12a
1208
(K12a
1208
)
A knot diagram
1
Linearized knot diagam
4 11 10 9 2 3 12 5 1 6 8 7
Solving Sequence
8,11 3,12
2 7 1 6 5 10 9 4
c
11
c
2
c
7
c
12
c
6
c
5
c
10
c
9
c
4
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2.07625 × 10
594
u
165
+ 5.47091 × 10
594
u
164
+ ··· + 1.02629 × 10
595
b + 3.00733 × 10
596
,
− 3.37299 × 10
595
u
165
+ 2.18527 × 10
596
u
164
+ ··· + 8.72344 × 10
596
a + 4.06613 × 10
598
,
u
166
+ 2u
165
+ ··· − 714u + 289i
I
u
2
= h1355679442634u
42
− 1138023218267u
41
+ ··· + 286979954013b − 2810619597407,
− 190977593434u
42
+ 27758049080035u
41
+ ··· + 860939862039a + 32882509966417,
u
43
+ u
42
+ ··· + 10u + 1i
* 2 irreducible components of dim
C
= 0, with total 209 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
= h2.08 × 10
594
u
165
+ 5.47 × 10
594
u
164
+ · · · + 1.03 × 10
595
b + 3.01 ×
10
596
, −3.37 × 10
595
u
165
+ 2.19 × 10
596
u
164
+ · · · + 8.72 × 10
596
a + 4.07 ×
10
598
, u
166
+ 2u
165
+ · · · − 714u + 289i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
3
=
0.0386659u
165
− 0.250505u
164
+ ··· + 103.290u − 46.6115
−0.202307u
165
− 0.533078u
164
+ ··· + 34.8210u − 29.3030
a
12
=
1
u
2
a
2
=
−0.163641u
165
− 0.783583u
164
+ ··· + 138.111u − 75.9146
−0.202307u
165
− 0.533078u
164
+ ··· + 34.8210u − 29.3030
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−1.21009u
165
− 3.04394u
164
+ ··· − 37.7098u − 83.1115
−0.0751152u
165
− 0.524075u
164
+ ··· + 127.144u − 55.8265
a
5
=
0.277604u
165
+ 0.563644u
164
+ ··· + 54.4908u − 3.35099
−1.15054u
165
− 3.71939u
164
+ ··· + 435.410u − 255.120
a
10
=
0.482406u
165
− 0.333118u
164
+ ··· + 660.458u − 236.350
−0.537254u
165
− 0.742007u
164
+ ··· − 231.635u + 55.4828
a
9
=
0.0940036u
165
− 0.413368u
164
+ ··· + 290.152u − 113.207
−0.869761u
165
− 0.726677u
164
+ ··· − 586.984u + 175.849
a
4
=
−0.0760578u
165
− 0.388130u
164
+ ··· + 98.5661u − 50.4660
−0.665368u
165
− 1.81042u
164
+ ··· + 115.272u − 91.2676
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.84451u
165
+ 4.84351u
164
+ ··· − 35.4126u + 139.634
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
166
+ 15u
165
+ ··· + 14u − 1
c
2
u
166
− 4u
165
+ ··· + 28476u + 667
c
3
u
166
− 3u
165
+ ··· − 8268033u + 335191
c
4
, c
8
u
166
− u
165
+ ··· − 228154u + 191449
c
5
u
166
− 2u
165
+ ··· + 2701472u − 273472
c
6
u
166
− 10u
165
+ ··· + 634u − 109
c
7
, c
11
, c
12
u
166
+ 2u
165
+ ··· − 714u + 289
c
9
u
166
− u
165
+ ··· − 67072u + 22016
c
10
u
166
+ 5u
165
+ ··· − 15u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
166
+ y
165
+ ··· − 14y + 1
c
2
y
166
− 2y
165
+ ··· − 1188891486y + 444889
c
3
y
166
+ 61y
165
+ ··· − 3152875669969y + 112353006481
c
4
, c
8
y
166
+ 117y
165
+ ··· + 1929765685298y + 36652719601
c
5
y
166
− 30y
165
+ ··· − 5537587637248y + 74786934784
c
6
y
166
+ 18y
165
+ ··· − 1172586y + 11881
c
7
, c
11
, c
12
y
166
+ 158y
165
+ ··· + 2222988y + 83521
c
9
y
166
+ 21y
165
+ ··· + 28523233280y + 484704256
c
10
y
166
+ 15y
165
+ ··· − 249y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.725948 + 0.683647I
a = −0.038423 + 0.619652I
b = 0.256542 − 0.112019I
0.02086 + 2.75664I 0
u = −0.725948 − 0.683647I
a = −0.038423 − 0.619652I
b = 0.256542 + 0.112019I
0.02086 − 2.75664I 0
u = 0.025517 + 0.986919I
a = −1.110390 + 0.549998I
b = 1.104750 − 0.503162I
0.89681 + 3.77593I 0
u = 0.025517 − 0.986919I
a = −1.110390 − 0.549998I
b = 1.104750 + 0.503162I
0.89681 − 3.77593I 0
u = −0.946801 + 0.396249I
a = 0.734629 + 0.455554I
b = 1.01961 − 1.14872I
0.4546 + 15.7472I 0
u = −0.946801 − 0.396249I
a = 0.734629 − 0.455554I
b = 1.01961 + 1.14872I
0.4546 − 15.7472I 0
u = −0.794890 + 0.511199I
a = −0.292218 + 0.368860I
b = 0.467134 + 0.346393I
−3.38316 + 0.71507I 0
u = −0.794890 − 0.511199I
a = −0.292218 − 0.368860I
b = 0.467134 − 0.346393I
−3.38316 − 0.71507I 0
u = 1.049290 + 0.235908I
a = 0.301042 + 0.002024I
b = 0.316727 + 0.503949I
1.78942 − 6.85416I 0
u = 1.049290 − 0.235908I
a = 0.301042 − 0.002024I
b = 0.316727 − 0.503949I
1.78942 + 6.85416I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.556720 + 0.733265I
a = 0.525878 + 0.156768I
b = −0.909625 + 0.665707I
−2.58532 + 5.21679I 0
u = 0.556720 − 0.733265I
a = 0.525878 − 0.156768I
b = −0.909625 − 0.665707I
−2.58532 − 5.21679I 0
u = 0.600379 + 0.688416I
a = −0.534562 − 0.328227I
b = −0.439443 − 0.877361I
−1.60622 − 2.48356I 0
u = 0.600379 − 0.688416I
a = −0.534562 + 0.328227I
b = −0.439443 + 0.877361I
−1.60622 + 2.48356I 0
u = 0.369614 + 1.033310I
a = 0.131564 − 0.169829I
b = 0.290813 + 0.632611I
4.88400 + 1.56084I 0
u = 0.369614 − 1.033310I
a = 0.131564 + 0.169829I
b = 0.290813 − 0.632611I
4.88400 − 1.56084I 0
u = −0.132622 + 1.117560I
a = 1.24662 + 0.98339I
b = −0.703852 + 0.079105I
4.07151 + 6.08335I 0
u = −0.132622 − 1.117560I
a = 1.24662 − 0.98339I
b = −0.703852 − 0.079105I
4.07151 − 6.08335I 0
u = 0.788182 + 0.368170I
a = 0.782020 − 0.769821I
b = 1.048490 + 0.884888I
−3.77502 − 9.90973I 0
u = 0.788182 − 0.368170I
a = 0.782020 + 0.769821I
b = 1.048490 − 0.884888I
−3.77502 + 9.90973I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.554858 + 0.666692I
a = −0.095827 − 0.534005I
b = −0.826350 + 0.668994I
−2.76581 + 4.07346I 0
u = −0.554858 − 0.666692I
a = −0.095827 + 0.534005I
b = −0.826350 − 0.668994I
−2.76581 − 4.07346I 0
u = −0.405250 + 0.744541I
a = −0.632404 + 0.871648I
b = 0.588314 + 0.139635I
−0.11721 + 2.83841I 0
u = −0.405250 − 0.744541I
a = −0.632404 − 0.871648I
b = 0.588314 − 0.139635I
−0.11721 − 2.83841I 0
u = −0.732834 + 0.338965I
a = −1.195570 − 0.003043I
b = −0.113109 + 0.305420I
2.24288 − 2.77835I 0
u = −0.732834 − 0.338965I
a = −1.195570 + 0.003043I
b = −0.113109 − 0.305420I
2.24288 + 2.77835I 0
u = −0.053658 + 1.192690I
a = 0.58502 + 3.52803I
b = 0.01778 − 1.61639I
1.35245 + 6.33268I 0
u = −0.053658 − 1.192690I
a = 0.58502 − 3.52803I
b = 0.01778 + 1.61639I
1.35245 − 6.33268I 0
u = −0.336940 + 0.717872I
a = −0.652905 + 1.059580I
b = 0.833983 − 0.388471I
0.97295 + 3.91183I 0
u = −0.336940 − 0.717872I
a = −0.652905 − 1.059580I
b = 0.833983 + 0.388471I
0.97295 − 3.91183I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.785466 + 0.089428I
a = −1.22500 + 0.71118I
b = −1.006870 − 0.678413I
−1.30016 − 4.36479I 0
u = 0.785466 − 0.089428I
a = −1.22500 − 0.71118I
b = −1.006870 + 0.678413I
−1.30016 + 4.36479I 0
u = −0.793606 + 0.916192I
a = 0.550045 − 0.061150I
b = −0.745314 − 1.088650I
1.92998 − 9.84732I 0
u = −0.793606 − 0.916192I
a = 0.550045 + 0.061150I
b = −0.745314 + 1.088650I
1.92998 + 9.84732I 0
u = −0.040204 + 1.222260I
a = −1.76830 + 0.36131I
b = 1.65751 − 0.03653I
0.54565 + 1.96085I 0
u = −0.040204 − 1.222260I
a = −1.76830 − 0.36131I
b = 1.65751 + 0.03653I
0.54565 − 1.96085I 0
u = 0.659388 + 0.402666I
a = 0.211715 + 0.689565I
b = −0.587173 + 1.037560I
3.42974 + 3.82141I 0
u = 0.659388 − 0.402666I
a = 0.211715 − 0.689565I
b = −0.587173 − 1.037560I
3.42974 − 3.82141I 0
u = −0.729954 + 0.247570I
a = −1.002790 + 0.123048I
b = −0.955453 − 0.985259I
−0.76173 − 3.67426I 0
u = −0.729954 − 0.247570I
a = −1.002790 − 0.123048I
b = −0.955453 + 0.985259I
−0.76173 + 3.67426I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.029942 + 1.230850I
a = 0.61461 − 1.51176I
b = 0.789132 + 0.782272I
5.14772 − 5.64701I 0
u = 0.029942 − 1.230850I
a = 0.61461 + 1.51176I
b = 0.789132 − 0.782272I
5.14772 + 5.64701I 0
u = −1.200860 + 0.304458I
a = −0.783677 − 0.133169I
b = −1.14324 + 1.40913I
0.31931 + 5.55081I 0
u = −1.200860 − 0.304458I
a = −0.783677 + 0.133169I
b = −1.14324 − 1.40913I
0.31931 − 5.55081I 0
u = 0.090973 + 1.239890I
a = 0.143791 + 0.749389I
b = 0.900131 − 0.470285I
1.94543 + 1.46866I 0
u = 0.090973 − 1.239890I
a = 0.143791 − 0.749389I
b = 0.900131 + 0.470285I
1.94543 − 1.46866I 0
u = 0.086497 + 1.251100I
a = −0.00903 − 3.04534I
b = 0.283185 + 0.150729I
1.67993 − 6.89070I 0
u = 0.086497 − 1.251100I
a = −0.00903 + 3.04534I
b = 0.283185 − 0.150729I
1.67993 + 6.89070I 0
u = 0.590527 + 0.453505I
a = −0.547503 + 0.679752I
b = −0.217537 − 0.878167I
3.19592 − 2.19949I 0
u = 0.590527 − 0.453505I
a = −0.547503 − 0.679752I
b = −0.217537 + 0.878167I
3.19592 + 2.19949I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.732939 + 0.103983I
a = −1.78445 − 0.51007I
b = −1.129710 + 0.342264I
−1.37174 + 4.38682I 0
u = 0.732939 − 0.103983I
a = −1.78445 + 0.51007I
b = −1.129710 − 0.342264I
−1.37174 − 4.38682I 0
u = 0.613741 + 0.411517I
a = 1.167490 − 0.507533I
b = 1.17963 + 1.08338I
3.52353 − 7.73326I 0
u = 0.613741 − 0.411517I
a = 1.167490 + 0.507533I
b = 1.17963 − 1.08338I
3.52353 + 7.73326I 0
u = −1.26807
a = 0.0715838
b = −0.0193289
−2.38908 0
u = 0.668235 + 0.289415I
a = −0.903820 + 0.162173I
b = −0.152832 − 0.662900I
2.72771 − 1.66856I 0
u = 0.668235 − 0.289415I
a = −0.903820 − 0.162173I
b = −0.152832 + 0.662900I
2.72771 + 1.66856I 0
u = −0.036979 + 1.280320I
a = −0.86818 − 3.14906I
b = 0.22425 + 2.00525I
0.320119 − 1.132360I 0
u = −0.036979 − 1.280320I
a = −0.86818 + 3.14906I
b = 0.22425 − 2.00525I
0.320119 + 1.132360I 0
u = −0.692433 + 0.108786I
a = −0.262714 − 0.144161I
b = −0.718367 + 0.295491I
−1.377630 − 0.063938I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.692433 − 0.108786I
a = −0.262714 + 0.144161I
b = −0.718367 − 0.295491I
−1.377630 + 0.063938I 0
u = 0.082398 + 1.297980I
a = −0.02656 + 2.50713I
b = −0.109061 − 0.148086I
0.032565 + 0.145382I 0
u = 0.082398 − 1.297980I
a = −0.02656 − 2.50713I
b = −0.109061 + 0.148086I
0.032565 − 0.145382I 0
u = −0.425785 + 1.231480I
a = −0.688572 − 0.013279I
b = 1.16183 + 0.98500I
4.09316 + 0.69217I 0
u = −0.425785 − 1.231480I
a = −0.688572 + 0.013279I
b = 1.16183 − 0.98500I
4.09316 − 0.69217I 0
u = 0.646752 + 0.254528I
a = −0.669782 + 0.783893I
b = −0.95342 − 1.08225I
−0.96365 − 6.74060I 0
u = 0.646752 − 0.254528I
a = −0.669782 − 0.783893I
b = −0.95342 + 1.08225I
−0.96365 + 6.74060I 0
u = −0.009787 + 1.311300I
a = −0.993443 − 0.460026I
b = 1.70773 + 0.53451I
0.73913 − 4.22237I 0
u = −0.009787 − 1.311300I
a = −0.993443 + 0.460026I
b = 1.70773 − 0.53451I
0.73913 + 4.22237I 0
u = 0.124052 + 1.319300I
a = −0.991384 + 0.092416I
b = −0.855687 − 0.027724I
0.55968 − 4.05266I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.124052 − 1.319300I
a = −0.991384 − 0.092416I
b = −0.855687 + 0.027724I
0.55968 + 4.05266I 0
u = 0.985453 + 0.885972I
a = −0.400218 + 0.097615I
b = 0.097629 − 1.180600I
2.10849 − 3.54917I 0
u = 0.985453 − 0.885972I
a = −0.400218 − 0.097615I
b = 0.097629 + 1.180600I
2.10849 + 3.54917I 0
u = −0.500222 + 0.447622I
a = 2.76284 + 0.55889I
b = 0.568813 − 0.452272I
0.21982 + 7.31370I −6.0000 − 13.3490I
u = −0.500222 − 0.447622I
a = 2.76284 − 0.55889I
b = 0.568813 + 0.452272I
0.21982 − 7.31370I −6.0000 + 13.3490I
u = 0.038523 + 1.331460I
a = −0.467909 + 0.043123I
b = −1.088600 − 0.262174I
4.02238 − 4.91225I 0
u = 0.038523 − 1.331460I
a = −0.467909 − 0.043123I
b = −1.088600 + 0.262174I
4.02238 + 4.91225I 0
u = −0.033022 + 1.336280I
a = 0.871766 − 0.883623I
b = −1.58004 + 0.11016I
4.78115 − 1.33167I 0
u = −0.033022 − 1.336280I
a = 0.871766 + 0.883623I
b = −1.58004 − 0.11016I
4.78115 + 1.33167I 0
u = −0.617037 + 0.178502I
a = −0.594347 − 0.228378I
b = −0.962127 + 0.749077I
−1.91522 + 0.34343I −10.92857 + 1.93540I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617037 − 0.178502I
a = −0.594347 + 0.228378I
b = −0.962127 − 0.749077I
−1.91522 − 0.34343I −10.92857 − 1.93540I
u = −0.138411 + 1.352910I
a = −0.217086 + 1.260970I
b = 1.257190 − 0.439498I
3.16771 + 1.68068I 0
u = −0.138411 − 1.352910I
a = −0.217086 − 1.260970I
b = 1.257190 + 0.439498I
3.16771 − 1.68068I 0
u = 0.331929 + 0.546548I
a = −0.255257 − 0.397058I
b = −0.835212 − 0.757564I
−1.56185 − 2.54859I −4.54183 + 6.73419I
u = 0.331929 − 0.546548I
a = −0.255257 + 0.397058I
b = −0.835212 + 0.757564I
−1.56185 + 2.54859I −4.54183 − 6.73419I
u = 0.506249 + 0.383063I
a = 1.282450 − 0.233467I
b = 1.33969 − 0.99782I
−0.33577 − 7.51283I −10.7158 + 11.6615I
u = 0.506249 − 0.383063I
a = 1.282450 + 0.233467I
b = 1.33969 + 0.99782I
−0.33577 + 7.51283I −10.7158 − 11.6615I
u = −0.480044 + 0.408777I
a = 0.60292 − 1.39775I
b = −0.298969 + 0.772807I
3.12353 + 6.46824I 0.73913 − 10.15279I
u = −0.480044 − 0.408777I
a = 0.60292 + 1.39775I
b = −0.298969 − 0.772807I
3.12353 − 6.46824I 0.73913 + 10.15279I
u = −0.203094 + 1.364630I
a = 1.73312 + 1.06332I
b = −1.30310 − 1.52212I
2.44790 + 5.28354I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.203094 − 1.364630I
a = 1.73312 − 1.06332I
b = −1.30310 + 1.52212I
2.44790 − 5.28354I 0
u = −0.233413 + 1.362470I
a = 0.08623 + 1.84107I
b = 0.81713 − 1.23061I
2.95350 + 3.42762I 0
u = −0.233413 − 1.362470I
a = 0.08623 − 1.84107I
b = 0.81713 + 1.23061I
2.95350 − 3.42762I 0
u = 0.133295 + 1.380780I
a = 0.92027 − 1.11902I
b = −0.001311 + 0.512264I
6.25299 + 0.52670I 0
u = 0.133295 − 1.380780I
a = 0.92027 + 1.11902I
b = −0.001311 − 0.512264I
6.25299 − 0.52670I 0
u = 0.240329 + 1.377430I
a = 0.491496 − 0.511370I
b = 0.189501 + 0.635128I
5.10956 + 1.83810I 0
u = 0.240329 − 1.377430I
a = 0.491496 + 0.511370I
b = 0.189501 − 0.635128I
5.10956 − 1.83810I 0
u = −0.228892 + 1.382180I
a = 0.117317 + 1.188650I
b = 0.556428 − 0.783561I
3.34633 + 3.06913I 0
u = −0.228892 − 1.382180I
a = 0.117317 − 1.188650I
b = 0.556428 + 0.783561I
3.34633 − 3.06913I 0
u = 0.25227 + 1.40551I
a = 0.03543 − 2.27765I
b = 0.86262 + 1.41048I
4.35063 − 10.02420I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25227 − 1.40551I
a = 0.03543 + 2.27765I
b = 0.86262 − 1.41048I
4.35063 + 10.02420I 0
u = −0.13339 + 1.42677I
a = 0.50672 − 1.98992I
b = −1.06454 + 0.97054I
6.57352 + 3.44110I 0
u = −0.13339 − 1.42677I
a = 0.50672 + 1.98992I
b = −1.06454 − 0.97054I
6.57352 − 3.44110I 0
u = 0.32254 + 1.39786I
a = 0.28885 − 2.01448I
b = 0.923664 + 1.004800I
3.60068 − 8.43394I 0
u = 0.32254 − 1.39786I
a = 0.28885 + 2.01448I
b = 0.923664 − 1.004800I
3.60068 + 8.43394I 0
u = −0.518527 + 0.214517I
a = 0.361565 + 0.426099I
b = 0.80056 + 1.42438I
−2.55081 + 2.60103I −12.9307 − 11.5295I
u = −0.518527 − 0.214517I
a = 0.361565 − 0.426099I
b = 0.80056 − 1.42438I
−2.55081 − 2.60103I −12.9307 + 11.5295I
u = 0.33778 + 1.42496I
a = 0.508109 − 1.087070I
b = 0.502588 + 0.790543I
8.09107 − 5.50368I 0
u = 0.33778 − 1.42496I
a = 0.508109 + 1.087070I
b = 0.502588 − 0.790543I
8.09107 + 5.50368I 0
u = −0.20032 + 1.45079I
a = −0.05306 + 1.92605I
b = 0.108526 − 1.070520I
9.10457 + 9.09493I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20032 − 1.45079I
a = −0.05306 − 1.92605I
b = 0.108526 + 1.070520I
9.10457 − 9.09493I 0
u = 0.20599 + 1.45240I
a = 1.57680 − 0.46057I
b = −2.03746 + 1.23721I
5.60714 − 10.22340I 0
u = 0.20599 − 1.45240I
a = 1.57680 + 0.46057I
b = −2.03746 − 1.23721I
5.60714 + 10.22340I 0
u = −0.17957 + 1.45625I
a = −0.37758 + 1.94844I
b = 0.90227 − 1.25699I
3.72229 + 6.43678I 0
u = −0.17957 − 1.45625I
a = −0.37758 − 1.94844I
b = 0.90227 + 1.25699I
3.72229 − 6.43678I 0
u = −0.20003 + 1.46621I
a = −0.915411 − 0.527789I
b = −0.821245 + 0.218176I
6.39257 + 9.98168I 0
u = −0.20003 − 1.46621I
a = −0.915411 + 0.527789I
b = −0.821245 − 0.218176I
6.39257 − 9.98168I 0
u = 0.23324 + 1.46146I
a = 0.18206 + 2.10390I
b = −1.45473 − 1.43064I
9.5600 − 10.8669I 0
u = 0.23324 − 1.46146I
a = 0.18206 − 2.10390I
b = −1.45473 + 1.43064I
9.5600 + 10.8669I 0
u = 0.21065 + 1.46806I
a = 0.01019 − 1.93348I
b = 0.93758 + 1.79722I
4.83665 − 5.23562I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21065 − 1.46806I
a = 0.01019 + 1.93348I
b = 0.93758 − 1.79722I
4.83665 + 5.23562I 0
u = 0.22202 + 1.46947I
a = 0.43697 − 1.72569I
b = 0.303575 + 1.114500I
9.39173 − 5.21294I 0
u = 0.22202 − 1.46947I
a = 0.43697 + 1.72569I
b = 0.303575 − 1.114500I
9.39173 + 5.21294I 0
u = −0.26248 + 1.46956I
a = 0.628599 + 0.826129I
b = 0.484751 − 0.429781I
8.16133 + 0.86157I 0
u = −0.26248 − 1.46956I
a = 0.628599 − 0.826129I
b = 0.484751 + 0.429781I
8.16133 − 0.86157I 0
u = 0.29888 + 1.46546I
a = −0.02359 + 1.92866I
b = −1.09492 − 1.07987I
2.12497 − 13.85470I 0
u = 0.29888 − 1.46546I
a = −0.02359 − 1.92866I
b = −1.09492 + 1.07987I
2.12497 + 13.85470I 0
u = −0.377529 + 0.327841I
a = −2.63328 − 0.36476I
b = −0.778590 + 0.560618I
−2.02929 − 0.12780I −10.74338 − 2.92051I
u = −0.377529 − 0.327841I
a = −2.63328 + 0.36476I
b = −0.778590 − 0.560618I
−2.02929 + 0.12780I −10.74338 + 2.92051I
u = 0.22806 + 1.48473I
a = −0.737285 + 1.180430I
b = 0.19151 − 1.48260I
9.63764 + 0.53038I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22806 − 1.48473I
a = −0.737285 − 1.180430I
b = 0.19151 + 1.48260I
9.63764 − 0.53038I 0
u = −0.492300
a = −0.880497
b = −0.767274
−1.03985 −9.78370
u = −0.36108 + 1.46548I
a = −0.194985 − 0.692778I
b = −0.260332 + 0.488777I
3.06785 + 5.46384I 0
u = −0.36108 − 1.46548I
a = −0.194985 + 0.692778I
b = −0.260332 − 0.488777I
3.06785 − 5.46384I 0
u = −0.16852 + 1.50024I
a = 0.35221 − 1.65697I
b = −0.646933 + 0.774698I
7.89567 + 6.01898I 0
u = −0.16852 − 1.50024I
a = 0.35221 + 1.65697I
b = −0.646933 − 0.774698I
7.89567 − 6.01898I 0
u = 0.09743 + 1.50655I
a = −0.418988 + 0.855912I
b = 0.268925 − 0.646170I
4.81503 + 3.13066I 0
u = 0.09743 − 1.50655I
a = −0.418988 − 0.855912I
b = 0.268925 + 0.646170I
4.81503 − 3.13066I 0
u = −0.22611 + 1.50968I
a = −0.008568 − 1.303240I
b = −0.480493 + 0.561248I
6.94963 + 5.98626I 0
u = −0.22611 − 1.50968I
a = −0.008568 + 1.303240I
b = −0.480493 − 0.561248I
6.94963 − 5.98626I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.466172 + 0.053820I
a = 2.74298 + 1.94383I
b = 0.557478 + 0.093884I
−3.69307 − 1.95755I −21.5246 + 4.3584I
u = 0.466172 − 0.053820I
a = 2.74298 − 1.94383I
b = 0.557478 − 0.093884I
−3.69307 + 1.95755I −21.5246 − 4.3584I
u = 0.40654 + 1.48266I
a = −0.174575 + 0.929955I
b = −0.664099 − 0.693623I
7.37799 − 12.05090I 0
u = 0.40654 − 1.48266I
a = −0.174575 − 0.929955I
b = −0.664099 + 0.693623I
7.37799 + 12.05090I 0
u = −0.36217 + 1.50053I
a = −0.18881 − 1.82911I
b = −1.18037 + 1.28798I
6.5397 + 20.4690I 0
u = −0.36217 − 1.50053I
a = −0.18881 + 1.82911I
b = −1.18037 − 1.28798I
6.5397 − 20.4690I 0
u = 0.01761 + 1.56111I
a = 0.40062 + 1.53699I
b = −0.40719 − 1.39963I
13.45800 + 0.73329I 0
u = 0.01761 − 1.56111I
a = 0.40062 − 1.53699I
b = −0.40719 + 1.39963I
13.45800 − 0.73329I 0
u = −0.42002 + 1.52310I
a = 0.30271 + 1.65901I
b = 1.25358 − 1.33361I
6.28714 + 11.19380I 0
u = −0.42002 − 1.52310I
a = 0.30271 − 1.65901I
b = 1.25358 + 1.33361I
6.28714 − 11.19380I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23918 + 1.56330I
a = −0.793867 − 0.051978I
b = 2.07607 − 0.62330I
4.46463 − 0.32332I 0
u = 0.23918 − 1.56330I
a = −0.793867 + 0.051978I
b = 2.07607 + 0.62330I
4.46463 + 0.32332I 0
u = −0.078937 + 0.395652I
a = 1.21565 − 0.97488I
b = −1.191190 + 0.608235I
−2.68361 + 4.42624I −17.0809 − 4.1958I
u = −0.078937 − 0.395652I
a = 1.21565 + 0.97488I
b = −1.191190 − 0.608235I
−2.68361 − 4.42624I −17.0809 + 4.1958I
u = 0.316419 + 0.196344I
a = −1.76905 − 2.53885I
b = 0.645438 − 0.416976I
0.24472 + 4.06950I −15.0900 − 3.4557I
u = 0.316419 − 0.196344I
a = −1.76905 + 2.53885I
b = 0.645438 + 0.416976I
0.24472 − 4.06950I −15.0900 + 3.4557I
u = −0.28601 + 1.60424I
a = −0.193252 − 0.089414I
b = 1.52095 + 0.48295I
4.88802 + 0.84151I 0
u = −0.28601 − 1.60424I
a = −0.193252 + 0.089414I
b = 1.52095 − 0.48295I
4.88802 − 0.84151I 0
u = 0.209703 + 0.292557I
a = −2.21950 − 0.86846I
b = −0.879647 + 0.862875I
−2.53441 + 0.87638I −11.93265 + 6.27963I
u = 0.209703 − 0.292557I
a = −2.21950 + 0.86846I
b = −0.879647 − 0.862875I
−2.53441 − 0.87638I −11.93265 − 6.27963I
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.078361 + 0.340629I
a = −1.72638 + 1.53643I
b = 0.720044 − 0.281910I
1.00286 + 1.79610I −0.49070 − 2.53110I
u = 0.078361 − 0.340629I
a = −1.72638 − 1.53643I
b = 0.720044 + 0.281910I
1.00286 − 1.79610I −0.49070 + 2.53110I
u = −0.195422 + 0.282160I
a = 0.50857 + 2.67042I
b = 0.988380 − 0.398161I
0.94576 + 1.84722I 1.10121 − 2.58190I
u = −0.195422 − 0.282160I
a = 0.50857 − 2.67042I
b = 0.988380 + 0.398161I
0.94576 − 1.84722I 1.10121 + 2.58190I
u = 0.01860 + 1.67391I
a = −0.222969 − 1.227730I
b = 0.269022 + 1.356990I
11.83490 − 7.06354I 0
u = 0.01860 − 1.67391I
a = −0.222969 + 1.227730I
b = 0.269022 − 1.356990I
11.83490 + 7.06354I 0
21
II.
I
u
2
= h1.36×10
12
u
42
−1.14×10
12
u
41
+· · ·+2.87×10
11
b−2.81×10
12
, −1.91×
10
11
u
42
+2.78×10
13
u
41
+· · ·+8.61×10
11
a+3.29×10
13
, u
43
+u
42
+· · ·+10u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
3
=
0.221825u
42
− 32.2416u
41
+ ··· − 299.443u − 38.1937
−4.72395u
42
+ 3.96551u
41
+ ··· + 68.4609u + 9.79378
a
12
=
1
u
2
a
2
=
−4.50213u
42
− 28.2761u
41
+ ··· − 230.982u − 28.4000
−4.72395u
42
+ 3.96551u
41
+ ··· + 68.4609u + 9.79378
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
1.26740u
42
− 25.2656u
41
+ ··· − 205.158u − 27.9026
−2.07515u
42
− 2.36787u
41
+ ··· − 62.5179u − 8.79318
a
5
=
−16.1530u
42
− 10.5518u
41
+ ··· − 63.9256u − 15.1660
12.9419u
42
+ 21.4444u
41
+ ··· + 37.9531u + 1.77918
a
10
=
−9.06365u
42
− 11.0607u
41
+ ··· + 71.8230u + 13.3274
3.06681u
42
+ 0.104786u
41
+ ··· − 49.4519u − 6.52750
a
9
=
−3.37370u
42
− 4.87295u
41
+ ··· + 22.7095u + 4.97731
10.7071u
42
+ 7.04464u
41
+ ··· − 46.0819u − 7.00358
a
4
=
−11.5047u
42
− 16.9836u
41
+ ··· − 194.799u − 25.3332
7.09211u
42
+ 25.4009u
41
+ ··· + 170.411u + 17.6561
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
54075895974472
860939862039
u
42
−
91712206252259
860939862039
u
41
+ ··· −
277470088274206
860939862039
u −
33734854727699
860939862039
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
43
− 18u
42
+ ··· + 12u
2
− 1
c
2
u
43
− 5u
42
+ ··· + 8u − 1
c
3
u
43
+ 15u
41
+ ··· + 3u − 9
c
4
u
43
+ 2u
42
+ ··· − 14u
2
− 1
c
5
u
43
− 3u
42
+ ··· + 22u + 1
c
6
u
43
− 3u
42
+ ··· + 2u − 1
c
7
u
43
− u
42
+ ··· + 10u − 1
c
8
u
43
− 2u
42
+ ··· + 14u
2
+ 1
c
9
u
43
+ 2u
42
+ ··· − u − 1
c
10
u
43
+ 2u
42
+ ··· + u + 1
c
11
, c
12
u
43
+ u
42
+ ··· + 10u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
43
− 6y
42
+ ··· + 24y −1
c
2
y
43
− 13y
42
+ ··· + 40y −1
c
3
y
43
+ 30y
42
+ ··· − 441y −81
c
4
, c
8
y
43
+ 34y
42
+ ··· − 28y −1
c
5
y
43
− 17y
42
+ ··· + 44y −1
c
6
y
43
+ 23y
42
+ ··· + 20y −1
c
7
, c
11
, c
12
y
43
+ 43y
42
+ ··· + 6y −1
c
9
y
43
+ 2y
42
+ ··· − 3y −1
c
10
y
43
− 26y
41
+ ··· − 21y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.994536 + 0.150816I
a = 0.906274 − 0.271769I
b = 1.11458 + 1.13376I
−0.22307 − 5.30082I −8.25420 + 7.03473I
u = 0.994536 − 0.150816I
a = 0.906274 + 0.271769I
b = 1.11458 − 1.13376I
−0.22307 + 5.30082I −8.25420 − 7.03473I
u = −0.708601 + 0.633712I
a = 0.191227 + 0.727984I
b = 0.649217 − 0.568399I
0.51627 + 3.47994I −7.74667 − 6.07604I
u = −0.708601 − 0.633712I
a = 0.191227 − 0.727984I
b = 0.649217 + 0.568399I
0.51627 − 3.47994I −7.74667 + 6.07604I
u = −0.447532 + 0.799937I
a = 0.801775 − 0.735958I
b = 0.196687 − 0.665448I
−2.57328 + 2.03942I −12.33316 − 1.81690I
u = −0.447532 − 0.799937I
a = 0.801775 + 0.735958I
b = 0.196687 + 0.665448I
−2.57328 − 2.03942I −12.33316 + 1.81690I
u = 0.011937 + 1.206330I
a = 1.33564 − 0.60332I
b = −1.57880 + 0.54168I
−0.18874 + 4.21692I 0
u = 0.011937 − 1.206330I
a = 1.33564 + 0.60332I
b = −1.57880 − 0.54168I
−0.18874 − 4.21692I 0
u = 0.741245 + 0.245069I
a = −0.718430 − 0.496296I
b = −0.513762 − 0.150614I
1.28665 − 6.29745I −7.03142 + 5.87693I
u = 0.741245 − 0.245069I
a = −0.718430 + 0.496296I
b = −0.513762 + 0.150614I
1.28665 + 6.29745I −7.03142 − 5.87693I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.040747 + 1.241710I
a = −0.85450 − 3.11424I
b = 0.344407 + 0.875309I
2.16762 + 6.44054I 0
u = −0.040747 − 1.241710I
a = −0.85450 + 3.11424I
b = 0.344407 − 0.875309I
2.16762 − 6.44054I 0
u = −1.25030
a = 0.0158832
b = −0.146461
−2.40936 −197.870
u = 0.086387 + 0.710392I
a = −0.230492 − 0.225732I
b = 1.182270 + 0.579007I
−2.16882 − 4.50883I −1.07557 + 6.25982I
u = 0.086387 − 0.710392I
a = −0.230492 + 0.225732I
b = 1.182270 − 0.579007I
−2.16882 + 4.50883I −1.07557 − 6.25982I
u = 0.028724 + 1.291820I
a = −0.520755 + 0.419157I
b = −1.022110 − 0.409951I
3.66390 − 4.55889I 0
u = 0.028724 − 1.291820I
a = −0.520755 − 0.419157I
b = −1.022110 + 0.409951I
3.66390 + 4.55889I 0
u = −0.068145 + 1.300850I
a = 0.50005 + 2.45482I
b = −0.424767 − 1.058000I
0.727086 − 0.489982I 0
u = −0.068145 − 1.300850I
a = 0.50005 − 2.45482I
b = −0.424767 + 1.058000I
0.727086 + 0.489982I 0
u = −0.257190 + 1.301560I
a = 0.732839 − 0.545164I
b = −1.61892 − 0.44519I
3.08345 + 0.58263I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.257190 − 1.301560I
a = 0.732839 + 0.545164I
b = −1.61892 + 0.44519I
3.08345 − 0.58263I 0
u = 0.004853 + 0.631885I
a = −0.48373 + 2.93246I
b = −0.283727 + 0.554739I
−0.20672 − 6.17992I −10.70052 + 5.69705I
u = 0.004853 − 0.631885I
a = −0.48373 − 2.93246I
b = −0.283727 − 0.554739I
−0.20672 + 6.17992I −10.70052 − 5.69705I
u = −0.251863 + 1.346230I
a = −0.774057 − 0.742338I
b = 0.549413 + 0.754159I
2.76284 + 4.64437I 0
u = −0.251863 − 1.346230I
a = −0.774057 + 0.742338I
b = 0.549413 − 0.754159I
2.76284 − 4.64437I 0
u = −0.190679 + 1.375190I
a = 0.03901 − 1.84667I
b = −0.69989 + 1.27425I
2.70702 + 3.95086I 0
u = −0.190679 − 1.375190I
a = 0.03901 + 1.84667I
b = −0.69989 − 1.27425I
2.70702 − 3.95086I 0
u = 0.29568 + 1.39265I
a = −0.23343 + 2.19845I
b = −0.92289 − 1.28590I
4.80069 − 9.55102I 0
u = 0.29568 − 1.39265I
a = −0.23343 − 2.19845I
b = −0.92289 + 1.28590I
4.80069 + 9.55102I 0
u = 0.27470 + 1.43631I
a = −0.540777 + 0.471902I
b = −0.088275 − 0.524413I
5.45011 + 2.16121I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27470 − 1.43631I
a = −0.540777 − 0.471902I
b = −0.088275 + 0.524413I
5.45011 − 2.16121I 0
u = 0.21977 + 1.45302I
a = 0.059220 − 0.136952I
b = 0.990880 − 0.094483I
7.02514 − 9.54845I 0
u = 0.21977 − 1.45302I
a = 0.059220 + 0.136952I
b = 0.990880 + 0.094483I
7.02514 + 9.54845I 0
u = −0.396732 + 0.292907I
a = −0.638609 − 0.563413I
b = 0.215097 − 0.849317I
−2.65156 + 1.72406I −12.69164 − 3.37048I
u = −0.396732 − 0.292907I
a = −0.638609 + 0.563413I
b = 0.215097 + 0.849317I
−2.65156 − 1.72406I −12.69164 + 3.37048I
u = −0.18265 + 1.50681I
a = 0.25510 − 1.57673I
b = −0.557755 + 0.756420I
7.66397 + 6.18308I 0
u = −0.18265 − 1.50681I
a = 0.25510 + 1.57673I
b = −0.557755 − 0.756420I
7.66397 − 6.18308I 0
u = −0.025242 + 0.455449I
a = −2.48479 + 0.91092I
b = 0.763287 − 0.466434I
0.56637 + 4.36746I −2.3969 − 17.9478I
u = −0.025242 − 0.455449I
a = −2.48479 − 0.91092I
b = 0.763287 + 0.466434I
0.56637 − 4.36746I −2.3969 + 17.9478I
u = 0.29189 + 1.67164I
a = 0.337666 + 0.013597I
b = −1.80615 + 0.49588I
5.13869 − 0.84939I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29189 − 1.67164I
a = 0.337666 − 0.013597I
b = −1.80615 − 0.49588I
5.13869 + 0.84939I 0
u = −0.255185 + 0.022593I
a = 1.31285 − 2.65318I
b = 1.084440 + 0.524226I
−2.15438 − 2.00272I −13.73059 + 2.44447I
u = −0.255185 − 0.022593I
a = 1.31285 + 2.65318I
b = 1.084440 − 0.524226I
−2.15438 + 2.00272I −13.73059 − 2.44447I
29
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
43
− 18u
42
+ ··· + 12u
2
− 1)(u
166
+ 15u
165
+ ··· + 14u − 1)
c
2
(u
43
− 5u
42
+ ··· + 8u − 1)(u
166
− 4u
165
+ ··· + 28476u + 667)
c
3
(u
43
+ 15u
41
+ ··· + 3u − 9)(u
166
− 3u
165
+ ··· − 8268033u + 335191)
c
4
(u
43
+ 2u
42
+ ··· − 14u
2
− 1)(u
166
− u
165
+ ··· − 228154u + 191449)
c
5
(u
43
− 3u
42
+ ··· + 22u + 1)(u
166
− 2u
165
+ ··· + 2701472u − 273472)
c
6
(u
43
− 3u
42
+ ··· + 2u − 1)(u
166
− 10u
165
+ ··· + 634u − 109)
c
7
(u
43
− u
42
+ ··· + 10u − 1)(u
166
+ 2u
165
+ ··· − 714u + 289)
c
8
(u
43
− 2u
42
+ ··· + 14u
2
+ 1)(u
166
− u
165
+ ··· − 228154u + 191449)
c
9
(u
43
+ 2u
42
+ ··· − u − 1)(u
166
− u
165
+ ··· − 67072u + 22016)
c
10
(u
43
+ 2u
42
+ ··· + u + 1)(u
166
+ 5u
165
+ ··· − 15u + 1)
c
11
, c
12
(u
43
+ u
42
+ ··· + 10u + 1)(u
166
+ 2u
165
+ ··· − 714u + 289)
30
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
43
− 6y
42
+ ··· + 24y −1)(y
166
+ y
165
+ ··· − 14y + 1)
c
2
(y
43
− 13y
42
+ ··· + 40y −1)
· (y
166
− 2y
165
+ ··· − 1188891486y + 444889)
c
3
(y
43
+ 30y
42
+ ··· − 441y −81)
· (y
166
+ 61y
165
+ ··· − 3152875669969y + 112353006481)
c
4
, c
8
(y
43
+ 34y
42
+ ··· − 28y −1)
· (y
166
+ 117y
165
+ ··· + 1929765685298y + 36652719601)
c
5
(y
43
− 17y
42
+ ··· + 44y −1)
· (y
166
− 30y
165
+ ··· − 5537587637248y + 74786934784)
c
6
(y
43
+ 23y
42
+ ··· + 20y −1)
· (y
166
+ 18y
165
+ ··· − 1172586y + 11881)
c
7
, c
11
, c
12
(y
43
+ 43y
42
+ ··· + 6y −1)
· (y
166
+ 158y
165
+ ··· + 2222988y + 83521)
c
9
(y
43
+ 2y
42
+ ··· − 3y −1)
· (y
166
+ 21y
165
+ ··· + 28523233280y + 484704256)
c
10
(y
43
− 26y
41
+ ··· − 21y −1)(y
166
+ 15y
165
+ ··· − 249y + 1)
31
