12a
0921
(K12a
0921
)
A knot diagram
1
Linearized knot diagam
4 6 9 10 11 3 12 1 2 5 8 7
Solving Sequence
4,10
5 11
2,6
1 9 3 7 8 12
c
4
c
10
c
5
c
1
c
9
c
3
c
6
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.48478 × 10
151
u
92
+ 2.29231 × 10
151
u
91
+ ··· + 4.90569 × 10
151
b − 2.80006 × 10
152
,
2.01917 × 10
152
u
92
− 3.99607 × 10
151
u
91
+ ··· + 9.81138 × 10
151
a + 9.96934 × 10
152
, u
93
+ u
92
+ ··· − 18u + 4i
I
u
2
= hu
20
− 9u
18
+ ··· − 2u
2
+ b, −u
19
+ 10u
17
+ ··· + a + 3, u
21
− 11u
19
+ ··· − 6u
2
+ 1i
I
u
3
= h−u
2
+ b, a − 1, u
15
− 3u
13
+ u
10
+ 5u
9
− 2u
8
− u
6
− 3u
5
+ 2u
4
− u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 129 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−9.48 × 10
151
u
92
+ 2.29 × 10
151
u
91
+ · · · + 4.91 × 10
151
b − 2.80 ×
10
152
, 2.02 × 10
152
u
92
− 4.00 × 10
151
u
91
+ · · · + 9.81 × 10
151
a + 9.97 ×
10
152
, u
93
+ u
92
+ · · · − 18u + 4i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
−2.05799u
92
+ 0.407289u
91
+ ··· + 12.6723u − 10.1610
1.93342u
92
− 0.467276u
91
+ ··· − 30.7332u + 5.70778
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
−0.124563u
92
− 0.0599871u
91
+ ··· − 18.0609u − 4.45321
1.93342u
92
− 0.467276u
91
+ ··· − 30.7332u + 5.70778
a
9
=
0.799139u
92
− 0.728059u
91
+ ··· − 46.3661u + 4.77657
1.44094u
92
− 0.629335u
91
+ ··· − 29.6189u + 5.05852
a
3
=
−1.94848u
92
+ 0.489593u
91
+ ··· + 11.8488u − 10.0698
1.92816u
92
− 0.456854u
91
+ ··· − 30.4428u + 5.56450
a
7
=
1.25578u
92
− 0.230053u
91
+ ··· − 14.2454u − 1.89595
−1.36128u
92
+ 0.166064u
91
+ ··· + 17.7972u − 4.51459
a
8
=
−1.51946u
92
+ 0.0968024u
91
+ ··· + 24.1105u − 2.93910
−2.91059u
92
+ 0.633840u
91
+ ··· + 41.0680u − 8.34160
a
12
=
0.632413u
92
− 0.385835u
91
+ ··· − 27.7370u + 0.504505
−0.480647u
92
+ 0.112108u
91
+ ··· − 0.601988u + 0.0953933
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.79061u
92
+ 1.91185u
91
+ ··· + 111.874u − 20.5189
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
93
− 7u
92
+ ··· + 87046u − 14548
c
2
, c
6
u
93
− 4u
92
+ ··· + 818u + 292
c
3
u
93
− u
92
+ ··· + 82u − 4
c
4
, c
5
, c
10
u
93
+ u
92
+ ··· − 18u + 4
c
7
, c
11
, c
12
u
93
− 5u
92
+ ··· − 62u + 4
c
8
u
93
+ 5u
92
+ ··· − 263654u + 40564
c
9
u
93
+ 3u
92
+ ··· − 3506u − 1364
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
93
− 19y
92
+ ··· + 9425154940y −211644304
c
2
, c
6
y
93
− 48y
92
+ ··· + 1643820y −85264
c
3
y
93
− 9y
92
+ ··· + 3164y −16
c
4
, c
5
, c
10
y
93
− 101y
92
+ ··· − 468y −16
c
7
, c
11
, c
12
y
93
+ 81y
92
+ ··· + 588y −16
c
8
y
93
− 27y
92
+ ··· + 67097196492y −1645438096
c
9
y
93
+ 21y
92
+ ··· − 67270084y −1860496
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.508441 + 0.865954I
a = −0.325096 + 1.247810I
b = 1.041020 − 0.783812I
0.20096 + 8.92280I 0
u = −0.508441 − 0.865954I
a = −0.325096 − 1.247810I
b = 1.041020 + 0.783812I
0.20096 − 8.92280I 0
u = 0.469257 + 0.915218I
a = −0.423152 − 1.219970I
b = 1.082360 + 0.876290I
5.41996 − 12.97790I 0
u = 0.469257 − 0.915218I
a = −0.423152 + 1.219970I
b = 1.082360 − 0.876290I
5.41996 + 12.97790I 0
u = −0.927529 + 0.448886I
a = −1.058270 + 0.051455I
b = 0.397945 + 0.501367I
8.09310 + 0.14930I 0
u = −0.927529 − 0.448886I
a = −1.058270 − 0.051455I
b = 0.397945 − 0.501367I
8.09310 − 0.14930I 0
u = 0.530707 + 0.896493I
a = −0.490200 + 0.098599I
b = 0.718569 − 0.370152I
2.47227 − 0.63691I 0
u = 0.530707 − 0.896493I
a = −0.490200 − 0.098599I
b = 0.718569 + 0.370152I
2.47227 + 0.63691I 0
u = 0.534102 + 0.752303I
a = −0.142930 − 1.371140I
b = 0.918907 + 0.670898I
2.25254 − 4.57716I 0
u = 0.534102 − 0.752303I
a = −0.142930 + 1.371140I
b = 0.918907 − 0.670898I
2.25254 + 4.57716I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.735519 + 0.867109I
a = −0.628196 + 0.018969I
b = 0.763287 + 0.500011I
−0.33868 − 3.16041I 0
u = −0.735519 − 0.867109I
a = −0.628196 − 0.018969I
b = 0.763287 − 0.500011I
−0.33868 + 3.16041I 0
u = −0.556116 + 0.577176I
a = 0.178244 − 1.271710I
b = −1.08666 + 0.99348I
2.06421 + 7.25817I 0
u = −0.556116 − 0.577176I
a = 0.178244 + 1.271710I
b = −1.08666 − 0.99348I
2.06421 − 7.25817I 0
u = 0.837532 + 0.861025I
a = −0.678478 − 0.091597I
b = 0.777681 − 0.589874I
4.46674 + 7.02318I 0
u = 0.837532 − 0.861025I
a = −0.678478 + 0.091597I
b = 0.777681 + 0.589874I
4.46674 − 7.02318I 0
u = 0.625041 + 0.460913I
a = 0.66228 − 1.43861I
b = 0.745720 + 0.381896I
1.99795 − 3.83741I 0
u = 0.625041 − 0.460913I
a = 0.66228 + 1.43861I
b = 0.745720 − 0.381896I
1.99795 + 3.83741I 0
u = −0.301204 + 0.688922I
a = −0.56454 + 1.82402I
b = 0.624251 − 0.868525I
9.88119 + 3.92848I 0
u = −0.301204 − 0.688922I
a = −0.56454 − 1.82402I
b = 0.624251 + 0.868525I
9.88119 − 3.92848I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.723386
a = 1.60032
b = 0.704568
−0.943143 −10.4180
u = −1.281680 + 0.000599I
a = −0.204360 + 1.175340I
b = −0.788781 − 1.123720I
1.54277 − 5.13635I 0
u = −1.281680 − 0.000599I
a = −0.204360 − 1.175340I
b = −0.788781 + 1.123720I
1.54277 + 5.13635I 0
u = 0.538824 + 0.470683I
a = 0.160205 + 1.374300I
b = −1.080240 − 0.790479I
−2.76079 − 3.81720I −9.13434 + 6.95796I
u = 0.538824 − 0.470683I
a = 0.160205 − 1.374300I
b = −1.080240 + 0.790479I
−2.76079 + 3.81720I −9.13434 − 6.95796I
u = 0.260333 + 0.634297I
a = 0.292242 + 1.114540I
b = −0.257972 − 1.062420I
4.35474 − 0.70676I 1.78969 + 4.36362I
u = 0.260333 − 0.634297I
a = 0.292242 − 1.114540I
b = −0.257972 + 1.062420I
4.35474 + 0.70676I 1.78969 − 4.36362I
u = −1.316730 + 0.162695I
a = −0.170965 − 0.295963I
b = 0.30737 + 2.10149I
2.22557 + 8.18081I 0
u = −1.316730 − 0.162695I
a = −0.170965 + 0.295963I
b = 0.30737 − 2.10149I
2.22557 − 8.18081I 0
u = 1.326910 + 0.070082I
a = −0.001160 + 0.218282I
b = 1.26981 − 1.26624I
3.28953 + 0.55896I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.326910 − 0.070082I
a = −0.001160 − 0.218282I
b = 1.26981 + 1.26624I
3.28953 − 0.55896I 0
u = −1.281140 + 0.367616I
a = −0.069228 − 0.910131I
b = −1.28880 + 0.64130I
−0.63612 + 2.02419I 0
u = −1.281140 − 0.367616I
a = −0.069228 + 0.910131I
b = −1.28880 − 0.64130I
−0.63612 − 2.02419I 0
u = 1.353450 + 0.161844I
a = −0.132542 + 0.363700I
b = 0.17474 − 1.64951I
−3.22563 − 5.08058I 0
u = 1.353450 − 0.161844I
a = −0.132542 − 0.363700I
b = 0.17474 + 1.64951I
−3.22563 + 5.08058I 0
u = 0.407933 + 0.464047I
a = −0.866007 + 0.691674I
b = 0.688589 − 0.455821I
2.66989 + 0.13790I 2.92063 − 0.32720I
u = 0.407933 − 0.464047I
a = −0.866007 − 0.691674I
b = 0.688589 + 0.455821I
2.66989 − 0.13790I 2.92063 + 0.32720I
u = −1.381120 + 0.098816I
a = 0.006521 − 0.340348I
b = 0.636543 + 1.106670I
−2.64960 + 1.68388I 0
u = −1.381120 − 0.098816I
a = 0.006521 + 0.340348I
b = 0.636543 − 1.106670I
−2.64960 − 1.68388I 0
u = 1.360210 + 0.260057I
a = −0.162811 + 0.802512I
b = −1.021440 − 0.796484I
−4.89754 − 3.66913I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.360210 − 0.260057I
a = −0.162811 − 0.802512I
b = −1.021440 + 0.796484I
−4.89754 + 3.66913I 0
u = 1.389140 + 0.012717I
a = −0.554931 + 1.201120I
b = −0.847473 − 0.644385I
−5.08356 − 2.17532I 0
u = 1.389140 − 0.012717I
a = −0.554931 − 1.201120I
b = −0.847473 + 0.644385I
−5.08356 + 2.17532I 0
u = 1.406690 + 0.094426I
a = −1.29452 − 1.03273I
b = −0.598145 − 0.021332I
−0.18126 − 7.44744I 0
u = 1.406690 − 0.094426I
a = −1.29452 + 1.03273I
b = −0.598145 + 0.021332I
−0.18126 + 7.44744I 0
u = −1.39601 + 0.23784I
a = −0.329690 − 0.575972I
b = −0.98291 + 1.39370I
−0.90850 + 3.86973I 0
u = −1.39601 − 0.23784I
a = −0.329690 + 0.575972I
b = −0.98291 − 1.39370I
−0.90850 − 3.86973I 0
u = −1.41760 + 0.04823I
a = −0.99595 + 1.26314I
b = −0.693903 − 0.244095I
−6.04675 + 2.86647I 0
u = −1.41760 − 0.04823I
a = −0.99595 − 1.26314I
b = −0.693903 + 0.244095I
−6.04675 − 2.86647I 0
u = −0.135731 + 0.564632I
a = −0.038430 − 1.246730I
b = 0.596702 + 1.029200I
1.44493 + 2.51937I 0.01028 − 7.23544I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135731 − 0.564632I
a = −0.038430 + 1.246730I
b = 0.596702 − 1.029200I
1.44493 − 2.51937I 0.01028 + 7.23544I
u = 0.047256 + 0.569881I
a = 0.11875 + 1.41024I
b = 0.79856 − 1.28376I
6.45729 − 5.60603I 5.38089 + 6.61393I
u = 0.047256 − 0.569881I
a = 0.11875 − 1.41024I
b = 0.79856 + 1.28376I
6.45729 + 5.60603I 5.38089 − 6.61393I
u = 1.43982 + 0.23261I
a = 0.553535 − 1.141840I
b = 0.815368 + 1.022160I
4.25414 − 7.21931I 0
u = 1.43982 − 0.23261I
a = 0.553535 + 1.141840I
b = 0.815368 − 1.022160I
4.25414 + 7.21931I 0
u = −0.467586 + 0.257946I
a = 0.02407 − 1.81471I
b = −1.094560 + 0.380639I
−0.223024 + 0.638682I −7.26593 − 1.08990I
u = −0.467586 − 0.257946I
a = 0.02407 + 1.81471I
b = −1.094560 − 0.380639I
−0.223024 − 0.638682I −7.26593 + 1.08990I
u = 1.48280 + 0.12522I
a = −0.584483 + 0.824508I
b = −1.39781 − 0.71566I
−6.64297 − 2.24828I 0
u = 1.48280 − 0.12522I
a = −0.584483 − 0.824508I
b = −1.39781 + 0.71566I
−6.64297 + 2.24828I 0
u = −1.49936 + 0.17405I
a = −0.571538 − 0.743869I
b = −1.53989 + 0.86367I
−9.39431 + 6.26075I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49936 − 0.17405I
a = −0.571538 + 0.743869I
b = −1.53989 − 0.86367I
−9.39431 − 6.26075I 0
u = 1.50553 + 0.20623I
a = −0.567957 + 0.697438I
b = −1.62262 − 0.98031I
−4.61612 − 10.16490I 0
u = 1.50553 − 0.20623I
a = −0.567957 − 0.697438I
b = −1.62262 + 0.98031I
−4.61612 + 10.16490I 0
u = 1.48132 + 0.41379I
a = 0.044885 + 0.816597I
b = −1.072630 − 0.146328I
−2.25116 − 8.01558I 0
u = 1.48132 − 0.41379I
a = 0.044885 − 0.816597I
b = −1.072630 + 0.146328I
−2.25116 + 8.01558I 0
u = −1.49735 + 0.35692I
a = 0.039185 − 0.774715I
b = −0.871253 + 0.182705I
−6.70226 + 4.67739I 0
u = −1.49735 − 0.35692I
a = 0.039185 + 0.774715I
b = −0.871253 − 0.182705I
−6.70226 − 4.67739I 0
u = −1.53475 + 0.12089I
a = 1.024310 + 0.928571I
b = 0.722740 − 0.376986I
−5.12025 + 5.82093I 0
u = −1.53475 − 0.12089I
a = 1.024310 − 0.928571I
b = 0.722740 + 0.376986I
−5.12025 − 5.82093I 0
u = −1.52693 + 0.26895I
a = 0.586700 + 0.990447I
b = 1.170260 − 0.787437I
−4.44470 + 8.33731I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52693 − 0.26895I
a = 0.586700 − 0.990447I
b = 1.170260 + 0.787437I
−4.44470 − 8.33731I 0
u = −0.235303 + 0.381265I
a = 0.96159 − 1.43797I
b = −0.610180 + 0.360523I
−0.375586 + 1.110620I −5.85320 − 5.23683I
u = −0.235303 − 0.381265I
a = 0.96159 + 1.43797I
b = −0.610180 − 0.360523I
−0.375586 − 1.110620I −5.85320 + 5.23683I
u = −1.52414 + 0.33387I
a = 0.521304 + 0.976377I
b = 1.39892 − 0.94174I
−1.0116 + 17.5021I 0
u = −1.52414 − 0.33387I
a = 0.521304 − 0.976377I
b = 1.39892 + 0.94174I
−1.0116 − 17.5021I 0
u = 1.56065
a = 1.42405
b = 0.642348
−8.44045 0
u = 1.53200 + 0.30838I
a = 0.544303 − 0.975626I
b = 1.32328 + 0.85818I
−6.4092 − 13.1952I 0
u = 1.53200 − 0.30838I
a = 0.544303 + 0.975626I
b = 1.32328 − 0.85818I
−6.4092 + 13.1952I 0
u = 1.54225 + 0.29438I
a = 0.069262 + 0.717819I
b = −0.570637 − 0.119504I
−3.25509 − 1.51532I 0
u = 1.54225 − 0.29438I
a = 0.069262 − 0.717819I
b = −0.570637 + 0.119504I
−3.25509 + 1.51532I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60036 + 0.03902I
a = 0.339371 + 0.487975I
b = 0.710583 − 0.058904I
−4.93556 − 4.01294I 0
u = −1.60036 − 0.03902I
a = 0.339371 − 0.487975I
b = 0.710583 + 0.058904I
−4.93556 + 4.01294I 0
u = 1.60243 + 0.10816I
a = 0.405139 − 0.408093I
b = 0.827639 + 0.088426I
−8.97902 − 0.30493I 0
u = 1.60243 − 0.10816I
a = 0.405139 + 0.408093I
b = 0.827639 − 0.088426I
−8.97902 + 0.30493I 0
u = −1.60735 + 0.20212I
a = 0.386947 + 0.314917I
b = 0.890916 − 0.105990I
−5.13275 + 4.82360I 0
u = −1.60735 − 0.20212I
a = 0.386947 − 0.314917I
b = 0.890916 + 0.105990I
−5.13275 − 4.82360I 0
u = 0.346577
a = −2.36075
b = 0.943840
2.83068 10.4240
u = −0.152629 + 0.293549I
a = −4.52463 − 0.47527I
b = −0.490294 + 0.609024I
4.95962 + 6.04460I 1.17092 − 11.50660I
u = −0.152629 − 0.293549I
a = −4.52463 + 0.47527I
b = −0.490294 − 0.609024I
4.95962 − 6.04460I 1.17092 + 11.50660I
u = −0.008205 + 0.246331I
a = −0.08505 − 3.19265I
b = 1.45669 + 0.61935I
7.62756 − 1.79977I 9.81021 + 0.38909I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.008205 − 0.246331I
a = −0.08505 + 3.19265I
b = 1.45669 − 0.61935I
7.62756 + 1.79977I 9.81021 − 0.38909I
u = 0.127305 + 0.126214I
a = −7.28555 − 3.50390I
b = −0.587613 − 0.256457I
−0.85046 − 2.18730I −11.9288 + 11.8413I
u = 0.127305 − 0.126214I
a = −7.28555 + 3.50390I
b = −0.587613 + 0.256457I
−0.85046 + 2.18730I −11.9288 − 11.8413I
14
II. I
u
2
=
hu
20
−9u
18
+· · ·−2u
2
+b, −u
19
+10u
17
+· · ·+a+3, u
21
−11u
19
+· · ·−6u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
u
19
− 10u
17
+ ··· + 9u
2
− 3
−u
20
+ 9u
18
+ ··· − u
3
+ 2u
2
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
−u
20
+ u
19
+ ··· + 11u
2
− 3
−u
20
+ 9u
18
+ ··· − u
3
+ 2u
2
a
9
=
−2u
18
+ 18u
16
+ ··· − 2u
2
− 3u
u
19
− 10u
17
+ ··· + 2u − 1
a
3
=
u
19
− 10u
17
+ ··· + 9u
2
− 2
−u
18
+ 9u
16
+ ··· + 4u
2
− u
a
7
=
−u
20
+ 10u
18
+ ··· + u + 3
−4u
20
− u
19
+ ··· + 5u + 1
a
8
=
5u
20
+ 8u
19
+ ··· − 8u − 7
5u
20
+ 8u
19
+ ··· − 4u − 8
a
12
=
7u
20
+ 9u
19
+ ··· − 8u − 9
4u
19
+ 4u
18
+ ··· + 9u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −4u
20
+ 6u
19
+ 39u
18
− 58u
17
− 158u
16
+ 228u
15
+ 345u
14
− 448u
13
− 453u
12
+
390u
11
+ 417u
10
+ 55u
9
−343u
8
−362u
7
+ 240u
6
+ 200u
5
−107u
4
−6u
3
+ 46u
2
+ 5u −20
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 6u
19
+ ··· + 9u − 1
c
2
u
21
− 3u
20
+ ··· − u + 1
c
3
u
21
+ u
19
+ ··· − 4u
3
− 1
c
4
, c
5
u
21
− 11u
19
+ ··· − 6u
2
+ 1
c
6
u
21
+ 3u
20
+ ··· − u − 1
c
7
u
21
+ u
20
+ ··· − 2u − 1
c
8
u
21
− u
20
+ ··· − 2u − 1
c
9
u
21
+ 4u
18
+ ··· − u
2
− 1
c
10
u
21
− 11u
19
+ ··· + 6u
2
− 1
c
11
, c
12
u
21
− u
20
+ ··· − 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 12y
20
+ ··· + 9y −1
c
2
, c
6
y
21
− 21y
20
+ ··· + 19y −1
c
3
y
21
+ 2y
20
+ ··· + 8y
2
− 1
c
4
, c
5
, c
10
y
21
− 22y
20
+ ··· + 12y −1
c
7
, c
11
, c
12
y
21
+ 21y
20
+ ··· + 14y −1
c
8
y
21
− 7y
20
+ ··· + 12y −1
c
9
y
21
− 8y
19
+ ··· − 2y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.255744 + 0.889960I
a = 0.672577 − 0.339366I
b = −0.727132 − 0.154624I
1.97479 + 1.31552I −5.85122 − 2.55614I
u = −0.255744 − 0.889960I
a = 0.672577 + 0.339366I
b = −0.727132 + 0.154624I
1.97479 − 1.31552I −5.85122 + 2.55614I
u = 1.255380 + 0.022059I
a = 0.841157 + 0.162242I
b = 1.93676 − 0.57055I
4.36898 + 1.63610I 2.61412 − 0.59366I
u = 1.255380 − 0.022059I
a = 0.841157 − 0.162242I
b = 1.93676 + 0.57055I
4.36898 − 1.63610I 2.61412 + 0.59366I
u = −1.26425
a = 0.931959
b = 1.79336
−0.221803 2.62670
u = −1.320610 + 0.146791I
a = 0.334116 − 0.914850I
b = −0.177692 + 1.239600I
1.41756 + 7.11034I −3.34752 − 5.62759I
u = −1.320610 − 0.146791I
a = 0.334116 + 0.914850I
b = −0.177692 − 1.239600I
1.41756 − 7.11034I −3.34752 + 5.62759I
u = −1.336660 + 0.309033I
a = −0.040182 − 0.647615I
b = −1.15216 + 0.84838I
−1.72885 + 2.95479I −7.19455 − 2.80057I
u = −1.336660 − 0.309033I
a = −0.040182 + 0.647615I
b = −1.15216 − 0.84838I
−1.72885 − 2.95479I −7.19455 + 2.80057I
u = 1.380070 + 0.215882I
a = −0.054776 + 0.872274I
b = −0.679947 − 0.858717I
−4.60051 − 4.33911I −7.30384 + 8.07755I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.380070 − 0.215882I
a = −0.054776 − 0.872274I
b = −0.679947 + 0.858717I
−4.60051 + 4.33911I −7.30384 − 8.07755I
u = −0.470407 + 0.375563I
a = −0.053666 − 1.392060I
b = −0.234865 − 0.689640I
4.67657 − 5.22027I −1.18453 + 2.23752I
u = −0.470407 − 0.375563I
a = −0.053666 + 1.392060I
b = −0.234865 + 0.689640I
4.67657 + 5.22027I −1.18453 − 2.23752I
u = 0.297006 + 0.518050I
a = 0.93330 + 1.24179I
b = −0.413320 + 0.328273I
−0.53747 + 1.63141I −4.38841 − 1.07862I
u = 0.297006 − 0.518050I
a = 0.93330 − 1.24179I
b = −0.413320 − 0.328273I
−0.53747 − 1.63141I −4.38841 + 1.07862I
u = 0.567113 + 0.064864I
a = −1.198340 + 0.359469I
b = 1.072880 + 0.452086I
6.99512 − 1.93767I −3.59564 + 3.74186I
u = 0.567113 − 0.064864I
a = −1.198340 − 0.359469I
b = 1.072880 − 0.452086I
6.99512 + 1.93767I −3.59564 − 3.74186I
u = −0.533430
a = −1.46571
b = 0.953611
2.54293 −18.1270
u = 1.57816 + 0.18852I
a = −0.597845 + 0.576829I
b = −0.711293 − 0.283542I
−4.68645 − 5.33753I −0.00830 + 5.00508I
u = 1.57816 − 0.18852I
a = −0.597845 − 0.576829I
b = −0.711293 + 0.283542I
−4.68645 + 5.33753I −0.00830 − 5.00508I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59095
a = −1.13893
b = −0.573444
−8.21101 8.01970
20
III. I
u
3
= h−u
2
+ b, a − 1, u
15
− 3u
13
+ · · · + u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
1
u
2
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
2
+ 1
u
2
a
9
=
−u
−u
3
+ u
a
3
=
u
4
− u
2
+ 1
u
6
− 2u
4
+ u
2
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
2
a
8
=
−u
7
+ 2u
3
−u
7
+ u
5
+ u
a
12
=
−u
12
+ u
11
+ u
10
− 2u
9
+ 3u
8
− u
7
− u
6
+ 2u
5
− 3u
4
+ u
3
− u + 1
u
13
− u
12
− 3u
11
+ 2u
10
+ u
9
+ u
8
+ 3u
7
− 2u
6
− u
5
− u
4
− 2u
3
+ u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
5
+ 4u
3
+ 4u − 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 6u
14
+ ··· + 2u − 1
c
2
, c
6
u
15
+ 6u
14
+ ··· + 2u + 1
c
3
u
15
+ 3u
13
+ ··· + 2u − 1
c
4
, c
5
, c
9
c
10
u
15
− 3u
13
+ u
10
+ 5u
9
− 2u
8
− u
6
− 3u
5
+ 2u
4
− u
3
+ u
2
− 1
c
7
, c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
5
c
8
(u
3
− u
2
+ 1)
5
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
15
− 18y
14
+ ··· + 10y −1
c
3
y
15
+ 6y
14
+ ··· + 22y −1
c
4
, c
5
, c
9
c
10
y
15
− 6y
14
+ ··· + 2y −1
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
5
c
8
(y
3
− y
2
+ 2y −1)
5
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.131335 + 0.994914I
a = 1.00000
b = −0.972606 − 0.261334I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.131335 − 0.994914I
a = 1.00000
b = −0.972606 + 0.261334I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.188117 + 0.879962I
a = 1.00000
b = −0.738945 + 0.331072I
−1.11345 −9.01951 + 0.I
u = 0.188117 − 0.879962I
a = 1.00000
b = −0.738945 − 0.331072I
−1.11345 −9.01951 + 0.I
u = −0.337905 + 0.833072I
a = 1.00000
b = −0.579829 − 0.562998I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.337905 − 0.833072I
a = 1.00000
b = −0.579829 + 0.562998I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −1.12246
a = 1.00000
b = 1.25992
−1.11345 −9.01950
u = 1.188510 + 0.170996I
a = 1.00000
b = 1.38332 + 0.40646I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 1.188510 − 0.170996I
a = 1.00000
b = 1.38332 − 0.40646I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.658707 + 0.399034I
a = 1.00000
b = 0.274667 + 0.525693I
3.02413 − 2.82812I −2.49024 + 2.97945I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.658707 − 0.399034I
a = 1.00000
b = 0.274667 − 0.525693I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 1.35788
a = 1.00000
b = 1.84385
−1.11345 −9.01950
u = −1.377980 + 0.066196I
a = 1.00000
b = 1.89445 − 0.18243I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −1.377980 − 0.066196I
a = 1.00000
b = 1.89445 + 0.18243I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.611656
a = 1.00000
b = 0.374123
−1.11345 −9.01950
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 6u
14
+ ··· + 2u − 1)(u
21
− 6u
19
+ ··· + 9u − 1)
· (u
93
− 7u
92
+ ··· + 87046u − 14548)
c
2
(u
15
+ 6u
14
+ ··· + 2u + 1)(u
21
− 3u
20
+ ··· − u + 1)
· (u
93
− 4u
92
+ ··· + 818u + 292)
c
3
(u
15
+ 3u
13
+ ··· + 2u − 1)(u
21
+ u
19
+ ··· − 4u
3
− 1)
· (u
93
− u
92
+ ··· + 82u − 4)
c
4
, c
5
(u
15
− 3u
13
+ u
10
+ 5u
9
− 2u
8
− u
6
− 3u
5
+ 2u
4
− u
3
+ u
2
− 1)
· (u
21
− 11u
19
+ ··· − 6u
2
+ 1)(u
93
+ u
92
+ ··· − 18u + 4)
c
6
(u
15
+ 6u
14
+ ··· + 2u + 1)(u
21
+ 3u
20
+ ··· − u − 1)
· (u
93
− 4u
92
+ ··· + 818u + 292)
c
7
((u
3
+ u
2
+ 2u + 1)
5
)(u
21
+ u
20
+ ··· − 2u − 1)
· (u
93
− 5u
92
+ ··· − 62u + 4)
c
8
((u
3
− u
2
+ 1)
5
)(u
21
− u
20
+ ··· − 2u − 1)
· (u
93
+ 5u
92
+ ··· − 263654u + 40564)
c
9
(u
15
− 3u
13
+ u
10
+ 5u
9
− 2u
8
− u
6
− 3u
5
+ 2u
4
− u
3
+ u
2
− 1)
· (u
21
+ 4u
18
+ ··· − u
2
− 1)(u
93
+ 3u
92
+ ··· − 3506u − 1364)
c
10
(u
15
− 3u
13
+ u
10
+ 5u
9
− 2u
8
− u
6
− 3u
5
+ 2u
4
− u
3
+ u
2
− 1)
· (u
21
− 11u
19
+ ··· + 6u
2
− 1)(u
93
+ u
92
+ ··· − 18u + 4)
c
11
, c
12
((u
3
+ u
2
+ 2u + 1)
5
)(u
21
− u
20
+ ··· − 2u + 1)
· (u
93
− 5u
92
+ ··· − 62u + 4)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 18y
14
+ ··· + 10y −1)(y
21
− 12y
20
+ ··· + 9y −1)
· (y
93
− 19y
92
+ ··· + 9425154940y −211644304)
c
2
, c
6
(y
15
− 18y
14
+ ··· + 10y −1)(y
21
− 21y
20
+ ··· + 19y −1)
· (y
93
− 48y
92
+ ··· + 1643820y −85264)
c
3
(y
15
+ 6y
14
+ ··· + 22y −1)(y
21
+ 2y
20
+ ··· + 8y
2
− 1)
· (y
93
− 9y
92
+ ··· + 3164y −16)
c
4
, c
5
, c
10
(y
15
− 6y
14
+ ··· + 2y −1)(y
21
− 22y
20
+ ··· + 12y −1)
· (y
93
− 101y
92
+ ··· − 468y −16)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
5
)(y
21
+ 21y
20
+ ··· + 14y −1)
· (y
93
+ 81y
92
+ ··· + 588y −16)
c
8
((y
3
− y
2
+ 2y −1)
5
)(y
21
− 7y
20
+ ··· + 12y −1)
· (y
93
− 27y
92
+ ··· + 67097196492y −1645438096)
c
9
(y
15
− 6y
14
+ ··· + 2y −1)(y
21
− 8y
19
+ ··· − 2y −1)
· (y
93
+ 21y
92
+ ··· − 67270084y −1860496)
27
