37270 + 1.91715I 0
u = −0.338470 + 0.671302I
a = 1.00000
b = −0.063362 − 1.273950I
−4.46772 − 0.64019I −2.99722 + 2.10098I
u = −0.338470 − 0.671302I
a = 1.00000
b = −0.063362 + 1.273950I
−4.46772 + 0.64019I −2.99722 − 2.10098I
u = 0.394993 + 0.596716I
a = 1.00000
b = 0.933205 + 0.993015I
2.14090 + 1.30641I 7.07669 − 7.35081I
u = 0.394993 − 0.596716I
a = 1.00000
b = 0.933205 − 0.993015I
2.14090 − 1.30641I 7.07669 + 7.35081I
u = 1.026820 + 0.792152I
a = 1.00000
b = −0.027990 + 0.832206I
0.92663 − 2.16938I 0
u = 1.026820 − 0.792152I
a = 1.00000
b = −0.027990 − 0.832206I
0.92663 + 2.16938I 0
u = 0.641768 + 1.157350I
a = 1.00000
b = 0.186450 + 1.239270I
−6.86303 − 3.75834I 0
u = 0.641768 − 1.157350I
a = 1.00000
b = 0.186450 − 1.239270I
−6.86303 + 3.75834I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.901999 + 1.045100I
a = 1.00000
b = 0.293959 − 1.351620I
−3.65978 − 3.90185I 0
u = −0.901999 − 1.045100I
a = 1.00000
b = 0.293959 + 1.351620I
−3.65978 + 3.90185I 0
u = 1.000200 + 0.965591I
a = 1.00000
b = 0.62065 + 1.29063I
2.08227 + 7.18268I 0
u = 1.000200 − 0.965591I
a = 1.00000
b = 0.62065 − 1.29063I
2.08227 − 7.18268I 0
u = −0.84268 + 1.17438I
a = 1.00000
b = 0.057255 − 1.186230I
−5.01603 − 5.20693I 0
u = −0.84268 − 1.17438I
a = 1.00000
b = 0.057255 + 1.186230I
−5.01603 + 5.20693I 0
u = 0.94208 + 1.19268I
a = 1.00000
b = 0.694329 + 1.176010I
2.17532 + 8.34585I 0
u = 0.94208 − 1.19268I
a = 1.00000
b = 0.694329 − 1.176010I
2.17532 − 8.34585I 0
u = −0.195613 + 0.426357I
a = 1.00000
b = −0.216338 + 0.544332I
0.50466 + 1.79559I 3.46378 − 3.10051I
u = −0.195613 − 0.426357I
a = 1.00000
b = −0.216338 − 0.544332I
0.50466 − 1.79559I 3.46378 + 3.10051I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.015924 + 0.425046I
a = 1.00000
b = 0.06103 + 1.82231I
−2.19516 − 9.28833I −7.03273 + 5.74266I
u = −0.015924 − 0.425046I
a = 1.00000
b = 0.06103 − 1.82231I
−2.19516 + 9.28833I −7.03273 − 5.74266I
u = 1.07924 + 1.18155I
a = 1.00000
b = 0.62297 + 1.37503I
2.04993 + 13.72580I 0
u = 1.07924 − 1.18155I
a = 1.00000
b = 0.62297 − 1.37503I
2.04993 − 13.72580I 0
u = −1.12239 + 1.17529I
a = 1.00000
b = 0.584184 − 1.132490I
3.25548 − 3.52615I 0
u = −1.12239 − 1.17529I
a = 1.00000
b = 0.584184 + 1.132490I
3.25548 + 3.52615I 0
u = −1.10707 + 1.25249I
a = 1.00000
b = 0.63231 − 1.34103I
0.8116 − 22.3107I 0
u = −1.10707 − 1.25249I
a = 1.00000
b = 0.63231 + 1.34103I
0.8116 + 22.3107I 0
u = −0.127947 + 0.260665I
a = 1.00000
b = −0.03961 − 2.00425I
−0.245250 − 0.513655I 1.5494 + 26.0988I
u = −0.127947 − 0.260665I
a = 1.00000
b = −0.03961 + 2.00425I
−0.245250 + 0.513655I 1.5494 − 26.0988I
9
II. I
u
2
= h1.63 × 10
1735
u
155
− 9.73 × 10
1735
u
154
+ · · · + 1.03 × 10
1738
b + 8.61 ×
10
1738
, 1.64 × 10
1736
u
155
− 2.99 × 10
1735
u
154
+ · · · + 4.74 × 10
1739
a + 1.16 ×
10
1741
, u
156
− 6u
155
+ · · · + 6790u + 1288i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−0.000346599u
155
+ 0.0000630564u
154
+ ··· − 49.7051u − 24.5222
−0.00158166u
155
+ 0.00944050u
154
+ ··· − 37.3726u − 8.35500
a
4
=
1
u
2
a
2
=
0.00204685u
155
− 0.0143357u
154
+ ··· + 1.80622u − 13.5699
−0.00179839u
155
+ 0.0108199u
154
+ ··· − 40.1971u − 8.30601
a
8
=
0.0101130u
155
− 0.0591571u
154
+ ··· + 470.090u + 66.8018
−0.00337653u
155
+ 0.0205497u
154
+ ··· − 77.3509u − 11.1044
a
12
=
0.00123506u
155
− 0.00937744u
154
+ ··· − 12.3325u − 16.1672
−0.00158166u
155
+ 0.00944050u
154
+ ··· − 37.3726u − 8.35500
a
6
=
0.00847347u
155
− 0.0528439u
154
+ ··· + 95.8064u − 2.97935
0.000148000u
155
− 0.00226143u
154
+ ··· − 32.9533u − 15.8318
a
7
=
−0.000693818u
155
+ 0.00122309u
154
+ ··· − 91.8035u − 44.3276
0.00200736u
155
− 0.0119787u
154
+ ··· + 42.5562u + 9.89170
a
10
=
0.0195170u
155
− 0.119912u
154
+ ··· + 571.122u + 56.6772
−0.00440003u
155
+ 0.0264988u
154
+ ··· − 105.520u − 18.8433
a
11
=
0.00770984u
155
− 0.0439725u
154
+ ··· + 433.571u + 68.3438
−0.000999740u
155
+ 0.00558199u
154
+ ··· − 45.2645u − 10.1410
a
3
=
0.0137587u
155
− 0.0844136u
154
+ ··· − 63.9818u − 42.9558
−0.00167335u
155
+ 0.0107474u
154
+ ··· − 17.9859u + 5.76366
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0125289u
155
+ 0.0675500u
154
+ ··· − 444.155u − 151.722
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(2u
78
+ 47u
77
+ ··· + 1391u + 71)
2
c
2
, c
7
u
156
− 2u
155
+ ··· − 932767u − 85726
c
3
, c
6
2(2u
156
− 11u
155
+ ··· − 10689u + 882)
c
4
, c
8
u
156
− 6u
155
+ ··· + 6790u + 1288
c
5
, c
12
4(2u
78
+ 29u
77
+ ··· + 2u − 1)
2
c
9
, c
11
2(2u
156
+ 9u
155
+ ··· − 1.96661 × 10
11
u + 9.82273 × 10
9
)
c
10
4(2u
78
− 33u
77
+ ··· − 13u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(4y
78
+ 67y
77
+ ··· − 256583y + 5041)
2
c
2
, c
7
y
156
+ 6y
155
+ ··· − 628310042425y + 7348947076
c
3
, c
6
4(4y
156
− y
155
+ ··· − 5.42417 × 10
7
y + 777924)
c
4
, c
8
y
156
− 6y
155
+ ··· + 68705644y + 1658944
c
5
, c
12
16(4y
78
+ 191y
77
+ ··· + 2y + 1)
2
c
9
, c
11
4(4y
156
− 225y
155
+ ··· − 3.03964 × 10
22
y + 9.64861 × 10
19
)
c
10
16(4y
78
− 37y
77
+ ··· − 57y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.479961 + 0.895187I
a = −1.50431 + 0.97086I
b = −0.315677 − 1.273790I
−2.85447 + 1.56373I 0
u = 0.479961 − 0.895187I
a = −1.50431 − 0.97086I
b = −0.315677 + 1.273790I
−2.85447 − 1.56373I 0
u = −0.878989 + 0.520454I
a = −1.203710 + 0.138500I
b = −1.112130 − 0.148145I
5.93146 − 6.69998I 0
u = −0.878989 − 0.520454I
a = −1.203710 − 0.138500I
b = −1.112130 + 0.148145I
5.93146 + 6.69998I 0
u = 0.853357 + 0.442102I
a = 0.583658 + 0.213614I
b = 1.162010 + 0.248983I
1.021380 − 0.881637I 0
u = 0.853357 − 0.442102I
a = 0.583658 − 0.213614I
b = 1.162010 − 0.248983I
1.021380 + 0.881637I 0
u = −0.797756 + 0.530173I
a = −0.694107 + 0.549397I
b = −0.573917 − 0.078814I
−1.06336 − 2.97038I 0
u = −0.797756 − 0.530173I
a = −0.694107 − 0.549397I
b = −0.573917 + 0.078814I
−1.06336 + 2.97038I 0
u = −0.919160 + 0.498496I
a = 1.040280 − 0.538311I
b = 0.913302 − 0.454713I
1.34644 − 8.47535I 0
u = −0.919160 − 0.498496I
a = 1.040280 + 0.538311I
b = 0.913302 + 0.454713I
1.34644 + 8.47535I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.015940 + 0.256287I
a = 1.09738 + 1.04498I
b = 0.520510 + 0.726816I
4.28368 + 0.07891I 0
u = 1.015940 − 0.256287I
a = 1.09738 − 1.04498I
b = 0.520510 − 0.726816I
4.28368 − 0.07891I 0
u = 0.425921 + 0.821163I
a = 0.487008 − 1.254460I
b = 0.0715166 + 0.0651013I
1.54820 − 2.23571I 0
u = 0.425921 − 0.821163I
a = 0.487008 + 1.254460I
b = 0.0715166 − 0.0651013I
1.54820 + 2.23571I 0
u = 0.898223 + 0.186166I
a = −0.09867 + 1.66261I
b = −0.402829 + 0.593899I
3.86806 + 1.53815I 0
u = 0.898223 − 0.186166I
a = −0.09867 − 1.66261I
b = −0.402829 − 0.593899I
3.86806 − 1.53815I 0
u = 0.319775 + 1.040490I
a = 0.398803 − 0.063093I
b = 0.44687 + 1.40191I
−3.55539 + 7.17927I 0
u = 0.319775 − 1.040490I
a = 0.398803 + 0.063093I
b = 0.44687 − 1.40191I
−3.55539 − 7.17927I 0
u = −1.068180 + 0.277813I
a = −0.15211 − 1.41616I
b = −0.349222 − 0.646022I
2.78026 − 9.68554I 0
u = −1.068180 − 0.277813I
a = −0.15211 + 1.41616I
b = −0.349222 + 0.646022I
2.78026 + 9.68554I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.049763 + 1.102890I
a = −0.401358 + 0.330207I
b = −0.344556 − 1.183320I
−4.65175 + 0.36929I 0
u = 0.049763 − 1.102890I
a = −0.401358 − 0.330207I
b = −0.344556 + 1.183320I
−4.65175 − 0.36929I 0
u = −0.879358 + 0.042817I
a = 1.30537 − 2.10299I
b = 0.225703 − 0.933087I
−0.214354 + 0.639866I 0
u = −0.879358 − 0.042817I
a = 1.30537 + 2.10299I
b = 0.225703 + 0.933087I
−0.214354 − 0.639866I 0
u = 1.101330 + 0.231138I
a = 0.057837 + 1.277300I
b = −0.285328 + 0.933415I
2.61817 − 2.36056I 0
u = 1.101330 − 0.231138I
a = 0.057837 − 1.277300I
b = −0.285328 − 0.933415I
2.61817 + 2.36056I 0
u = −0.803023 + 0.297798I
a = 0.40574 + 1.39575I
b = 0.265780 + 1.020500I
−0.86266 + 2.73725I 0
u = −0.803023 − 0.297798I
a = 0.40574 − 1.39575I
b = 0.265780 − 1.020500I
−0.86266 − 2.73725I 0
u = 0.262452 + 0.806281I
a = −0.885768 + 0.701100I
b = −0.573917 + 0.078814I
−1.06336 + 2.97038I 0
u = 0.262452 − 0.806281I
a = −0.885768 − 0.701100I
b = −0.573917 − 0.078814I
−1.06336 − 2.97038I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.740443 + 0.887906I
a = −1.60594 + 0.05731I
b = −0.354683 + 1.128330I
−3.97260 − 6.43264I 0
u = −0.740443 − 0.887906I
a = −1.60594 − 0.05731I
b = −0.354683 − 1.128330I
−3.97260 + 6.43264I 0
u = −0.774548 + 0.870533I
a = −1.337020 + 0.116561I
b = −0.690391 + 1.231120I
−2.00603 − 7.84989I 0
u = −0.774548 − 0.870533I
a = −1.337020 − 0.116561I
b = −0.690391 − 1.231120I
−2.00603 + 7.84989I 0
u = 0.840314 + 0.825520I
a = −1.039640 + 0.096434I
b = −1.002090 + 0.203248I
2.16176 + 7.58809I 0
u = 0.840314 − 0.825520I
a = −1.039640 − 0.096434I
b = −1.002090 − 0.203248I
2.16176 − 7.58809I 0
u = 0.698682 + 0.954916I
a = 1.56245 − 0.27544I
b = 0.361274 + 1.324060I
−3.98422 + 12.55590I 0
u = 0.698682 − 0.954916I
a = 1.56245 + 0.27544I
b = 0.361274 − 1.324060I
−3.98422 − 12.55590I 0
u = 1.18829
a = 0.448510
b = 0.520389
1.95670 0
u = 0.797052 + 0.078604I
a = −1.24946 − 0.88650I
b = −0.954726 − 0.270295I
2.17712 − 2.41882I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.797052 − 0.078604I
a = −1.24946 + 0.88650I
b = −0.954726 + 0.270295I
2.17712 + 2.41882I 0
u = −0.886514 + 0.828920I
a = 1.322770 − 0.203441I
b = 0.421697 − 1.345190I
−4.00440 − 4.24597I 0
u = −0.886514 − 0.828920I
a = 1.322770 + 0.203441I
b = 0.421697 + 1.345190I
−4.00440 + 4.24597I 0
u = −0.174617 + 0.759086I
a = −0.596104 + 0.082537I
b = −0.317853 − 1.311150I
−2.97182 − 3.18788I 0
u = −0.174617 − 0.759086I
a = −0.596104 − 0.082537I
b = −0.317853 + 1.311150I
−2.97182 + 3.18788I 0
u = −0.687839 + 1.013370I
a = 0.758242 + 0.392365I
b = 0.913302 − 0.454713I
1.34644 − 8.47535I 0
u = −0.687839 − 1.013370I
a = 0.758242 − 0.392365I
b = 0.913302 + 0.454713I
1.34644 + 8.47535I 0
u = −0.926201 + 0.804801I
a = −0.532357 − 0.377712I
b = −0.954726 + 0.270295I
2.17712 + 2.41882I 0
u = −0.926201 − 0.804801I
a = −0.532357 + 0.377712I
b = −0.954726 − 0.270295I
2.17712 − 2.41882I 0
u = −0.095480 + 0.765392I
a = −0.969354 + 0.245670I
b = −0.720411
−3.19854 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.095480 − 0.765392I
a = −0.969354 − 0.245670I
b = −0.720411
−3.19854 0
u = −0.953234 + 0.777211I
a = −0.953664 + 0.088459I
b = −1.002090 − 0.203248I
2.16176 − 7.58809I 0
u = −0.953234 − 0.777211I
a = −0.953664 − 0.088459I
b = −1.002090 + 0.203248I
2.16176 + 7.58809I 0
u = 0.985966 + 0.748216I
a = −0.819909 + 0.094339I
b = −1.112130 + 0.148145I
5.93146 + 6.69998I 0
u = 0.985966 − 0.748216I
a = −0.819909 − 0.094339I
b = −1.112130 − 0.148145I
5.93146 − 6.69998I 0
u = 1.132990 + 0.505041I
a = −0.492554 − 0.248408I
b = −0.592022 − 1.242280I
−0.84280 + 8.08701I 0
u = 1.132990 − 0.505041I
a = −0.492554 + 0.248408I
b = −0.592022 + 1.242280I
−0.84280 − 8.08701I 0
u = 1.237540 + 0.134389I
a = 0.268939 − 0.692748I
b = 0.0715166 − 0.0651013I
1.54820 + 2.23571I 0
u = 1.237540 − 0.134389I
a = 0.268939 + 0.692748I
b = 0.0715166 + 0.0651013I
1.54820 − 2.23571I 0
u = −0.741466 + 0.999991I
a = 0.192043 + 0.660636I
b = 0.265780 − 1.020500I
−0.86266 − 2.73725I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741466 − 0.999991I
a = 0.192043 − 0.660636I
b = 0.265780 + 1.020500I
−0.86266 + 2.73725I 0
u = −0.635285 + 1.075650I
a = −1.144020 + 0.110753I
b = −0.403537 + 1.180610I
−6.63749 − 4.04388I 0
u = −0.635285 − 1.075650I
a = −1.144020 − 0.110753I
b = −0.403537 − 1.180610I
−6.63749 + 4.04388I 0
u = 1.260380 + 0.147986I
a = 0.653556 + 0.968643I
b = 0.082652 + 0.796113I
1.08265 − 2.16413I 0
u = 1.260380 − 0.147986I
a = 0.653556 − 0.968643I
b = 0.082652 − 0.796113I
1.08265 + 2.16413I 0
u = −1.290730 + 0.215380I
a = −0.766949 + 1.023580I
b = −0.314582 + 0.971329I
3.16527 − 8.27221I 0
u = −1.290730 − 0.215380I
a = −0.766949 − 1.023580I
b = −0.314582 − 0.971329I
3.16527 + 8.27221I 0
u = −0.432602 + 0.530204I
a = −1.61856 − 0.81628I
b = −0.592022 + 1.242280I
−0.84280 − 8.08701I 0
u = −0.432602 − 0.530204I
a = −1.61856 + 0.81628I
b = −0.592022 − 1.242280I
−0.84280 + 8.08701I 0
u = −0.213303 + 1.322530I
a = −1.062750 + 0.027144I
b = −0.724784 + 1.022780I
−5.34834 − 2.90068I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.213303 − 1.322530I
a = −1.062750 − 0.027144I
b = −0.724784 − 1.022780I
−5.34834 + 2.90068I 0
u = 0.403630 + 0.440325I
a = 1.51094 − 0.55299I
b = 1.162010 + 0.248983I
1.021380 − 0.881637I 0
u = 0.403630 − 0.440325I
a = 1.51094 + 0.55299I
b = 1.162010 − 0.248983I
1.021380 + 0.881637I 0
u = 0.19079 + 1.41130I
a = −0.940343 + 0.024017I
b = −0.724784 − 1.022780I
−5.34834 + 2.90068I 0
u = 0.19079 − 1.41130I
a = −0.940343 − 0.024017I
b = −0.724784 + 1.022780I
−5.34834 − 2.90068I 0
u = −0.384153 + 0.426220I
a = −1.48582 + 1.22242I
b = −0.344556 + 1.183320I
−4.65175 − 0.36929I −3.63498 + 0.I
u = −0.384153 − 0.426220I
a = −1.48582 − 1.22242I
b = −0.344556 − 1.183320I
−4.65175 + 0.36929I −3.63498 + 0.I
u = 0.60765 + 1.30092I
a = −0.865996 + 0.083837I
b = −0.403537 − 1.180610I
−6.63749 + 4.04388I 0
u = 0.60765 − 1.30092I
a = −0.865996 − 0.083837I
b = −0.403537 + 1.180610I
−6.63749 − 4.04388I 0
u = −0.23154 + 1.42010I
a = 0.035378 − 0.781299I
b = −0.285328 + 0.933415I
2.61817 − 2.36056I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23154 − 1.42010I
a = 0.035378 + 0.781299I
b = −0.285328 − 0.933415I
2.61817 + 2.36056I 0
u = 0.548296 + 0.111887I
a = −2.67612 − 0.90805I
b = −0.366656 + 0.571064I
4.29109 + 5.26116I 9.28004 − 1.66680I
u = 0.548296 − 0.111887I
a = −2.67612 + 0.90805I
b = −0.366656 − 0.571064I
4.29109 − 5.26116I 9.28004 + 1.66680I
u = −1.39210 + 0.45988I
a = 0.293750 − 0.010120I
b = 0.526504 + 0.674952I
4.41001 + 4.13048I 0
u = −1.39210 − 0.45988I
a = 0.293750 + 0.010120I
b = 0.526504 − 0.674952I
4.41001 − 4.13048I 0
u = 0.532960
a = 2.22960
b = 0.520389
1.95670 8.30610
u = −0.491251 + 0.194866I
a = 2.35079 + 2.41938I
b = 0.279715 − 0.895923I
0.29144 − 4.39387I 3.3530 + 14.1192I
u = −0.491251 − 0.194866I
a = 2.35079 − 2.41938I
b = 0.279715 + 0.895923I
0.29144 + 4.39387I 3.3530 − 14.1192I
u = 0.68038 + 1.31757I
a = 0.478654 − 0.709418I
b = 0.082652 + 0.796113I
1.08265 − 2.16413I 0
u = 0.68038 − 1.31757I
a = 0.478654 + 0.709418I
b = 0.082652 − 0.796113I
1.08265 + 2.16413I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273976 + 0.391212I
a = −8.50504 − 0.10618I
b = 0.065464 + 0.938318I
0.17888 − 1.82981I −51.4632 + 40.8262I
u = −0.273976 − 0.391212I
a = −8.50504 + 0.10618I
b = 0.065464 − 0.938318I
0.17888 + 1.82981I −51.4632 − 40.8262I
u = −0.39815 + 1.47503I
a = −0.035570 − 0.599352I
b = −0.402829 + 0.593899I
3.86806 + 1.53815I 0
u = −0.39815 − 1.47503I
a = −0.035570 + 0.599352I
b = −0.402829 − 0.593899I
3.86806 − 1.53815I 0
u = 0.041437 + 0.466906I
a = −1.64600 + 0.22791I
b = −0.317853 + 1.311150I
−2.97182 + 3.18788I −1.27247 − 9.49415I
u = 0.041437 − 0.466906I
a = −1.64600 − 0.22791I
b = −0.317853 − 1.311150I
−2.97182 − 3.18788I −1.27247 + 9.49415I
u = 0.193175 + 0.394775I
a = 2.44627 + 0.38702I
b = 0.44687 + 1.40191I
−3.55539 + 7.17927I −1.80110 − 4.96138I
u = 0.193175 − 0.394775I
a = 2.44627 − 0.38702I
b = 0.44687 − 1.40191I
−3.55539 − 7.17927I −1.80110 + 4.96138I
u = 0.93412 + 1.25420I
a = −0.742290 + 0.064713I
b = −0.690391 − 1.231120I
−2.00603 + 7.84989I 0
u = 0.93412 − 1.25420I
a = −0.742290 − 0.064713I
b = −0.690391 + 1.231120I
−2.00603 − 7.84989I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273496 + 0.334247I
a = −0.32690 − 3.69989I
b = −0.306294 + 0.673772I
3.37148 − 0.42279I 10.67920 + 9.23860I
u = −0.273496 − 0.334247I
a = −0.32690 + 3.69989I
b = −0.306294 − 0.673772I
3.37148 + 0.42279I 10.67920 − 9.23860I
u = −0.404274 + 0.149178I
a = 3.40022 + 0.11714I
b = 0.526504 + 0.674952I
4.41001 + 4.13048I 12.00147 − 6.90127I
u = −0.404274 − 0.149178I
a = 3.40022 − 0.11714I
b = 0.526504 − 0.674952I
4.41001 − 4.13048I 12.00147 + 6.90127I
u = −0.119964 + 0.411107I
a = −0.491215 + 0.559006I
b = −1.24456 − 1.70824I
0.006574 − 0.227616I 1.8034 − 40.7693I
u = −0.119964 − 0.411107I
a = −0.491215 − 0.559006I
b = −1.24456 + 1.70824I
0.006574 + 0.227616I 1.8034 + 40.7693I
u = 0.327035 + 0.276267I
a = −1.72607 + 4.94236I
b = −0.313034 − 0.942204I
1.92493 + 12.66990I 5.2608 − 13.7782I
u = 0.327035 − 0.276267I
a = −1.72607 − 4.94236I
b = −0.313034 + 0.942204I
1.92493 − 12.66990I 5.2608 + 13.7782I
u = 0.55591 + 1.47045I
a = −0.074979 + 0.698079I
b = −0.349222 − 0.646022I
2.78026 − 9.68554I 0
u = 0.55591 − 1.47045I
a = −0.074979 − 0.698079I
b = −0.349222 + 0.646022I
2.78026 + 9.68554I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16123 + 1.06821I
a = −0.0478892 + 0.1124320I
b = −0.119517 + 1.210060I
−0.70607 + 1.63222I 0
u = −1.16123 − 1.06821I
a = −0.0478892 − 0.1124320I
b = −0.119517 − 1.210060I
−0.70607 − 1.63222I 0
u = 1.20710 + 1.01716I
a = −1.010050 − 0.187305I
b = −0.59012 − 1.29731I
2.34263 + 12.68040I 0
u = 1.20710 − 1.01716I
a = −1.010050 + 0.187305I
b = −0.59012 + 1.29731I
2.34263 − 12.68040I 0
u = −1.36571 + 0.79730I
a = −0.335095 − 0.113703I
b = −0.366656 − 0.571064I
4.29109 − 5.26116I 0
u = −1.36571 − 0.79730I
a = −0.335095 + 0.113703I
b = −0.366656 + 0.571064I
4.29109 + 5.26116I 0
u = 0.84705 + 1.34288I
a = 0.477905 − 0.455087I
b = 0.520510 + 0.726816I
4.28368 + 0.07891I 0
u = 0.84705 − 1.34288I
a = 0.477905 + 0.455087I
b = 0.520510 − 0.726816I
4.28368 − 0.07891I 0
u = 1.32608 + 0.90264I
a = −0.023695 + 0.268185I
b = −0.306294 + 0.673772I
3.37148 − 0.42279I 0
u = 1.32608 − 0.90264I
a = −0.023695 − 0.268185I
b = −0.306294 − 0.673772I
3.37148 + 0.42279I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.05646 + 1.21992I
a = −1.081890 − 0.015420I
b = −0.576006 + 1.262350I
−1.13829 − 13.26270I 0
u = −1.05646 − 1.21992I
a = −1.081890 + 0.015420I
b = −0.576006 − 1.262350I
−1.13829 + 13.26270I 0
u = −1.02871 + 1.25347I
a = −0.957138 − 0.177493I
b = −0.59012 + 1.29731I
2.34263 − 12.68040I 0
u = −1.02871 − 1.25347I
a = −0.957138 + 0.177493I
b = −0.59012 − 1.29731I
2.34263 + 12.68040I 0
u = −1.00402 + 1.27683I
a = 0.738518 + 0.113583I
b = 0.421697 − 1.345190I
−4.00440 − 4.24597I 0
u = −1.00402 − 1.27683I
a = 0.738518 − 0.113583I
b = 0.421697 + 1.345190I
−4.00440 + 4.24597I 0
u = −0.177799 + 0.284302I
a = 0.23215 − 6.03439I
b = −0.327024 + 0.965735I
2.80080 − 4.67456I 10.8864 + 12.5236I
u = −0.177799 − 0.284302I
a = 0.23215 + 6.03439I
b = −0.327024 − 0.965735I
2.80080 + 4.67456I 10.8864 − 12.5236I
u = 0.76946 + 1.48634I
a = −0.468819 + 0.625689I
b = −0.314582 − 0.971329I
3.16527 + 8.27221I 0
u = 0.76946 − 1.48634I
a = −0.468819 − 0.625689I
b = −0.314582 + 0.971329I
3.16527 − 8.27221I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170883 + 0.269002I
a = −0.887022 + 1.009440I
b = −1.24456 + 1.70824I
0.006574 + 0.227616I 1.8034 + 40.7693I
u = −0.170883 − 0.269002I
a = −0.887022 − 1.009440I
b = −1.24456 − 1.70824I
0.006574 − 0.227616I 1.8034 − 40.7693I
u = 1.16179 + 1.30353I
a = −0.924120 − 0.013171I
b = −0.576006 − 1.262350I
−1.13829 + 13.26270I 0
u = 1.16179 − 1.30353I
a = −0.924120 + 0.013171I
b = −0.576006 + 1.262350I
−1.13829 − 13.26270I 0
u = −1.62628 + 0.73043I
a = 0.206579 + 0.212607I
b = 0.279715 + 0.895923I
0.29144 + 4.39387I 0
u = −1.62628 − 0.73043I
a = 0.206579 − 0.212607I
b = 0.279715 − 0.895923I
0.29144 − 4.39387I 0
u = −0.064491 + 0.181715I
a = −3.20664 + 7.52841I
b = −0.119517 − 1.210060I
−0.70607 − 1.63222I 4.82942 + 8.80654I
u = −0.064491 − 0.181715I
a = −3.20664 − 7.52841I
b = −0.119517 + 1.210060I
−0.70607 + 1.63222I 4.82942 − 8.80654I
u = −1.59111 + 0.88066I
a = −0.469289 + 0.302872I
b = −0.315677 + 1.273790I
−2.85447 − 1.56373I 0
u = −1.59111 − 0.88066I
a = −0.469289 − 0.302872I
b = −0.315677 − 1.273790I
−2.85447 + 1.56373I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.125336 + 0.097188I
a = 10.3674 − 21.8568I
b = 0.088562 + 0.896331I
0.41240 + 2.22393I −7.29347 − 8.95816I
u = 0.125336 − 0.097188I
a = 10.3674 + 21.8568I
b = 0.088562 − 0.896331I
0.41240 − 2.22393I −7.29347 + 8.95816I
u = 1.13823 + 1.46836I
a = −0.621895 + 0.022192I
b = −0.354683 − 1.128330I
−3.97260 + 6.43264I 0
u = 1.13823 − 1.46836I
a = −0.621895 − 0.022192I
b = −0.354683 + 1.128330I
−3.97260 − 6.43264I 0
u = 1.35467 + 1.29957I
a = 0.620731 + 0.109425I
b = 0.361274 + 1.324060I
−3.98422 + 12.55590I 0
u = 1.35467 − 1.29957I
a = 0.620731 − 0.109425I
b = 0.361274 − 1.324060I
−3.98422 − 12.55590I 0
u = 1.67431 + 1.13891I
a = 0.006366 + 0.165472I
b = −0.327024 + 0.965735I
2.80080 − 4.67456I 0
u = 1.67431 − 1.13891I
a = 0.006366 − 0.165472I
b = −0.327024 − 0.965735I
2.80080 + 4.67456I 0
u = −1.05784 + 1.90517I
a = 0.213067 + 0.343259I
b = 0.225703 − 0.933087I
−0.214354 + 0.639866I 0
u = −1.05784 − 1.90517I
a = 0.213067 − 0.343259I
b = 0.225703 + 0.933087I
−0.214354 − 0.639866I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.92990 + 1.13947I
a = −0.062981 − 0.180337I
b = −0.313034 − 0.942204I
1.92493 + 12.66990I 0
u = −1.92990 − 1.13947I
a = −0.062981 + 0.180337I
b = −0.313034 + 0.942204I
1.92493 − 12.66990I 0
u = 3.42362 + 1.73184I
a = 0.0177160 − 0.0373491I
b = 0.088562 − 0.896331I
0.41240 − 2.22393I 0
u = 3.42362 − 1.73184I
a = 0.0177160 + 0.0373491I
b = 0.088562 + 0.896331I
0.41240 + 2.22393I 0
u = 2.37172 + 3.29818I
a = −0.1175590 − 0.0014677I
b = 0.065464 − 0.938318I
0.17888 + 1.82981I 0
u = 2.37172 − 3.29818I
a = −0.1175590 + 0.0014677I
b = 0.065464 + 0.938318I
0.17888 − 1.82981I 0
28
III. I
u
3
= h−5.52 × 10
28
u
32
+ 2.59 × 10
28
u
31
+ · · · + 5.80 × 10
28
b − 5.01 ×
10
27
, a + 1, u
33
+ 5u
31
+ · · · + 4u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−1
0.951964u
32
− 0.446840u
31
+ ··· − 2.06786u + 0.0863895
a
4
=
1
u
2
a
2
=
−0.951964u
32
+ 0.446840u
31
+ ··· + 2.06786u − 1.08639
0.918252u
32
− 0.501484u
31
+ ··· − 2.90326u − 0.360451
a
8
=
−u
−0.446840u
32
+ 0.0337128u
31
+ ··· − 2.72147u − 0.951964
a
12
=
−0.951964u
32
+ 0.446840u
31
+ ··· + 2.06786u − 1.08639
0.951964u
32
− 0.446840u
31
+ ··· − 2.06786u + 0.0863895
a
6
=
1.32269u
32
− 0.513435u
31
+ ··· + 3.38292u + 0.101967
−0.370724u
32
+ 0.0665946u
31
+ ··· − 5.45078u + 0.984423
a
7
=
0.112955u
32
− 0.130314u
31
+ ··· − 1.88373u − 0.604599
0.218417u
32
− 0.192748u
31
+ ··· + 0.199599u + 0.800773
a
10
=
0.172309u
32
− 0.0566887u
31
+ ··· + 12.9481u + 1.16770
−0.0583181u
32
+ 0.439758u
31
+ ··· − 10.4006u − 1.51968
a
11
=
−0.673417u
32
+ 0.306715u
31
+ ··· + 2.79891u − 0.572955
0.568895u
32
− 0.174923u
31
+ ··· − 1.25992u + 0.200380
a
3
=
1.05987u
32
− 0.239711u
31
+ ··· + 4.85356u + 1.60317
−0.894227u
32
+ 0.157890u
31
+ ··· − 6.15318u − 0.927171
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8.95876u
32
− 2.84222u
31
+ ··· − 12.0440u + 4.31329
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
33
− 18u
32
+ ··· − 90u + 25
c
2
, c
7
u
33
− u
32
+ ··· + 2u − 1
c
3
, c
6
u
33
− u
32
+ ··· + 8u − 1
c
4
, c
8
u
33
+ 5u
31
+ ··· + 4u + 1
c
5
u
33
+ 8u
32
+ ··· − 45u − 11
c
9
, c
11
u
33
− 2u
32
+ ··· − 28u − 4
c
10
u
33
− 16u
32
+ ··· + u − 1
c
12
u
33
− 8u
32
+ ··· − 45u + 11
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
− 4y
32
+ ··· − 3500y −625
c
2
, c
7
y
33
+ y
32
+ ··· + 22y −1
c
3
, c
6
y
33
+ y
32
+ ··· − 6y −1
c
4
, c
8
y
33
+ 10y
32
+ ··· − 14y −1
c
5
, c
12
y
33
+ 30y
32
+ ··· − 2353y −121
c
9
, c
11
y
33
− 12y
32
+ ··· + 432y −16
c
10
y
33
+ 8y
32
+ ··· + 19y −1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.168715 + 0.904319I
a = −1.00000
b = 0.211967 + 0.998704I
−0.20592 + 3.02064I 4.66691 − 3.97543I
u = −0.168715 − 0.904319I
a = −1.00000
b = 0.211967 − 0.998704I
−0.20592 − 3.02064I 4.66691 + 3.97543I
u = −0.593938 + 0.634380I
a = −1.00000
b = 0.278636 + 0.519226I
3.36803 − 0.36624I 10.78955 + 1.90553I
u = −0.593938 − 0.634380I
a = −1.00000
b = 0.278636 − 0.519226I
3.36803 + 0.36624I 10.78955 − 1.90553I
u = −0.734685 + 0.460453I
a = −1.00000
b = −1.019540 + 0.561361I
2.05075 + 0.83990I 11.12891 − 0.28641I
u = −0.734685 − 0.460453I
a = −1.00000
b = −1.019540 − 0.561361I
2.05075 − 0.83990I 11.12891 + 0.28641I
u = −0.812625 + 0.853439I
a = −1.00000
b = 0.248656 + 0.916833I
2.66313 + 3.69897I 8.75583 − 4.73989I
u = −0.812625 − 0.853439I
a = −1.00000
b = 0.248656 − 0.916833I
2.66313 − 3.69897I 8.75583 + 4.73989I
u = 0.958958 + 0.691328I
a = −1.00000
b = −0.922919 + 0.036438I
3.94821 + 7.37230I 8.53206 − 8.71708I
u = 0.958958 − 0.691328I
a = −1.00000
b = −0.922919 − 0.036438I
3.94821 − 7.37230I 8.53206 + 8.71708I
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.079670 + 0.808678I
a = −1.00000
b = −0.368861 − 0.958181I
−3.60784 − 2.31209I −6.62484 + 2.31830I
u = −0.079670 − 0.808678I
a = −1.00000
b = −0.368861 + 0.958181I
−3.60784 + 2.31209I −6.62484 − 2.31830I
u = 0.980087 + 0.718284I
a = −1.00000
b = 0.224126 − 0.824618I
1.94588 − 11.52120I 4.47395 + 6.03943I
u = 0.980087 − 0.718284I
a = −1.00000
b = 0.224126 + 0.824618I
1.94588 + 11.52120I 4.47395 − 6.03943I
u = 0.983806 + 0.738529I
a = −1.00000
b = −0.140001 − 0.536790I
3.81043 + 6.56313I 7.47883 − 6.51008I
u = 0.983806 − 0.738529I
a = −1.00000
b = −0.140001 + 0.536790I
3.81043 − 6.56313I 7.47883 + 6.51008I
u = 0.320744 + 1.249490I
a = −1.00000
b = −0.596108 − 1.053050I
−6.09846 + 2.54463I −8.70429 + 1.92607I
u = 0.320744 − 1.249490I
a = −1.00000
b = −0.596108 + 1.053050I
−6.09846 − 2.54463I −8.70429 − 1.92607I
u = 0.926206 + 1.029530I
a = −1.00000
b = −0.34866 − 1.39004I
−3.84906 + 3.62349I 0. + 10.49967I
u = 0.926206 − 1.029530I
a = −1.00000
b = −0.34866 + 1.39004I
−3.84906 − 3.62349I 0. − 10.49967I
33
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.790710 + 1.154890I
a = −1.00000
b = 0.093645 + 0.904158I
0.40815 − 1.75689I 5.38092 + 2.46903I
u = −0.790710 − 1.154890I
a = −1.00000
b = 0.093645 − 0.904158I
0.40815 + 1.75689I 5.38092 − 2.46903I
u = 0.82028 + 1.15606I
a = −1.00000
b = −0.198156 − 1.132650I
−4.61541 + 4.46442I 0. − 3.67106I
u = 0.82028 − 1.15606I
a = −1.00000
b = −0.198156 + 1.132650I
−4.61541 − 4.46442I 0. + 3.67106I
u = −0.19236 + 1.40778I
a = −1.00000
b = −0.751362 + 1.010120I
−4.90547 − 2.98394I 16.1588 + 5.9851I
u = −0.19236 − 1.40778I
a = −1.00000
b = −0.751362 − 1.010120I
−4.90547 + 2.98394I 16.1588 − 5.9851I
u = −0.407596 + 0.343971I
a = −1.00000
b = −0.30865 + 1.72803I
−1.82389 − 9.59720I 5.5996 + 15.8899I
u = −0.407596 − 0.343971I
a = −1.00000
b = −0.30865 − 1.72803I
−1.82389 + 9.59720I 5.5996 − 15.8899I
u = −0.398810
a = −1.00000
b = 0.915287
4.06063 9.55440
u = −1.12238 + 1.19264I
a = −1.00000
b = −0.551807 + 1.289240I
0.21835 − 12.79100I 0
34
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12238 − 1.19264I
a = −1.00000
b = −0.551807 − 1.289240I
0.21835 + 12.79100I 0
u = 0.111994 + 0.285752I
a = −1.00000
b = −0.30860 − 2.04071I
−0.272015 − 0.346641I −6.5809 − 19.6542I
u = 0.111994 − 0.285752I
a = −1.00000
b = −0.30860 + 2.04071I
−0.272015 + 0.346641I −6.5809 + 19.6542I
35
IV.
I
u
4
= h−4.84 × 10
5
u
11
− 2.83 × 10
6
u
10
+ · · · + 2.43 × 10
7
b + 7.31 × 10
6
, 1.98 ×
10
7
u
11
+1.38×10
8
u
10
+· · · +4.85×10
7
a−1.92×10
8
, u
12
+7u
11
+· · · − 6u +8i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−0.408452u
11
− 2.85189u
10
+ ··· − 2.55780u + 3.94871
0.0199533u
11
+ 0.116604u
10
+ ··· + 0.779717u − 0.301249
a
4
=
1
u
2
a
2
=
−0.476546u
11
− 3.18766u
10
+ ··· − 0.0262394u + 4.19174
−0.00267315u
11
+ 0.0649243u
10
+ ··· + 2.16980u − 1.42835
a
8
=
0.888765u
11
+ 6.38892u
10
+ ··· + 5.61669u − 17.5644
−0.150658u
11
− 1.00425u
10
+ ··· − 1.16846u + 0.454089
a
12
=
−0.428405u
11
− 2.96849u
10
+ ··· − 3.33752u + 4.24996
0.0199533u
11
+ 0.116604u
10
+ ··· + 0.779717u − 0.301249
a
6
=
−0.136342u
11
− 1.17244u
10
+ ··· − 7.99051u − 1.17488
0.0795807u
11
+ 0.624457u
10
+ ··· + 0.962199u + 0.346989
a
7
=
−0.602023u
11
− 4.06803u
10
+ ··· − 1.61564u + 1.97057
−0.0352751u
11
+ 0.00747723u
10
+ ··· + 3.81404u − 1.20267
a
10
=
0.533024u
11
+ 3.66862u
10
+ ··· + 1.61252u − 13.8248
−0.215035u
11
− 1.53280u
10
+ ··· − 1.81856u + 2.09220
a
11
=
0.886566u
11
+ 6.19636u
10
+ ··· + 3.13455u − 15.5687
−0.329372u
11
− 2.41312u
10
+ ··· − 2.73127u + 1.09288
a
3
=
0.560376u
11
+ 5.37265u
10
+ ··· + 49.1407u + 26.3999
0.0452092u
11
+ 0.241021u
10
+ ··· − 2.54129u − 5.12788
(ii) Obstruction class = 1
(iii) Cusp Shapes =
215900093
194102032
u
11
+
3183931527
388204064
u
10
+ ··· −
1918294387
194102032
u −
8300245477
388204064
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(2u
6
+ u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
2
, c
7
u
12
− 3u
11
+ ··· − 7u + 2
c
3
, c
6
2(2u
12
− 5u
11
+ ··· − u + 2)
c
4
, c
8
u
12
+ 7u
11
+ ··· − 6u + 8
c
5
4(2u
6
− 5u
5
+ 9u
4
− 9u
3
+ 7u
2
− 4u + 1)
2
c
9
, c
11
2(2u
12
− 3u
11
+ ··· − 160u + 64)
c
10
4(2u
6
+ 9u
5
+ 19u
4
+ 23u
3
+ 18u
2
+ 7u + 1)
2
c
12
4(2u
6
+ 5u
5
+ 9u
4
+ 9u
3
+ 7u
2
+ 4u + 1)
2
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(4y
6
+ 3y
5
+ y
4
− y
2
+ y + 1)
2
c
2
, c
7
y
12
+ 11y
11
+ ··· + 23y + 4
c
3
, c
6
4(4y
12
+ 35y
11
+ ··· + 67y + 4)
c
4
, c
8
y
12
− 17y
11
+ ··· + 76y + 64
c
5
, c
12
16(4y
6
+ 11y
5
+ 19y
4
+ 9y
3
− 5y
2
− 2y + 1)
2
c
9
, c
11
4(4y
12
+ 35y
11
+ ··· − 5120y + 4096)
c
10
16(4y
6
− 5y
5
+ 19y
4
+ 33y
3
+ 40y
2
− 13y + 1)
2
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.001170 + 0.097095I
a = 0.741262 − 0.844341I
b = 0.583572 − 0.120772I
2.72171 + 2.00437I 12.08084 − 3.25701I
u = −1.001170 − 0.097095I
a = 0.741262 + 0.844341I
b = 0.583572 + 0.120772I
2.72171 − 2.00437I 12.08084 + 3.25701I
u = 0.579882 + 0.747128I
a = 1.58668 − 0.23717I
b = 0.672863 + 1.178830I
−1.42405 + 8.53123I 1.8254 − 14.9556I
u = 0.579882 − 0.747128I
a = 1.58668 + 0.23717I
b = 0.672863 − 1.178830I
−1.42405 − 8.53123I 1.8254 + 14.9556I
u = 0.660150 + 0.917304I
a = 0.587193 − 0.668848I
b = 0.583572 + 0.120772I
2.72171 − 2.00437I 12.08084 + 3.25701I
u = 0.660150 − 0.917304I
a = 0.587193 + 0.668848I
b = 0.583572 − 0.120772I
2.72171 + 2.00437I 12.08084 − 3.25701I
u = 0.318121 + 0.468569I
a = 4.07880 − 3.54728I
b = −0.006436 + 0.874144I
0.34727 − 1.97215I −20.8593 − 1.2683I
u = 0.318121 − 0.468569I
a = 4.07880 + 3.54728I
b = −0.006436 − 0.874144I
0.34727 + 1.97215I −20.8593 + 1.2683I
u = −1.09729 + 1.04792I
a = 0.616472 − 0.092147I
b = 0.672863 − 1.178830I
−1.42405 − 8.53123I 1.8254 + 14.9556I
u = −1.09729 − 1.04792I
a = 0.616472 + 0.092147I
b = 0.672863 + 1.178830I
−1.42405 + 8.53123I 1.8254 − 14.9556I
39
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −2.95970 + 0.78273I
a = 0.139590 − 0.121400I
b = −0.006436 − 0.874144I
0.34727 + 1.97215I −20.8593 + 1.2683I
u = −2.95970 − 0.78273I
a = 0.139590 + 0.121400I
b = −0.006436 + 0.874144I
0.34727 − 1.97215I −20.8593 − 1.2683I
40
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(2u
6
+ u
5
+ ··· + u + 1)
2
(u
33
− 18u
32
+ ··· − 90u + 25)
· (u
50
− 37u
49
+ ··· − 1343488u + 65536)
· (2u
78
+ 47u
77
+ ··· + 1391u + 71)
2
c
2
, c
7
(u
12
− 3u
11
+ ··· − 7u + 2)(u
33
− u
32
+ ··· + 2u − 1)
· (u
50
+ u
49
+ ··· + u + 1)(u
156
− 2u
155
+ ··· − 932767u − 85726)
c
3
, c
6
4(2u
12
− 5u
11
+ ··· − u + 2)(u
33
− u
32
+ ··· + 8u − 1)
· (u
50
+ u
49
+ ··· + u + 1)(2u
156
− 11u
155
+ ··· − 10689u + 882)
c
4
, c
8
(u
12
+ 7u
11
+ ··· − 6u + 8)(u
33
+ 5u
31
+ ··· + 4u + 1)
· (u
50
+ 5u
48
+ ··· + 5u + 1)(u
156
− 6u
155
+ ··· + 6790u + 1288)
c
5
16(2u
6
− 5u
5
+ 9u
4
− 9u
3
+ 7u
2
− 4u + 1)
2
· (u
33
+ 8u
32
+ ··· − 45u − 11)(u
50
− 27u
49
+ ··· − 45312u + 2560)
· (2u
78
+ 29u
77
+ ··· + 2u − 1)
2
c
9
, c
11
4(2u
12
− 3u
11
+ ··· − 160u + 64)(u
33
− 2u
32
+ ··· − 28u − 4)
· (u
50
+ 2u
49
+ ··· − 284u + 148)
· (2u
156
+ 9u
155
+ ··· − 196661110784u + 9822734336)
c
10
16(2u
6
+ 9u
5
+ 19u
4
+ 23u
3
+ 18u
2
+ 7u + 1)
2
· (u
33
− 16u
32
+ ··· + u − 1)(u
50
+ 33u
49
+ ··· + 3584u + 256)
· (2u
78
− 33u
77
+ ··· − 13u + 1)
2
c
12
16(2u
6
+ 5u
5
+ 9u
4
+ 9u
3
+ 7u
2
+ 4u + 1)
2
· (u
33
− 8u
32
+ ··· − 45u + 11)(u
50
− 27u
49
+ ··· − 45312u + 2560)
· (2u
78
+ 29u
77
+ ··· + 2u − 1)
2
41
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
256(4y
6
+ 3y
5
+ ··· + y + 1)
2
(y
33
− 4y
32
+ ··· − 3500y −625)
· (y
50
+ 15y
49
+ ··· + 68719476736y + 4294967296)
· (4y
78
+ 67y
77
+ ··· − 256583y + 5041)
2
c
2
, c
7
(y
12
+ 11y
11
+ ··· + 23y + 4)(y
33
+ y
32
+ ··· + 22y −1)
· (y
50
− 23y
49
+ ··· − 51y + 1)
· (y
156
+ 6y
155
+ ··· − 628310042425y + 7348947076)
c
3
, c
6
16(4y
12
+ 35y
11
+ ··· + 67y + 4)(y
33
+ y
32
+ ··· − 6y −1)
· (y
50
+ 5y
49
+ ··· + 29y + 1)
· (4y
156
− y
155
+ ··· − 54241677y + 777924)
c
4
, c
8
(y
12
− 17y
11
+ ··· + 76y + 64)(y
33
+ 10y
32
+ ··· − 14y −1)
· (y
50
+ 10y
49
+ ··· + 37y + 1)
· (y
156
− 6y
155
+ ··· + 68705644y + 1658944)
c
5
, c
12
256(4y
6
+ 11y
5
+ 19y
4
+ 9y
3
− 5y
2
− 2y + 1)
2
· (y
33
+ 30y
32
+ ··· − 2353y −121)
· (y
50
+ 35y
49
+ ··· + 254345216y + 6553600)
· (4y
78
+ 191y
77
+ ··· + 2y + 1)
2
c
9
, c
11
16(4y
12
+ 35y
11
+ ··· − 5120y + 4096)
· (y
33
− 12y
32
+ ··· + 432y −16)(y
50
− 12y
49
+ ··· − 46320y + 21904)
· (4y
156
− 225y
155
+ ··· − 3.04 × 10
22
y + 9.65 × 10
19
)
c
10
256(4y
6
− 5y
5
+ 19y
4
+ 33y
3
+ 40y
2
− 13y + 1)
2
· (y
33
+ 8y
32
+ ··· + 19y −1)(y
50
+ 7y
49
+ ··· + 1769472y + 65536)
· (4y
78
− 37y
77
+ ··· − 57y + 1)
2
42
