12a
1043
(K12a
1043
)
A knot diagram
1
Linearized knot diagam
4 7 8 1 12 11 10 5 2 3 6 9
Solving Sequence
5,12 6,9
1 4 2 8 3 11 7 10
c
5
c
12
c
4
c
1
c
8
c
3
c
11
c
6
c
10
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h309279332727u
39
− 6570519786366u
38
+ ··· + 25449616384b − 304514848348160,
− 446066672385u
39
+ 9504187459743u
38
+ ··· + 25449616384a + 483336474422784,
3u
40
− 66u
39
+ ··· − 43008u + 2048i
I
u
2
= h1.99934 × 10
105
a
21
u
3
+ 1.76754 × 10
105
a
20
u
3
+ ··· + 2.92106 × 10
102
a + 2.33669 × 10
103
,
a
21
u
3
− 5a
20
u
3
+ ··· + 24254a − 4243, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
3
= h1279125u
24
− 1287228u
23
+ ··· + 965461b − 3643883,
10931649u
24
+ 12210774u
23
+ ··· + 965461a − 9081154, 3u
25
+ 3u
24
+ ··· − 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 153 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
= h3.09 × 10
11
u
39
− 6.57 × 10
12
u
38
+ · · · + 2.54 × 10
10
b − 3.05 ×
10
14
, −4.46 × 10
11
u
39
+ 9.50 × 10
12
u
38
+ · · · + 2.54 × 10
10
a + 4.83 ×
10
14
, 3u
40
− 66u
39
+ · · · − 43008u + 2048i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
17.5274u
39
− 373.451u
38
+ ··· + 369493.u − 18991.9
−12.1526u
39
+ 258.178u
38
+ ··· − 232282.u + 11965.4
a
1
=
15.7231u
39
− 330.923u
38
+ ··· + 230269.u − 11844.6
−14.9846u
39
+ 317.152u
38
+ ··· − 213560.u + 10733.6
a
4
=
17.7712u
39
− 381.885u
38
+ ··· + 379671.u − 19416.9
3.42698u
39
− 69.4386u
38
+ ··· − 31264.6u + 1902.33
a
2
=
1.54086u
39
− 32.5131u
38
+ ··· + 7256.97u − 270.009
5.16740u
39
− 111.458u
38
+ ··· + 131235.u − 6838.08
a
8
=
5.37483u
39
− 115.274u
38
+ ··· + 137212.u − 7026.50
−12.1526u
39
+ 258.178u
38
+ ··· − 232282.u + 11965.4
a
3
=
11.4025u
39
− 244.818u
38
+ ··· + 259388.u − 13416.8
1.38575u
39
− 29.6174u
38
+ ··· + 21819.7u − 1051.89
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
16.5400u
39
− 352.658u
38
+ ··· + 288678.u − 14393.4
−1.36215u
39
+ 27.8518u
38
+ ··· − 32059.5u + 1831.54
(ii) Obstruction class = −1
(iii) Cusp Shapes =
10816413693
6362404096
u
39
−
115564318683
3181202048
u
38
+ ···+
489218830366
24853141
u −
20767219470
24853141
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
3(3u
40
− 63u
39
+ ··· − 4480u + 256)
c
2
, c
10
u
40
+ 4u
38
+ ··· − 3u + 3
c
3
, c
9
u
40
− 3u
39
+ ··· + 10u + 25
c
5
, c
6
, c
11
3(3u
40
− 66u
39
+ ··· − 43008u + 2048)
c
7
3(3u
40
− 90u
39
+ ··· − 96u + 16)
c
8
, c
12
u
40
+ u
39
+ ··· + 36u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
9(9y
40
+ 207y
39
+ ··· + 876544y + 65536)
c
2
, c
10
y
40
+ 8y
39
+ ··· − 63y + 9
c
3
, c
9
y
40
− 19y
39
+ ··· − 1150y + 625
c
5
, c
6
, c
11
9(9y
40
+ 306y
39
+ ··· + 2097152y + 4194304)
c
7
9(9y
40
− 36y
39
+ ··· − 12928y + 256)
c
8
, c
12
y
40
+ y
39
+ ··· + 324y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.430076 + 0.939129I
a = 0.709951 − 0.050908I
b = −0.353142 − 0.644841I
2.91207 + 3.15877I 0
u = 0.430076 − 0.939129I
a = 0.709951 + 0.050908I
b = −0.353142 + 0.644841I
2.91207 − 3.15877I 0
u = 0.231231 + 0.892892I
a = −0.389877 − 0.824893I
b = −0.646388 + 0.538859I
−0.74157 + 1.76866I 0
u = 0.231231 − 0.892892I
a = −0.389877 + 0.824893I
b = −0.646388 − 0.538859I
−0.74157 − 1.76866I 0
u = 0.797794 + 0.829732I
a = 0.079070 + 1.281020I
b = 0.99982 − 1.08760I
−0.4120 + 15.0532I 0
u = 0.797794 − 0.829732I
a = 0.079070 − 1.281020I
b = 0.99982 + 1.08760I
−0.4120 − 15.0532I 0
u = 1.143770 + 0.218983I
a = 0.669280 + 0.663411I
b = −0.620227 − 0.905352I
1.46137 − 8.89771I 0
u = 1.143770 − 0.218983I
a = 0.669280 − 0.663411I
b = −0.620227 + 0.905352I
1.46137 + 8.89771I 0
u = 1.061750 + 0.531482I
a = −0.592784 − 0.312411I
b = 0.463345 + 0.646754I
−0.374138 + 0.723530I 0
u = 1.061750 − 0.531482I
a = −0.592784 + 0.312411I
b = 0.463345 − 0.646754I
−0.374138 − 0.723530I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.366980 + 1.149690I
a = −0.587719 − 1.101030I
b = −1.05016 + 1.07975I
1.86448 + 4.61004I 0
u = 0.366980 − 1.149690I
a = −0.587719 + 1.101030I
b = −1.05016 − 1.07975I
1.86448 − 4.61004I 0
u = 0.962991 + 0.729062I
a = 0.057833 − 1.141700I
b = −0.888065 + 1.057290I
−0.88372 + 5.83229I 0
u = 0.962991 − 0.729062I
a = 0.057833 + 1.141700I
b = −0.888065 − 1.057290I
−0.88372 − 5.83229I 0
u = 0.895035 + 0.886441I
a = −0.165708 + 0.723991I
b = 0.790089 − 0.501107I
−4.31918 + 8.60646I 0
u = 0.895035 − 0.886441I
a = −0.165708 − 0.723991I
b = 0.790089 + 0.501107I
−4.31918 − 8.60646I 0
u = 0.714926 + 0.070491I
a = −0.80903 + 1.42994I
b = 0.679194 − 0.965270I
5.53685 + 0.79423I 0
u = 0.714926 − 0.070491I
a = −0.80903 − 1.42994I
b = 0.679194 + 0.965270I
5.53685 − 0.79423I 0
u = 0.434361 + 0.523139I
a = −0.45056 − 1.78531I
b = −0.738261 + 1.011170I
1.76895 + 1.27338I 0. − 4.56377I
u = 0.434361 − 0.523139I
a = −0.45056 + 1.78531I
b = −0.738261 − 1.011170I
1.76895 − 1.27338I 0. + 4.56377I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.519767 + 0.325027I
a = −0.567043 − 0.806038I
b = 0.032746 + 0.603256I
0.90033 + 1.11286I 3.57927 − 3.43616I
u = 0.519767 − 0.325027I
a = −0.567043 + 0.806038I
b = 0.032746 − 0.603256I
0.90033 − 1.11286I 3.57927 + 3.43616I
u = 0.400531 + 0.362017I
a = −1.56564 − 0.64119I
b = 0.394968 + 0.823605I
2.18207 + 1.75911I 3.60232 − 4.80724I
u = 0.400531 − 0.362017I
a = −1.56564 + 0.64119I
b = 0.394968 − 0.823605I
2.18207 − 1.75911I 3.60232 + 4.80724I
u = 0.10737 + 1.52582I
a = 0.394221 + 0.366834I
b = 0.517395 − 0.640896I
−5.33866 + 3.18854I 0
u = 0.10737 − 1.52582I
a = 0.394221 − 0.366834I
b = 0.517395 + 0.640896I
−5.33866 − 3.18854I 0
u = 0.10832 + 1.54869I
a = 0.689279 + 0.757629I
b = 1.09867 − 1.14955I
−5.20346 + 3.15092I 0
u = 0.10832 − 1.54869I
a = 0.689279 − 0.757629I
b = 1.09867 + 1.14955I
−5.20346 − 3.15092I 0
u = 0.25142 + 1.65145I
a = −0.569813 − 0.870066I
b = −1.29361 + 1.15977I
−8.6562 + 19.0603I 0
u = 0.25142 − 1.65145I
a = −0.569813 + 0.870066I
b = −1.29361 − 1.15977I
−8.6562 − 19.0603I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29257 + 1.65671I
a = 0.538073 + 0.853110I
b = 1.25593 − 1.14103I
−8.82937 + 10.53240I 0
u = 0.29257 − 1.65671I
a = 0.538073 − 0.853110I
b = 1.25593 + 1.14103I
−8.82937 − 10.53240I 0
u = 0.26892 + 1.66392I
a = −0.295163 − 0.749259I
b = −1.167330 + 0.692615I
−12.7100 + 12.9921I 0
u = 0.26892 − 1.66392I
a = −0.295163 + 0.749259I
b = −1.167330 − 0.692615I
−12.7100 − 12.9921I 0
u = 1.38555 + 0.97091I
a = 0.086799 − 0.325668I
b = −0.436459 + 0.366956I
−2.92234 − 0.70874I 0
u = 1.38555 − 0.97091I
a = 0.086799 + 0.325668I
b = −0.436459 − 0.366956I
−2.92234 + 0.70874I 0
u = 0.29238 + 1.71673I
a = 0.277808 + 0.672154I
b = 1.072680 − 0.673445I
−11.76900 + 4.97311I 0
u = 0.29238 − 1.71673I
a = 0.277808 − 0.672154I
b = 1.072680 + 0.673445I
−11.76900 − 4.97311I 0
u = 0.33425 + 1.71922I
a = −0.008980 − 0.357256I
b = −0.611201 + 0.134853I
−7.92682 + 6.50746I 0
u = 0.33425 − 1.71922I
a = −0.008980 + 0.357256I
b = −0.611201 − 0.134853I
−7.92682 − 6.50746I 0
8
II. I
u
2
= h2.00 × 10
105
a
21
u
3
+ 1.77 × 10
105
a
20
u
3
+ · · · + 2.92 × 10
102
a +
2.34 × 10
103
, a
21
u
3
− 5a
20
u
3
+ · · · + 24254a − 4243, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
a
−78.5727a
21
u
3
− 69.4631a
20
u
3
+ ··· − 0.114796a − 0.918302
a
1
=
−a
2
u
−8.74081a
21
u
3
− 5.12626a
20
u
3
+ ··· + 0.385900a − 0.158208
a
4
=
−1.89040a
21
u
3
+ 4.17765a
20
u
3
+ ··· − 0.411276a + 1.19408
−6.23246a
21
u
3
− 3.30996a
20
u
3
+ ··· + 0.0353917a + 0.000856252
a
2
=
2.63867a
21
u
3
+ 13.9877a
20
u
3
+ ··· − 0.685670a + 0.182322
−40.5506a
21
u
3
+ 7.86725a
20
u
3
+ ··· + 0.957810a − 0.211076
a
8
=
−78.5727a
21
u
3
− 69.4631a
20
u
3
+ ··· + 0.885204a − 0.918302
−78.5727a
21
u
3
− 69.4631a
20
u
3
+ ··· − 0.114796a − 0.918302
a
3
=
−87.9371a
21
u
3
− 42.3152a
20
u
3
+ ··· − 0.483802a + 0.569188
−101.333a
21
u
3
− 79.9473a
20
u
3
+ ··· − 0.395275a − 0.785595
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
10
=
−57.6236a
21
u
3
− 64.1783a
20
u
3
+ ··· + 1.49037a + 0.268510
−22.6994a
21
u
3
− 62.7768a
20
u
3
+ ··· − 1.47511a − 0.286750
(ii) Obstruction class = −1
(iii) Cusp Shapes = 139.745a
21
u
3
+ 269.849a
20
u
3
+ ··· + 8.18196a − 11.5585
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
11
+ 3u
10
+ ··· + 2u + 1)
8
c
2
, c
10
u
88
+ 3u
87
+ ··· + 313760u + 32689
c
3
, c
9
u
88
+ u
87
+ ··· + 7015212u + 14269049
c
5
, c
6
, c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
22
c
7
(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
8
c
8
, c
12
u
88
− u
87
+ ··· − 584u + 83
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
11
+ 7y
10
+ ··· − 6y −1)
8
c
2
, c
10
y
88
+ 35y
87
+ ··· + 45878166472y + 1068570721
c
3
, c
9
y
88
− 41y
87
+ ··· − 6370049061361272y + 203605759364401
c
5
, c
6
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
22
c
7
(y
11
− y
10
+ ··· + 6y −1)
8
c
8
, c
12
y
88
− 21y
87
+ ··· − 714888y + 6889
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 0.907790 + 0.226548I
b = −0.647304 + 1.109790I
3.19680 + 3.58563I 3.66733 − 1.31877I
u = −0.395123 + 0.506844I
a = −0.017246 − 0.753773I
b = −1.163050 + 0.611843I
−2.23683 + 1.28930I −7.64088 + 4.99207I
u = −0.395123 + 0.506844I
a = 1.277480 + 0.112709I
b = −0.886862 + 0.535701I
0.32630 + 4.50932I −7.34372 − 5.11480I
u = −0.395123 + 0.506844I
a = 0.578173 + 1.190000I
b = −0.944476 − 0.408288I
−3.81269 − 1.41510I −16.4346 + 4.9087I
u = −0.395123 + 0.506844I
a = −0.281884 + 0.537705I
b = 1.71358 − 1.04898I
−1.29627 − 6.63139I −4.6093 + 13.9215I
u = −0.395123 + 0.506844I
a = −0.72321 − 1.21563I
b = 0.189954 − 0.056607I
−1.85793 + 0.83268I −7.80908 − 0.15485I
u = −0.395123 + 0.506844I
a = 0.43939 + 1.37682I
b = −0.568100 − 0.987543I
−1.85793 − 3.66289I −7.80908 + 9.97234I
u = −0.395123 + 0.506844I
a = 0.53617 + 1.38915I
b = 0.292755 − 1.302630I
−2.23683 − 4.11951I −7.64088 + 4.82542I
u = −0.395123 + 0.506844I
a = 0.40425 − 1.54629I
b = 1.31383 + 1.13328I
3.19680 − 6.41584I 3.66733 + 11.13625I
u = −0.395123 + 0.506844I
a = −0.40252 − 1.54965I
b = 0.831592 + 0.177152I
−3.81269 − 1.41510I −16.4346 + 4.9087I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −1.50585 − 0.57585I
b = 0.561889 − 0.602950I
0.32630 + 4.50932I −7.34372 − 5.11480I
u = −0.395123 + 0.506844I
a = 0.251194 + 0.178954I
b = −0.901890 − 0.113767I
−1.85793 + 0.83268I −7.80908 − 0.15485I
u = −0.395123 + 0.506844I
a = 0.66841 − 1.64193I
b = 0.871448 + 0.321314I
−1.85793 − 3.66289I −7.80908 + 9.97234I
u = −0.395123 + 0.506844I
a = −1.81056 + 0.60810I
b = −1.292500 − 0.105875I
−1.29627 + 3.80118I 0
u = −0.395123 + 0.506844I
a = −1.98119 + 0.26736I
b = 0.473513 − 0.370593I
3.19680 + 3.58563I 0
u = −0.395123 + 0.506844I
a = −1.10659 − 1.68743I
b = −0.407184 + 1.157940I
−1.29627 + 3.80118I 0
u = −0.395123 + 0.506844I
a = −1.86351 − 0.84193I
b = −0.388860 − 0.289092I
−2.23683 + 1.28930I 0
u = −0.395123 + 0.506844I
a = 0.08448 + 2.04846I
b = −0.924867 − 1.064220I
0.32630 − 7.33953I 0
u = −0.395123 + 0.506844I
a = 1.87864 − 0.88694I
b = 0.915937 + 0.277129I
−2.23683 − 4.11951I 0
u = −0.395123 + 0.506844I
a = 0.42118 − 2.15310I
b = 1.071630 + 0.766574I
0.32630 − 7.33953I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.13382 + 2.69650I
b = −0.624000 − 0.815866I
3.19680 − 6.41584I 0
u = −0.395123 + 0.506844I
a = 2.92664 + 1.09934I
b = 0.161153 + 0.355331I
−1.29627 − 6.63139I 0
u = −0.395123 − 0.506844I
a = 0.907790 − 0.226548I
b = −0.647304 − 1.109790I
3.19680 − 3.58563I 3.66733 + 1.31877I
u = −0.395123 − 0.506844I
a = −0.017246 + 0.753773I
b = −1.163050 − 0.611843I
−2.23683 − 1.28930I −7.64088 − 4.99207I
u = −0.395123 − 0.506844I
a = 1.277480 − 0.112709I
b = −0.886862 − 0.535701I
0.32630 − 4.50932I −7.34372 + 5.11480I
u = −0.395123 − 0.506844I
a = 0.578173 − 1.190000I
b = −0.944476 + 0.408288I
−3.81269 + 1.41510I −16.4346 − 4.9087I
u = −0.395123 − 0.506844I
a = −0.281884 − 0.537705I
b = 1.71358 + 1.04898I
−1.29627 + 6.63139I −4.6093 − 13.9215I
u = −0.395123 − 0.506844I
a = −0.72321 + 1.21563I
b = 0.189954 + 0.056607I
−1.85793 − 0.83268I −7.80908 + 0.15485I
u = −0.395123 − 0.506844I
a = 0.43939 − 1.37682I
b = −0.568100 + 0.987543I
−1.85793 + 3.66289I −7.80908 − 9.97234I
u = −0.395123 − 0.506844I
a = 0.53617 − 1.38915I
b = 0.292755 + 1.302630I
−2.23683 + 4.11951I −7.64088 − 4.82542I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 − 0.506844I
a = 0.40425 + 1.54629I
b = 1.31383 − 1.13328I
3.19680 + 6.41584I 3.66733 − 11.13625I
u = −0.395123 − 0.506844I
a = −0.40252 + 1.54965I
b = 0.831592 − 0.177152I
−3.81269 + 1.41510I −16.4346 − 4.9087I
u = −0.395123 − 0.506844I
a = −1.50585 + 0.57585I
b = 0.561889 + 0.602950I
0.32630 − 4.50932I −7.34372 + 5.11480I
u = −0.395123 − 0.506844I
a = 0.251194 − 0.178954I
b = −0.901890 + 0.113767I
−1.85793 − 0.83268I −7.80908 + 0.15485I
u = −0.395123 − 0.506844I
a = 0.66841 + 1.64193I
b = 0.871448 − 0.321314I
−1.85793 + 3.66289I −7.80908 − 9.97234I
u = −0.395123 − 0.506844I
a = −1.81056 − 0.60810I
b = −1.292500 + 0.105875I
−1.29627 − 3.80118I 0
u = −0.395123 − 0.506844I
a = −1.98119 − 0.26736I
b = 0.473513 + 0.370593I
3.19680 − 3.58563I 0
u = −0.395123 − 0.506844I
a = −1.10659 + 1.68743I
b = −0.407184 − 1.157940I
−1.29627 − 3.80118I 0
u = −0.395123 − 0.506844I
a = −1.86351 + 0.84193I
b = −0.388860 + 0.289092I
−2.23683 − 1.28930I 0
u = −0.395123 − 0.506844I
a = 0.08448 − 2.04846I
b = −0.924867 + 1.064220I
0.32630 + 7.33953I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 − 0.506844I
a = 1.87864 + 0.88694I
b = 0.915937 − 0.277129I
−2.23683 + 4.11951I 0
u = −0.395123 − 0.506844I
a = 0.42118 + 2.15310I
b = 1.071630 − 0.766574I
0.32630 + 7.33953I 0
u = −0.395123 − 0.506844I
a = −0.13382 − 2.69650I
b = −0.624000 + 0.815866I
3.19680 + 6.41584I 0
u = −0.395123 − 0.506844I
a = 2.92664 − 1.09934I
b = 0.161153 − 0.355331I
−1.29627 + 6.63139I 0
u = −0.10488 + 1.55249I
a = −0.461183 + 0.892316I
b = −1.063630 − 0.517160I
−10.81440 − 3.16396I −20.0881 + 2.5648I
u = −0.10488 + 1.55249I
a = 0.495958 − 0.888062I
b = 1.24404 + 1.37283I
−6.67544 − 9.08839I −10.9972 + 12.5883I
u = −0.10488 + 1.55249I
a = −0.218137 + 1.032250I
b = −0.442822 − 0.518019I
−8.85968 − 0.91618I −11.46256 − 2.49880I
u = −0.10488 + 1.55249I
a = −0.938059 + 0.686154I
b = −1.114430 − 0.398815I
−8.85968 − 5.41175I −11.46256 + 7.62840I
u = −0.10488 + 1.55249I
a = −0.626036 + 0.515485I
b = −1.90563 − 1.18371I
−3.80495 − 8.16470I 0.01385 + 8.79231I
u = −0.10488 + 1.55249I
a = −0.826373 + 0.857145I
b = −1.32669 − 0.86311I
−6.67544 − 9.08839I −10.9972 + 12.5883I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 + 1.55249I
a = 0.207448 − 0.731849I
b = 0.96687 + 1.52829I
−8.85968 − 5.41175I −11.46256 + 7.62840I
u = −0.10488 + 1.55249I
a = 0.285531 − 0.704398I
b = 1.33695 + 0.80957I
−10.81440 − 3.16396I −20.0881 + 2.5648I
u = −0.10488 + 1.55249I
a = 0.690763 − 0.277309I
b = 0.279626 − 0.077482I
−3.80495 + 1.83677I 0.01385 − 3.66271I
u = −0.10488 + 1.55249I
a = 0.267837 + 0.681491I
b = 0.96295 − 1.99576I
−8.29802 + 2.05233I −8.26277 − 6.44798I
u = −0.10488 + 1.55249I
a = 0.607253 + 1.124130I
b = 0.352803 − 0.362834I
−9.23857 − 0.45956I −11.29436 + 2.64813I
u = −0.10488 + 1.55249I
a = −0.035023 − 0.663384I
b = −0.29712 + 2.09193I
−9.23857 − 5.86837I −11.29436 + 2.48147I
u = −0.10488 + 1.55249I
a = −0.026839 + 0.644591I
b = −0.483773 − 0.157378I
−6.67544 + 2.76046I −10.99719 − 7.45875I
u = −0.10488 + 1.55249I
a = −1.354220 − 0.099900I
b = −1.033570 − 0.015201I
−9.23857 − 5.86837I −11.29436 + 2.48147I
u = −0.10488 + 1.55249I
a = 1.32139 + 0.53100I
b = 1.086100 − 0.344342I
−8.29802 + 2.05233I −8.26277 − 6.44798I
u = −0.10488 + 1.55249I
a = 0.67645 − 1.27316I
b = 0.734630 + 1.025980I
−3.80495 − 8.16470I 0. + 8.79231I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 + 1.55249I
a = 0.312972 − 0.306376I
b = 1.57967 + 0.44691I
−8.85968 − 0.91618I −11.46256 − 2.49880I
u = −0.10488 + 1.55249I
a = 0.079956 − 0.317012I
b = 0.997908 + 0.109270I
−6.67544 + 2.76046I −10.99719 − 7.45875I
u = −0.10488 + 1.55249I
a = 0.247931 + 0.210501I
b = 1.80889 − 0.82486I
−9.23857 − 0.45956I −11.29436 + 2.64813I
u = −0.10488 + 1.55249I
a = 0.061794 + 0.175940I
b = −0.358075 − 1.101490I
−3.80495 + 1.83677I 0.01385 − 3.66271I
u = −0.10488 + 1.55249I
a = −0.065207 − 0.143109I
b = −2.24387 + 1.80044I
−8.29802 − 8.38025I −8.2628 + 11.5776I
u = −0.10488 + 1.55249I
a = −1.25164 − 1.36078I
b = −0.229015 + 0.086225I
−8.29802 − 8.38025I 0
u = −0.10488 − 1.55249I
a = −0.461183 − 0.892316I
b = −1.063630 + 0.517160I
−10.81440 + 3.16396I −20.0881 − 2.5648I
u = −0.10488 − 1.55249I
a = 0.495958 + 0.888062I
b = 1.24404 − 1.37283I
−6.67544 + 9.08839I −10.9972 − 12.5883I
u = −0.10488 − 1.55249I
a = −0.218137 − 1.032250I
b = −0.442822 + 0.518019I
−8.85968 + 0.91618I −11.46256 + 2.49880I
u = −0.10488 − 1.55249I
a = −0.938059 − 0.686154I
b = −1.114430 + 0.398815I
−8.85968 + 5.41175I −11.46256 − 7.62840I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 − 1.55249I
a = −0.626036 − 0.515485I
b = −1.90563 + 1.18371I
−3.80495 + 8.16470I 0.01385 − 8.79231I
u = −0.10488 − 1.55249I
a = −0.826373 − 0.857145I
b = −1.32669 + 0.86311I
−6.67544 + 9.08839I −10.9972 − 12.5883I
u = −0.10488 − 1.55249I
a = 0.207448 + 0.731849I
b = 0.96687 − 1.52829I
−8.85968 + 5.41175I −11.46256 − 7.62840I
u = −0.10488 − 1.55249I
a = 0.285531 + 0.704398I
b = 1.33695 − 0.80957I
−10.81440 + 3.16396I −20.0881 − 2.5648I
u = −0.10488 − 1.55249I
a = 0.690763 + 0.277309I
b = 0.279626 + 0.077482I
−3.80495 − 1.83677I 0.01385 + 3.66271I
u = −0.10488 − 1.55249I
a = 0.267837 − 0.681491I
b = 0.96295 + 1.99576I
−8.29802 − 2.05233I −8.26277 + 6.44798I
u = −0.10488 − 1.55249I
a = 0.607253 − 1.124130I
b = 0.352803 + 0.362834I
−9.23857 + 0.45956I −11.29436 − 2.64813I
u = −0.10488 − 1.55249I
a = −0.035023 + 0.663384I
b = −0.29712 − 2.09193I
−9.23857 + 5.86837I −11.29436 − 2.48147I
u = −0.10488 − 1.55249I
a = −0.026839 − 0.644591I
b = −0.483773 + 0.157378I
−6.67544 − 2.76046I −10.99719 + 7.45875I
u = −0.10488 − 1.55249I
a = −1.354220 + 0.099900I
b = −1.033570 + 0.015201I
−9.23857 + 5.86837I −11.29436 − 2.48147I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 − 1.55249I
a = 1.32139 − 0.53100I
b = 1.086100 + 0.344342I
−8.29802 − 2.05233I −8.26277 + 6.44798I
u = −0.10488 − 1.55249I
a = 0.67645 + 1.27316I
b = 0.734630 − 1.025980I
−3.80495 + 8.16470I 0. − 8.79231I
u = −0.10488 − 1.55249I
a = 0.312972 + 0.306376I
b = 1.57967 − 0.44691I
−8.85968 + 0.91618I −11.46256 + 2.49880I
u = −0.10488 − 1.55249I
a = 0.079956 + 0.317012I
b = 0.997908 − 0.109270I
−6.67544 − 2.76046I −10.99719 + 7.45875I
u = −0.10488 − 1.55249I
a = 0.247931 − 0.210501I
b = 1.80889 + 0.82486I
−9.23857 + 0.45956I −11.29436 − 2.64813I
u = −0.10488 − 1.55249I
a = 0.061794 − 0.175940I
b = −0.358075 + 1.101490I
−3.80495 − 1.83677I 0.01385 + 3.66271I
u = −0.10488 − 1.55249I
a = −0.065207 + 0.143109I
b = −2.24387 − 1.80044I
−8.29802 + 8.38025I −8.2628 − 11.5776I
u = −0.10488 − 1.55249I
a = −1.25164 + 1.36078I
b = −0.229015 − 0.086225I
−8.29802 + 8.38025I 0
20
III.
I
u
3
= h1.28 × 10
6
u
24
− 1.29 × 10
6
u
23
+ · · · + 9.65 × 10
5
b − 3.64 × 10
6
, 1.09 ×
10
7
u
24
+1.22×10
7
u
23
+· · ·+9.65×10
5
a−9.08×10
6
, 3u
25
+3u
24
+· · ·−3u+1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
−11.3227u
24
− 12.6476u
23
+ ··· − 24.9129u + 9.40603
−1.32489u
24
+ 1.33328u
23
+ ··· − 1.91670u + 3.77424
a
1
=
0.704452u
24
+ 0.00409856u
23
+ ··· + 7.42560u − 3.81888
−0.700354u
24
− 0.804853u
23
+ ··· − 2.11443u − 0.234817
a
4
=
1.90570u
24
+ 0.232011u
23
+ ··· + 3.36279u − 3.03538
−1.56919u
24
− 1.80857u
23
+ ··· − 1.19451u − 0.868684
a
2
=
−1.33728u
24
− 3.30659u
23
+ ··· + 2.81981u − 4.40145
−1.83443u
24
− 0.976439u
23
+ ··· − 3.23603u + 0.156149
a
8
=
−12.6476u
24
− 11.3143u
23
+ ··· − 26.8296u + 13.1803
−1.32489u
24
+ 1.33328u
23
+ ··· − 1.91670u + 3.77424
a
3
=
−2.43776u
24
− 3.00552u
23
+ ··· − 3.83884u − 2.32182
−1.96931u
24
− 0.702641u
23
+ ··· − 5.73873u + 0.445761
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−5.83876u
24
− 1.95916u
23
+ ··· − 19.7988u + 6.79115
−0.687315u
24
+ 1.97683u
23
+ ··· − 2.76064u + 3.16448
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16337289
965461
u
24
+
20341383
965461
u
23
+ ··· +
53054017
965461
u −
16958173
965461
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
25
− 24u
24
+ ··· + 8u − 1)
c
2
, c
10
u
25
+ 6u
23
+ ··· + 3u − 3
c
3
, c
9
u
25
+ u
24
+ ··· + 14u − 3
c
4
3(3u
25
+ 24u
24
+ ··· + 8u + 1)
c
5
, c
6
3(3u
25
+ 3u
24
+ ··· − 3u + 1)
c
7
3(3u
25
− 33u
24
+ ··· − 5u
2
+ 1)
c
8
, c
12
u
25
− u
24
+ ··· + 18u + 9
c
11
3(3u
25
− 3u
24
+ ··· − 3u − 1)
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
9(9y
25
+ 144y
24
+ ··· − 44y −1)
c
2
, c
10
y
25
+ 12y
24
+ ··· − 9y −9
c
3
, c
9
y
25
− 11y
24
+ ··· + 46y −9
c
5
, c
6
, c
11
9(9y
25
+ 261y
24
+ ··· − 23y −1)
c
7
9(9y
25
− 27y
24
+ ··· + 10y −1)
c
8
, c
12
y
25
− 7y
24
+ ··· + 756y −81
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139409 + 0.935691I
a = 0.84933 − 1.28204I
b = 1.08118 + 0.97344I
1.33306 − 5.44425I −3.58587 + 7.46892I
u = −0.139409 − 0.935691I
a = 0.84933 + 1.28204I
b = 1.08118 − 0.97344I
1.33306 + 5.44425I −3.58587 − 7.46892I
u = −1.29971
a = −0.393591
b = 0.511554
−2.82749 −24.4960
u = −0.065043 + 0.681628I
a = 0.849488 + 0.907455I
b = −0.673799 + 0.520011I
2.05503 + 4.77815I −2.21061 − 7.54120I
u = −0.065043 − 0.681628I
a = 0.849488 − 0.907455I
b = −0.673799 − 0.520011I
2.05503 − 4.77815I −2.21061 + 7.54120I
u = −0.527060 + 0.342003I
a = −0.45508 − 1.98170I
b = 0.917604 + 0.888839I
0.58769 − 6.44489I −3.50337 + 5.24964I
u = −0.527060 − 0.342003I
a = −0.45508 + 1.98170I
b = 0.917604 − 0.888839I
0.58769 + 6.44489I −3.50337 − 5.24964I
u = −0.07693 + 1.45578I
a = −0.140733 + 0.544149I
b = −0.781335 − 0.246736I
−6.47742 + 1.78174I −8.59786 + 1.29099I
u = −0.07693 − 1.45578I
a = −0.140733 − 0.544149I
b = −0.781335 + 0.246736I
−6.47742 − 1.78174I −8.59786 − 1.29099I
u = 0.333604 + 0.407699I
a = 1.52958 − 0.56643I
b = 0.741208 + 0.434646I
−2.22833 − 2.22988I −8.23719 + 4.92806I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.333604 − 0.407699I
a = 1.52958 + 0.56643I
b = 0.741208 − 0.434646I
−2.22833 + 2.22988I −8.23719 − 4.92806I
u = 0.355757 + 0.361090I
a = −2.20095 + 0.15407I
b = −0.838634 − 0.739932I
−1.37213 + 5.75583I −4.99345 − 3.86999I
u = 0.355757 − 0.361090I
a = −2.20095 − 0.15407I
b = −0.838634 + 0.739932I
−1.37213 − 5.75583I −4.99345 + 3.86999I
u = 0.10906 + 1.50963I
a = −0.733282 + 0.691650I
b = −1.12411 − 1.03156I
−8.40480 − 0.76829I −7.10287 + 0.I
u = 0.10906 − 1.50963I
a = −0.733282 − 0.691650I
b = −1.12411 + 1.03156I
−8.40480 + 0.76829I −7.10287 + 0.I
u = 0.09232 + 1.53624I
a = 0.765943 − 0.674345I
b = 1.10667 + 1.11442I
−7.96724 + 7.26085I −4.39305 − 3.18345I
u = 0.09232 − 1.53624I
a = 0.765943 + 0.674345I
b = 1.10667 − 1.11442I
−7.96724 − 7.26085I −4.39305 + 3.18345I
u = −0.11080 + 1.54481I
a = −0.657300 + 0.877205I
b = −1.28228 − 1.11260I
−6.06586 − 8.44559I −3.25508 + 4.03663I
u = −0.11080 − 1.54481I
a = −0.657300 − 0.877205I
b = −1.28228 + 1.11260I
−6.06586 + 8.44559I −3.25508 − 4.03663I
u = −0.11068 + 1.56442I
a = −0.373565 + 0.755507I
b = −1.140590 − 0.668030I
−9.98771 − 3.11005I −7.23130 + 1.80254I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11068 − 1.56442I
a = −0.373565 − 0.755507I
b = −1.140590 + 0.668030I
−9.98771 + 3.11005I −7.23130 − 1.80254I
u = 0.17655 + 1.58755I
a = 0.358080 − 0.208144I
b = 0.393656 + 0.531720I
−7.17425 + 5.89770I −4.52396 − 3.09477I
u = 0.17655 − 1.58755I
a = 0.358080 + 0.208144I
b = 0.393656 − 0.531720I
−7.17425 − 5.89770I −4.52396 + 3.09477I
u = 0.112488 + 0.335309I
a = 1.90528 − 1.87984I
b = 0.844648 + 0.427399I
−2.23230 − 2.18556I −9.78413 + 4.86470I
u = 0.112488 − 0.335309I
a = 1.90528 + 1.87984I
b = 0.844648 − 0.427399I
−2.23230 + 2.18556I −9.78413 − 4.86470I
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
9(u
11
+ 3u
10
+ ··· + 2u + 1)
8
(3u
25
− 24u
24
+ ··· + 8u − 1)
· (3u
40
− 63u
39
+ ··· − 4480u + 256)
c
2
, c
10
(u
25
+ 6u
23
+ ··· + 3u − 3)(u
40
+ 4u
38
+ ··· − 3u + 3)
· (u
88
+ 3u
87
+ ··· + 313760u + 32689)
c
3
, c
9
(u
25
+ u
24
+ ··· + 14u − 3)(u
40
− 3u
39
+ ··· + 10u + 25)
· (u
88
+ u
87
+ ··· + 7015212u + 14269049)
c
4
9(u
11
+ 3u
10
+ ··· + 2u + 1)
8
(3u
25
+ 24u
24
+ ··· + 8u + 1)
· (3u
40
− 63u
39
+ ··· − 4480u + 256)
c
5
, c
6
9(u
4
+ u
3
+ 3u
2
+ 2u + 1)
22
(3u
25
+ 3u
24
+ ··· − 3u + 1)
· (3u
40
− 66u
39
+ ··· − 43008u + 2048)
c
7
9(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
8
· (3u
25
− 33u
24
+ ··· − 5u
2
+ 1)(3u
40
− 90u
39
+ ··· − 96u + 16)
c
8
, c
12
(u
25
− u
24
+ ··· + 18u + 9)(u
40
+ u
39
+ ··· + 36u + 9)
· (u
88
− u
87
+ ··· − 584u + 83)
c
11
9(u
4
+ u
3
+ 3u
2
+ 2u + 1)
22
(3u
25
− 3u
24
+ ··· − 3u − 1)
· (3u
40
− 66u
39
+ ··· − 43008u + 2048)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
81(y
11
+ 7y
10
+ ··· − 6y −1)
8
(9y
25
+ 144y
24
+ ··· − 44y −1)
· (9y
40
+ 207y
39
+ ··· + 876544y + 65536)
c
2
, c
10
(y
25
+ 12y
24
+ ··· − 9y −9)(y
40
+ 8y
39
+ ··· − 63y + 9)
· (y
88
+ 35y
87
+ ··· + 45878166472y + 1068570721)
c
3
, c
9
(y
25
− 11y
24
+ ··· + 46y −9)(y
40
− 19y
39
+ ··· − 1150y + 625)
· (y
88
− 41y
87
+ ··· − 6370049061361272y + 203605759364401)
c
5
, c
6
, c
11
81(y
4
+ 5y
3
+ ··· + 2y + 1)
22
(9y
25
+ 261y
24
+ ··· − 23y −1)
· (9y
40
+ 306y
39
+ ··· + 2097152y + 4194304)
c
7
81(y
11
− y
10
+ ··· + 6y −1)
8
(9y
25
− 27y
24
+ ··· + 10y −1)
· (9y
40
− 36y
39
+ ··· − 12928y + 256)
c
8
, c
12
(y
25
− 7y
24
+ ··· + 756y −81)(y
40
+ y
39
+ ··· + 324y + 81)
· (y
88
− 21y
87
+ ··· − 714888y + 6889)
28
