12a
0955
(K12a
0955
)
A knot diagram
1
Linearized knot diagam
4 6 10 9 11 3 12 5 1 2 8 7
Solving Sequence
3,10 4,6
7 2 11 1 5 9 8 12
c
3
c
6
c
2
c
10
c
1
c
5
c
9
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.91588 × 10
1054
u
135
+ 6.69620 × 10
1054
u
134
+ ··· + 1.75763 × 10
1054
b + 3.05109 × 10
1055
,
− 2.92192 × 10
1056
u
135
+ 2.42676 × 10
1056
u
134
+ ··· + 1.75763 × 10
1054
a + 1.61676 × 10
1057
,
u
136
− u
135
+ ··· − 90u + 1i
I
u
2
= h1.29910 × 10
75
u
39
+ 6.04417 × 10
73
u
38
+ ··· + 7.64937 × 10
75
b − 2.92334 × 10
75
,
3.00344 × 10
74
u
39
+ 4.01392 × 10
74
u
38
+ ··· + 7.64937 × 10
75
a + 1.89389 × 10
76
, u
40
+ 6u
38
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 176 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−9.92 × 10
1054
u
135
+ 6.70 × 10
1054
u
134
+ · · · + 1.76 × 10
1054
b +
3.05 × 10
1055
, −2.92 × 10
1056
u
135
+ 2.43 × 10
1056
u
134
+ · · · + 1.76 ×
10
1054
a + 1.62 × 10
1057
, u
136
− u
135
+ · · · − 90u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
166.241u
135
− 138.070u
134
+ ··· + 84755.9u − 919.851
5.64160u
135
− 3.80978u
134
+ ··· + 1561.92u − 17.3591
a
7
=
171.883u
135
− 141.880u
134
+ ··· + 86317.8u − 937.210
5.64160u
135
− 3.80978u
134
+ ··· + 1561.92u − 17.3591
a
2
=
−112.241u
135
+ 97.0441u
134
+ ··· − 67403.4u + 879.171
10.4249u
135
− 6.60479u
134
+ ··· + 1875.62u − 20.2786
a
11
=
−160.594u
135
+ 137.593u
134
+ ··· − 96574.1u + 1237.25
−0.205345u
135
+ 2.30610u
134
+ ··· − 3591.94u + 45.2540
a
1
=
−103.598u
135
+ 92.1701u
134
+ ··· − 66783.3u + 874.089
9.12403u
135
− 5.70219u
134
+ ··· + 1545.05u − 16.5096
a
5
=
147.567u
135
− 121.755u
134
+ ··· + 73520.8u − 834.757
0.975785u
135
+ 0.194203u
134
+ ··· − 1776.12u + 23.0939
a
9
=
−175.798u
135
+ 152.843u
134
+ ··· − 109261.u + 1393.02
−8.58222u
135
+ 7.48626u
134
+ ··· − 5293.45u + 64.5618
a
8
=
163.248u
135
− 136.229u
134
+ ··· + 85190.3u − 925.173
6.21223u
135
− 4.81821u
134
+ ··· + 2835.38u − 33.0506
a
12
=
35.9075u
135
− 30.6827u
134
+ ··· + 21883.0u − 266.266
−0.370479u
135
− 0.414086u
134
+ ··· + 989.079u − 12.4810
(ii) Obstruction class = −1
(iii) Cusp Shapes = −178.426u
135
+ 121.516u
134
+ ··· − 41107.4u + 451.503
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
136
− 11u
135
+ ··· − 99138u + 6727
c
2
, c
6
u
136
− 3u
135
+ ··· − 1044u + 4261
c
3
u
136
+ u
135
+ ··· + 90u + 1
c
4
, c
8
u
136
+ 4u
135
+ ··· − 238658u + 29957
c
5
u
136
+ u
135
+ ··· − 958173436u + 138684577
c
7
, c
11
, c
12
u
136
+ 72u
134
+ ··· − 558u + 71
c
9
u
136
+ 19u
134
+ ··· − 157163u + 21971
c
10
u
136
− 15u
134
+ ··· + 28235809u + 4063723
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
136
+ 33y
135
+ ··· + 1941216156y + 45252529
c
2
, c
6
y
136
− 89y
135
+ ··· − 722664720y + 18156121
c
3
y
136
+ 5y
135
+ ··· − 3718y + 1
c
4
, c
8
y
136
+ 122y
135
+ ··· − 20806491988y + 897421849
c
5
y
136
+ 79y
135
+ ··· + 1981830159489008108y + 19233411897668929
c
7
, c
11
, c
12
y
136
+ 144y
135
+ ··· + 122872y + 5041
c
9
y
136
+ 38y
135
+ ··· + 7897021639y + 482724841
c
10
y
136
− 30y
135
+ ··· − 461058800492953y + 16513844620729
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002500 + 0.063014I
a = 2.26750 − 0.41171I
b = −1.233320 + 0.422915I
14.1826 − 7.7014I 0
u = −1.002500 − 0.063014I
a = 2.26750 + 0.41171I
b = −1.233320 − 0.422915I
14.1826 + 7.7014I 0
u = −0.268691 + 0.984175I
a = 0.504189 + 0.133192I
b = 0.318734 + 0.297660I
−0.41282 − 1.61897I 0
u = −0.268691 − 0.984175I
a = 0.504189 − 0.133192I
b = 0.318734 − 0.297660I
−0.41282 + 1.61897I 0
u = 0.605736 + 0.838936I
a = −0.728686 + 0.627850I
b = −0.409253 + 0.667357I
3.53391 − 2.67721I 0
u = 0.605736 − 0.838936I
a = −0.728686 − 0.627850I
b = −0.409253 − 0.667357I
3.53391 + 2.67721I 0
u = −0.479470 + 0.830260I
a = −0.438130 − 0.008324I
b = 0.432698 − 0.924634I
2.55578 − 3.30889I 0
u = −0.479470 − 0.830260I
a = −0.438130 + 0.008324I
b = 0.432698 + 0.924634I
2.55578 + 3.30889I 0
u = 0.816298 + 0.498199I
a = 2.30208 − 1.08177I
b = −1.095330 − 0.444551I
6.58510 + 5.02708I 0
u = 0.816298 − 0.498199I
a = 2.30208 + 1.08177I
b = −1.095330 + 0.444551I
6.58510 − 5.02708I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.727375 + 0.755504I
a = 0.351811 − 0.182094I
b = −0.616455 − 1.037090I
6.10494 + 2.29566I 0
u = −0.727375 − 0.755504I
a = 0.351811 + 0.182094I
b = −0.616455 + 1.037090I
6.10494 − 2.29566I 0
u = −0.389122 + 0.843441I
a = 0.321785 − 0.000734I
b = 0.062580 + 0.521542I
−0.36394 − 1.54443I 0
u = −0.389122 − 0.843441I
a = 0.321785 + 0.000734I
b = 0.062580 − 0.521542I
−0.36394 + 1.54443I 0
u = −0.398424 + 0.801121I
a = −0.621530 + 0.078693I
b = −0.418336 + 0.507954I
0.74586 − 4.82761I 0
u = −0.398424 − 0.801121I
a = −0.621530 − 0.078693I
b = −0.418336 − 0.507954I
0.74586 + 4.82761I 0
u = −0.658120 + 0.599733I
a = −1.39914 − 0.59882I
b = 1.47290 − 0.66787I
12.7343 − 10.3334I 0
u = −0.658120 − 0.599733I
a = −1.39914 + 0.59882I
b = 1.47290 + 0.66787I
12.7343 + 10.3334I 0
u = −1.048210 + 0.371939I
a = −1.86845 − 0.10856I
b = 1.324620 − 0.352471I
10.73120 − 5.00750I 0
u = −1.048210 − 0.371939I
a = −1.86845 + 0.10856I
b = 1.324620 + 0.352471I
10.73120 + 5.00750I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.712861 + 0.488127I
a = −0.412892 + 0.500570I
b = −0.167658 − 0.583468I
4.00300 − 1.05980I 0
u = −0.712861 − 0.488127I
a = −0.412892 − 0.500570I
b = −0.167658 + 0.583468I
4.00300 + 1.05980I 0
u = −0.187510 + 0.833352I
a = 0.840276 − 0.688063I
b = 0.813280 − 0.195468I
−0.70171 − 2.24730I 0
u = −0.187510 − 0.833352I
a = 0.840276 + 0.688063I
b = 0.813280 + 0.195468I
−0.70171 + 2.24730I 0
u = 0.239091 + 0.819586I
a = −1.47388 − 0.99592I
b = −1.151490 − 0.233690I
11.5671 + 8.5371I 0
u = 0.239091 − 0.819586I
a = −1.47388 + 0.99592I
b = −1.151490 + 0.233690I
11.5671 − 8.5371I 0
u = −0.793679 + 0.163901I
a = 0.403955 + 1.273500I
b = 0.259003 + 0.463813I
3.19544 − 2.72879I 0
u = −0.793679 − 0.163901I
a = 0.403955 − 1.273500I
b = 0.259003 − 0.463813I
3.19544 + 2.72879I 0
u = −0.088010 + 0.799434I
a = −2.24733 + 0.36788I
b = −1.039660 + 0.072164I
3.55213 − 3.56061I 0
u = −0.088010 − 0.799434I
a = −2.24733 − 0.36788I
b = −1.039660 − 0.072164I
3.55213 + 3.56061I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.887942 + 0.814621I
a = 0.066964 − 0.228052I
b = 0.129749 − 1.058500I
−1.56586 + 3.74407I 0
u = 0.887942 − 0.814621I
a = 0.066964 + 0.228052I
b = 0.129749 + 1.058500I
−1.56586 − 3.74407I 0
u = −0.692156 + 0.990198I
a = 1.47593 + 0.13370I
b = −0.878064 − 0.164448I
4.10114 + 0.66022I 0
u = −0.692156 − 0.990198I
a = 1.47593 − 0.13370I
b = −0.878064 + 0.164448I
4.10114 − 0.66022I 0
u = −1.027430 + 0.637510I
a = 1.60176 + 0.29050I
b = −1.50451 + 0.23809I
16.3588 − 3.0418I 0
u = −1.027430 − 0.637510I
a = 1.60176 − 0.29050I
b = −1.50451 − 0.23809I
16.3588 + 3.0418I 0
u = −0.553504 + 0.558455I
a = 1.008670 + 0.672872I
b = −0.980509 + 0.372582I
1.89932 − 1.74077I 0
u = −0.553504 − 0.558455I
a = 1.008670 − 0.672872I
b = −0.980509 − 0.372582I
1.89932 + 1.74077I 0
u = 0.121197 + 0.762928I
a = 0.541844 + 0.084245I
b = −0.014393 + 0.583516I
−0.80117 − 1.41412I 0
u = 0.121197 − 0.762928I
a = 0.541844 − 0.084245I
b = −0.014393 − 0.583516I
−0.80117 + 1.41412I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.596209 + 0.479918I
a = 1.39245 + 1.03343I
b = −1.34852 + 0.65533I
8.40609 − 5.75438I 0
u = −0.596209 − 0.479918I
a = 1.39245 − 1.03343I
b = −1.34852 − 0.65533I
8.40609 + 5.75438I 0
u = −0.660020 + 0.385811I
a = −1.178570 − 0.050631I
b = 1.39664 + 0.63986I
7.54221 − 2.75018I 0
u = −0.660020 − 0.385811I
a = −1.178570 + 0.050631I
b = 1.39664 − 0.63986I
7.54221 + 2.75018I 0
u = 0.837017 + 0.915713I
a = −0.226742 + 0.092602I
b = −0.014695 + 1.060940I
3.44137 + 8.50029I 0
u = 0.837017 − 0.915713I
a = −0.226742 − 0.092602I
b = −0.014695 − 1.060940I
3.44137 − 8.50029I 0
u = 0.565967 + 1.144860I
a = −0.094721 + 0.616456I
b = 1.008800 + 0.175200I
5.15870 + 5.32280I 0
u = 0.565967 − 1.144860I
a = −0.094721 − 0.616456I
b = 1.008800 − 0.175200I
5.15870 − 5.32280I 0
u = 0.958967 + 0.871863I
a = −1.55424 + 0.69528I
b = 1.187340 + 0.441105I
2.79943 + 5.61282I 0
u = 0.958967 − 0.871863I
a = −1.55424 − 0.69528I
b = 1.187340 − 0.441105I
2.79943 − 5.61282I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.765743 + 1.085720I
a = −0.328234 − 0.289606I
b = 0.562214 + 0.242411I
1.30346 − 3.92039I 0
u = −0.765743 − 1.085720I
a = −0.328234 + 0.289606I
b = 0.562214 − 0.242411I
1.30346 + 3.92039I 0
u = 0.791285 + 1.067280I
a = −1.143380 + 0.775089I
b = 1.150870 − 0.080158I
7.61172 − 0.99607I 0
u = 0.791285 − 1.067280I
a = −1.143380 − 0.775089I
b = 1.150870 + 0.080158I
7.61172 + 0.99607I 0
u = 0.785394 + 1.073990I
a = −0.427491 + 0.713269I
b = 0.910080 + 0.222265I
5.10789 + 5.30901I 0
u = 0.785394 − 1.073990I
a = −0.427491 − 0.713269I
b = 0.910080 − 0.222265I
5.10789 − 5.30901I 0
u = 0.615778 + 0.258179I
a = 0.48844 − 1.51099I
b = 0.100617 + 0.656427I
10.40450 + 3.59236I 0
u = 0.615778 − 0.258179I
a = 0.48844 + 1.51099I
b = 0.100617 − 0.656427I
10.40450 − 3.59236I 0
u = 1.299960 + 0.324998I
a = −1.083360 − 0.026428I
b = 1.63019 − 0.35452I
16.8741 + 5.7954I 0
u = 1.299960 − 0.324998I
a = −1.083360 + 0.026428I
b = 1.63019 + 0.35452I
16.8741 − 5.7954I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.250060 + 0.491063I
a = 1.195670 + 0.003182I
b = −1.228970 − 0.245647I
3.66584 + 0.57684I 0
u = −1.250060 − 0.491063I
a = 1.195670 − 0.003182I
b = −1.228970 + 0.245647I
3.66584 − 0.57684I 0
u = 0.946176 + 0.971207I
a = 0.961632 − 0.604019I
b = −0.953124 − 0.659253I
7.32100 + 3.63789I 0
u = 0.946176 − 0.971207I
a = 0.961632 + 0.604019I
b = −0.953124 + 0.659253I
7.32100 − 3.63789I 0
u = 0.970389 + 0.962515I
a = 1.48843 − 0.67039I
b = −1.37225 − 0.39614I
7.91599 + 7.79466I 0
u = 0.970389 − 0.962515I
a = 1.48843 + 0.67039I
b = −1.37225 + 0.39614I
7.91599 − 7.79466I 0
u = −0.326293 + 1.331470I
a = 0.391756 − 0.149787I
b = −0.733453 − 0.039222I
−0.181456 − 0.824990I 0
u = −0.326293 − 1.331470I
a = 0.391756 + 0.149787I
b = −0.733453 + 0.039222I
−0.181456 + 0.824990I 0
u = −0.506818 + 0.332194I
a = −1.64596 − 2.31339I
b = 1.199610 − 0.596259I
13.04380 − 1.33924I 0
u = −0.506818 − 0.332194I
a = −1.64596 + 2.31339I
b = 1.199610 + 0.596259I
13.04380 + 1.33924I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.068370 + 0.896863I
a = −0.137972 − 0.075513I
b = −0.152161 − 1.282390I
10.7662 − 12.1647I 0
u = −1.068370 − 0.896863I
a = −0.137972 + 0.075513I
b = −0.152161 + 1.282390I
10.7662 + 12.1647I 0
u = 0.388015 + 0.427820I
a = −2.91520 + 1.62097I
b = 1.016000 + 0.292192I
1.77191 + 4.25174I 0. − 10.36937I
u = 0.388015 − 0.427820I
a = −2.91520 − 1.62097I
b = 1.016000 − 0.292192I
1.77191 − 4.25174I 0. + 10.36937I
u = 1.00155 + 1.01256I
a = −0.256009 + 0.230430I
b = 0.690240 − 0.696246I
7.41627 + 3.66701I 0
u = 1.00155 − 1.01256I
a = −0.256009 − 0.230430I
b = 0.690240 + 0.696246I
7.41627 − 3.66701I 0
u = 0.461023 + 0.321603I
a = −1.66934 + 0.25789I
b = 1.60627 + 0.54957I
5.49438 + 4.60657I 6.1450 − 15.7932I
u = 0.461023 − 0.321603I
a = −1.66934 − 0.25789I
b = 1.60627 − 0.54957I
5.49438 − 4.60657I 6.1450 + 15.7932I
u = 0.477951 + 0.228463I
a = 1.83816 − 0.83096I
b = −1.225920 − 0.559909I
2.04680 + 2.93313I −4.00000 − 7.70322I
u = 0.477951 − 0.228463I
a = 1.83816 + 0.83096I
b = −1.225920 + 0.559909I
2.04680 − 2.93313I −4.00000 + 7.70322I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.86123 + 1.20580I
a = 0.489954 + 0.234127I
b = −0.608678 + 0.375773I
3.92341 + 2.36412I 0
u = 0.86123 − 1.20580I
a = 0.489954 − 0.234127I
b = −0.608678 − 0.375773I
3.92341 − 2.36412I 0
u = −0.511567 + 0.037095I
a = −3.21381 + 3.28057I
b = −0.397714 + 0.141416I
9.05237 + 6.53367I −1.42833 + 1.74114I
u = −0.511567 − 0.037095I
a = −3.21381 − 3.28057I
b = −0.397714 − 0.141416I
9.05237 − 6.53367I −1.42833 − 1.74114I
u = 0.420727 + 0.270479I
a = −0.146294 − 0.722424I
b = −0.421680 − 1.047550I
−0.88286 + 2.88516I −5.78499 + 11.42640I
u = 0.420727 − 0.270479I
a = −0.146294 + 0.722424I
b = −0.421680 + 1.047550I
−0.88286 − 2.88516I −5.78499 − 11.42640I
u = 0.074926 + 0.490562I
a = −1.89688 − 3.53029I
b = 0.576351 + 0.285810I
10.50980 + 3.34688I 7.60713 − 1.33462I
u = 0.074926 − 0.490562I
a = −1.89688 + 3.53029I
b = 0.576351 − 0.285810I
10.50980 − 3.34688I 7.60713 + 1.33462I
u = 0.463444 + 0.139671I
a = 2.37154 + 0.95293I
b = −1.255360 + 0.045964I
3.71404 + 2.01864I 5.51705 − 1.86309I
u = 0.463444 − 0.139671I
a = 2.37154 − 0.95293I
b = −1.255360 − 0.045964I
3.71404 − 2.01864I 5.51705 + 1.86309I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32571 + 0.75177I
a = 0.078249 + 0.258186I
b = 0.119889 + 1.399890I
4.20104 − 5.36025I 0
u = −1.32571 − 0.75177I
a = 0.078249 − 0.258186I
b = 0.119889 − 1.399890I
4.20104 + 5.36025I 0
u = −1.26946 + 0.87372I
a = −1.334030 − 0.083329I
b = 1.157180 + 0.001078I
6.28349 − 4.35744I 0
u = −1.26946 − 0.87372I
a = −1.334030 + 0.083329I
b = 1.157180 − 0.001078I
6.28349 + 4.35744I 0
u = 0.456842 + 0.023233I
a = −3.62121 − 1.42336I
b = 0.996680 − 0.466465I
6.74551 − 1.77319I 6.89232 + 0.99553I
u = 0.456842 − 0.023233I
a = −3.62121 + 1.42336I
b = 0.996680 + 0.466465I
6.74551 + 1.77319I 6.89232 − 0.99553I
u = 1.29737 + 0.83550I
a = −1.52539 + 0.32309I
b = 1.036890 + 0.328272I
2.90263 + 6.75650I 0
u = 1.29737 − 0.83550I
a = −1.52539 − 0.32309I
b = 1.036890 − 0.328272I
2.90263 − 6.75650I 0
u = −1.33508 + 0.78876I
a = −1.58569 − 0.47217I
b = 0.893175 − 0.523408I
8.01886 − 8.38965I 0
u = −1.33508 − 0.78876I
a = −1.58569 + 0.47217I
b = 0.893175 + 0.523408I
8.01886 + 8.38965I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.07362 + 1.13981I
a = 1.27707 + 0.72580I
b = −1.35272 + 0.53335I
7.6233 − 14.1804I 0
u = −1.07362 − 1.13981I
a = 1.27707 − 0.72580I
b = −1.35272 − 0.53335I
7.6233 + 14.1804I 0
u = 0.404418 + 0.133429I
a = −0.445258 + 0.806474I
b = −0.422704 − 1.028030I
5.35849 + 0.81312I 4.06819 − 2.00701I
u = 0.404418 − 0.133429I
a = −0.445258 − 0.806474I
b = −0.422704 + 1.028030I
5.35849 − 0.81312I 4.06819 + 2.00701I
u = −0.62254 + 1.49088I
a = −0.612380 − 0.790840I
b = 1.242770 − 0.114162I
13.69740 − 3.47264I 0
u = −0.62254 − 1.49088I
a = −0.612380 + 0.790840I
b = 1.242770 + 0.114162I
13.69740 + 3.47264I 0
u = −1.13705 + 1.17245I
a = −1.165560 − 0.663334I
b = 1.296720 − 0.529973I
2.15662 − 9.34279I 0
u = −1.13705 − 1.17245I
a = −1.165560 + 0.663334I
b = 1.296720 + 0.529973I
2.15662 + 9.34279I 0
u = −1.37742 + 0.93861I
a = −1.086560 − 0.191967I
b = 1.257740 + 0.268629I
8.32935 + 5.72247I 0
u = −1.37742 − 0.93861I
a = −1.086560 + 0.191967I
b = 1.257740 − 0.268629I
8.32935 − 5.72247I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298162 + 0.097877I
a = −0.101249 − 0.637838I
b = 0.62019 + 1.64062I
8.65752 − 2.24574I 32.4612 − 14.6799I
u = 0.298162 − 0.097877I
a = −0.101249 + 0.637838I
b = 0.62019 − 1.64062I
8.65752 + 2.24574I 32.4612 + 14.6799I
u = 0.18075 + 1.69000I
a = 0.290240 + 0.120261I
b = −1.078440 − 0.004368I
5.02250 − 0.25714I 0
u = 0.18075 − 1.69000I
a = 0.290240 − 0.120261I
b = −1.078440 + 0.004368I
5.02250 + 0.25714I 0
u = 1.19788 + 1.22102I
a = 1.152210 − 0.689156I
b = −1.38581 − 0.64138I
14.7054 + 18.8851I 0
u = 1.19788 − 1.22102I
a = 1.152210 + 0.689156I
b = −1.38581 + 0.64138I
14.7054 − 18.8851I 0
u = 0.286273
a = 3.31127
b = 0.415258
−1.14438 −9.87290
u = 1.24672 + 1.23588I
a = 1.257460 − 0.411902I
b = −1.041830 − 0.154203I
1.08261 + 2.17619I 0
u = 1.24672 − 1.23588I
a = 1.257460 + 0.411902I
b = −1.041830 + 0.154203I
1.08261 − 2.17619I 0
u = −0.60047 + 1.71440I
a = −0.081253 − 0.827842I
b = −0.660091 − 1.074370I
9.11350 + 5.02216I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.60047 − 1.71440I
a = −0.081253 + 0.827842I
b = −0.660091 + 1.074370I
9.11350 − 5.02216I 0
u = 0.144317 + 0.005571I
a = −7.50699 − 11.88810I
b = −0.749599 − 0.093849I
2.76729 − 2.67367I −0.40334 − 2.26799I
u = 0.144317 − 0.005571I
a = −7.50699 + 11.88810I
b = −0.749599 + 0.093849I
2.76729 + 2.67367I −0.40334 + 2.26799I
u = 1.31322 + 1.32237I
a = −0.986907 + 0.591761I
b = 1.43640 + 0.60904I
8.5998 + 12.2951I 0
u = 1.31322 − 1.32237I
a = −0.986907 − 0.591761I
b = 1.43640 − 0.60904I
8.5998 − 12.2951I 0
u = −0.96962 + 1.60627I
a = 0.723616 + 0.817787I
b = −1.25005 + 0.68230I
5.33250 − 3.06203I 0
u = −0.96962 − 1.60627I
a = 0.723616 − 0.817787I
b = −1.25005 − 0.68230I
5.33250 + 3.06203I 0
u = −1.46239 + 1.33953I
a = 1.181910 + 0.523487I
b = −1.039450 + 0.331730I
5.24762 − 5.44019I 0
u = −1.46239 − 1.33953I
a = 1.181910 − 0.523487I
b = −1.039450 − 0.331730I
5.24762 + 5.44019I 0
u = 0.0167571
a = 88.2974
b = 0.703402
−1.11227 −11.6150
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.00277 + 0.36986I
a = 0.889022 + 0.021614I
b = −1.58650 + 0.29439I
10.63410 − 1.18271I 0
u = 2.00277 − 0.36986I
a = 0.889022 − 0.021614I
b = −1.58650 − 0.29439I
10.63410 + 1.18271I 0
u = 1.72432 + 1.18066I
a = −0.861788 + 0.103902I
b = 1.38253 − 0.33823I
15.2827 − 9.1211I 0
u = 1.72432 − 1.18066I
a = −0.861788 − 0.103902I
b = 1.38253 + 0.33823I
15.2827 + 9.1211I 0
u = 1.37717 + 2.17321I
a = 0.563590 − 0.550051I
b = −1.55956 − 0.80089I
11.65750 + 3.05874I 0
u = 1.37717 − 2.17321I
a = 0.563590 + 0.550051I
b = −1.55956 + 0.80089I
11.65750 − 3.05874I 0
18
II.
I
u
2
= h1.30 × 10
75
u
39
+ 6.04 × 10
73
u
38
+ · · · + 7.65 × 10
75
b − 2.92 × 10
75
, 3.00 ×
10
74
u
39
+4.01×10
74
u
38
+· · ·+7.65×10
75
a+1.89×10
76
, u
40
+6u
38
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
−0.0392638u
39
− 0.0524739u
38
+ ··· + 0.606930u − 2.47588
−0.169830u
39
− 0.00790152u
38
+ ··· − 5.66165u + 0.382167
a
7
=
−0.209094u
39
− 0.0603754u
38
+ ··· − 5.05472u − 2.09371
−0.169830u
39
− 0.00790152u
38
+ ··· − 5.66165u + 0.382167
a
2
=
0.523060u
39
− 0.0751174u
38
+ ··· + 13.6209u + 0.319118
−0.181403u
39
− 0.0222854u
38
+ ··· − 8.97741u − 1.32005
a
11
=
0.653272u
39
− 0.391160u
38
+ ··· − 7.84448u + 1.99508
−0.375237u
39
+ 0.218175u
38
+ ··· + 6.38692u − 0.0825126
a
1
=
0.383856u
39
− 0.120476u
38
+ ··· + 4.27063u − 0.925810
−0.174249u
39
− 0.0314766u
38
+ ··· − 9.20734u − 1.36540
a
5
=
0.329544u
39
− 0.0318034u
38
+ ··· + 2.41934u + 1.86609
−0.0499788u
39
− 0.0514062u
38
+ ··· − 2.10243u − 1.67809
a
9
=
0.413042u
39
− 0.107330u
38
+ ··· + 1.67777u + 1.91333
−0.127500u
39
+ 0.131798u
38
+ ··· + 5.20467u − 0.497728
a
8
=
−0.402858u
39
+ 0.171998u
38
+ ··· + 2.22164u − 1.67341
0.0927416u
39
− 0.0628101u
38
+ ··· − 2.06166u + 1.00230
a
12
=
0.338358u
39
− 0.192969u
38
+ ··· − 3.15479u + 1.74535
−0.314398u
39
+ 0.0984837u
38
+ ··· − 0.441439u − 0.368607
(ii) Obstruction class = 1
(iii) Cusp Shapes = −0.851008u
39
− 0.484788u
38
+ ··· − 62.4749u − 6.17641
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
− 4u
39
+ ··· + 6u
2
+ 1
c
2
u
40
+ 2u
39
+ ··· − 16u
2
+ 1
c
3
u
40
+ 6u
38
+ ··· + 2u + 1
c
4
u
40
+ u
39
+ ··· + 4u + 1
c
5
u
40
+ 5u
38
+ ··· + 226u + 37
c
6
u
40
− 2u
39
+ ··· − 16u
2
+ 1
c
7
u
40
+ u
39
+ ··· − 2u + 1
c
8
u
40
− u
39
+ ··· − 4u + 1
c
9
u
40
+ 5u
39
+ ··· − u + 1
c
10
u
40
− u
39
+ ··· − 5u + 1
c
11
, c
12
u
40
− u
39
+ ··· + 2u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
+ 8y
39
+ ··· + 12y + 1
c
2
, c
6
y
40
− 22y
39
+ ··· − 32y + 1
c
3
y
40
+ 12y
39
+ ··· + 30y + 1
c
4
, c
8
y
40
+ 37y
39
+ ··· + 28y + 1
c
5
y
40
+ 10y
39
+ ··· + 45716y + 1369
c
7
, c
11
, c
12
y
40
+ 43y
39
+ ··· + 24y + 1
c
9
y
40
+ 17y
39
+ ··· + 3y + 1
c
10
y
40
+ 13y
39
+ ··· − y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.796206 + 0.351155I
a = 1.051500 + 0.299097I
b = −1.054250 + 0.633032I
5.01478 + 0.50916I 5.83747 − 2.93176I
u = 0.796206 − 0.351155I
a = 1.051500 − 0.299097I
b = −1.054250 − 0.633032I
5.01478 − 0.50916I 5.83747 + 2.93176I
u = 0.067408 + 1.164890I
a = −0.184864 + 0.371657I
b = −0.751676 + 0.011062I
0.35050 + 1.85110I 2.99827 − 3.67948I
u = 0.067408 − 1.164890I
a = −0.184864 − 0.371657I
b = −0.751676 − 0.011062I
0.35050 − 1.85110I 2.99827 + 3.67948I
u = −0.955477 + 0.684517I
a = −0.090499 + 0.681133I
b = −0.115268 + 0.832906I
2.93569 − 4.19999I −1.49983 + 5.26459I
u = −0.955477 − 0.684517I
a = −0.090499 − 0.681133I
b = −0.115268 − 0.832906I
2.93569 + 4.19999I −1.49983 − 5.26459I
u = 0.805319 + 0.172926I
a = −1.49322 + 1.12153I
b = 1.308480 − 0.354168I
13.2214 − 8.1179I 3.48258 + 6.14970I
u = 0.805319 − 0.172926I
a = −1.49322 − 1.12153I
b = 1.308480 + 0.354168I
13.2214 + 8.1179I 3.48258 − 6.14970I
u = 0.439552 + 1.105110I
a = 0.406443 − 0.451885I
b = −0.761999 − 0.169824I
−0.20418 + 1.56599I −5.22807 − 4.02362I
u = 0.439552 − 1.105110I
a = 0.406443 + 0.451885I
b = −0.761999 + 0.169824I
−0.20418 − 1.56599I −5.22807 + 4.02362I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.737294 + 0.318440I
a = −1.48663 − 2.99524I
b = 0.597362 − 0.105154I
9.36711 − 6.94685I 8.05447 + 10.02472I
u = −0.737294 − 0.318440I
a = −1.48663 + 2.99524I
b = 0.597362 + 0.105154I
9.36711 + 6.94685I 8.05447 − 10.02472I
u = 0.647043 + 1.054320I
a = −0.018902 + 0.484212I
b = 0.687876 − 0.132743I
1.78821 + 4.07878I 6.64587 − 4.68971I
u = 0.647043 − 1.054320I
a = −0.018902 − 0.484212I
b = 0.687876 + 0.132743I
1.78821 − 4.07878I 6.64587 + 4.68971I
u = −0.571213 + 0.449556I
a = 1.61367 + 0.59318I
b = −1.294590 + 0.354516I
3.04497 − 2.81941I 2.78869 + 7.19991I
u = −0.571213 − 0.449556I
a = 1.61367 − 0.59318I
b = −1.294590 − 0.354516I
3.04497 + 2.81941I 2.78869 − 7.19991I
u = 0.555686 + 0.441278I
a = 0.001021 − 0.269896I
b = −0.316054 − 1.061020I
−0.79791 + 3.15337I 2.4481 − 14.9170I
u = 0.555686 − 0.441278I
a = 0.001021 + 0.269896I
b = −0.316054 + 1.061020I
−0.79791 − 3.15337I 2.4481 + 14.9170I
u = −1.097080 + 0.724650I
a = −1.65995 − 0.35445I
b = 1.134360 − 0.373387I
3.88443 − 6.41404I 4.53460 + 6.66931I
u = −1.097080 − 0.724650I
a = −1.65995 + 0.35445I
b = 1.134360 + 0.373387I
3.88443 + 6.41404I 4.53460 − 6.66931I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.244411 + 0.571122I
a = 2.88253 + 2.47488I
b = 0.763694 + 0.014160I
2.52572 + 3.16079I −8.21754 − 9.16753I
u = 0.244411 − 0.571122I
a = 2.88253 − 2.47488I
b = 0.763694 − 0.014160I
2.52572 − 3.16079I −8.21754 + 9.16753I
u = −1.01325 + 1.03698I
a = 0.801511 + 0.680746I
b = −0.871894 + 0.338195I
4.54439 − 4.55226I 0
u = −1.01325 − 1.03698I
a = 0.801511 − 0.680746I
b = −0.871894 − 0.338195I
4.54439 + 4.55226I 0
u = −0.31846 + 1.43705I
a = 0.990036 − 0.026463I
b = −0.547814 + 0.111721I
3.25955 + 0.19369I 0
u = −0.31846 − 1.43705I
a = 0.990036 + 0.026463I
b = −0.547814 − 0.111721I
3.25955 − 0.19369I 0
u = −0.70686 + 1.39444I
a = 0.742529 + 1.050330I
b = −1.145230 + 0.653615I
5.10594 − 3.10337I 0
u = −0.70686 − 1.39444I
a = 0.742529 − 1.050330I
b = −1.145230 − 0.653615I
5.10594 + 3.10337I 0
u = −0.94792 + 1.28866I
a = −0.631620 − 0.041139I
b = 0.639127 + 0.234313I
4.20396 − 4.23338I 0
u = −0.94792 − 1.28866I
a = −0.631620 + 0.041139I
b = 0.639127 − 0.234313I
4.20396 + 4.23338I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.37956 + 1.55763I
a = 0.395941 − 1.206920I
b = −0.868175 − 0.790254I
9.25452 + 4.30867I 0
u = 0.37956 − 1.55763I
a = 0.395941 + 1.206920I
b = −0.868175 + 0.790254I
9.25452 − 4.30867I 0
u = −0.344912 + 0.080803I
a = −3.52289 + 0.70225I
b = 1.308950 − 0.405254I
5.31373 − 4.02937I 1.09577 + 2.14504I
u = −0.344912 − 0.080803I
a = −3.52289 − 0.70225I
b = 1.308950 + 0.405254I
5.31373 + 4.02937I 1.09577 − 2.14504I
u = 1.43420 + 1.05243I
a = −1.328130 + 0.473695I
b = 1.067980 + 0.416029I
5.97147 + 7.29999I 0
u = 1.43420 − 1.05243I
a = −1.328130 − 0.473695I
b = 1.067980 − 0.416029I
5.97147 − 7.29999I 0
u = 0.035720 + 0.201543I
a = −2.28495 + 0.06055I
b = 0.68977 − 1.35787I
8.52959 + 2.35400I −5.1591 − 14.8120I
u = 0.035720 − 0.201543I
a = −2.28495 − 0.06055I
b = 0.68977 + 1.35787I
8.52959 − 2.35400I −5.1591 + 14.8120I
u = 1.28735 + 1.33079I
a = 0.816468 − 0.657189I
b = −1.47065 − 0.63385I
11.38220 + 2.64327I 0
u = 1.28735 − 1.33079I
a = 0.816468 + 0.657189I
b = −1.47065 + 0.63385I
11.38220 − 2.64327I 0
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
40
− 4u
39
+ ··· + 6u
2
+ 1)(u
136
− 11u
135
+ ··· − 99138u + 6727)
c
2
(u
40
+ 2u
39
+ ··· − 16u
2
+ 1)(u
136
− 3u
135
+ ··· − 1044u + 4261)
c
3
(u
40
+ 6u
38
+ ··· + 2u + 1)(u
136
+ u
135
+ ··· + 90u + 1)
c
4
(u
40
+ u
39
+ ··· + 4u + 1)(u
136
+ 4u
135
+ ··· − 238658u + 29957)
c
5
(u
40
+ 5u
38
+ ··· + 226u + 37)
· (u
136
+ u
135
+ ··· − 958173436u + 138684577)
c
6
(u
40
− 2u
39
+ ··· − 16u
2
+ 1)(u
136
− 3u
135
+ ··· − 1044u + 4261)
c
7
(u
40
+ u
39
+ ··· − 2u + 1)(u
136
+ 72u
134
+ ··· − 558u + 71)
c
8
(u
40
− u
39
+ ··· − 4u + 1)(u
136
+ 4u
135
+ ··· − 238658u + 29957)
c
9
(u
40
+ 5u
39
+ ··· − u + 1)(u
136
+ 19u
134
+ ··· − 157163u + 21971)
c
10
(u
40
− u
39
+ ··· − 5u + 1)
· (u
136
− 15u
134
+ ··· + 28235809u + 4063723)
c
11
, c
12
(u
40
− u
39
+ ··· + 2u + 1)(u
136
+ 72u
134
+ ··· − 558u + 71)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
40
+ 8y
39
+ ··· + 12y + 1)
· (y
136
+ 33y
135
+ ··· + 1941216156y + 45252529)
c
2
, c
6
(y
40
− 22y
39
+ ··· − 32y + 1)
· (y
136
− 89y
135
+ ··· − 722664720y + 18156121)
c
3
(y
40
+ 12y
39
+ ··· + 30y + 1)(y
136
+ 5y
135
+ ··· − 3718y + 1)
c
4
, c
8
(y
40
+ 37y
39
+ ··· + 28y + 1)
· (y
136
+ 122y
135
+ ··· − 20806491988y + 897421849)
c
5
(y
40
+ 10y
39
+ ··· + 45716y + 1369)
· (y
136
+ 79y
135
+ ··· + 1981830159489008108y + 19233411897668929)
c
7
, c
11
, c
12
(y
40
+ 43y
39
+ ··· + 24y + 1)(y
136
+ 144y
135
+ ··· + 122872y + 5041)
c
9
(y
40
+ 17y
39
+ ··· + 3y + 1)
· (y
136
+ 38y
135
+ ··· + 7897021639y + 482724841)
c
10
(y
40
+ 13y
39
+ ··· − y + 1)
· (y
136
− 30y
135
+ ··· − 461058800492953y + 16513844620729)
27
