Type: [I{0-0-0}], p. 155
[1, Mat([7, 0]), [x^5 + x^3 - 2*x^2 + 3*x + 1, 0], [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, 0], [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, 0], [7, [1, []], ["(tame) [I
I] page 155", []]]]
[9, Mat([3, 2]), [x^6 + 12*x^4 - 9*x^2 + 27, 0], [3, [1, []], ["[II] page 15
5", []]]]
Type: [III], p. 155
[2401, Mat([7, 4]), [x^6 + 28*x^3 + 49, 0], [7, [1, []], ["[III] page 155", 
[3, 3]]]]
Type: [IV], p. 155
[2401, Mat([7, 4]), [7*x^6 + 245*x^3 + 343, 0], [7, [4, []], ["[III*{3}] pag
e 184", []]]]
Type: [V], p. 156
[2401, Mat([7, 4]), [x^6 + 7, 0], [7, [1, []], ["[V] page 156", [3]]]]
Type: [V*], p. 156
[2401, Mat([7, 4]), [49*x^6 + 7, 0], [7, [1, []], ["[V*] page 156", [3]]]]
Type: [VI], p. 156
[2401, Mat([7, 4]), [x^5 + 21*x^3 + 49*x, 0], [7, [1, []], ["(tame) [VI] pag
e 156", [2, 2]]]]
Type: [VII], p. 156
[2401, Mat([7, 4]), [x^5 + 7*x, 0], [7, [1, []], ["[VII] page 156", [2]]]]
Type: [VII*], p. 156
[2401, Mat([7, 4]), [7*x^5 + 49*x, 0], [7, [1, []], ["[VII*] page 156", [2]]
]]
Type: [VIII-1], p. 156
[2401, Mat([7, 4]), [x^5 + 7, 0], [7, [1, []], ["[VIII-1] page 156", []]]]
Type: [VIII-2], p. 157
[2401, Mat([7, 4]), [x^5 + 343, 0], [7, [1, []], ["[VIII-2] page 157", []]]]
Type: [VIII-3], p. 157
[2401, Mat([7, 4]), [7*x^5 + 343, 0], [7, [1, []], ["[VIII-3] page 157", []]
]]
Type: [VIII-4], p. 157
[2401, Mat([7, 4]), [49*x^5 + 7, 0], [7, [1, []], ["[VIII-4] page 157", []]]
]
Type: [IX-1], p. 157
[2401, Mat([7, 4]), [x^5 + 49, 0], [7, [1, []], ["[IX-1] page 157", [5]]]]
Type: [IX-2], p. 157
[2401, Mat([7, 4]), [7*x^5 + 1, 0], [7, [1, []], ["[IX-2] page 157", [5]]]]
Type: [IX-3], p. 157
[2401, Mat([7, 4]), [7*x^5 + 49, 0], [7, [1, []], ["[IX-3] page 157", [5]]]]
Type: [IX-4], p. 158
[2401, Mat([7, 4]), [49*x^5 + 1, 0], [7, [1, []], ["[IX-4] page 158", [5]]]]
Type: [I{0}-I{0}-10], p. 158
[1, Mat([7, 0]), [x^6 + 63668057609090279857414351392240013*x^4 + 5080218607
39623365322188197652216501772434524836002*x^3 + 1910041728272708395722430541
76720030*x^2 + 1524065582218870159634622202046929362731654966748013*x + 5080
21860739623365322188197652216501772434524836001, 0], [7, [5, [Mod(2, 7), Mod
(5, 7)]], ["(tame) [I{0}-I{0}-10] page 158", []]]]
[1, Mat([3, 0]), [x^6 + 12157665459056928800*x^4 + 4239115827521620351429443
3202*x^3 - 12157665459056928801*x^2 - 42391158263058538055237504400*x + 4239
1158275216203514294433201, 0], [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]), [x^6 - 3*x^5 + 3119734822845423713013303218219760640*x^4
 + 174251498233690804946306083258439121068035387359467068*x^3 - 522754494701
071974956308228570573828328352393092171529*x^2 + 261377247350536227541748732
24064163053785883855665547000*x + 339790421555697087895745575999685007210492
83193655926885, 0], [7, [5, [Mod(2, 7), Mod(2, 7)]], ["(tame) [I*{0}-I*{0}-1
0] page 158", [2, 2, 2, 2]]]]
[81, Mat([3, 4]), [x^6 - 3*x^5 + 109418989131512359203*x^4 + 114456127310258
0527491412618835*x^3 - 3433683820949026419446923244535*x^2 - 686736763675536
0349712765606247*x + 40059644570079312321008239374945, 0], [3, [5, [Mod(0, 3
), Mod(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]), [x^6 + 3119734822845423713013303218219760493*x^4 + 1742514
98233690814305510551794710260107945042018748344*x^3 + 9359204468536271139039
909654659281470*x^2 + 522754494701072446036266478229554493337138344276005519
*x + 174251498233690814305510551794710260107945042018748343, 0], [7, [5, [Mo
d(2, 7), Mod(5, 7)]], ["(tame) [I{0}-I*{0}-10] page 159", [2, 2]]]]
[9, Mat([3, 2]), [x^6 + 109418989131512359208*x^4 + 114456127343083749488594
9696428*x^3 - 109418989131512359209*x^2 - 1144561273321418505754437337218*x 
+ 1144561273430837494885949696427, 0], [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 + 26517308418364
47612787128678837, 0], [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, 0], [
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 + 5411695603795
2111668959660849*x - 574743694141699243546, 0], [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 + 5411695603795
2111668959660849*x - 574743694141699243546, 0], [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]), [x^5 + 3*x^4 + x^3 + 3556153025177363557255317383565515512
407041673852007*x^2 + 10668459075532090671765952150696546537221125021556021*
x + 3556153025177363557255317383565515512407041673852007, 0], [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]), [x^5 + 3*x^4 + x^3 + 8538323413450849900970017037940802745
289307058918668807*x^2 + 256149702403525497029100511138224082358679211767560
06421*x + 8538323413450849900970017037940802745289307058918668807, 0], [7, [
5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I{0}-II*-10] page 160", []]]]
[243, Mat([3, 5]), [x^5 + 3*x^4 + x^3 + 10301051460877537453973547267843*x^2
 + 30903154382632612361920641803529*x + 10301051460877537453973547267843, 0]
, [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]), [x^5 + 3*x^4 + x^3 + 2489307117624154490078722168495860858
6849291716964049*x^2 + 74679213528724634702361665054875825760547875150892147
*x + 24893071176241544900787221684958608586849291716964049, 0], [7, [5, [Mod
(0, 7), Mod(2, 7)]], ["(tame) [I{0}-IV-10] page 160", [3]]]]
[243, Mat([3, 5]), [x^5 + 3*x^4 + x^3 + 381520424476945831628649898809*x^2 +
 1144561273430837494885949696427*x + 381520424476945831628649898809, 0], [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]), [x^5 + 3*x^4 + x^3 + 1219760487635835700138573862562971820
755615294131238401*x^2 + 365928146290750710041572158768891546226684588239371
5203*x + 1219760487635835700138573862562971820755615294131238401, 0], [7, [5
, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I{0}-IV*-10] page 160", [3]]]]
[243, Mat([3, 5]), [x^5 + 3*x^4 + x^3 + 3433683820292512484657849089281*x^2 
+ 10301051460877537453973547267843*x + 3433683820292512484657849089281, 0], 
[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]), [49*x^5 + 21*x^4 + x^3 + 1742514982336908143055105517947
10260107945042018748343*x^2 + 7467921352872463470236166505487582576054787515
0892147*x + 3556153025177363557255317383565515512407041673852007, 0], [7, [5
, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I*{0}-II-10] page 160", [2, 2]]]]
[2187, Mat([3, 7]), [9*x^5 + 9*x^4 + x^3 + 1144561273430837494885949696427*x
^2 + 1144561273430837494885949696427*x + 127173474825648610542883299603, 0],
 [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]), [49*x^5 + 21*x^4 + x^3 + 4183778472590916451475308348590
99334519176045887014771543*x^2 + 1793047916824678479203703577967568576510754
48237292044947*x + 8538323413450849900970017037940802745289307058918668807, 
0], [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I*{0}-II*-10] page 160", [2, 
2]]]]
[2187, Mat([3, 7]), [9*x^5 + 9*x^4 + x^3 + 92709463147897837085761925410587*
x^2 + 92709463147897837085761925410587*x + 10301051460877537453973547267843,
 0], [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]), [49*x^5 + 21*x^4 + x^3 + 1219760487635835700138573862562
971820755615294131238401*x^2 + 522754494701072442916531655384130780323835126
056245029*x + 24893071176241544900787221684958608586849291716964049, 0], [7,
 [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I*{0}-IV-10] page 161", [6, 2]]]]
Type: [I{0}*-IV*-10], p. 161
[2401, Mat([7, 4]), [49*x^5 + 21*x^4 + x^3 + 5976826389415594930679011926558
5619217025149412430681649*x^2 + 25614970240352549702910051113822408235867921
176756006421*x + 1219760487635835700138573862562971820755615294131238401, 0]
, [7, [5, [Mod(0, 7), Mod(2, 7)]], ["(tame) [I*{0}-IV*-10] page 161", [6, 2]
]]]
Type: [I{0}-III-10], p. 161
[49, Mat([7, 2]), [x^5 + 3*x^4 + 44567640326363195900190045974568008*x^3 + 1
33702920979089587700570137923704021*x^2 + 4456764032636319590019004597456800
7*x, 0], [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]), [x^5 + 3*x^4 + 2183814375991796599109312252753832344*x^3 +
 6551443127975389797327936758261497029*x^2 + 2183814375991796599109312252753
832343*x, 0], [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]), [49*x^5 + 21*x^4 + 2183814375991796599109312252753832344
*x^3 + 935920446853627113903990965465928147*x^2 + 44567640326363195900190045
974568007*x, 0], [7, [5, [Mod(2, 7), Mod(6, 7)]], ["(tame) [I*{0}-III-10] pa
ge 162", [2, 2, 2]]]]
Type: [I{0}*-III*-10], p. 162
[2401, Mat([7, 4]), [49*x^5 + 21*x^4 + 1070069044235980333563563003849377848
08*x^3 + 45860101895827728581295557307830479203*x^2 + 2183814375991796599109
312252753832343*x, 0], [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, 0], [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, 0], [
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, 0], [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, 0], 
[3, [5, [Mod(0, 3), Mod(0, 3)]], ["[2II*-10] page 163", []]]]
Type: [II-II-10], p. 163
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 3*x^4 + 355615302517736355725531738356551
5512407041673852013*x^3 - 10668459075532090671765952150696546537221125021556
021*x^2 + 10668459075532090671765952150696546537221125021556021*x + 21336918
151064181343531904301393093074442250043112042, 0], [7, [5, [Mod(0, 7), Mod(0
, 7)]], ["(tame) [II-II-10] page 163", []]]]
Type: [II-II*-10], p. 163
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 3*x^4 + 355615302517736355725531738356551
5512407041673868813*x^3 - 10668459075532090671765952150696546537221125021556
021*x^2 + 10668459075532090671765952150696546537221125021556021*x + 59764707
741130771943232863948202053701512742370756829642, 0], [7, [5, [Mod(0, 7), Mo
d(0, 7)]], ["(tame) [II-II*-10] page 163", []]]]
Type: [II*-II*-10], p. 163
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 3*x^4 + 853832341345084990097001703794080
2745289307058918685613*x^3 - 25614970240352549702910051113822408235867921176
756006421*x^2 + 25614970240352549702910051113822408235867921176756006421*x +
 143495063286454983435702106339633130937332094432187147970442, 0], [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, 0], [7, [5, [Mod(0, 7), Mod(0, 7)]], ["(tame) [II*-II*--1] page 163"
, []]]]
Type: [II-IV-10], p. 164
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 3*x^4 + 355615302517736355725531738356551
5512407041673852055*x^3 - 10668459075532090671765952150696546537221125021556
021*x^2 + 10668459075532090671765952150696546537221125021556021*x + 17069534
5208513450748255234411144744595538000344896336, 0], [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]), [x^6 - 3*x^5 + 3*x^4 + 355615302517736355725531738356551
5512407041673854407*x^3 - 10668459075532090671765952150696546537221125021556
021*x^2 + 10668459075532090671765952150696546537221125021556021*x + 85347672
60425672537412761720557237229776900017244816800, 0], [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]), [x^6 - 3*x^5 + 3*x^4 + 853832341345084990097001703794080
2745289307058918668855*x^3 - 25614970240352549702910051113822408235867921176
756006421*x^2 + 25614970240352549702910051113822408235867921176756006421*x +
 409839523845640795246560817821158531773886738828096102736, 0], [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, 0], [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]), [343*x^6 - 147*x^5 + 21*x^4 + 41837784725909164514753083
4859099334519176045887014771591*x^3 - 17930479168246784792037035779675685765
1075448237292044947*x^2 + 25614970240352549702910051113822408235867921176756
006421*x + 58548503406520113606651545403022647396269534118299443248, 0], [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,
 0], [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, 0], [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
, 0], [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, 0], [3, [5,
 [Mod(0, 3), Mod(0, 3)]], ["[2IV*-10] page 165", [3]]]]
Type: [IV-IV-10], p. 165
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 3*x^4 + 248930711762415449007872216849586
08586849291716964097*x^3 - 7467921352872463470236166505487582576054787515089
2147*x^2 + 74679213528724634702361665054875825760547875150892147*x + 1194867
416459594155237786640878013212168766002414274352, 0], [7, [5, [Mod(0, 7), Mo
d(0, 7)]], ["(tame) [IV-IV-10] page 165", [3, 3]]]]
Type: [IV-IV*-10], p. 165
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 3*x^4 + 248930711762415449007872216849586
08586849291716966449*x^3 - 7467921352872463470236166505487582576054787515089
2147*x^2 + 74679213528724634702361665054875825760547875150892147*x + 5974337
0822979707761889332043900660608438300120713717600, 0], [7, [5, [Mod(0, 7), M
od(0, 7)]], ["(tame) [IV-IV*-10] page 165", [3, 3]]]]
Type: [IV*-IV*-10], p. 166
[2401, Mat([7, 4]), [343*x^6 - 147*x^5 + 21*x^4 + 41837784725909164514753083
4859099334519176045887014771549*x^3 - 17930479168246784792037035779675685765
1075448237292044947*x^2 + 25614970240352549702910051113822408235867921176756
006421*x + 7318562925815014200831443175377830924533691764787430406, 0], [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]), [x^6 - 3*x^5 + 44567640326363195900190045974568010*x^4 -
 133702920979089587700570137923704015*x^3 + 13370292097908958770057013792370
4021*x^2 + 267405841958179175401140275847408042*x, 0], [7, [5, [Mod(0, 7), M
od(6, 7)]], ["(tame) [II-III-10] page 166", [2]]]]
Type: [II-III*-10], p. 166
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 2183814375991796599109312252753832346*x^4
 - 6551443127975389797327936758261497023*x^3 + 65514431279753897973279367582
61497029*x^2 + 13102886255950779594655873516522994058*x, 0], [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]), [x^6 - 3*x^5 + 44567640326363195900190045974568010*x^4 -
 133702920979089587700570137923687215*x^3 + 13370292097908958770057013792370
4021*x^2 + 749003763324859870298593912648589925642*x, 0], [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, 0], [7, [5, [Mod(0, 7), Mod
(6, 7)]], ["[II*-III-(-1)] page 167", [2]]]]
Type: [II*-III*-10], p. 167
[2401, Mat([7, 4]), [343*x^6 - 147*x^5 + 74904833096518623349449410269456449
3670*x^4 - 321020713270794100069068901154813354373*x^3 + 4586010189582772858
1295557307830479203*x^2 + 104823090047606236757246988132183952464*x, 0], [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]), [x^6 - 3*x^5 + 44567640326363195900190045974568010*x^4 -
 133702920979089587700570137923703973*x^3 + 13370292097908958770057013792370
4021*x^2 + 2139246735665433403209122206779264336*x, 0], [7, [5, [Mod(0, 7), 
Mod(6, 7)]], ["(tame) [III-IV-10] page 167", [6]]]]
[2187, Mat([3, 7]), [x^6 - 3*x^5 + 36472996377170786406*x^4 - 10941898913151
2359201*x^3 + 109418989131512359209*x^2 + 291783971017366291224*x, 0], [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]), [x^6 - 3*x^5 + 2183814375991796599109312252753832346*x^4
 - 6551443127975389797327936758261496981*x^3 + 65514431279753897973279367582
61497029*x^2 + 104823090047606236757246988132183952464*x, 0], [7, [5, [Mod(0
, 7), Mod(6, 7)]], ["(tame) [III*-IV-10] page 167", [6]]]]
[2187, Mat([3, 7]), [x^6 - 3*x^5 + 328256967394537077630*x^4 - 9847709021836
11232873*x^3 + 984770902183611232881*x^2 + 2626055739156296621016*x, 0], [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, 0], [7, [5, [Mod(0, 7), Mod
(6, 7)]], ["[IV-III*-(-1)] page 167", [6]]]]
Type: [IV*-III-10], p. 168
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 44567640326363195900190045974568010*x^4 -
 133702920979089587700570137923701621*x^3 + 13370292097908958770057013792370
4021*x^2 + 106962336783271670160456110338963216800*x, 0], [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]), [343*x^6 - 147*x^5 + 74904833096518623349449410269456449
3670*x^4 - 321020713270794100069068901154813354415*x^3 + 4586010189582772858
1295557307830479203*x^2 + 13102886255950779594655873516522994058*x, 0], [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 - 2736
8747340080916343*x - 343, 0], [7, [5, [Mod(6, 7), Mod(6, 7)]], ["(tame) [2II
I-10] page 168", [2]]]]
[81, Mat([3, 4]), [x^6 - 9*x^4 + 31381059609*x^3 + 27*x^2 - 94143178827*x - 
27, 0], [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 - 191
581231380566414401*x - 343, 0], [7, [5, [Mod(6, 7), Mod(6, 7)]], ["(tame) [2
III*-10] page 168", [2]]]]
[81, Mat([3, 4]), [x^6 - 9*x^4 + 94143178827*x^3 + 27*x^2 - 282429536481*x -
 27, 0], [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[2III*-10] page 168", [2]]]]
Type: [III-III-10], p. 169
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 44567640326363195900190045974568017*x^4 -
 133702920979089587700570137923704029*x^3 + 44567640326363195900190045974568
0070*x^2 - 356541122610905567201520367796544056*x, 0], [7, [5, [Mod(6, 7), M
od(6, 7)]], ["(tame) [III-III-10] page 169", [2, 2]]]]
Type: [III-III*-10], p. 169
[2401, Mat([7, 4]), [x^6 - 3*x^5 + 44567640326363195900190045974568353*x^4 -
 133702920979089587700570137923704365*x^3 + 15420403552921665781465755907200
530422*x^2 - 15331268272268939389665375815251394408*x, 0], [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]), [343*x^6 - 147*x^5 + 74904833096518623349449410269456449
3719*x^4 - 321020713270794100069068901154813354429*x^3 + 1528670063194257619
37651857692768264010*x^2 - 17470515007934372792874498022030658744*x, 0], [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, 0], [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]), [x^5 - 2*x^4 + 19100417282727083957224305458025611*x^3 + 50
8021860739623327121353632198048587323823689491995*x^2 - 10160437207084759789
80782478311514614647856768035178*x + 205005150237173513518523762302840650436
56128020898248641608, 0], [7, [6, [Mod(2, 7)]], ["(tame) [I{0}-I{9}-10] page
 170", [9]]]]
[3, Mat([3, 1]), [x^5 - 2*x^4 - 12157665459056909117*x^3 + 42391158299531534
432408290803*x^2 - 84782555861919303105175385286*x + 83442755948935574997537
1623128484, 0], [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 + 5
08021860739623479924691894014720245118274940175011*x^3 + 3556153062945129319
148051483501814963799504492542834*x^2 + 100452521126907926660581690807062797
6335864597950580018666977*x + 7031676478883553015620189472307296962082581739
484589084102397, 0], [7, [6, [Mod(2, 7)]], ["(tame) [I{0}-I*{9}-10] page 170
", [4]]]]
[9, Mat([3, 2]), [x^6 - 12157665459056751660*x^4 + 4239115825090087259618057
5607*x^3 + 127171321168158531362286712374*x^2 + 7509466510672336877795600427
053229*x + 22528399551400256301066821173173441, 0], [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]), [x^5 - 2*x^4 + 935920446853627113903990965506281755*x^3 +
 174251498233690812433669658087456032299963111086892049*x^2 - 34850299642961
3861779505001656767519159936482237292310*x + 7031676653135051513685365046987
434309974051911168099284071544, 0], [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
, 0], [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 + 1219760489486
456222471317833459850493873847680657395212*x^2 + 344552147465294121823456159
637489836481536621034944927824583035*x + 24118650322570587620837872021372610
10629601295382324365507824195, 0], [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, 0], [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, 0], [7, [2, [Mod(0, 7)]], ["(tame) [II*{9-0}] page 172"
, []]]]
Type: [II-I{9}-10], p. 172
[343, Mat([7, 3]), [x^5 - 2*x^4 + 40353608*x^3 + 355615302517736355725531738
3565515512407041673852007*x^2 - 71123060503547271145106347671310310248140833
47704014*x + 143503605166021459462966633611988455305592896146287740491256, 0
], [7, [6, [Mod(0, 7)]], ["(tame) [I{9}-II-10] page 172", [9]]]]
Type: [II*-I{9}-10], p. 172
[343, Mat([7, 3]), [x^5 - 2*x^4 + 40353608*x^3 + 853832341345084990097001703
7940802745289307058918668807*x^2 - 17076646826901699801940034075881605490578
614117837337614*x + 34455215600361752417058288730238428118872854364723686491
9505656, 0], [7, [6, [Mod(0, 7)]], ["(tame) [I{9}-II*-10] page 172", [9]]]]
Type: [IV-I{9}-10], p. 173
[343, Mat([7, 3]), [x^5 - 2*x^4 + 40353608*x^3 + 248930711762415449007872216
84958608586849291716964049*x^2 - 4978614235248308980157444336991721717369858
3433928098*x + 1004525236162150216240766435283919187139150273024014183438792
, 0], [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]), [x^5 - 2*x^4 + 40353608*x^3 + 121976048763583570013857386
2562971820755615294131238401*x^2 - 24395209752716714002771477251259436415112
30588262476802*x + 492217365719453605957975553289120401698183633781766949885
00808, 0], [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]), [x^6 + 4*x^5 + 1977326732*x^4 + 355615302517736355725531
7383565515512407053537812471*x^3 + 14224612100709454229021269534262062049628
166695408028*x^2 + 703167643976587000304355161166839129604312116674559885295
1124*x + 42190058894638237831031485792393199392975843893780593635051248, 0],
 [7, [6, [Mod(0, 7)]], ["(tame) [I*{9}-II-10] page 173", [4]]]]
Type: [II*-I*{9}-10], p. 174
[2401, Mat([7, 4]), [x^6 + 4*x^5 + 1977326732*x^4 + 853832341345084990097001
7037940802745289307070782629271*x^3 + 34153293653803399603880068151763210981
157228235674675228*x^2 + 168830551318778538773075674196158075017995339213561
82845935648724*x + 101298331406026409032306597387536071742535001188967205317
758046448, 0], [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 + 1384
1287544, 0], [7, [6, [Mod(0, 7)]], ["(tame) [I*{9}-II*--1] page 174", [4]]]]
Type: [IV-I*{9}-10], p. 174
[2401, Mat([7, 4]), [x^6 + 4*x^5 + 1977326732*x^4 + 248930711762415449007872
21684958608586849303580924513*x^3 + 9957228470496617960314888673983443434739
7166867856196*x^2 + 49221735078361090021304861281678739072301848167219191970
657868*x + 295330412262467664817220400546752395750830907256464155445358736, 
0], [7, [6, [Mod(0, 7)]], ["(tame) [I*{9}-IV-10] page 174", [12]]]]
Type: [IV*-I*{9}-10], p. 174
[2401, Mat([7, 4]), [x^6 + 4*x^5 + 1977326732*x^4 + 121976048763583570013857
3862562971820755615305995198865*x^3 + 48790419505433428005542954502518872830
22461176524953604*x^2 + 2411865018839693411043938202802258214542790560193740
406562235532*x + 14471190200860915576043799626790867391790714455566743616822
578064, 0], [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 + 197732
6792, 0], [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, 0], 
[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, 0], [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, 0], [
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, 0], [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, 0], [
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, 0], [7, [2, [Mod(0, 7)]],
 ["[IV*-II{0}] page 175", []]]]
[729, Mat([3, 6]), [3*x^5 + 9*x^3 + 9*x^2 + 27, 0], [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, 0], [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, 0], [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 + 1977
326792*x, 0], [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, 
0], [3, [6, [Mod(0, 3)]], ["[II*-II*{9}] page 176", [2, 2]]]]
Type: [III-I{9}-10], p. 176
[343, Mat([7, 3]), [x^5 - 2*x^4 + 44567640326363195900190046014921615*x^3 - 
89135280652726391800380091949136014*x^2 + 1798465087215052472983476240759695
323819256*x, 0], [7, [6, [Mod(6, 7)]], ["(tame) [I{9}-III-10] page 176", [18
]]]]
[27, Mat([3, 3]), [x^5 - 2*x^4 + 36472996377170806087*x^3 - 7294599275434157
2806*x^2 + 717934460688229759556652*x, 0], [3, [6, [Mod(0, 3)]], ["[I{9}-III
-10] pages 159-177", [18]]]]
Type: [III*-I{9}-10], p. 176
[343, Mat([7, 3]), [x^5 - 2*x^4 + 2183814375991796599109312252794185951*x^3 
- 4367628751983593198218624505507664686*x^2 + 881247892735375711761903357972
25070867143544*x, 0], [7, [6, [Mod(6, 7)]], ["(tame) [I{9}-III*-10] page 176
", [18]]]]
[27, Mat([3, 3]), [x^5 - 2*x^4 + 328256967394537097311*x^3 - 656513934789074
155254*x^2 + 6461410146194067836009868*x, 0], [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 + 88124786777749712899851365386582
460699453771*x^2 + 528748722538339171106362420127476948226402066*x - 6168735
09628062366290756156815389740634465608, 0], [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 - 1938324566
7680019897328164, 0], [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 + 4318114552109735932092716903
942542282683541067*x^2 + 25908687404378619384211758586246368564860027954*x -
 30226801971775055948247051683954096626707029144, 0], [7, [6, [Mod(6, 7)]], 
["(tame) [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 - 174449
211009120179071701948, 0], [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,
 0], [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, 0
], [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
, 0], [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, 0], [7, [2, [Mod(6, 7)]],
 ["(tame) [II{0}-III*] page 178", []]]]
Type: [III-II*{9}], p. 178
[2401, Mat([7, 4]), [x^6 + 282475249*x^4 + 7*x^2 + 1977326743, 0], [7, [2, [
Mod(6, 7)]], ["(tame) [II*{9}-III] page 178", [8]]]]
Type: [III*-II*{9}], p. 178
[2401, Mat([7, 4]), [49*x^6 + 1977326743*x^4 + 7*x^2 + 282475249, 0], [7, [2
, [Mod(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, 0], [7, [3, []], ["(tame) [I{8-9-0}] page 179", [72]]]
]
Type: [I{9}-I{8}-10}], p. 179
[49, Mat([7, 2]), [x^5 + 79792266297611999*x^4 + 256923577521058878088611317
639703031862407*x^3 + 205005145156954900983818558659781116742032881369987397
51195*x^2 - 41001029029909867670917466553668751161754024538661404934400*x + 
118181407081110395672359026541012872529905940276396171922010844814, 0], [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 + 1628413
315435200*x - 1628413880385698, 0], [7, [3, []], ["(tame) [I*{8-9-0}] page 1
80", [4, 2, 2]]]]
[81, Mat([3, 4]), [3*x^5 + 3*x^4 + 78729*x^3 + 39363*x^2 + 387361440*x - 387
479538, 0], [3, [3, []], ["(tame) [I*{8-9-0}] page 180", [4, 2, 2]]]]
Type: [I*{9}-I*{8}-10], p. 180
[2401, Mat([7, 4]), [x^6 + 558545864083284011*x^5 + 125892552985318850263419
64618171002060370009*x^4 + 7031676478883553330351571935604422778407017230014
542438128339*x^3 + 281267059190903660066737582393121131015113920617862950327
59138*x^2 + 1986274486911633708389059586001471994720392681842749646477323061
061338*x + 11917647427750508601928684316018206546318610433380303440718925199
651500, 0], [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]), [x^5 + 558545864083284005*x^4 + 1798465042647412146620279
223477921223036843*x^3 + 100452521126907903640229144920187323147932185427354
5939119501*x^2 - 20090504224655835266657461170142416866476292458123049372930
94*x + 40536216601669598101144906108238208297572724431553769920914920922744,
 0], [7, [7, []], ["(tame) [I{9}-I*{8}-10] page 180", [18, 2]]]]
[27, Mat([3, 3]), [x^5 + 10460353201*x^4 + 717897987691831668083527*x^3 + 75
09466513543928828768912373164901*x^2 - 15018918898855459881467074562933778*x
 + 147816338880860903040887156922341555148, 0], [3, [7, []], ["[I{9}-I*{8}-1
0] page 180", [18, 2]]]]
Type: [2I{8}-10], p. 181
[343, Mat([7, 3]), [x^6 + 1977326722*x^4 + 9387480337620071731394*x^2 + 1856
2115855305211939015772541728, 0], [7, [7, []], ["(tame) [2I{8}-10] page 181"
, [8]]]]
[27, Mat([3, 3]), [x^6 + 177138*x^4 + 2541864765474*x^2 + 450276280295106672
, 0], [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 - 2768
2574255*x^2 + 18562115855305211938918883531664*x + 96889010064, 0], [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, 0], [7, [3, []], ["(t
ame) [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, 0], 
[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 + 65712
362363534280139690*x^2 + 129934811447123020117269034708856*x - 4599865365447
39960977144, 0], [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, 0], [3, [7, []], ["[2I*{8}-10] p
ages 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 - 
343, 0], [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 + 232630877169
677*x^2 - 564950498*x + 1628413880385698, 0], [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 - 118
098*x + 387479538, 0], [3, [3, []], ["[II{9-8}] page 182", [36]]]]
Type: [III{8}], p. 182
[2401, Mat([7, 4]), [49*x^5 - 14*x^3 + 2402*x, 0], [7, [3, []], ["(tame) [II
I{8}] page 182", [2, 2]]]]
Type: [III{9}], p. 182
[2401, Mat([7, 4]), [49*x^5 - 14*x^3 + 16807*x^2 + x, 0], [7, [3, []], ["(ta
me) [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 + 233406173743
369*x^2 - 931878986337810*x + 3910752249023424154, 0], [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 + 16338
43216203583*x^2 - 6523152904364670*x + 27375265743163969078, 0], [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 - 2353
96*x + 678505665796, 0], [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 + 48
42756, 0], [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 + 
678223190400*x + 282475298, 0], [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, 0], [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, 0], [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, 0], [7, [4, []], ["(tame) [II*{9-9}] page
 184", [9]]]]
Type: [III{12}], p. 184
[2401, Mat([7, 4]), [x^6 - 14*x^3 + 117698, 0], [7, [4, []], ["[III{12}] pag
e 184", [3, 3]]]]
[59049, Mat([3, 10]), [x^6 - 6*x^3 + 738, 0], [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, 0], [7, [4, []], ["[III{1
3}] page 184", [9]]]]
[59049, Mat([3, 10]), [x^6 - 6*x^3 + 729*x + 9, 0], [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, 0], [7, [4, []], ["[III
{14}] page 184", [9]]]]
[59049, Mat([3, 10]), [x^6 - 6*x^3 + 729*x^2 + 9, 0], [3, [4, []], ["[III{14
}] page 184", [9]]]]
Type: [III*{6}], p. 184
[2401, Mat([7, 4]), [7*x^6 - 98*x^3 + 17150, 0], [7, [4, []], ["[III*{6}] pa
ge 184", []]]]
[59049, Mat([3, 10]), [3*x^6 - 18*x^3 + 270, 0], [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, 0], [7, [4, []], ["[III
*{7}] page 184", []]]]
[59049, Mat([3, 10]), [3*x^6 - 18*x^3 + 243*x + 27, 0], [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, 0], [7, [4, []], ["[III{8
}] page 184", [9]]]]
[59049, Mat([3, 10]), [x^6 - 6*x^3 + 81*x^2 + 9, 0], [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, 0], [3, [7, []], ["(tame) [I*{1}-I*{1}-
0] page 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, 0], [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]), [3*x^6 + 3*x^4 + 3*x^3 + x^2 - 5*x - 5, 0], [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]), [-3*x^6 + 6*x^5 - x^4 + 6*x^3 - 6*x^2 - x - 6, 0], [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]), [x^6 + 9*x^5 + 2*x^4 + 6580*x^3 + 9*x^2 + 13122*x + 6561, 0
], [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]), [x^6 + 4*x^5 - 24*x^4 - 16*x^3 - 52*x^2 - 48*x, 0], [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]), [x^6 + 4*x^5 + 24*x^4 + 32*x^3 + 56*x^2 + 48*x + 24, 0], [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]), [24*x^5 + 56*x^4 + 76*x^3 + 33*x^2 - 4*x - 20, 0], [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]), [-3*x^6 + 6*x^5 - 25*x^4 + 36*x^3 - 69*x^2 + 38*x - 39, 0],
 [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]), [-5*x^5 + 5*x^4 + 10*x^3 - 7, 1], [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]), [-5*x^6 - 3*x^5 - 10*x^4 - 10*x^3 - 7, 1], [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]), [3*x^5 + 5*x^4 + 5*x - 4, 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]), [-9*x^6 + 6*x^5 - 8*x^4 - 5*x^3 + 5*x^2 - 10*x + 3, x^2 + x
], [3, [6, [Mod(0, 3)]], ["(tame) [I{0}-I{12}-1] page 170", [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]), [-7*x^6 + 5*x^3 + 5*x^2 - 6*x + 1, x^3 + 1], [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 + 97*x^4 + 118*x^3 + 60*x^2 + 13*x + 1, 0], [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]), [-x^6 - 3*x^4 - 10*x^2 - 1, x], [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], [-60*x^6 - 203*x^5 - 291*x^4 - 244*x^3 - 129*x^2 - 41*x
 - 7, x^3 + x^2 + x + 1], [[2, [5, [Mod(0, 2), Mod(0, 2)]], []], [3, [5, [Mo
d(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 + 5*x^4 + x^2 + 1, 0], [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^3 + 1, x^3 + 1], [[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]), [25*x^5 + 5, 0], [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]), [2730000*x^6 - 15573200*x^5 - 448376300*x^4 + 2975633192*
x^3 + 2276184980*x^2 + 39645936*x - 26954928, 0], [5, [6, [Mod(3, 5)]], ["(t
ame) [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 - 2808*x^5 + 1962*x^4 - 676*x^3 + 113*x^2 - 4*x
, 0], [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, 0], [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, 0], [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[2I*{0}-
0] pages 159, 181", [2, 2]]]]
? genus2red(150*x^6+180*x^5-270*x^4+2040*x^3-1350*x^2+3060*x+270,3)
[81, Mat([3, 4]), [1350*x^6 - 2160*x^5 + 1080*x^4 + 640*x^3 - 960*x^2 + 480*
x - 80, 0], [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[III*-III*-0] pages 162-177",
 [2, 2]]]]
? genus2red(-3*x^6-36*x^5-72*x^4+270*x^3+3,3)
[2187, Mat([3, 7]), [-27*x^6 - 162*x^5 - 297*x^4 - 146*x^3 - 3*x^2 + 12*x + 
2, 0], [3, [5, [Mod(0, 3), Mod(0, 3)]], ["[IV*-IV*-0] pages 160-175", [3, 3]
]]]
? print("Total time spent: ",gettime);
Total time spent: 49
