class_group 0.6.0

Type: [I{0-0-0}], p. 155
[1, Mat([7, 0]), x^5 + x^3 - 2*x^2 + 3*x + 1, [7, [1, []], ["(tame) [I{0-0-0
}] page 155", []]]]
Type: [I*{0-0-0}], p. 155
[2401, Mat([7, 4]), 7*x^5 + 7*x^3 - 14*x^2 + 21*x + 7, [7, [1, []], ["(tame)
 [I*{0-0-0}] page 155", [2, 2, 2, 2]]]]
Type: [II], p. 155
[49, Mat([7, 2]), x^6 + 28*x^4 - 49*x^2 + 343, [7, [1, []], ["(tame) [II] pa
ge 155", []]]]
[9, Mat([3, 2]), x^6 + 12*x^4 - 9*x^2 + 27, [3, [1, []], ["[II] page 155", [
]]]]
Type: [III], p. 155
[2401, Mat([7, 4]), x^6 + 28*x^3 + 49, [7, [1, []], ["[III] page 155", [3, 3
]]]]
Type: [IV], p. 155
[2401, Mat([7, 4]), 7*x^6 + 245*x^3 + 343, [7, [4, []], ["[III*{3}] page 184
", []]]]
Type: [V], p. 156
[2401, Mat([7, 4]), x^6 + 7, [7, [1, []], ["[V] page 156", [3]]]]
Type: [V*], p. 156
[2401, Mat([7, 4]), 7*x^6 + 49, [7, [1, []], ["[V*] page 156", [3]]]]
Type: [VI], p. 156
[2401, Mat([7, 4]), x^5 + 21*x^3 + 49*x, [7, [1, []], ["(tame) [VI] page 156
", [2, 2]]]]
Type: [VII], p. 156
[2401, Mat([7, 4]), x^5 + 7*x, [7, [1, []], ["[VII] page 156", [2]]]]
Type: [VII*], p. 156
[2401, Mat([7, 4]), 7*x^5 + 49*x, [7, [1, []], ["[VII*] page 156", [2]]]]
Type: [VIII-1], p. 156
[2401, Mat([7, 4]), x^5 + 7, [7, [1, []], ["[VIII-1] page 156", []]]]
Type: [VIII-2], p. 157
[2401, Mat([7, 4]), x^5 + 343, [7, [1, []], ["[VIII-2] page 157", []]]]
Type: [VIII-3], p. 157
[2401, Mat([7, 4]), 7*x^5 + 343, [7, [1, []], ["[VIII-3] page 157", []]]]
Type: [VIII-4], p. 157
[2401, Mat([7, 4]), 7*x^6 + 49*x, [7, [1, []], ["[VIII-4] page 157", []]]]
Type: [IX-1], p. 157
[2401, Mat([7, 4]), x^5 + 49, [7, [1, []], ["[IX-1] page 157", [5]]]]
Type: [IX-2], p. 157
[2401, Mat([7, 4]), x^6 + 7*x, [7, [1, []], ["[IX-2] page 157", [5]]]]
Type: [IX-3], p. 157
[2401, Mat([7, 4]), 7*x^5 + 49, [7, [1, []], ["[IX-3] page 157", [5]]]]
Type: [IX-4], p. 158
[2401, Mat([7, 4]), x^6 + 49*x, [7, [1, []], ["[IX-4] page 158", [5]]]]
Type: [I{0}-I{0}-10], p. 158
[1, Mat([7, 0]), 508021860739623365322188197652216501772434524836001*x^6 + 5
080218607396233653221881976522165257101144141196013*x^4 + 508021860739623365
322188197652216501772434524836002*x^3 + 2393767988928360030*x^2 + 2393767988
92836013*x + 1, [7, [5, [Mod(2, 7), Mod(5, 7)]], ["(tame) [I{0}-I{0}-10] pag
e 158", []]]]
[1, Mat([3, 0]), 42391158275216203514294433201*x^6 + 42391158275216203510807
648800*x^4 + 42391158275216203514294433202*x^3 - 3486784401*x^2 - 3486784400
*x + 1, [3, [5, [Mod(0, 3), Mod(1, 3)]], ["[I{0}-I{0}-10] page 158", []]]]
Type: [I{0}*-I{0}*-10], p. 158
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 24893071176241544900787221684958
6097837332861811440640*x^4 + 17425149823369080494630608325843912106803538735
9467068*x^3 - 6551443127975383932596363883779423529*x^2 + 410531210101213754
7000*x + 66885, [7, [5, [Mod(2, 7), Mod(2, 7)]], ["(tame) [I*{0}-I*{0}-10] p
age 158", [2, 2, 2, 2]]]]
[81, Mat([3, 4]), 42391158275216203514294433201*x^6 - 36472996377170786403*x
^5 + 381520424476945831607729192403*x^4 + 1144561273102580527491412618835*x^
3 - 984770902371897590535*x^2 - 564859072647*x + 945, [3, [5, [Mod(0, 3), Mo
d(0, 3)]], ["[I*{0}-I*{0}-10] page 158", [2, 2, 2, 2]]]]
Type: [I{0}-I{0}*-10], p. 159
[49, Mat([7, 2]), 508021860739623365322188197652216501772434524836001*x^6 + 
248930711762415449007872216849586086107869716062476493*x^4 + 174251498233690
814305510551794710260107945042018748344*x^3 + 117294631457489641470*x^2 + 82
106242020242749519*x + 343, [7, [5, [Mod(2, 7), Mod(5, 7)]], ["(tame) [I{0}-
I*{0}-10] page 159", [2, 2]]]]
[9, Mat([3, 2]), 42391158275216203514294433201*x^6 + 38152042447694583162516
3114408*x^4 + 1144561273430837494885949696428*x^3 - 31381059609*x^2 - 941431
78818*x + 27, [3, [5, [Mod(0, 3), Mod(1, 3)]], ["[I{0}-I*{0}-10] page 159", 
[2, 2]]]]
Type: [2I{0}-11], p. 159
[49, Mat([7, 2]), x^6 - 21*x^4 + 574743694141699243350*x^2 + 265173084183644
7612787128678837, [7, [5, [Mod(2, 7), Mod(2, 7)]], ["(tame) [2I{0}-11] page 
159", []]]]
[9, Mat([3, 2]), x^6 - 9*x^4 - 282429536454*x^2 + 150095482585608537, [3, [5
, [Mod(0, 3), Mod(0, 3)]], ["[2I{0}-11] page 159", []]]]
Type: [2I{0}*-10], p. 159
[2401, Mat([7, 4]), x^6 - 21*x^4 + 82106242020242749176*x^2 + 54116956037952
111668959660849*x - 574743694141699243546, [7, [5, [Mod(2, 7), Mod(2, 7)]], 
["(tame) [2I*{0}-10] page 159", [2, 2]]]]
Type: [2I{0}*-10], p. 159
[2401, Mat([7, 4]), x^6 - 21*x^4 + 82106242020242749176*x^2 + 54116956037952
111668959660849*x - 574743694141699243546, [7, [5, [Mod(2, 7), Mod(2, 7)]], 
["(tame) [2I*{0}-10] page 159", [2, 2]]]]
Type: [I{0}-II-10], p. 159
[49, Mat([7, 2]), 6366805760909027985741435139224001*x^5 + 23937679889283600
3*x^4 + x^3 + 44567640326363195900190045974568007*x^2 + 1675637592249852021*
x + 7, [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I{0}-II-10] page 159", []]
]]
Type: [I{0}-II*-10], p. 160
[49, Mat([7, 2]), 6366805760909027985741435139224001*x^5 + 23937679889283600
3*x^4 + x^3 + 107006904423598033356356300384937784807*x^2 + 4023205858991894
702421*x + 16807, [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I{0}-II*-10] pa
ge 160", []]]]
[243, Mat([3, 5]), 12157665459056928801*x^5 + 10460353203*x^4 + x^3 + 295431
2706550833698643*x^2 + 2541865828329*x + 243, [3, [5, [Mod(0, 3), Mod(0, 3)]
], ["[I{0}-II*-10] pages 159-177", []]]]
Type: [I{0}-IV-10], p. 160
[49, Mat([7, 2]), 6366805760909027985741435139224001*x^5 + 23937679889283600
3*x^4 + x^3 + 311973482284542371301330321821976049*x^2 + 1172946314574896414
7*x + 49, [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I{0}-IV-10] page 160", 
[3]]]]
[243, Mat([3, 5]), 12157665459056928801*x^5 + 10460353203*x^4 + x^3 + 109418
989131512359209*x^2 + 94143178827*x + 9, [3, [5, [Mod(0, 3), Mod(0, 3)]], ["
[I{0}-IV-10] pages 159-177", [3]]]]
Type: [I{0}-IV*-10], p. 160
[49, Mat([7, 2]), 6366805760909027985741435139224001*x^5 + 23937679889283600
3*x^4 + x^3 + 15286700631942576193765185769276826401*x^2 + 57474369414169924
3203*x + 2401, [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I{0}-IV*-10] page 
160", [3]]]]
[243, Mat([3, 5]), 12157665459056928801*x^5 + 10460353203*x^4 + x^3 + 984770
902183611232881*x^2 + 847288609443*x + 81, [3, [5, [Mod(0, 3), Mod(0, 3)]], 
["[I{0}-IV*-10] pages 159-177", [3]]]]
Type: [I{0}*-II-10], p. 160
[2401, Mat([7, 4]), 311973482284542371301330321821976049*x^5 + 1675637592249
852021*x^4 + x^3 + 2183814375991796599109312252753832343*x^2 + 1172946314574
8964147*x + 7, [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I*{0}-II-10] page 
160", [2, 2]]]]
[2187, Mat([3, 7]), 109418989131512359209*x^5 + 31381059609*x^4 + x^3 + 3282
56967394537077627*x^2 + 94143178827*x + 3, [3, [5, [Mod(0, 3), Mod(0, 3)]], 
["[I*{0}-II-10] pages 159-177", [2, 2]]]]
Type: [I{0}*-II*-10], p. 160-161
[2401, Mat([7, 4]), 311973482284542371301330321821976049*x^5 + 1675637592249
852021*x^4 + x^3 + 5243338316756303634461458718861951455543*x^2 + 2816244101
2943262916947*x + 16807, [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I*{0}-II
*-10] page 160", [2, 2]]]]
[2187, Mat([3, 7]), 109418989131512359209*x^5 + 31381059609*x^4 + x^3 + 2658
8814358957503287787*x^2 + 7625597484987*x + 243, [3, [5, [Mod(0, 3), Mod(0, 
3)]], ["[I*{0}-II*-10] pages 159-177", [2, 2]]]]
Type: [I{0}*-IV-10], p. 161
[2401, Mat([7, 4]), 311973482284542371301330321821976049*x^5 + 1675637592249
852021*x^4 + x^3 + 15286700631942576193765185769276826401*x^2 + 821062420202
42749029*x + 49, [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I*{0}-IV-10] pag
e 161", [6, 2]]]]
Type: [I{0}*-IV*-10], p. 161
[2401, Mat([7, 4]), 311973482284542371301330321821976049*x^5 + 1675637592249
852021*x^4 + x^3 + 749048330965186233494494102694564493649*x^2 + 40232058589
91894702421*x + 2401, [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I*{0}-IV*-1
0] page 161", [6, 2]]]]
Type: [I{0}-III-10], p. 161
[49, Mat([7, 2]), 6366805760909027985741435139224001*x^5 + 23937679889283600
3*x^4 + 44567640326363195900190045974568008*x^3 + 1675637592249852021*x^2 + 
7*x, [7, [5, [Mod(2, 7), Mod(6, 7)]], ["(tame) [I{0}-III-10] page 161", [2]]
]]
Type: [I{0}-III*-10], p. 162
[49, Mat([7, 2]), 6366805760909027985741435139224001*x^5 + 23937679889283600
3*x^4 + 2183814375991796599109312252753832344*x^3 + 82106242020242749029*x^2
 + 343*x, [7, [5, [Mod(2, 7), Mod(6, 7)]], ["(tame) [I{0}-III*-10] page 162"
, [2]]]]
Type: [I{0}*-III-10], p. 162
[2401, Mat([7, 4]), 311973482284542371301330321821976049*x^5 + 1675637592249
852021*x^4 + 2183814375991796599109312252753832344*x^3 + 1172946314574896414
7*x^2 + 7*x, [7, [5, [Mod(2, 7), Mod(6, 7)]], ["(tame) [I*{0}-III-10] page 1
62", [2, 2, 2]]]]
Type: [I{0}*-III*-10], p. 162
[2401, Mat([7, 4]), 311973482284542371301330321821976049*x^5 + 1675637592249
852021*x^4 + 107006904423598033356356300384937784808*x^3 + 57474369414169924
3203*x^2 + 343*x, [7, [5, [Mod(2, 7), Mod(6, 7)]], ["(tame) [I*{0}-III*-10] 
page 162", [2, 2, 2]]]]
Type: [2II-10], p. 162
[2401, Mat([7, 4]), x^6 - 21*x^4 + 147*x^2 + 7730993719707444524137094407*x 
- 343, [7, [5, [Mod(0, 7), Mod(0, 7)]], ["(tame) [2II-10] page 162", []]]]
[59049, Mat([3, 10]), x^6 - 9*x^4 + 27*x^2 + 5559060566555523*x - 27, [3, [5
, [Mod(0, 3), Mod(0, 3)]], ["[2II-10] page 162", []]]]
Type: [2II*-10], p. 163
[2401, Mat([7, 4]), x^6 - 21*x^4 + 147*x^2 + 378818692265664781682717625943*
x - 343, [7, [5, [Mod(0, 7), Mod(0, 7)]], ["(tame) [2II*-10] page 163", []]]
]
[59049, Mat([3, 10]), x^6 - 9*x^4 + 27*x^2 + 50031545098999707*x - 27, [3, [
5, [Mod(0, 3), Mod(0, 3)]], ["[2II*-10] page 163", []]]]
Type: [II-II-10], p. 163
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 239376798892836003*x^4 + 3556153
025177363557255317383565515512407041673852013*x^3 - 133702920979089587700570
137923704021*x^2 + 1675637592249852021*x + 42, [7, [5, [Mod(0, 7), Mod(0, 7)
]], ["(tame) [II-II-10] page 163", []]]]
Type: [II-II*-10], p. 163
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 239376798892836003*x^4 + 3556153
025177363557255317383565515512407041673868813*x^3 - 133702920979089587700570
137923704021*x^2 + 1675637592249852021*x + 117642, [7, [5, [Mod(0, 7), Mod(0
, 7)]], ["(tame) [II-II*-10] page 163", []]]]
Type: [II*-II*-10], p. 163
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 239376798892836003*x^4 + 8538323
413450849900970017037940802745289307058918685613*x^3 - 321020713270794100069
068901154813354421*x^2 + 4023205858991894702421*x + 282458442, [7, [5, [Mod(
0, 7), Mod(0, 7)]], ["(tame) [II*-II*-10] page 163", []]]]
Type: [II*-II*-(-1)], p. 163
[2401, Mat([7, 4]), 7*x^6 - 21*x^5 + 21*x^4 + 679*x^3 - 1029*x^2 + 1029*x + 
16464, [7, [5, [Mod(0, 7), Mod(0, 7)]], ["(tame) [II*-II*--1] page 163", []]
]]
Type: [II-IV-10], p. 164
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 239376798892836003*x^4 + 3556153
025177363557255317383565515512407041673852055*x^3 - 133702920979089587700570
137923704021*x^2 + 1675637592249852021*x + 336, [7, [5, [Mod(0, 7), Mod(0, 7
)]], ["(tame) [II-IV-10] page 164", [3]]]]
Type: [II-IV*-10], p. 164
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 239376798892836003*x^4 + 3556153
025177363557255317383565515512407041673854407*x^3 - 133702920979089587700570
137923704021*x^2 + 1675637592249852021*x + 16800, [7, [5, [Mod(0, 7), Mod(0,
 7)]], ["(tame) [II-IV*-10] page 164", [3]]]]
Type: [II*-IV-10], p. 164
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 239376798892836003*x^4 + 8538323
413450849900970017037940802745289307058918668855*x^3 - 321020713270794100069
068901154813354421*x^2 + 4023205858991894702421*x + 806736, [7, [5, [Mod(0, 
7), Mod(0, 7)]], ["(tame) [II*-IV-10] page 164", [3]]]]
Type: [II*-IV-(-1)], p. 164
[2401, Mat([7, 4]), x^6 + 56*x^3 + 343, [7, [5, [Mod(0, 7), Mod(0, 7)]], ["[
II*-IV-(-1)] page 164", [3]]]]
Type: [II*-IV*-10], p. 164-165
[2401, Mat([7, 4]), 174251498233690814305510551794710260107945042018748343*x
^6 - 935920446853627113903990965465928147*x^5 + 1675637592249852021*x^4 + 41
8377847259091645147530834859099334519176045887014771591*x^3 - 22471449928955
58700483482308083693480947*x^2 + 4023205858991894702421*x + 115248, [7, [5, 
[Mod(0, 7), Mod(0, 7)]], ["(tame) [II*-IV*-10] page 164", [3]]]]
Type: [2IV-10], p. 165
[2401, Mat([7, 4]), x^6 - 21*x^4 + 147*x^2 + 54116956037952111668959660506, 
[7, [5, [Mod(0, 7), Mod(0, 7)]], ["(tame) [2IV-10] page 165", [3]]]]
[59049, Mat([3, 10]), x^6 - 9*x^4 + 27*x^2 + 16677181699666542, [3, [5, [Mod
(0, 3), Mod(0, 3)]], ["[2IV-10] page 165", [3]]]]
Type: [2IV*-10], p. 165
[2401, Mat([7, 4]), x^6 - 21*x^4 + 147*x^2 + 378818692265664781682717625600,
 [7, [5, [Mod(0, 7), Mod(0, 7)]], ["(tame) [2IV*-10] page 165", [3]]]]
[59049, Mat([3, 10]), x^6 - 9*x^4 + 27*x^2 + 50031545098999680, [3, [5, [Mod
(0, 3), Mod(0, 3)]], ["[2IV*-10] page 165", [3]]]]
Type: [IV-IV-10], p. 165
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 239376798892836003*x^4 + 2489307
1176241544900787221684958608586849291716964097*x^3 - 93592044685362711390399
0965465928147*x^2 + 11729463145748964147*x + 2352, [7, [5, [Mod(0, 7), Mod(0
, 7)]], ["(tame) [IV-IV-10] page 165", [3, 3]]]]
Type: [IV-IV*-10], p. 165
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 239376798892836003*x^4 + 2489307
1176241544900787221684958608586849291716966449*x^3 - 93592044685362711390399
0965465928147*x^2 + 11729463145748964147*x + 117600, [7, [5, [Mod(0, 7), Mod
(0, 7)]], ["(tame) [IV-IV*-10] page 165", [3, 3]]]]
Type: [IV*-IV*-10], p. 166
[2401, Mat([7, 4]), 174251498233690814305510551794710260107945042018748343*x
^6 - 935920446853627113903990965465928147*x^5 + 1675637592249852021*x^4 + 41
8377847259091645147530834859099334519176045887014771549*x^3 - 22471449928955
58700483482308083693480947*x^2 + 4023205858991894702421*x + 14406, [7, [5, [
Mod(0, 7), Mod(0, 7)]], ["(tame) [IV*-IV*-10] page 166", [3, 3]]]]
Type: [II-III-10], p. 166
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 35561530251773635572553173835655
15751783840566688010*x^4 - 133702920979089587700570137923704015*x^3 + 167563
7592249852021*x^2 + 42*x, [7, [5, [Mod(0, 7), Mod(6, 7)]], ["(tame) [II-III-
10] page 166", [2]]]]
Type: [II-III*-10], p. 166
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 17425149823369081430551055179471
0260347321840911584346*x^4 - 6551443127975389797327936758261497023*x^3 + 821
06242020242749029*x^2 + 2058*x, [7, [5, [Mod(0, 7), Mod(6, 7)]], ["(tame) [I
I-III*-10] page 166", [2]]]]
Type: [II*-III-10], p. 166
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 35561530251773635572553173835655
15751783840566688010*x^4 - 133702920979089587700570137923687215*x^3 + 167563
7592249852021*x^2 + 117642*x, [7, [5, [Mod(0, 7), Mod(6, 7)]], ["(tame) [II*
-III-10] page 166", [2]]]]
Type: [II*-III-(-1)], p. 167
[2401, Mat([7, 4]), x^5 + 7*x^3 + 49*x^2 + 343, [7, [5, [Mod(0, 7), Mod(6, 7
)]], ["[II*-III-(-1)] page 167", [2]]]]
Type: [II*-III*-10], p. 167
[2401, Mat([7, 4]), 174251498233690814305510551794710260107945042018748343*x
^6 - 935920446853627113903990965465928147*x^5 + 5976826389415594930679011926
5585619218700787004680533670*x^4 - 321020713270794100069068901154813354373*x
^3 + 574743694141699243203*x^2 + 16464*x, [7, [5, [Mod(0, 7), Mod(6, 7)]], [
"(tame) [II*-III*-10] page 167", [2]]]]
Type: [IV-III-10], p. 167
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 35561530251773635572553173835655
15751783840566688010*x^4 - 133702920979089587700570137923703973*x^3 + 167563
7592249852021*x^2 + 336*x, [7, [5, [Mod(0, 7), Mod(6, 7)]], ["(tame) [III-IV
-10] page 167", [6]]]]
[2187, Mat([3, 7]), 42391158275216203514294433201*x^6 - 36472996377170786403
*x^5 + 127173474825648610553343652806*x^4 - 109418989131512359201*x^3 + 3138
1059609*x^2 + 24*x, [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[III-IV-10] pages 161
-177", [6]]]]
Type: [IV-III*-10], p. 167
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 17425149823369081430551055179471
0260347321840911584346*x^4 - 6551443127975389797327936758261496981*x^3 + 821
06242020242749029*x^2 + 16464*x, [7, [5, [Mod(0, 7), Mod(6, 7)]], ["(tame) [
III*-IV-10] page 167", [6]]]]
[2187, Mat([3, 7]), 42391158275216203514294433201*x^6 - 36472996377170786403
*x^5 + 1144561273430837494896410049630*x^4 - 984770902183611232873*x^3 + 282
429536481*x^2 + 216*x, [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[III*-IV-10] pages
 162-177", [6]]]]
Type: [IV-III*-(-1)], p. 167
[2401, Mat([7, 4]), x^6 + 7*x^4 + 7*x^3 + 49*x, [7, [5, [Mod(0, 7), Mod(6, 7
)]], ["[IV-III*-(-1)] page 167", [6]]]]
Type: [IV*-III-10], p. 168
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 35561530251773635572553173835655
15751783840566688010*x^4 - 133702920979089587700570137923701621*x^3 + 167563
7592249852021*x^2 + 16800*x, [7, [5, [Mod(0, 7), Mod(6, 7)]], ["(tame) [III-
IV*-10] page 168", [6]]]]
Type: [IV*-III*-10], p. 168
[2401, Mat([7, 4]), 174251498233690814305510551794710260107945042018748343*x
^6 - 935920446853627113903990965465928147*x^5 + 5976826389415594930679011926
5585619218700787004680533670*x^4 - 321020713270794100069068901154813354415*x
^3 + 574743694141699243203*x^2 + 2058*x, [7, [5, [Mod(0, 7), Mod(6, 7)]], ["
(tame) [III*-IV*-10] page 168", [6]]]]
Type: [2III-10], p. 168
[2401, Mat([7, 4]), x^6 - 21*x^4 + 3909821048582988049*x^3 + 147*x^2 - 27368
747340080916343*x - 343, [7, [5, [Mod(6, 7), Mod(6, 7)]], ["(tame) [2III-10]
 page 168", [2]]]]
[81, Mat([3, 4]), x^6 - 9*x^4 + 31381059609*x^3 + 27*x^2 - 94143178827*x - 2
7, [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[2III-10] page 168", [2]]]]
Type: [2III*-10], p. 168
[2401, Mat([7, 4]), x^6 - 21*x^4 + 27368747340080916343*x^3 + 147*x^2 - 1915
81231380566414401*x - 343, [7, [5, [Mod(6, 7), Mod(6, 7)]], ["(tame) [2III*-
10] page 168", [2]]]]
[81, Mat([3, 4]), x^6 - 9*x^4 + 94143178827*x^3 + 27*x^2 - 282429536481*x - 
27, [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[2III*-10] page 168", [2]]]]
Type: [III-III-10], p. 169
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 35561530251773635572553173835655
16310329704649972017*x^4 - 133702920979089587700570137923704029*x^3 + 558545
8640832840070*x^2 - 56*x, [7, [5, [Mod(6, 7), Mod(6, 7)]], ["(tame) [III-III
-10] page 169", [2, 2]]]]
Type: [III-III*-10], p. 169
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
- 19100417282727083957224305417672003*x^5 + 35561530251773635572553173835655
43120531180647604353*x^4 - 133702920979089587700570137923704365*x^3 + 193256
868972816266422*x^2 - 2408*x, [7, [5, [Mod(6, 7), Mod(6, 7)]], ["(tame) [III
-III*-10] page 169", [2, 2]]]]
Type: [III*-III*-{10}], p. 169
[2401, Mat([7, 4]), 174251498233690814305510551794710260107945042018748343*x
^6 - 935920446853627113903990965465928147*x^5 + 5976826389415594930679011926
5585619222610608053263521719*x^4 - 321020713270794100069068901154813354429*x
^3 + 1915812313805664144010*x^2 - 2744*x, [7, [5, [Mod(6, 7), Mod(6, 7)]], [
"(tame) [III*-III*-10] page 169", [2, 2]]]]
Type: [I{9-0-0}], p. 170
[7, Mat([7, 1]), x^5 + 40353610*x^3 + x^2 + 121060821*x + 40353607, [7, [2, 
[Mod(2, 7)]], ["(tame) [I{9-0-0}] page 170", [9]]]]
Type: [I{9}-I{0}-10], p. 170
[7, Mat([7, 1]), 6366805760909027985741435139224001*x^5 - 159584532595224002
*x^4 + 19100417282727083957224305458025611*x^3 + 636680576090902750698783735
3551995*x^2 - 159584532474163178*x + 40353608, [7, [6, [Mod(2, 7)]], ["(tame
) [I{0}-I{9}-10] page 170", [9]]]]
[3, Mat([3, 1]), 12157665459056928801*x^5 - 6973568802*x^4 - 121576654590569
09117*x^3 + 12157665466030497603*x^2 - 6973588486*x + 19684, [3, [6, [Mod(0,
 3)]], ["(tame) [I{0}-I{9}-10] page 170", [9]]]]
Type: [I{0}-I*{9}-10], p. 170
[49, Mat([7, 2]), x^6 + 4*x^5 + 19100417282727083957224307394998728*x^4 + 50
8021860739623479924691894014720245118274940175011*x^3 + 35561530629451293191
48051483501814963799504492542834*x^2 + 1004525211269079266605816908070627976
335864597950580018666977*x + 70316764788835530156201894723072969620825817394
84589084102397, [7, [6, [Mod(2, 7)]], ["(tame) [I{0}-I*{9}-10] page 170", [4
]]]]
[9, Mat([3, 2]), x^6 - 12157665459056751660*x^4 + 42391158250900872596180575
607*x^3 + 127171321168158531362286712374*x^2 + 75094665106723368777956004270
53229*x + 22528399551400256301066821173173441, [3, [6, [Mod(0, 3)]], ["[I{0}
-I*{9}-10] page 170", [4]]]]
Type: [I{9}-I{0}*-10], p. 171
[343, Mat([7, 3]), 6366805760909027985741435139224001*x^5 - 1595845325952240
02*x^4 + 935920446853627113903990965506281755*x^3 + 218381437599179657565038
5961255904049*x^2 - 54737494674229852310*x + 13841287544, [7, [6, [Mod(2, 7)
]], ["(tame) [I{9}-I*{0}-10] page 170", [18, 2]]]]
Type: [I*{9-0-0}], p. 171
[2401, Mat([7, 4]), 7*x^5 + 282475270*x^3 + 7*x^2 + 847425747*x + 282475249,
 [7, [2, [Mod(2, 7)]], ["(tame) [I*{9-0-0}] page 171", [4, 2, 2]]]]
Type: [I*{9}-I{0}*-10], p. 171
[2401, Mat([7, 4]), x^6 + 4*x^5 + 935920446853627113903990967443254872*x^4 +
 174251498233690819921033232916472943531890842723624217*x^3 + 12197604894864
56222471317833459850493873847680657395212*x^2 + 3445521474652941218234561596
37489836481536621034944927824583035*x + 241186503225705876208378720213726101
0629601295382324365507824195, [7, [6, [Mod(2, 7)]], ["(tame) [I*{0}-I*{9}-10
] page 171", [4, 2, 2]]]]
Type: [II{9-0}], p. 171
[343, Mat([7, 3]), x^6 - 2*x^5 + 5764823*x^4 - 42*x^3 + 121060891*x^2 - 98*x
 + 282475298, [7, [2, [Mod(0, 7)]], ["(tame) [II{9-0}] page 171", [36]]]]
Type: [II*{9-0}], p. 172
[49, Mat([7, 2]), 7*x^6 - 14*x^5 + 40353761*x^4 - 294*x^3 + 847426237*x^2 - 
686*x + 1977327086, [7, [2, [Mod(0, 7)]], ["(tame) [II*{9-0}] page 172", []]
]]
Type: [II-I{9}-10], p. 172
[343, Mat([7, 3]), 6366805760909027985741435139224001*x^5 - 1595845325952240
02*x^4 + 40353608*x^3 + 44567640326363195900190045974568007*x^2 - 1117091728
166568014*x + 282475256, [7, [6, [Mod(0, 7)]], ["(tame) [I{9}-II-10] page 17
2", [9]]]]
Type: [II*-I{9}-10], p. 172
[343, Mat([7, 3]), 6366805760909027985741435139224001*x^5 - 1595845325952240
02*x^4 + 40353608*x^3 + 107006904423598033356356300384937784807*x^2 - 268213
7239327929801614*x + 678223089656, [7, [6, [Mod(0, 7)]], ["(tame) [I{9}-II*-
10] page 172", [9]]]]
Type: [IV-I{9}-10], p. 173
[343, Mat([7, 3]), 6366805760909027985741435139224001*x^5 - 1595845325952240
02*x^4 + 40353608*x^3 + 311973482284542371301330321821976049*x^2 - 781964209
7165976098*x + 1977326792, [7, [6, [Mod(0, 7)]], ["(tame) [I{9}-IV-10] page 
173", [9, 3]]]]
Type: [IV*-I{9}-10], p. 173
[343, Mat([7, 3]), 6366805760909027985741435139224001*x^5 - 1595845325952240
02*x^4 + 40353608*x^3 + 15286700631942576193765185769276826401*x^2 - 3831624
62761132828802*x + 96889012808, [7, [6, [Mod(0, 7)]], ["(tame) [I{9}-IV*-10]
 page 173", [9, 3]]]]
Type: [II-I*{9}-10], p. 173
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
+ 25467223043636111942965740556896004*x^5 + 157775381157130877341310732*x^4 
+ 3556153025177363557255317383565515512407053537812471*x^3 + 178270561305452
783600760183898272028*x^2 + 1104427668099916141389175124*x + 83047723248, [7
, [6, [Mod(0, 7)]], ["(tame) [I*{9}-II-10] page 173", [4]]]]
Type: [II*-I*{9}-10], p. 174
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
+ 25467223043636111942965740556896004*x^5 + 157775381157130877341310732*x^4 
+ 8538323413450849900970017037940802745289307070782629271*x^3 + 428027617694
392133425425201539751139228*x^2 + 2651730831107898655475409472724*x + 199397
583518448, [7, [6, [Mod(0, 7)]], ["(tame) [I*{9}-II*-10] page 174", [4]]]]
Type: [II*-I*{9}-(-1)], p. 174
[2401, Mat([7, 4]), 7*x^5 - 14*x^4 + 282475256*x^3 + 343*x^2 - 686*x + 13841
287544, [7, [6, [Mod(0, 7)]], ["(tame) [I*{9}-II*--1] page 174", [4]]]]
Type: [IV-I*{9}-10], p. 174
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
+ 25467223043636111942965740556896004*x^5 + 157775381157130877341310732*x^4 
+ 24893071176241544900787221684958608586849303580924513*x^3 + 12478939291381
69485205321287287904196*x^2 + 7730993676699412989724225868*x + 581334062736,
 [7, [6, [Mod(0, 7)]], ["(tame) [I*{9}-IV-10] page 174", [12]]]]
Type: [IV*-I*{9}-10], p. 174
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
+ 25467223043636111942965740556896004*x^5 + 157775381157130877341310732*x^4 
+ 1219760487635835700138573862562971820755615305995198865*x^3 + 611468025277
70304775060743077107305604*x^2 + 378818690158271236496487067532*x + 28485369
074064, [7, [6, [Mod(0, 7)]], ["(tame) [I*{9}-IV*-10] page 174", [12]]]]
Type: [IV*-I*{9}-(-1)], p. 175
[2401, Mat([7, 4]), 7*x^5 - 14*x^4 + 282475256*x^3 + 49*x^2 - 98*x + 1977326
792, [7, [6, [Mod(0, 7)]], ["(tame) [I*{9}-IV*--1] page 174", [12]]]]
[2187, Mat([3, 7]), 3*x^5 - 6*x^4 + 59052*x^3 + 9*x^2 - 18*x + 177156, [3, [
6, [Mod(0, 3)]], ["[I*{9}-IV*--1] pages 159-177", [12]]]]
Type: [IV-II{9}], p. 175
[343, Mat([7, 3]), x^6 - 2*x^5 + 40353608*x^4 + 7*x^3 - 14*x^2 + 282475256*x
, [7, [2, [Mod(0, 7)]], ["(tame) [II{9}-IV] page 175", [29]]]]
[729, Mat([3, 6]), x^6 - 2*x^5 + 19684*x^4 + 3*x^3 - 6*x^2 + 59052*x, [3, [6
, [Mod(0, 3)]], ["[IV-II{9}] page 175", [29]]]]
Type: [IV*-II{9}], p. 175
[343, Mat([7, 3]), x^6 - 2*x^5 + 5764802*x^4 + 49*x^3 - 98*x^2 + 282475298*x
, [7, [2, [Mod(0, 7)]], ["(tame) [II{9}-IV*] page 175", [28]]]]
[729, Mat([3, 6]), x^6 - 2*x^5 + 6562*x^4 + 9*x^3 - 18*x^2 + 59058*x, [3, [6
, [Mod(0, 3)]], ["[IV*-II{9}] page 175", [28]]]]
Type: [IV*-II{0}], p. 175
[343, Mat([7, 3]), 7*x^5 + 49*x^3 + 49*x^2 + 343, [7, [2, [Mod(0, 7)]], ["[I
V*-II{0}] page 175", []]]]
[729, Mat([3, 6]), 3*x^5 + 9*x^3 + 9*x^2 + 27, [3, [6, [Mod(0, 3)]], ["[IV*-
II{0}] page 175", []]]]
Type: [II-II*{9}], p. 176
[2401, Mat([7, 4]), x^5 + 282475249*x^3 + 7*x^2 + 1977326743, [7, [2, [Mod(0
, 7)]], ["[II-II*{9}] page 176", [2, 2]]]]
[2187, Mat([3, 7]), x^5 + 59049*x^3 + 3*x^2 + 177147, [3, [6, [Mod(0, 3)]], 
["[II-II*{9}] page 176", [2, 2]]]]
Type: [II*-II*{9}], p. 176
[2401, Mat([7, 4]), 7*x^6 - 14*x^5 + 282475256*x^4 + 49*x^3 - 98*x^2 + 19773
26792*x, [7, [2, [Mod(0, 7)]], ["(tame) [II*-II*{9}] page 176", [2, 2]]]]
[2187, Mat([3, 7]), 3*x^6 - 6*x^5 + 59052*x^4 + 9*x^3 - 18*x^2 + 177156*x, [
3, [6, [Mod(0, 3)]], ["[II*-II*{9}] page 176", [2, 2]]]]
Type: [III-I{9}-10], p. 176
[343, Mat([7, 3]), 6366805760909027985741435139224001*x^5 - 1595845325952240
02*x^4 + 44567640326363195900190046014921615*x^3 - 1117091728166568014*x^2 +
 282475256*x, [7, [6, [Mod(6, 7)]], ["(tame) [I{9}-III-10] page 176", [18]]]
]
[27, Mat([3, 3]), 12157665459056928801*x^5 - 6973568802*x^4 + 36472996377170
806087*x^3 - 20920706406*x^2 + 59052*x, [3, [6, [Mod(0, 3)]], ["[I{9}-III-10
] pages 159-177", [18]]]]
Type: [III*-I{9}-10], p. 176
[343, Mat([7, 3]), 6366805760909027985741435139224001*x^5 - 1595845325952240
02*x^4 + 2183814375991796599109312252794185951*x^3 - 54737494680161832686*x^
2 + 13841287544*x, [7, [6, [Mod(6, 7)]], ["(tame) [I{9}-III*-10] page 176", 
[18]]]]
[27, Mat([3, 3]), 12157665459056928801*x^5 - 6973568802*x^4 + 32825696739453
7097311*x^3 - 188286357654*x^2 + 531468*x, [3, [6, [Mod(0, 3)]], ["[I{9}-III
*-10] pages 159-177", [18]]]]
Type: [III-I*{9}-10], p. 177
[2401, Mat([7, 4]), x^6 + 4*x^5 + 44567640326363195900190047951894732*x^4 + 
267405841958179175401140283756715034*x^3 + 881247867777497128998513653865824
60699453771*x^2 + 528748722538339171106362420127476948226402066*x - 61687350
9628062366290756156815389740634465608, [7, [6, [Mod(6, 7)]], ["(tame) [I*{9}
-III-10] page 177", [4, 2]]]]
[81, Mat([3, 4]), x^6 + 36472996377170963544*x^4 + 72945992754341572814*x^3 
+ 6460972470237541785510147*x^2 + 12922163778453346599281658*x - 19383245667
680019897328164, [3, [6, [Mod(0, 3)]], ["[I*{9}-III-10] pages 159-177", [4, 
2]]]]
Type: [III*-I*{9}-10], p. 177
[2401, Mat([7, 4]), x^6 + 4*x^5 + 2183814375991796599109312254731159068*x^4 
+ 13102886255950779594655873524432301050*x^3 + 43181145521097359320927169039
42542282683541067*x^2 + 25908687404378619384211758586246368564860027954*x - 
30226801971775055948247051683954096626707029144, [7, [6, [Mod(6, 7)]], ["(ta
me) [I*{9}-III*-10] page 177", [4, 2]]]]
[81, Mat([3, 4]), x^6 + 328256967394537254768*x^4 + 656513934789074155262*x^
3 + 58148752232137876078094403*x^2 + 116299474006080119382197514*x - 1744492
11009120179071701948, [3, [6, [Mod(0, 3)]], ["[I*{9}-III*-10] pages 159-177"
, [4, 2]]]]
Type: [III*-I*{9}-(-1)], p. 177
[2401, Mat([7, 4]), 7*x^5 - 14*x^4 + 282475305*x^3 - 98*x^2 + 1977326792*x, 
[7, [6, [Mod(6, 7)]], ["(tame) [I*{9}-III*--1] page 177", [4, 2]]]]
Type: [III-II{9}], p. 177
[343, Mat([7, 3]), x^6 - 2*x^5 + 40353608*x^4 + 7*x^2 - 14*x + 282475256, [7
, [2, [Mod(6, 7)]], ["(tame) [II{9}-III] page 177", [19]]]]
Type: [III*-II{9}], p. 178
[343, Mat([7, 3]), x^6 - 2*x^5 + 5764802*x^4 + 343*x^2 - 686*x + 1977327086,
 [7, [2, [Mod(6, 7)]], ["(tame) [II{9}-III*] page 178", [19]]]]
Type: [III*-II{0}], p. 178
[343, Mat([7, 3]), 7*x^6 + 49*x^4 + 49*x^2 + 343, [7, [2, [Mod(6, 7)]], ["(t
ame) [II{0}-III*] page 178", []]]]
Type: [III-II*{9}], p. 178
[2401, Mat([7, 4]), x^6 + 282475249*x^4 + 7*x^2 + 1977326743, [7, [2, [Mod(6
, 7)]], ["(tame) [II*{9}-III] page 178", [8]]]]
Type: [III*-II*{9}], p. 178
[2401, Mat([7, 4]), 282475249*x^6 + 7*x^4 + 1977326743*x^2 + 49, [7, [2, [Mo
d(6, 7)]], ["(tame) [II*{9}-III*] page 178", [8]]]]
Type: [I{9-8-0}], p. 179
[49, Mat([7, 2]), x^5 + x^4 + 46118407*x^3 + 34588805*x^2 + 232630473633600*
x - 232630554340814, [7, [3, []], ["(tame) [I{8-9-0}] page 179", [72]]]]
Type: [I{9}-I{8}-10}], p. 179
[49, Mat([7, 2]), 6366805760909027985741435139224001*x^5 + 63668057609090278
26156902543999999*x^4 + 256923577521058878088611317639703031862407*x^3 + 256
923577521058871648799965597876173411195*x^2 - 6439811511393728899334400*x + 
232630554340814, [7, [7, []], ["(tame) [I{8}-I{9}-10] page 179", [72]]]]
Type: [I*{9-8-0}], p. 180
[2401, Mat([7, 4]), 7*x^5 + 7*x^4 + 322828849*x^3 + 242121635*x^2 + 16284133
15435200*x - 1628413880385698, [7, [3, []], ["(tame) [I*{8-9-0}] page 180", 
[4, 2, 2]]]]
[81, Mat([3, 4]), 3*x^5 + 3*x^4 + 78729*x^3 + 39363*x^2 + 387361440*x - 3874
79538, [3, [3, []], ["(tame) [I*{8-9-0}] page 180", [4, 2, 2]]]]
Type: [I*{9}-I*{8}-10], p. 180
[2401, Mat([7, 4]), 508021860739623365322188197652216501772434524836001*x^6 
+ 3556153025177363582722540427201627455372782230748011*x^5 + 100452521126907
9039999221712767258830172664699912235178878009*x^4 + 70316764788835533303515
71935604422778407017230014542438128339*x^3 + 3524991484034604193284089402685
37457526303138*x^2 + 311973470135837957969478408827349338*x + 23458926374545
651500, [7, [7, []], ["(tame) [I*{8}-I*{9}-10] page 180", [4, 2, 2]]]]
Type: [I{9}-I*{8}-10], p. 180
[343, Mat([7, 3]), 6366805760909027985741435139224001*x^5 + 4456764032636319
5740605513379344005*x^4 + 1798465042647412146620279223477921223036843*x^3 + 
12589255298531884981263281802603029551507501*x^2 - 3155507640582927177622370
94*x + 79792268274938744, [7, [7, []], ["(tame) [I{9}-I*{8}-10] page 180", [
18, 2]]]]
[27, Mat([3, 3]), 12157665459056928801*x^5 + 36472996370197217601*x^4 + 7178
97987691831668083527*x^3 + 2153693962663775502180501*x^2 - 1235345630247378*
x + 3486961548, [3, [7, []], ["[I{9}-I*{8}-10] page 180", [18, 2]]]]
Type: [2I{8}-10], p. 181
[343, Mat([7, 3]), x^6 + 1977326722*x^4 + 9387480337620071731394*x^2 + 18562
115855305211939015772541728, [7, [7, []], ["(tame) [2I{8}-10] page 181", [8]
]]]
[27, Mat([3, 3]), x^6 + 177138*x^4 + 2541864765474*x^2 + 450276280295106672,
 [3, [7, []], ["[2I{8}-10] page 181", [8]]]]
Type: [2I{9}-10}], p. 181
[343, Mat([7, 3]), x^6 + 1977326722*x^4 + 9387480337647754305649*x^3 - 27682
574255*x^2 + 18562115855305211938918883531664*x + 96889010064, [7, [7, []], 
["(tame) [2I{9}-10] page 181", [9]]]]
Type: [2I{8}-0], p. 181
[343, Mat([7, 3]), x^6 - 7*x^4 + 117600*x^2 + 823886, [7, [3, []], ["(tame) 
[2I{8}-0] page 181", [8]]]]
Type: [2I{9}-0], p. 181
[343, Mat([7, 3]), x^6 - 7*x^4 + 117649*x^3 - 49*x^2 + 823543*x + 343, [7, [
3, []], ["(tame) [2I{9}-0] page 181", [9]]]]
Type: [2I*{8}-10}], p. 181
[2401, Mat([7, 4]), x^6 + 1977326743*x^5 - 21*x^4 - 27682574402*x^3 + 657123
62363534280139690*x^2 + 129934811447123020117269034708856*x - 45998653654473
9960977144, [7, [7, []], ["(tame) [2I*{8}-10] page 181", [2, 2]]]]
[81, Mat([3, 4]), x^6 + 177147*x^5 - 9*x^4 - 1062882*x^3 + 7625597485014*x^2
 + 1350851717674586412*x - 22876792454988, [3, [7, []], ["[2I*{8}-10] pages 
159, 181", [2, 2]]]]
Type: [2I*{9}-10}], p. 181
[2401, Mat([7, 4]), x^6 + 1977326743*x^5 - 21*x^4 + 65712362363506597565141*
x^3 + 129934811447123020117172145698596*x^2 - 459986536544643071966394*x - 3
43, [7, [7, []], ["(tame) [2I*{9}-10] page 181", [4]]]]
Type: [II{9-8}], p. 182
[343, Mat([7, 3]), x^6 - 2*x^5 + 46118416*x^4 - 80707228*x^3 + 2326308771696
77*x^2 - 564950498*x + 1628413880385698, [7, [3, []], ["[II{9-8}] page 182",
 [36]]]]
[27, Mat([3, 3]), x^6 - 2*x^5 + 26248*x^4 - 39372*x^3 + 129238581*x^2 - 1180
98*x + 387479538, [3, [3, []], ["[II{9-8}] page 182", [36]]]]
Type: [III{8}], p. 182
[2401, Mat([7, 4]), 2402*x^5 - 14*x^3 + 49*x, [7, [3, []], ["(tame) [III{8}]
 page 182", [2, 2]]]]
Type: [III{9}], p. 182
[2401, Mat([7, 4]), x^5 + 16807*x^4 - 14*x^3 + 49*x, [7, [3, []], ["(tame) [
III{9}] page 182", [4]]]]
Type: [I{9-8-5}], pp. 182-183
[49, Mat([7, 2]), x^6 - 6*x^5 + 46135228*x^4 - 265214472*x^3 + 2334061737433
69*x^2 - 931878986337810*x + 3910752249023424154, [7, [4, []], ["(tame) [I{5
-8-9}] page 182", [157]]]]
Type: [I*{9-8-5}], pp. 183
[2401, Mat([7, 4]), 7*x^6 - 42*x^5 + 322946596*x^4 - 1856501304*x^3 + 163384
3216203583*x^2 - 6523152904364670*x + 27375265743163969078, [7, [4, []], ["(
tame) [I*{5-8-9}] page 183", [4, 4]]]]
Type: [II{9-8}], p. 183
[343, Mat([7, 3]), x^6 - 2*x^5 + 5764788*x^4 + 28*x^3 - 80589530*x^2 - 23539
6*x + 678505665796, [7, [4, []], ["(tame) [II{9-8}] page 183", [44]]]]
[27, Mat([3, 3]), x^6 - 2*x^5 + 6556*x^4 + 12*x^3 - 38634*x^2 - 1476*x + 484
2756, [3, [4, []], ["(tame) [II{9-8}] page 183", [44]]]]
Type: [II{9-9}], p. 183
[343, Mat([7, 3]), x^6 - 2*x^5 + 5764788*x^4 + 117677*x^3 - 80942477*x^2 + 6
78223190400*x + 282475298, [7, [4, []], ["(tame) [II{9-9}] page 183", [45]]]
]
[27, Mat([3, 3]), x^6 - 2*x^5 + 6556*x^4 + 741*x^3 - 40821*x^2 + 4783680*x +
 59058, [3, [4, []], ["(tame) [II{9-9}] page 183", [45]]]]
Type: [II*{9-8}], p. 184
[343, Mat([7, 3]), 7*x^6 - 14*x^5 + 40353516*x^4 + 196*x^3 - 564126710*x^2 -
 1647772*x + 4749539660572, [7, [4, []], ["(tame) [II*{9-8}] page 184", [8]]
]]
Type: [II*{9-9}], p. 184
[343, Mat([7, 3]), 7*x^6 - 14*x^5 + 40353516*x^4 + 823739*x^3 - 566597339*x^
2 + 4747562332800*x + 1977327086, [7, [4, []], ["(tame) [II*{9-9}] page 184"
, [9]]]]
Type: [III{12}], p. 184
[2401, Mat([7, 4]), x^6 - 14*x^3 + 117698, [7, [4, []], ["[III{12}] page 184
", [3, 3]]]]
[59049, Mat([3, 10]), x^6 - 6*x^3 + 738, [3, [4, []], ["[III{12}] page 184",
 [3, 3]]]]
Type: [III{13}], p. 184
[2401, Mat([7, 4]), x^6 - 14*x^3 + 117649*x + 49, [7, [4, []], ["[III{13}] p
age 184", [9]]]]
[59049, Mat([3, 10]), x^6 - 6*x^3 + 729*x + 9, [3, [4, []], ["[III{13}] page
 184", [9]]]]
Type: [III{14}], p. 184
[2401, Mat([7, 4]), x^6 - 14*x^3 + 117649*x^2 + 49, [7, [4, []], ["[III{14}]
 page 184", [9]]]]
[59049, Mat([3, 10]), x^6 - 6*x^3 + 729*x^2 + 9, [3, [4, []], ["[III{14}] pa
ge 184", [9]]]]
Type: [III*{6}], p. 184
[2401, Mat([7, 4]), 7*x^6 - 98*x^3 + 17150, [7, [4, []], ["[III*{6}] page 18
4", []]]]
[59049, Mat([3, 10]), 3*x^6 - 18*x^3 + 270, [3, [5, [Mod(0, 3), Mod(0, 3)]],
 ["[III*{6}] page 184", []]]]
Type: [III*{7}], p. 184
[2401, Mat([7, 4]), 7*x^6 - 98*x^3 + 16807*x + 343, [7, [4, []], ["[III*{7}]
 page 184", []]]]
[59049, Mat([3, 10]), 3*x^6 - 18*x^3 + 243*x + 27, [3, [5, [Mod(0, 3), Mod(0
, 3)]], ["[III*{7}] page 184", []]]]
Type: [III{8}], p. 184
[2401, Mat([7, 4]), x^6 - 14*x^3 + 2401*x^2 + 49, [7, [4, []], ["[III{8}] pa
ge 184", [9]]]]
[59049, Mat([3, 10]), x^6 - 6*x^3 + 81*x^2 + 9, [3, [5, [Mod(0, 3), Mod(0, 3
)]], ["[III{8}] page 184", [9]]]]
   echo = 1
? genus2red(-x^6-6*x^2-7,3)
[81, Mat([3, 4]), -x^6 - 6*x^2 - 7, [3, [7, []], ["(tame) [I*{1}-I*{1}-0] pa
ge 180", [4, 4]]]]
? genus2red(-9*x^6+6*x^5-8*x^4-5*x^3+5*x^2-10*x+3,3)
[9, Mat([3, 2]), -9*x^6 + 6*x^5 - 8*x^4 - 5*x^3 + 5*x^2 - 10*x + 3, [3, [3, 
[]], ["(tame) [I{2-8-0}] page 179", [8, 2]]]]
? genus2red(3*x^6+3*x^4+3*x^3+x^2-5*x-5,3)
[27, Mat([3, 3]), -5*x^6 - 5*x^5 + x^4 + 3*x^3 + 3*x^2 + 3, [3, [2, [Mod(0, 
3)]], ["(tame) [II{4}-III] page 177", [9]]]]
? genus2red(-3*x^6+6*x^5-1*x^4+6*x^3-6*x^2-1*x-6,3)
[3, Mat([3, 1]), -2187*x^6 - 2430*x^5 - 1089*x^4 - 242*x^3 - 26*x^2 - x, [3,
 [6, [Mod(2, 3)]], ["(tame) [I{0}-I{1}-1] page 170", []]]]
? genus2red((x^3+2*x+1)*(x^3+3^2*x^2+3^8),3)
[3, Mat([3, 1]), 729*x^6 + 729*x^5 + 18*x^4 + 6580*x^3 + x^2 + 162*x + 9, [3
, [6, [Mod(1, 3)]], ["(tame) [I{0}-I{2}-1] page 170", [2]]]]
? P=x^6+4*x^5-24*x^4-16*x^3-52*x^2-48*x;
? genus2red(P,3)
[9, Mat([3, 2]), 729*x^6 + 2268*x^5 + 2664*x^4 + 1520*x^3 + 428*x^2 + 48*x, 
[3, [7, []], ["(tame) [I{2}-I{2}-1] page 179", [2, 2]]]]
? P=x^6+4*x^5+24*x^4+32*x^3+56*x^2+48*x+24;
? genus2red(P,3)
[9, Mat([3, 2]), 729*x^6 + 2268*x^5 + 3096*x^4 + 2336*x^3 + 1016*x^2 + 240*x
 + 24, [3, [7, []], ["(tame) [I{1}-I{1}-1] page 179", []]]]
? P=24*x^5+56*x^4+76*x^3+33*x^2-4*x-20;
? genus2red(P,3)
[9, Mat([3, 2]), 1944*x^5 + 5904*x^4 + 7196*x^3 + 4397*x^2 + 1346*x + 165, [
3, [7, []], ["(tame) [I{2}-I{2}-1] page 179", [2, 2]]]]
? P=-3*x^6+6*x^5-25*x^4+36*x^3-69*x^2+38*x-39;
? genus2red(P,3)
[9, Mat([3, 2]), -2187*x^6 - 6804*x^5 - 9000*x^4 - 6464*x^3 - 2656*x^2 - 592
*x - 56, [3, [7, []], ["(tame) [I{1}-I{1}-1] page 179", []]]]
? P=-5*x^5+5*x^4+10*x^3-7;
? genus2red([P,1],3)
[9, Mat([3, 2]), -1620*x^5 - 2520*x^4 - 1520*x^3 - 440*x^2 - 60*x - 3, [3, [
7, []], ["(tame) [I{1}-I{2}-1] page 179", [2]]]]
? P=-5*x^6-3*x^5-10*x^4-10*x^3-7;
? genus2red([P,1],3)
[3, Mat([3, 1]), -14580*x^6 - 59292*x^5 - 100800*x^4 - 91720*x^3 - 47120*x^2
 - 12960*x - 1491, [3, [6, [Mod(1, 3)]], ["(tame) [I{0}-I{1}-1] page 170", [
]]]]
? P=3*x^5+5*x^4+5*x-4;
? genus2red([P,1],3)
[3, Mat([3, 1]), 972*x^5 + 1260*x^4 + 640*x^3 + 160*x^2 + 20*x + 1, [3, [6, 
[Mod(1, 3)]], ["(tame) [I{0}-I{2}-1] page 170", [2]]]]
? Q=x^2+x;P=-9*x^6+6*x^5-8*x^4-5*x^3+5*x^2-10*x+3;
? genus2red([P,Q],3)
[3, Mat([3, 1]), -26244*x^6 - 138024*x^5 - 302679*x^4 - 354290*x^3 - 233475*
x^2 - 82136*x - 12052, [3, [6, [Mod(0, 3)]], ["(tame) [I{0}-I{12}-1] page 17
0", [12]]]]
? Q=x^3+1;P=-7*x^6+5*x^3+5*x^2-6*x+1;
? genus2red([P,Q],3)
[3, Mat([3, 1]), -27*x^6 + 22*x^3 + 20*x^2 - 24*x + 5, [3, [6, [Mod(2, 3)]],
 ["(tame) [I{0}-I{1}-1] page 170", []]]]
? genus2red(27*x^5+97*x^4+118*x^3+60*x^2+13*x+1,3)
[729, Mat([3, 6]), 27*x^5 + 367*x^4 + 1974*x^3 + 5256*x^2 + 6933*x + 3627, [
3, [6, [Mod(0, 3)]], ["[IV-II{6}] page 175", [20]]]]
? genus2red([-x^6-3*x^4-10*x^2-1,x],3)
[729, Mat([3, 6]), -4*x^6 - 12*x^4 - 39*x^2 - 4, [3, [5, [Mod(0, 3), Mod(0, 
3)]], ["[IV*-IV*-0] pages 160-175", [3, 3]]]]
? genus2red([-60*x^6-203*x^5-291*x^4-244*x^3-129*x^2-41*x-7,x^3+x^2+x+1])
[729, [2, -1; 3, 6], -239*x^6 - 810*x^5 - 1161*x^4 - 972*x^3 - 513*x^2 - 162
*x - 27, [[2, [5, [Mod(0, 2), Mod(0, 2)]], []], [3, [5, [Mod(0, 3), Mod(0, 3
)]], ["[2IV*-0] page 165", [3]]]]]
? genus2red(6*x^6+5*x^4+x^2+1,7)
[2401, Mat([7, 4]), 6*x^6 + 180*x^5 + 2255*x^4 + 15100*x^3 + 57001*x^2 + 115
010*x + 96901, [7, [5, [Mod(0, 7), Mod(0, 7)]], ["(tame) [II-II-0] page 163"
, []]]]
? genus2red([1,x^3-1])
[18225, [3, 6; 5, 2], x^6 - 2*x^3 + 5, [[3, [5, [Mod(0, 3), Mod(0, 3)]], ["[
II-II-0] pages 159-174", []]], [5, [5, [Mod(0, 5), Mod(0, 5)]], ["[I{0}-II-0
] page 159", []]]]]
? genus2red(x^5+1/5,5)
[1953125, Mat([5, 9]), 5*x^6 + 25*x, [5, [1, []], ["[VIII-4] page 157", []]]
]
? genus2red(273*x^6-38933/5*x^5-4483763/4*x^4+371954149/10*x^3+569046245/4*x^2+12389355*x-42117075,5)
[125, Mat([5, 3]), 682500*x^6 - 3893300*x^5 - 112094075*x^4 + 743908298*x^3 
+ 569046245*x^2 + 9911484*x - 6738732, [5, [6, [Mod(3, 5)]], ["(tame) [I{4}-
I*{0}-0] page 170", [4, 2, 2]]]]
? genus2red(177*x^6+126*x^5-63*x^4+72*x+84,3)
[729, Mat([3, 6]), 1593*x^6 + 6750*x^5 + 11817*x^4 + 10952*x^3 + 5672*x^2 + 
1560*x + 180, [3, [6, [Mod(0, 3)]], ["[I{5}-IV*-0] pages 159-177", [15]]]]
? genus2red(3*(4*x^6+6*x^5+3*x^4+8*x^3+9*x^2-3),3)
[59049, Mat([3, 10]), 108*x^6 + 270*x^5 + 279*x^4 + 160*x^3 + 57*x^2 + 12*x 
+ 1, [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[II-IV*-0] pages 159-174", [3]]]]
? genus2red(x^6+27,3)
[81, Mat([3, 4]), x^6 + 27, [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[2I*{0}-0] pa
ges 159, 181", [2, 2]]]]
? print("Total time spent: ",gettime);
Total time spent: 72