LMFDB - Abstract group data

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Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
abelian_quotient	text
all_subgroups_known	boolean
almost_simple	boolean
aut_abelian	boolean
aut_cyclic	boolean
aut_derived_length	smallint
aut_exponent	numeric
aut_gen_orders	numeric[]
aut_gens	numeric[]
aut_group	text
aut_hash	bigint
aut_nilpotency_class	smallint
aut_nilpotent	boolean
aut_order	numeric
aut_permdeg	integer
aut_perms	numeric[]
aut_phi_ratio	double precision
aut_solvable	boolean
aut_stats	numeric[]
aut_supersolvable	boolean
aut_tex	text
autcent_abelian	boolean
autcent_cyclic	boolean
autcent_exponent	numeric
autcent_group	text
autcent_hash	bigint
autcent_nilpotent	boolean
autcent_order	numeric
autcent_solvable	boolean
autcent_split	boolean
autcent_supersolvable	boolean
autcent_tex	text
autcentquo_abelian	boolean
autcentquo_cyclic	boolean
autcentquo_exponent	numeric
autcentquo_group	text
autcentquo_hash	bigint
autcentquo_nilpotent	boolean
autcentquo_order	numeric
autcentquo_solvable	boolean
autcentquo_supersolvable	boolean
autcentquo_tex	text
cc_stats	numeric[]
center_label	text
center_order	numeric
central_product	boolean
central_quotient	text
commutator_count	integer
commutator_label	text
complements_known	boolean
complete	boolean
complex_characters_known	boolean
composition_factors	text[]
composition_length	smallint
conjugacy_classes_known	boolean
counter	integer
cyclic	boolean
derived_length	smallint
dihedral	boolean
direct_factorization	jsonb
direct_product	boolean
div_stats	numeric[]
element_repr_type	text
elementary	integer
eulerian_function	numeric
exponent	numeric
exponents_of_order	smallint[]
factors_of_aut_order	integer[]
factors_of_order	smallint[]
faithful_reps	numeric[]
familial	boolean
frattini_label	text
frattini_quotient	text
hash	bigint
hyperelementary	integer
inner_abelian	boolean
inner_cyclic	boolean
inner_exponent	numeric
inner_gen_orders	numeric[]
inner_gens	numeric[]
inner_hash	bigint
inner_nilpotent	boolean
inner_order	numeric
inner_split	boolean
inner_tex	text
inner_used	smallint[]
irrC_degree	integer
irrQ_degree	integer
irrQ_dim	integer
irrR_degree	integer
irrep_stats	numeric[]
label	text
linC_count	numeric
linC_degree	integer
linFp_degree	integer
linFq_degree	integer
linQ_degree	integer
linQ_degree_count	numeric
linQ_dim	integer
linQ_dim_count	numeric
linR_count	numeric
linR_degree	integer
maximal_subgroups_known	boolean
metabelian	boolean
metacyclic	boolean
monomial	boolean
name	text
ngens	smallint
nilpotency_class	smallint
nilpotent	boolean
normal_counts	integer[]
normal_index_bound	numeric
normal_order_bound	numeric
normal_subgroups_known	boolean
number_autjugacy_classes	integer
number_characteristic_subgroups	integer
number_conjugacy_classes	integer
number_divisions	integer
number_normal_subgroups	integer
number_subgroup_autclasses	integer
number_subgroup_classes	integer
number_subgroups	numeric
old_label	text
order	numeric
order_factorization_type	integer
order_stats	numeric[]
outer_abelian	boolean
outer_cyclic	boolean
outer_equivalence	boolean
outer_exponent	numeric
outer_gen_orders	numeric[]
outer_gen_pows	numeric[]
outer_gens	numeric[]
outer_group	text
outer_hash	bigint
outer_nilpotent	boolean
outer_order	numeric
outer_permdeg	integer
outer_perms	numeric[]
outer_solvable	boolean
outer_supersolvable	boolean
outer_tex	text
pc_rank	smallint
perfect	boolean
permutation_degree	integer
pgroup	smallint
primary_abelian_invariants	integer[]
quasisimple	boolean
rank	smallint
rational	boolean
rational_characters_known	boolean
ratrep_stats	numeric[]
representations	jsonb
schur_multiplier	integer[]
semidirect_product	boolean
simple	boolean
smith_abelian_invariants	integer[]
solvability_type	smallint
solvable	boolean
subgroup_inclusions_known	boolean
subgroup_index_bound	numeric
supersolvable	boolean
sylow_subgroups_known	boolean
tex_name	text
transitive_degree	integer
wreath_data	text[]
wreath_product	boolean

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '27.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 18, 'aut_gen_orders': [18, 6, 6, 6], 'aut_gens': [[29229310, 2502841, 24446350, 15060466], [29229310, 36121126, 10453195, 29585035], [14884750, 11852707, 34368049, 709318], [14882563, 12066628, 38975320, 29409346], [29231497, 40548334, 19845613, 15060466]], 'aut_group': None, 'aut_hash': 225813103164118894, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 472392, 'aut_permdeg': 486, 'aut_perms': [10599004142300759331335384723344946915887111451186028556604084154641668291746846120748198818352557307897930800716143653305096140977712545965920461222566593099765923852957098312323971766032434670609256022811520515111594390755480877894885724962740680175931286751219859408811657706306035500850301312561228081875699085337537717309129348731746816968556642396024537338086270873052453940395809470596637446373311846957978630673468322734031925102801214941535974735263965184198133864604361516334010637398278580895890532750337868955681200290496744814155100397597571971617445676199352943381251586034926330726616937487885680305370103183559520923458316507939648724094758081003752832866920094372968558966491616591683747055257929944731349953104672131259215055431020946923107225229368956757005702178971752123950806554238010329120985792992198013672513987126370753195702402852371163156832019553617569723283976513429582910052521216832737088491457370360041152640963546350058316752068514480183901482928562891865130789917483172420435320598906408930168678503073607696367832457094100600505770940523640513269593608550514164, 17771259680173230676728333266015025368033758164364332393186699017445623411282236911297186926838264269932220901016455350635492427590088354775755768763456819307420816230044118353191951997987729559614556299207630625045244585279153891874738173196733886744786159538968463785026175221941215486608152117625726645424136423516794143653137793847465544457286904635383789769549656628941987317312686060374785501286511510623314008993342913006735667515616597448123192497145097126517632305775003855632841736277044979174860001537673654882317386649204822395990640187174373951954321014580056956556371294114834670745482066723142094752151178027904638094273746349628965387642172561268803758923130018041180570132204947873120606071542697427610280818708682161869414428275701385605415891223902874279903848331022641401611335803082156829038916282621302646987027739323589807259300297509768480836254860300175408560504152231644481321950482633284101528863985610068931173605781321945819058160001261090815916961060391398627841458677429278985792607196873362359411493326230940284256429427377337547403070163632094861816313062713585476, 12737349902127916189660759969127766912202678345861251846687024653066717910307681302758340184461587082764288302233300677801462817688410510216704407470792582094531625320858220305147550067205872081398582025680653143018157738357264152665611428324218237968893290717347226005454653963686959911597359992936874212118323750448252991467105585384113801005708788617761995075256752868351594390099364242023141222829526102649145128478315917791487580045988971079191683135215788187434724671443554399130482115640631937981116512012474770577212490156285990119031467464054815803904911263924733454155587991744161055600483293111707559953687333389313163822097888113027559682654879571720834781686077145212537028273442080469752287270273337547193938314693626316259698413190100898181477319344378165861317252886328194333263344091416031241341428741828123922184711143304039999418808679744054502851896532557343682078510916020542709849497675503714643399092584933632457483178054280816813659053727838813132788312276809515937739717874193349060581113291356946971944581555203833444220441096298282124444793331874710193183023474274185025, 17662644813090335159670991093949577659208128731324212157374470596406505039199113914384541473001555892311808461494945336283692268796745689410108780466394988435223362417422241878698992495479447931185058591238613002879230349981332359310162798672422937984039353024282523026029516155913990938208412858933080542113636981163711074054817963271933834666436286977023602985545693784841998280952036944469751417280400590000722632620850722472038648747857370354654656037700907686379387534699598376296430003070358699533987773632645258464379777918565545336456766015965778445686639656884653727916083062340196473055202512274815866905105917000002438282390673912371505282922105798677973875796425621512008499933158369210605091010156840564282859604404852380133871915767025941852564800958414262122730953754275538160028772763296406508258758675005053216857749211636068274170898571326884208538824730133227634381478863511047298004336351011994429695560103770942715943278827876649185682981284632278713466422318114602751463103986698802637061985139572383810237559808928513054095428151563507141118318851297487478067635682850917564], 'aut_phi_ratio': 972.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1], [3, 1, 6, 1], [3, 3, 2, 1], [3, 3, 4, 1], [3, 27, 18, 1], [9, 3, 6, 1], [9, 3, 12, 1], [9, 3, 54, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3^4.\\He_3.C_3^3.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '486.183', 'autcent_hash': 183, 'autcent_nilpotent': False, 'autcent_order': 486, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^4:S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': '972.447', 'autcentquo_hash': 447, 'autcentquo_nilpotent': False, 'autcentquo_order': 972, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_3^3.S_3^2', 'cc_stats': [[1, 1, 1], [3, 1, 8], [3, 3, 6], [3, 27, 18], [9, 3, 72]], 'center_label': '9.2', 'center_order': 9, 'central_product': True, 'central_quotient': '81.9', 'commutator_count': 1, 'commutator_label': '27.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 395, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['243.26', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 4], [3, 3, 2, 3], [3, 27, 2, 9], [9, 3, 6, 12]], 'element_repr_type': 'GLZq', 'elementary': 3, 'eulerian_function': 468, 'exponent': 9, 'exponents_of_order': [6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '27.2', 'frattini_quotient': '27.5', 'hash': 395, 'hyperelementary': 3, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 9, 'inner_gen_orders': [1, 3, 9, 3], 'inner_gens': [[29229310, 2502841, 24446350, 15060466], [29229310, 2502841, 10279639, 29409346], [29229310, 2322778, 24446350, 15060466], [29229310, 31202869, 24446350, 15060466]], 'inner_hash': 9, 'inner_nilpotent': True, 'inner_order': 81, 'inner_split': False, 'inner_tex': '\\He_3:C_3', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 27], [3, 78]], 'label': '729.395', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C9^2:C3^2', 'ngens': 3, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 105, 'number_divisions': 29, 'number_normal_subgroups': 40, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 130, 'number_subgroups': 850, 'old_label': None, 'order': 729, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 512], [9, 216]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6, 6, 6, 3, 3, 3], 'outer_gen_pows': [531442, 889381, 531442, 531442, 531442, 531442], 'outer_gens': [[29229310, 16849588, 5314456, 29589409], [29229310, 31340326, 19663336, 29409346], [14882563, 40548334, 34016644, 29409346], [29229310, 31202896, 24446350, 15060466], [29229310, 16849588, 24450724, 15060466], [29233684, 2502841, 24446350, 15060466]], 'outer_group': '5832.il', 'outer_hash': 1624906626852756491, 'outer_nilpotent': False, 'outer_order': 5832, 'outer_permdeg': 21, 'outer_perms': [249735734048329856, 262560264661149198, 10103723861066051513, 98499, 13017804187112762164, 859343615985254400], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^3.S_3^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 30, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 13], [6, 3], [18, 12]], 'representations': {'PC': {'code': 5331097505850465300, 'gens': [1, 2, 3, 5], 'pres': [6, 3, 3, 3, 3, 3, 3, 2330, 68, 2169, 1360, 118]}, 'GLZq': {'d': 2, 'q': 81, 'gens': [531469, 29587195, 2147089, 14880376, 533629, 34012270]}, 'Perm': {'d': 30, 'gens': [9801602063944636128240532004184, 1230961227294315343161203776083, 19275850533684766814617041722404, 28433801669260121289866091797424, 18056322351962255673484449395184, 19275850533684766814617041722400]}}, 'schur_multiplier': [3, 3, 3, 9], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_9^2:C_3^2', 'transitive_degree': 81, 'wreath_data': None, 'wreath_product': False}

Column	Type
aut_label	text
centralizer	text
counter	integer
group_counter	integer
group_order	numeric
label	text
order	integer
powers	integer[]
representative	numeric
size	numeric

gps_conj_classes • Show schema
Showing the first 100 of 105 matching records in this table.

id: 176520359
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 395, 'group_order': 729, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 531442, 'size': 1}
id: 176520376
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 395, 'group_order': 729, 'label': '3A1', 'order': 3, 'powers': [3, 1], 'representative': 29229310, 'size': 1}
id: 176520387
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 395, 'group_order': 729, 'label': '3A-1', 'order': 3, 'powers': [2, 1], 'representative': 14880376, 'size': 1}
id: 176520398
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 395, 'group_order': 729, 'label': '3B1', 'order': 3, 'powers': [5, 1], 'representative': 29231497, 'size': 1}
id: 176520409
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 395, 'group_order': 729, 'label': '3B-1', 'order': 3, 'powers': [4, 1], 'representative': 14884750, 'size': 1}
id: 176520420
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 395, 'group_order': 729, 'label': '3C1', 'order': 3, 'powers': [7, 1], 'representative': 29233684, 'size': 1}
id: 176520431
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 7, 'group_counter': 395, 'group_order': 729, 'label': '3C-1', 'order': 3, 'powers': [6, 1], 'representative': 14882563, 'size': 1}
id: 176520442
{'aut_label': '3D1', 'centralizer': '1.a1', 'counter': 8, 'group_counter': 395, 'group_order': 729, 'label': '3D1', 'order': 3, 'powers': [9, 1], 'representative': 533629, 'size': 1}
id: 176520453
{'aut_label': '3D1', 'centralizer': '1.a1', 'counter': 9, 'group_counter': 395, 'group_order': 729, 'label': '3D-1', 'order': 3, 'powers': [8, 1], 'representative': 535816, 'size': 1}
id: 176520360
{'aut_label': '3E1', 'centralizer': '3.b1', 'counter': 10, 'group_counter': 395, 'group_order': 729, 'label': '3E1', 'order': 3, 'powers': [11, 1], 'representative': 14880349, 'size': 3}
id: 176520367
{'aut_label': '3E1', 'centralizer': '3.b1', 'counter': 11, 'group_counter': 395, 'group_order': 729, 'label': '3E-1', 'order': 3, 'powers': [10, 1], 'representative': 29229256, 'size': 3}
id: 176520368
{'aut_label': '3E1', 'centralizer': '3.b1', 'counter': 12, 'group_counter': 395, 'group_order': 729, 'label': '3F1', 'order': 3, 'powers': [13, 1], 'representative': 531469, 'size': 3}
id: 176520369
{'aut_label': '3E1', 'centralizer': '3.b1', 'counter': 13, 'group_counter': 395, 'group_order': 729, 'label': '3F-1', 'order': 3, 'powers': [12, 1], 'representative': 531496, 'size': 3}
id: 176520370
{'aut_label': '3G1', 'centralizer': '3.b1', 'counter': 14, 'group_counter': 395, 'group_order': 729, 'label': '3G1', 'order': 3, 'powers': [15, 1], 'representative': 29229283, 'size': 3}
id: 176520371
{'aut_label': '3G1', 'centralizer': '3.b1', 'counter': 15, 'group_counter': 395, 'group_order': 729, 'label': '3G-1', 'order': 3, 'powers': [14, 1], 'representative': 14880403, 'size': 3}
id: 176520372
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 16, 'group_counter': 395, 'group_order': 729, 'label': '3H1', 'order': 3, 'powers': [17, 1], 'representative': 2502841, 'size': 27}
id: 176520373
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 17, 'group_counter': 395, 'group_order': 729, 'label': '3H-1', 'order': 3, 'powers': [16, 1], 'representative': 40548334, 'size': 27}
id: 176520374
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 18, 'group_counter': 395, 'group_order': 729, 'label': '3I1', 'order': 3, 'powers': [19, 1], 'representative': 11715223, 'size': 27}
id: 176520375
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 19, 'group_counter': 395, 'group_order': 729, 'label': '3I-1', 'order': 3, 'powers': [18, 1], 'representative': 16815757, 'size': 27}
id: 176520377
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 20, 'group_counter': 395, 'group_order': 729, 'label': '3J1', 'order': 3, 'powers': [21, 1], 'representative': 31202896, 'size': 27}
id: 176520378
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 21, 'group_counter': 395, 'group_order': 729, 'label': '3J-1', 'order': 3, 'powers': [20, 1], 'representative': 11852653, 'size': 27}
id: 176520379
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 22, 'group_counter': 395, 'group_order': 729, 'label': '3K1', 'order': 3, 'powers': [23, 1], 'representative': 21459046, 'size': 27}
id: 176520380
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 23, 'group_counter': 395, 'group_order': 729, 'label': '3K-1', 'order': 3, 'powers': [22, 1], 'representative': 7421125, 'size': 27}
id: 176520381
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 24, 'group_counter': 395, 'group_order': 729, 'label': '3L1', 'order': 3, 'powers': [25, 1], 'representative': 26203774, 'size': 27}
id: 176520382
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 25, 'group_counter': 395, 'group_order': 729, 'label': '3L-1', 'order': 3, 'powers': [24, 1], 'representative': 16849588, 'size': 27}
id: 176520383
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 26, 'group_counter': 395, 'group_order': 729, 'label': '3M1', 'order': 3, 'powers': [27, 1], 'representative': 40415197, 'size': 27}
id: 176520384
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 27, 'group_counter': 395, 'group_order': 729, 'label': '3M-1', 'order': 3, 'powers': [26, 1], 'representative': 31160236, 'size': 27}
id: 176520385
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 28, 'group_counter': 395, 'group_order': 729, 'label': '3N1', 'order': 3, 'powers': [29, 1], 'representative': 7105738, 'size': 27}
id: 176520386
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 29, 'group_counter': 395, 'group_order': 729, 'label': '3N-1', 'order': 3, 'powers': [28, 1], 'representative': 21772165, 'size': 27}
id: 176520388
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 30, 'group_counter': 395, 'group_order': 729, 'label': '3O1', 'order': 3, 'powers': [31, 1], 'representative': 36123286, 'size': 27}
id: 176520389
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 31, 'group_counter': 395, 'group_order': 729, 'label': '3O-1', 'order': 3, 'powers': [30, 1], 'representative': 35805793, 'size': 27}
id: 176520390
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 32, 'group_counter': 395, 'group_order': 729, 'label': '3P1', 'order': 3, 'powers': [33, 1], 'representative': 26061970, 'size': 27}
id: 176520391
{'aut_label': '3H1', 'centralizer': '27.e1', 'counter': 33, 'group_counter': 395, 'group_order': 729, 'label': '3P-1', 'order': 3, 'powers': [32, 1], 'representative': 2464636, 'size': 27}
id: 176520392
{'aut_label': '9A1', 'centralizer': '3.b1', 'counter': 34, 'group_counter': 395, 'group_order': 729, 'label': '9A1', 'order': 9, 'powers': [36, 8], 'representative': 15060466, 'size': 3}
id: 176520393
{'aut_label': '9A1', 'centralizer': '3.b1', 'counter': 35, 'group_counter': 395, 'group_order': 729, 'label': '9A-1', 'order': 9, 'powers': [37, 9], 'representative': 29587222, 'size': 3}
id: 176520394
{'aut_label': '9A1', 'centralizer': '3.b1', 'counter': 36, 'group_counter': 395, 'group_order': 729, 'label': '9A2', 'order': 9, 'powers': [38, 9], 'representative': 29589409, 'size': 3}
id: 176520395
{'aut_label': '9A1', 'centralizer': '3.b1', 'counter': 37, 'group_counter': 395, 'group_order': 729, 'label': '9A-2', 'order': 9, 'powers': [39, 8], 'representative': 15058279, 'size': 3}
id: 176520396
{'aut_label': '9A1', 'centralizer': '3.b1', 'counter': 38, 'group_counter': 395, 'group_order': 729, 'label': '9A4', 'order': 9, 'powers': [35, 8], 'representative': 15062653, 'size': 3}
id: 176520397
{'aut_label': '9A1', 'centralizer': '3.b1', 'counter': 39, 'group_counter': 395, 'group_order': 729, 'label': '9A-4', 'order': 9, 'powers': [34, 9], 'representative': 29585035, 'size': 3}
id: 176520399
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 40, 'group_counter': 395, 'group_order': 729, 'label': '9B1', 'order': 9, 'powers': [42, 14], 'representative': 24446350, 'size': 3}
id: 176520400
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 41, 'group_counter': 395, 'group_order': 729, 'label': '9B-1', 'order': 9, 'powers': [43, 15], 'representative': 19663336, 'size': 3}
id: 176520401
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 42, 'group_counter': 395, 'group_order': 729, 'label': '9B2', 'order': 9, 'powers': [44, 15], 'representative': 5314456, 'size': 3}
id: 176520402
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 43, 'group_counter': 395, 'group_order': 729, 'label': '9B-2', 'order': 9, 'powers': [45, 14], 'representative': 38795230, 'size': 3}
id: 176520403
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 44, 'group_counter': 395, 'group_order': 729, 'label': '9B4', 'order': 9, 'powers': [41, 14], 'representative': 10097389, 'size': 3}
id: 176520404
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 45, 'group_counter': 395, 'group_order': 729, 'label': '9B-4', 'order': 9, 'powers': [40, 15], 'representative': 34012297, 'size': 3}
id: 176520405
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 46, 'group_counter': 395, 'group_order': 729, 'label': '9C1', 'order': 9, 'powers': [48, 14], 'representative': 24448537, 'size': 3}
id: 176520406
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 47, 'group_counter': 395, 'group_order': 729, 'label': '9C-1', 'order': 9, 'powers': [49, 15], 'representative': 34372423, 'size': 3}
id: 176520407
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 48, 'group_counter': 395, 'group_order': 729, 'label': '9C2', 'order': 9, 'powers': [50, 15], 'representative': 5318830, 'size': 3}
id: 176520408
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 49, 'group_counter': 395, 'group_order': 729, 'label': '9C-2', 'order': 9, 'powers': [51, 14], 'representative': 38797417, 'size': 3}
id: 176520410
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 50, 'group_counter': 395, 'group_order': 729, 'label': '9C4', 'order': 9, 'powers': [47, 14], 'representative': 38975293, 'size': 3}
id: 176520411
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 51, 'group_counter': 395, 'group_order': 729, 'label': '9C-4', 'order': 9, 'powers': [46, 15], 'representative': 34016671, 'size': 3}
id: 176520412
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 52, 'group_counter': 395, 'group_order': 729, 'label': '9D1', 'order': 9, 'powers': [54, 8], 'representative': 711532, 'size': 3}
id: 176520413
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 53, 'group_counter': 395, 'group_order': 729, 'label': '9D-1', 'order': 9, 'powers': [55, 9], 'representative': 889435, 'size': 3}
id: 176520414
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 54, 'group_counter': 395, 'group_order': 729, 'label': '9D2', 'order': 9, 'powers': [56, 9], 'representative': 891622, 'size': 3}
id: 176520415
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 55, 'group_counter': 395, 'group_order': 729, 'label': '9D-2', 'order': 9, 'powers': [57, 8], 'representative': 709345, 'size': 3}
id: 176520416
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 56, 'group_counter': 395, 'group_order': 729, 'label': '9D4', 'order': 9, 'powers': [53, 8], 'representative': 713719, 'size': 3}
id: 176520417
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 57, 'group_counter': 395, 'group_order': 729, 'label': '9D-4', 'order': 9, 'powers': [52, 9], 'representative': 887248, 'size': 3}
id: 176520418
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 58, 'group_counter': 395, 'group_order': 729, 'label': '9E1', 'order': 9, 'powers': [60, 14], 'representative': 10097416, 'size': 3}
id: 176520419
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 59, 'group_counter': 395, 'group_order': 729, 'label': '9E-1', 'order': 9, 'powers': [61, 15], 'representative': 34012270, 'size': 3}
id: 176520421
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 60, 'group_counter': 395, 'group_order': 729, 'label': '9E2', 'order': 9, 'powers': [62, 15], 'representative': 19663390, 'size': 3}
id: 176520422
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 61, 'group_counter': 395, 'group_order': 729, 'label': '9E-2', 'order': 9, 'powers': [63, 14], 'representative': 24446296, 'size': 3}
id: 176520423
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 62, 'group_counter': 395, 'group_order': 729, 'label': '9E4', 'order': 9, 'powers': [59, 14], 'representative': 38795257, 'size': 3}
id: 176520424
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 63, 'group_counter': 395, 'group_order': 729, 'label': '9E-4', 'order': 9, 'powers': [58, 15], 'representative': 5314429, 'size': 3}
id: 176520425
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 64, 'group_counter': 395, 'group_order': 729, 'label': '9F1', 'order': 9, 'powers': [66, 14], 'representative': 24450724, 'size': 3}
id: 176520426
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 65, 'group_counter': 395, 'group_order': 729, 'label': '9F-1', 'order': 9, 'powers': [67, 15], 'representative': 19665523, 'size': 3}
id: 176520427
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 66, 'group_counter': 395, 'group_order': 729, 'label': '9F2', 'order': 9, 'powers': [68, 15], 'representative': 5316643, 'size': 3}
id: 176520428
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 67, 'group_counter': 395, 'group_order': 729, 'label': '9F-2', 'order': 9, 'powers': [69, 14], 'representative': 38799604, 'size': 3}
id: 176520429
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 68, 'group_counter': 395, 'group_order': 729, 'label': '9F4', 'order': 9, 'powers': [65, 14], 'representative': 38977480, 'size': 3}
id: 176520430
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 69, 'group_counter': 395, 'group_order': 729, 'label': '9F-4', 'order': 9, 'powers': [64, 15], 'representative': 34014484, 'size': 3}
id: 176520432
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 70, 'group_counter': 395, 'group_order': 729, 'label': '9G1', 'order': 9, 'powers': [72, 9], 'representative': 15240475, 'size': 3}
id: 176520433
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 71, 'group_counter': 395, 'group_order': 729, 'label': '9G-1', 'order': 9, 'powers': [73, 8], 'representative': 29407132, 'size': 3}
id: 176520434
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 72, 'group_counter': 395, 'group_order': 729, 'label': '9G2', 'order': 9, 'powers': [74, 8], 'representative': 29411506, 'size': 3}
id: 176520435
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 73, 'group_counter': 395, 'group_order': 729, 'label': '9G-2', 'order': 9, 'powers': [75, 9], 'representative': 15236101, 'size': 3}
id: 176520436
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 74, 'group_counter': 395, 'group_order': 729, 'label': '9G4', 'order': 9, 'powers': [71, 9], 'representative': 15238288, 'size': 3}
id: 176520437
{'aut_label': '9D1', 'centralizer': '3.b1', 'counter': 75, 'group_counter': 395, 'group_order': 729, 'label': '9G-4', 'order': 9, 'powers': [70, 8], 'representative': 29409319, 'size': 3}
id: 176520438
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 76, 'group_counter': 395, 'group_order': 729, 'label': '9H1', 'order': 9, 'powers': [78, 15], 'representative': 34012243, 'size': 3}
id: 176520439
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 77, 'group_counter': 395, 'group_order': 729, 'label': '9H-1', 'order': 9, 'powers': [79, 14], 'representative': 10097443, 'size': 3}
id: 176520440
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 78, 'group_counter': 395, 'group_order': 729, 'label': '9H2', 'order': 9, 'powers': [80, 14], 'representative': 24446323, 'size': 3}
id: 176520441
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 79, 'group_counter': 395, 'group_order': 729, 'label': '9H-2', 'order': 9, 'powers': [81, 15], 'representative': 19663363, 'size': 3}
id: 176520443
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 80, 'group_counter': 395, 'group_order': 729, 'label': '9H4', 'order': 9, 'powers': [77, 15], 'representative': 5314483, 'size': 3}
id: 176520444
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 81, 'group_counter': 395, 'group_order': 729, 'label': '9H-4', 'order': 9, 'powers': [76, 14], 'representative': 38795203, 'size': 3}
id: 176520445
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 82, 'group_counter': 395, 'group_order': 729, 'label': '9I1', 'order': 9, 'powers': [84, 14], 'representative': 10099603, 'size': 3}
id: 176520446
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 83, 'group_counter': 395, 'group_order': 729, 'label': '9I-1', 'order': 9, 'powers': [85, 15], 'representative': 5674555, 'size': 3}
id: 176520447
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 84, 'group_counter': 395, 'group_order': 729, 'label': '9I2', 'order': 9, 'powers': [86, 15], 'representative': 19667764, 'size': 3}
id: 176520448
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 85, 'group_counter': 395, 'group_order': 729, 'label': '9I-2', 'order': 9, 'powers': [87, 14], 'representative': 24448483, 'size': 3}
id: 176520449
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 86, 'group_counter': 395, 'group_order': 729, 'label': '9I4', 'order': 9, 'powers': [83, 14], 'representative': 24626359, 'size': 3}
id: 176520450
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 87, 'group_counter': 395, 'group_order': 729, 'label': '9I-4', 'order': 9, 'powers': [82, 15], 'representative': 5318803, 'size': 3}
id: 176520451
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 88, 'group_counter': 395, 'group_order': 729, 'label': '9J1', 'order': 9, 'powers': [90, 14], 'representative': 10101790, 'size': 3}
id: 176520452
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 89, 'group_counter': 395, 'group_order': 729, 'label': '9J-1', 'order': 9, 'powers': [91, 15], 'representative': 34014457, 'size': 3}
id: 176520454
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 90, 'group_counter': 395, 'group_order': 729, 'label': '9J2', 'order': 9, 'powers': [92, 15], 'representative': 19665577, 'size': 3}
id: 176520455
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 91, 'group_counter': 395, 'group_order': 729, 'label': '9J-2', 'order': 9, 'powers': [93, 14], 'representative': 24450670, 'size': 3}
id: 176520456
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 92, 'group_counter': 395, 'group_order': 729, 'label': '9J4', 'order': 9, 'powers': [89, 14], 'representative': 24628546, 'size': 3}
id: 176520457
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 93, 'group_counter': 395, 'group_order': 729, 'label': '9J-4', 'order': 9, 'powers': [88, 15], 'representative': 5316616, 'size': 3}
id: 176520458
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 94, 'group_counter': 395, 'group_order': 729, 'label': '9K1', 'order': 9, 'powers': [96, 15], 'representative': 34014430, 'size': 3}
id: 176520459
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 95, 'group_counter': 395, 'group_order': 729, 'label': '9K-1', 'order': 9, 'powers': [97, 14], 'representative': 10101817, 'size': 3}
id: 176520460
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 96, 'group_counter': 395, 'group_order': 729, 'label': '9K2', 'order': 9, 'powers': [98, 14], 'representative': 10279693, 'size': 3}
id: 176520461
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 97, 'group_counter': 395, 'group_order': 729, 'label': '9K-2', 'order': 9, 'powers': [99, 15], 'representative': 19665550, 'size': 3}
id: 176520462
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 98, 'group_counter': 395, 'group_order': 729, 'label': '9K4', 'order': 9, 'powers': [95, 15], 'representative': 5316670, 'size': 3}
id: 176520463
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 99, 'group_counter': 395, 'group_order': 729, 'label': '9K-4', 'order': 9, 'powers': [94, 14], 'representative': 38799577, 'size': 3}
id: 176520361
{'aut_label': '9B1', 'centralizer': '3.b1', 'counter': 100, 'group_counter': 395, 'group_order': 729, 'label': '9L1', 'order': 9, 'powers': [102, 14], 'representative': 38797390, 'size': 3}

Column	Type
cdim	integer
counter	smallint
faithful	boolean
group	text
group_order	numeric
image	text
label	text
multiplicity	smallint
nt	integer[]
qdim	integer
qvalues	integer[]
schur_index	smallint

gps_qchar • Show schema

id: 18465392
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 18465403
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1b', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
id: 18465414
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, -1, 2, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
id: 18465415
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1d', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2], 'schur_index': 1}
id: 18465416
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
id: 18465417
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1f', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2], 'schur_index': 1}
id: 18465418
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1g', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
id: 18465419
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1h', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2], 'schur_index': 1}
id: 18465420
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
id: 18465393
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1j', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
id: 18465394
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1k', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
id: 18465395
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1l', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1], 'schur_index': 1}
id: 18465396
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1m', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1], 'schur_index': 1}
id: 18465397
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.1n', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1], 'schur_index': 1}
id: 18465398
{'cdim': 3, 'counter': 15, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3a', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, -3, -3, -3, 6, 6, -3, -3, -3, 6, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, -3, -3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, 0, 0, 6, 6, 0, 0, 0, 6, 0], 'schur_index': 1}
id: 18465399
{'cdim': 3, 'counter': 16, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3b', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, -3, -3, -3, 6, 6, -3, -3, -3, 6, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 6, 0, 0, -3, 6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, -3, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, -3, -3, 0, 0, 0, -3, 0], 'schur_index': 1}
id: 18465400
{'cdim': 3, 'counter': 17, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3c', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, -3, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, -3, -3, 0, 0, 0, -3, 0], 'schur_index': 1}
id: 18465401
{'cdim': 3, 'counter': 18, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3d', 'multiplicity': 6, 'nt': [27, 23], 'qdim': 18, 'qvalues': [18, -9, -9, -9, 18, 18, -9, -9, -9, -9, -9, -9, 18, -9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 18465402
{'cdim': 3, 'counter': 19, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3e', 'multiplicity': 6, 'nt': [27, 23], 'qdim': 18, 'qvalues': [18, -9, -9, -9, 18, 18, -9, -9, -9, -9, 18, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 18465404
{'cdim': 3, 'counter': 20, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3f', 'multiplicity': 6, 'nt': [27, 23], 'qdim': 18, 'qvalues': [18, 18, 18, 18, 18, 18, 18, 18, 18, -9, -9, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 18465405
{'cdim': 3, 'counter': 21, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3g', 'multiplicity': 6, 'nt': [27, 104], 'qdim': 18, 'qvalues': [18, -9, -9, 18, -9, -9, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, 6, -3, 0, 0, -3, 6, 6, 6, -3, 0, -3, 6, -3, -3, -3, 6, 0, 6, 0, -3, -3, 0, 0, -3, -3, -3, -3, 6, 0, -3, -3, -3, -3, -3, -3, 6, -3, -3, -3, 0, 0, 0, 0, 6, 0, -3, 6, -3, 6, -3, -3, 6, -3, 6, 6, -3, 6, -3, 0, 0, 6, -3, 0, 0, 6, -3, -3, 0, -3], 'schur_index': 1}
id: 18465406
{'cdim': 3, 'counter': 22, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3h', 'multiplicity': 6, 'nt': [27, 104], 'qdim': 18, 'qvalues': [18, -9, -9, 18, -9, -9, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 6, -3, -3, 0, 0, -3, -3, -3, -3, 6, 0, 6, -3, -3, -3, 6, -3, 0, -3, 0, 6, 6, 0, 0, -3, 6, 6, -3, -3, 0, -3, -3, 6, 6, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, -3, 0, 6, -3, 6, -3, -3, 6, -3, -3, -3, -3, 6, -3, 6, 0, 0, -3, -3, 0, 0, -3, 6, 6, 0, -3], 'schur_index': 1}
id: 18465407
{'cdim': 3, 'counter': 23, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3i', 'multiplicity': 6, 'nt': [27, 104], 'qdim': 18, 'qvalues': [18, -9, -9, 18, -9, -9, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, -3, 6, 0, 0, 6, -3, -3, -3, -3, 0, -3, -3, 6, 6, -3, -3, 0, -3, 0, -3, -3, 0, 0, 6, -3, -3, 6, -3, 0, 6, 6, -3, -3, 6, 6, -3, -3, 6, 6, 0, 0, 0, 0, -3, 0, -3, -3, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, -3, 0, 0, -3, 6, 0, 0, -3, -3, -3, 0, 6], 'schur_index': 1}
id: 18465408
{'cdim': 3, 'counter': 24, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3j', 'multiplicity': 6, 'nt': [27, 104], 'qdim': 18, 'qvalues': [18, -9, 18, -9, -9, -9, -9, -9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 6, 6, -3, 0, 0, -3, -3, -3, 6, -3, 0, -3, -3, -3, -3, -3, -3, 0, -3, 0, -3, -3, 0, 0, 6, -3, -3, -3, -3, 0, -3, -3, 6, -3, 6, 6, -3, -3, 6, 6, 0, 0, 0, 0, -3, 0, 6, 6, 6, 6, -3, -3, -3, -3, -3, 6, 6, -3, 6, 0, 0, 6, -3, 0, 0, -3, -3, -3, 0, 6], 'schur_index': 1}
id: 18465409
{'cdim': 3, 'counter': 25, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3k', 'multiplicity': 6, 'nt': [27, 104], 'qdim': 18, 'qvalues': [18, -9, 18, -9, -9, -9, -9, -9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, -3, -3, 6, 0, 0, 6, 6, -3, -3, 6, 0, -3, -3, -3, 6, -3, 6, 0, -3, 0, 6, 6, 0, 0, -3, -3, 6, 6, 6, 0, -3, -3, -3, -3, -3, -3, 6, -3, -3, -3, 0, 0, 0, 0, 6, 0, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, -3, 6, -3, 0, 0, -3, -3, 0, 0, -3, -3, 6, 0, -3], 'schur_index': 1}
id: 18465410
{'cdim': 3, 'counter': 26, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3l', 'multiplicity': 6, 'nt': [27, 104], 'qdim': 18, 'qvalues': [18, -9, 18, -9, -9, -9, -9, -9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, -3, -3, -3, 0, 0, -3, -3, 6, -3, -3, 0, 6, 6, 6, -3, 6, -3, 0, 6, 0, -3, -3, 0, 0, -3, 6, -3, -3, -3, 0, 6, 6, -3, 6, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, -3, 0, -3, -3, -3, -3, -3, -3, 6, 6, 6, -3, -3, -3, -3, 0, 0, -3, 6, 0, 0, 6, 6, -3, 0, -3], 'schur_index': 1}
id: 18465411
{'cdim': 3, 'counter': 27, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3m', 'multiplicity': 6, 'nt': [27, 104], 'qdim': 18, 'qvalues': [18, 18, -9, -9, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, 0, 0, -3, -3, 6, -3, 6, 0, -3, 6, -3, -3, -3, -3, 0, 6, 0, 6, 6, 0, 0, 6, -3, 6, -3, -3, 0, -3, -3, -3, -3, 6, 6, -3, -3, 6, 6, 0, 0, 0, 0, -3, 0, -3, -3, -3, -3, -3, 6, 6, -3, 6, -3, -3, -3, -3, 0, 0, -3, -3, 0, 0, 6, -3, 6, 0, 6], 'schur_index': 1}
id: 18465412
{'cdim': 3, 'counter': 28, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3n', 'multiplicity': 6, 'nt': [27, 104], 'qdim': 18, 'qvalues': [18, 18, -9, -9, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, -3, 6, 6, 0, 0, 6, -3, -3, 6, -3, 0, 6, -3, -3, 6, 6, -3, 0, -3, 0, -3, -3, 0, 0, -3, 6, -3, 6, -3, 0, -3, -3, -3, 6, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, -3, 0, -3, 6, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, -3, 0, 0, 6, -3, 0, 0, -3, 6, -3, 0, -3], 'schur_index': 1}
id: 18465413
{'cdim': 3, 'counter': 29, 'faithful': False, 'group': '729.395', 'group_order': 729, 'image': None, 'label': '729.395.3o', 'multiplicity': 6, 'nt': [27, 104], 'qdim': 18, 'qvalues': [18, 18, -9, -9, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, 6, -3, -3, 0, 0, -3, 6, -3, -3, -3, 0, -3, -3, 6, -3, -3, 6, 0, -3, 0, -3, -3, 0, 0, -3, -3, -3, -3, 6, 0, 6, 6, 6, -3, -3, -3, 6, -3, -3, -3, 0, 0, 0, 0, 6, 0, 6, -3, 6, -3, -3, -3, -3, 6, -3, -3, 6, 6, 6, 0, 0, -3, 6, 0, 0, -3, -3, -3, 0, -3], 'schur_index': 1}

Column	Type
center	text
center_index	numeric
center_order	numeric
counter	smallint
cyclotomic_n	integer
dim	integer
faithful	boolean
field	numeric[]
group	text
group_counter	integer
group_order	numeric
image	text
image_isoclass	text
image_order	numeric
indicator	smallint
kernel	text
kernel_order	numeric
label	text
nt	integer[]
q_character	text
values	jsonb

gps_char • Show schema
Showing the first 100 of 105 matching records in this table.

id: 39706391
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 729, 'label': '729.395.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 39706408
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 2, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1b1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]]]}
id: 39706419
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1b2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]]]}
id: 39706430
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
id: 39706441
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
id: 39706452
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1d1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]]]}
id: 39706463
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1d2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]]]}
id: 39706474
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
id: 39706485
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
id: 39706392
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1f1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]]]}
id: 39706399
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1f2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]]]}
id: 39706400
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1g1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]]]}
id: 39706401
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1g2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]]]}
id: 39706402
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1h1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]]]}
id: 39706403
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1h2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]]]}
id: 39706404
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1i1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]]]}
id: 39706405
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1i2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]]]}
id: 39706406
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 243, 'label': '729.395.1j1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
id: 39706407
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id: 39706409
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 243, 'label': '729.395.1k1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 39706410
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 243, 'label': '729.395.1k2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 39706411
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 243, 'label': '729.395.1l1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]]]}
id: 39706412
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 243, 'label': '729.395.1l2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]]]}
id: 39706413
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 243, 'label': '729.395.1m1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]]]}
id: 39706414
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 25, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 243, 'label': '729.395.1m2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]]]}
id: 39706415
{'center': '1.a1', 'center_index': 1, 'center_order': 729, 'counter': 26, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 243, 'label': '729.395.1n1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]]]}
id: 39706416
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id: 39706417
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id: 39706418
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id: 39706420
{'center': '9.a1', 'center_index': 9, 'center_order': 81, 'counter': 30, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.c1', 'kernel_order': 27, 'label': '729.395.3b1', 'nt': [9, 7], 'q_character': None, 'values': [[[3, 0]], [[3, -1]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]]]}
id: 39706421
{'center': '9.a1', 'center_index': 9, 'center_order': 81, 'counter': 31, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.c1', 'kernel_order': 27, 'label': '729.395.3b2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 1]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]]]}
id: 39706422
{'center': '9.a1', 'center_index': 9, 'center_order': 81, 'counter': 32, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.a1', 'kernel_order': 27, 'label': '729.395.3c1', 'nt': [9, 7], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]]]}
id: 39706423
{'center': '9.a1', 'center_index': 9, 'center_order': 81, 'counter': 33, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.a1', 'kernel_order': 27, 'label': '729.395.3c2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]]]}
id: 39706424
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 34, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3d1', 'nt': [27, 23], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]]]}
id: 39706425
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 35, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3d2', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [-2, -4]]]}
id: 39706426
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 36, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3d3', 'nt': [27, 23], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [2, 4]]]}
id: 39706427
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 37, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3d4', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]]]}
id: 39706428
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 38, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3d5', 'nt': [27, 23], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[0, 0]], [[-2, 1], [-1, 4]]]}
id: 39706429
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 39, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3d6', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]]]}
id: 39706431
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 40, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3e1', 'nt': [27, 23], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[0, 0]], [[2, 2], [1, -4]]]}
id: 39706432
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 41, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3e2', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[0, 0]], [[-2, 1], [-1, 4]]]}
id: 39706433
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 42, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3e3', 'nt': [27, 23], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [2, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]]]}
id: 39706434
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 43, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3e4', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [-1, 4]]]}
id: 39706435
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 44, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3e5', 'nt': [27, 23], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]]]}
id: 39706436
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 45, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 9, 'label': '729.395.3e6', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 3]], [[3, 3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, -3]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]]]}
id: 39706437
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 46, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.a1', 'kernel_order': 9, 'label': '729.395.3f1', 'nt': [27, 23], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]]]}
id: 39706438
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 47, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.a1', 'kernel_order': 9, 'label': '729.395.3f2', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [1, -4]]]}
id: 39706439
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 48, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.a1', 'kernel_order': 9, 'label': '729.395.3f3', 'nt': [27, 23], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[0, 0]], [[0, 0]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[0, 0]], [[2, 2], [1, -4]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[0, 0]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[0, 0]], [[-2, 1], [-1, 4]]]}
id: 39706440
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id: 39706442
{'center': '27.a1', 'center_index': 27, 'center_order': 27, 'counter': 50, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '81.9', 'image_order': 81, 'indicator': 0, 'kernel': '81.a1', 'kernel_order': 9, 'label': '729.395.3f5', 'nt': [27, 23], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[0, 0]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 4]], [[0, 0]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[0, 0]], [[0, 0]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[-2, 1], [-1, 4]], [[0, 0]], [[1, 1], [-1, 4]]]}
id: 39706443
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id: 39706444
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id: 39706445
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 53, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3g2', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [-2, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 2], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [2, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]]]}
id: 39706446
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id: 39706447
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id: 39706448
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 56, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3g5', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [2, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[2, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]]]}
id: 39706449
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 57, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3g6', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [2, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-2, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]]]}
id: 39706450
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id: 39706451
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id: 39706453
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 60, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3h3', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-2, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [2, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [2, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 3], [1, -2], [1, -1]], [[2, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]]]}
id: 39706454
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 61, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3h4', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[2, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [2, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-2, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]]]}
id: 39706455
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id: 39706456
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 63, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3h6', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[2, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [-2, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [-2, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [2, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-2, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]]]}
id: 39706457
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 64, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3i1', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [2, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-2, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[2, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]]]}
id: 39706458
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 65, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3i2', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[-1, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[2, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [-2, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [-2, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [2, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]]]}
id: 39706459
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id: 39706460
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id: 39706461
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 68, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3i5', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[1, 2], [1, 3], [1, 4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [-2, -4]], [[2, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-2, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]]]}
id: 39706462
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 69, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3i6', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [-2, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[2, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[2, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [2, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]]]}
id: 39706464
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id: 39706465
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id: 39706466
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 72, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3j3', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [-2, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[2, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]]]}
id: 39706467
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 73, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3j4', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]]]}
id: 39706468
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id: 39706469
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 75, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3j6', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-2, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-2, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[1, 0], [1, 4], [1, -4]]]}
id: 39706470
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 76, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3k1', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [2, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [-2, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]]]}
id: 39706471
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 77, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3k2', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [2, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [2, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [2, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]]]}
id: 39706472
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id: 39706473
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id: 39706475
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id: 39706476
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id: 39706477
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id: 39706478
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id: 39706479
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 84, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3l3', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, -3]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [-2, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 2], [-2, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-2, 1], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[2, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [2, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [2, 4]], [[1, 1], [1, 3], [1, -4]]]}
id: 39706480
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 85, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3l4', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[2, 2], [1, -4]], [[-1, 2], [-2, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]]]}
id: 39706481
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id: 39706482
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 87, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3l6', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 3]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [2, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [2, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [2, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [-2, -4]], [[-1, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]]]}
id: 39706483
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 88, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3m1', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[-1, 2], [-2, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [2, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]]]}
id: 39706484
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 89, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3m2', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [-2, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-2, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]]]}
id: 39706486
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id: 39706487
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 91, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3m4', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [2, 4]], [[-1, 2], [-2, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-2, 1], [-1, 4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [-2, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-2, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]]]}
id: 39706488
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 92, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3m5', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [2, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-2, 1], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[2, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]]]}
id: 39706489
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 93, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3m6', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [-2, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[2, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[2, 2], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[-2, 1], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [2, 4]], [[1, 0], [1, 4], [1, -4]]]}
id: 39706490
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id: 39706491
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id: 39706492
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 96, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3n3', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[-2, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[2, 2], [1, -4]], [[2, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [2, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [-2, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[2, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]]]}
id: 39706493
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id: 39706494
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 98, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3n5', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [-1, 4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-2, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [2, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[2, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]]]}
id: 39706495
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 99, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3n6', 'nt': [27, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 3]], [[3, -3]], [[3, -3]], [[3, 3]], [[3, 0]], [[3, 3]], [[3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [-1, 4]], [[2, 2], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[2, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 1], [2, 4]], [[1, 1], [2, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[2, 2], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[-1, 2], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-2, 1], [-1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-2, 1], [-1, 4]], [[-1, 2], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [2, 4]], [[1, 3], [1, -2], [1, -1]]]}
id: 39706393
{'center': '81.a1', 'center_index': 81, 'center_order': 9, 'counter': 100, 'cyclotomic_n': 9, 'dim': 3, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '729.395', 'group_counter': 395, 'group_order': 729, 'image': None, 'image_isoclass': '243.26', 'image_order': 243, 'indicator': 0, 'kernel': '243.a1', 'kernel_order': 3, 'label': '729.395.3o1', 'nt': [27, 104], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -3]], [[3, 3]], [[3, 3]], [[3, -3]], [[3, 0]], [[3, -3]], [[3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 4], [1, -4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[-2, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 1], [-1, 4]], [[1, 3], [1, -2], [1, -1]], [[1, 3], [1, -2], [1, -1]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [2, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 2], [1, -4]], [[-1, 2], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-2, 1], [-1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 2], [1, 3], [1, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 1], [-1, 4]], [[-1, 2], [-2, -4]], [[1, 1], [2, 4]], [[2, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 0], [1, 1], [1, 2], [-1, 3]], [[1, 3], [1, -2], [1, -1]], [[1, 2], [1, 3], [1, 4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [-1, -4]], [[1, 0], [1, 4], [1, -4]], [[-1, 2], [-2, -4]], [[1, 1], [-1, 4]], [[1, 1], [1, 3], [1, -4]], [[1, 0], [1, 4], [1, -4]], [[2, 2], [1, -4]], [[1, 1], [2, 4]], [[1, 1], [1, 3], [1, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, -4]], [[1, 2], [1, 3], [1, 4]], [[-1, 2], [1, -4]], [[1, 3], [1, -2], [1, -1]]]}

Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
ambient	text
ambient_counter	integer
ambient_order	numeric
ambient_tex	text
central	boolean
central_factor	boolean
centralizer_order	numeric
characteristic	boolean
core_order	numeric
counter	integer
cyclic	boolean
direct	boolean
hall	numeric
label	text
maximal	boolean
maximal_normal	boolean
metabelian	boolean
metacyclic	boolean
minimal	boolean
minimal_normal	boolean
nilpotent	boolean
normal	boolean
old_label	text
outer_equivalence	boolean
perfect	boolean
proper	boolean
quotient	text
quotient_Agroup	boolean
quotient_abelian	boolean
quotient_cyclic	boolean
quotient_hash	bigint
quotient_metabelian	boolean
quotient_nilpotent	boolean
quotient_order	numeric
quotient_simple	boolean
quotient_solvable	boolean
quotient_supersolvable	boolean
quotient_tex	text
simple	boolean
solvable	boolean
special_labels	text[]
split	boolean
standard_generators	boolean
stem	boolean
subgroup	text
subgroup_hash	bigint
subgroup_order	numeric
subgroup_tex	text
supersolvable	boolean
sylow	smallint

gps_subgroup_search • Show schema

id: 273112564
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 729, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 3, 'label': '729.395.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '729.395', 'subgroup_hash': 395, 'subgroup_order': 729, 'subgroup_tex': 'C_9^2:C_3^2', 'supersolvable': True, 'sylow': 3}
id: 273112575
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.53', 'subgroup_hash': 53, 'subgroup_order': 243, 'subgroup_tex': '\\He_3:C_3^2', 'supersolvable': True, 'sylow': 0}
id: 273112586
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 243, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.3.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.31', 'subgroup_hash': 31, 'subgroup_order': 243, 'subgroup_tex': 'C_3\\times C_9^2', 'supersolvable': True, 'sylow': 0}
id: 273112594
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': True, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '729.395.3.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.26', 'subgroup_hash': 26, 'subgroup_order': 243, 'subgroup_tex': 'C_9^2:C_3', 'supersolvable': True, 'sylow': 0}
id: 273112595
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 81, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 273112596
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.9', 'subgroup_hash': 9, 'subgroup_order': 81, 'subgroup_tex': '\\He_3:C_3', 'supersolvable': True, 'sylow': 0}
id: 273112597
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 81, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.9.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.2', 'subgroup_hash': 2, 'subgroup_order': 81, 'subgroup_tex': 'C_9^2', 'supersolvable': True, 'sylow': 0}
id: 273112598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.9.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 273112599
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.9.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 273112565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.9.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.9', 'subgroup_hash': 9, 'subgroup_order': 81, 'subgroup_tex': '\\He_3:C_3', 'supersolvable': True, 'sylow': 0}
id: 273112566
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.9.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.2', 'subgroup_hash': 2, 'subgroup_order': 81, 'subgroup_tex': 'C_9^2', 'supersolvable': True, 'sylow': 0}
id: 273112567
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 27, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3', 'simple': False, 'solvable': True, 'special_labels': ['U2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 273112568
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 27, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 273112569
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 273112570
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.27.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 273112571
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.27.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 273112572
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.27.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 273112573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.27.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 273112574
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.27.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 273112576
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.27.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 273112577
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.27.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 273112578
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 729, 'characteristic': True, 'core_order': 9, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '81.9', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 81, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3:C_3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 273112579
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '81.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '81.9', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 81, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3:C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 273112580
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 9, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '729.395.81.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '81.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '81.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 81, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 273112581
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.81.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 273112582
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.81.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 273112583
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '729.395.81.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 273112584
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '729.395.81.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 273112585
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '729.395.81.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 273112587
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '729.395.81.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 273112588
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 3, 'counter': 31, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '729.395.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '243.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '243.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 243, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9^2:C_3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 273112589
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 729, 'characteristic': True, 'core_order': 3, 'counter': 32, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '729.395.243.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '243.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '243.53', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 53, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 243, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3:C_3^2', 'simple': True, 'solvable': True, 'special_labels': ['L3', 'C5'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 273112590
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '729.395.243.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 273112591
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '729.395.243.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 273112592
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '729.395.243.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 273112593
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.395', 'ambient_counter': 395, 'ambient_order': 729, 'ambient_tex': 'C_9^2:C_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 729, 'characteristic': True, 'core_order': 1, 'counter': 36, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '729.395.729.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '729.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '729.395', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 395, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 729, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9^2:C_3^2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U4', 'L4', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

Column	Type
ambient	text
aut_centralizer_order	numeric
aut_label	text
aut_quo_index	numeric
aut_stab_index	numeric
aut_weyl_group	text
aut_weyl_index	numeric
centralizer	text
complements	text[]
conjugacy_class_count	numeric
contained_in	text[]
contains	text[]
core	text
coset_action_label	text
count	numeric
diagramx	smallint[]
generators	numeric[]
label	text
mobius_quo	bigint
mobius_sub	bigint
normal_closure	text
normal_contained_in	text[]
normal_contains	text[]
normalizer	text
old_label	text
projective_image	text
quotient_action_image	text
quotient_action_kernel	text
quotient_action_kernel_order	numeric
quotient_fusion	jsonb
short_label	text
subgroup_fusion	integer[]
weyl_group	text

gps_subgroup_data • Show schema

id: 273112564
{'ambient': '729.395', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1', 'complements': ['729.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['3.a1', '3.b1', '3.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4731, 4320, 4846, 4265], 'generators': [29229310, 2502841, 24446350], 'label': '729.395.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['3.a1', '3.b1', '3.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '81.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '81.9'}
id: 273112565
{'ambient': '729.395', 'aut_centralizer_order': 27, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '972.447', 'aut_weyl_index': 486, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['3.a1'], 'contains': ['27.c1', '27.i1'], 'core': '27.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [6866, -1, 7035, -1], 'generators': [15062599, 11888725], 'label': '729.395.9.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '9.f1', 'projective_image': '243.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
id: 273112566
{'ambient': '729.395', 'aut_centralizer_order': 243, 'aut_label': '9.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '324.138', 'aut_weyl_index': 1458, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.b1'], 'contains': ['27.c1', '27.j1'], 'core': '27.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [3777, -1, 3870, -1], 'generators': [15062599, 24446350], 'label': '729.395.9.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '9.g1', 'projective_image': '243.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112567
{'ambient': '729.395', 'aut_centralizer_order': 6561, 'aut_label': '27.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 6561, 'centralizer': '3.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.d1', '9.e1'], 'contains': ['81.a1', '81.b1', '81.c1', '81.d1'], 'core': '27.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2683, 7941, 2749, 8421], 'generators': [29229310, 29229283, 533629], 'label': '729.395.27.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '27.a1', 'normal_contained_in': ['9.a1'], 'normal_contains': ['81.a1', '81.b1', '81.c1'], 'normalizer': '1.a1', 'old_label': '27.a1', 'projective_image': '81.9', 'quotient_action_image': '3.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112568
{'ambient': '729.395', 'aut_centralizer_order': 13122, 'aut_label': '27.b1', 'aut_quo_index': 52, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 13122, 'centralizer': '3.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1', '9.c1'], 'contains': ['81.c1', '81.g1'], 'core': '27.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3645, 3437, 3734, 3975], 'generators': [29411533, 29229283], 'label': '729.395.27.b1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '27.b1', 'normal_contained_in': ['9.a1', '9.b1', '9.c1'], 'normal_contains': ['81.c1'], 'normalizer': '1.a1', 'old_label': '27.b1', 'projective_image': '243.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112569
{'ambient': '729.395', 'aut_centralizer_order': 6561, 'aut_label': '27.c1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 13122, 'centralizer': '3.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['9.a1', '9.f1', '9.g1'], 'contains': ['81.c1', '81.h1'], 'core': '27.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [4845, 5937, 4964, 6443], 'generators': [15062599, 29229283], 'label': '729.395.27.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '27.c1', 'normal_contained_in': ['9.a1'], 'normal_contains': ['81.c1'], 'normalizer': '1.a1', 'old_label': '27.c1', 'projective_image': '243.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '27.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112570
{'ambient': '729.395', 'aut_centralizer_order': 486, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '36.12', 'aut_weyl_index': 13122, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['9.e1'], 'contains': ['81.d1', '81.i1'], 'core': '243.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [520, -1, 533, -1], 'generators': [29229310, 24446350], 'label': '729.395.27.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '27.d1', 'projective_image': '243.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112571
{'ambient': '729.395', 'aut_centralizer_order': 81, 'aut_label': '27.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '216.102', 'aut_weyl_index': 2187, 'centralizer': '27.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.d1'], 'contains': ['81.a1', '81.e1', '81.f1'], 'core': '81.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9480, -1, 9711, -1], 'generators': [29229310, 11888725, 533629], 'label': '729.395.27.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '27.e1', 'projective_image': '81.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112572
{'ambient': '729.395', 'aut_centralizer_order': 4374, 'aut_label': '27.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 13122, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1'], 'contains': ['81.a1', '81.g1', '81.h1'], 'core': '81.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7246, -1, 7423, -1], 'generators': [29229310, 15062653], 'label': '729.395.27.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '27.f1', 'projective_image': '81.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112573
{'ambient': '729.395', 'aut_centralizer_order': 81, 'aut_label': '27.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '108.17', 'aut_weyl_index': 4374, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['9.d1'], 'contains': ['81.b1', '81.f1'], 'core': '81.b1', 'coset_action_label': None, 'count': 54, 'diagramx': [8799, -1, 9014, -1], 'generators': [14880349, 11717410], 'label': '729.395.27.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '27.g1', 'projective_image': '243.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.g1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 273112574
{'ambient': '729.395', 'aut_centralizer_order': 2187, 'aut_label': '27.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.12', 'aut_weyl_index': 13122, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.a1'], 'contains': ['81.b1', '81.g1', '81.h1'], 'core': '81.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6046, -1, 6194, -1], 'generators': [531469, 15062653], 'label': '729.395.27.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '27.h1', 'projective_image': '243.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112575
{'ambient': '729.395', 'aut_centralizer_order': 9, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 27, 'centralizer': '81.a1', 'complements': ['243.e1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['9.a1', '9.b1', '9.d1', '9.f1'], 'core': '3.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6302, 4320, 6456, 4265], 'generators': [29229310, 11888725, 29411533], 'label': '729.395.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.a1', '9.b1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '81.9', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '81.9'}
id: 273112576
{'ambient': '729.395', 'aut_centralizer_order': 162, 'aut_label': '27.i1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '108.17', 'aut_weyl_index': 4374, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['9.b1', '9.d1', '9.f1'], 'contains': ['81.c1', '81.f1'], 'core': '81.c1', 'coset_action_label': None, 'count': 27, 'diagramx': [8164, -1, 8363, -1], 'generators': [11888725, 29229283], 'label': '729.395.27.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.i1', 'projective_image': '243.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.i1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
id: 273112577
{'ambient': '729.395', 'aut_centralizer_order': 1458, 'aut_label': '27.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '36.12', 'aut_weyl_index': 13122, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.c1', '9.e1', '9.g1'], 'contains': ['81.c1', '81.i1'], 'core': '81.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [1721, -1, 1763, -1], 'generators': [24446350, 533629], 'label': '729.395.27.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '27.j1', 'projective_image': '243.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112578
{'ambient': '729.395', 'aut_centralizer_order': 39366, 'aut_label': '81.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 39366, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.e1', '27.f1'], 'contains': ['243.a1', '243.b1'], 'core': '81.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7246, 8952, 7423, 9419], 'generators': [29229310, 533629], 'label': '729.395.81.a1', 'mobius_quo': 3, 'mobius_sub': 0, 'normal_closure': '81.a1', 'normal_contained_in': ['27.a1'], 'normal_contains': ['243.a1', '243.b1'], 'normalizer': '1.a1', 'old_label': '81.a1', 'projective_image': '81.9', 'quotient_action_image': '1.1', 'quotient_action_kernel': '81.9', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112579
{'ambient': '729.395', 'aut_centralizer_order': 19683, 'aut_label': '81.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 39366, 'centralizer': '3.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['27.a1', '27.g1', '27.h1'], 'contains': ['243.b1', '243.c1'], 'core': '81.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5251, 7445, 5380, 7931], 'generators': [14880349, 533629], 'label': '729.395.81.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '81.b1', 'normal_contained_in': ['27.a1'], 'normal_contains': ['243.b1'], 'normalizer': '1.a1', 'old_label': '81.b1', 'projective_image': '243.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '27.2', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112580
{'ambient': '729.395', 'aut_centralizer_order': 39366, 'aut_label': '81.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 39366, 'centralizer': '3.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.b1', '27.c1', '27.i1', '27.j1'], 'contains': ['243.b1', '243.d1'], 'core': '81.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4087, 5937, 4186, 6443], 'generators': [29229283, 533629], 'label': '729.395.81.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '81.c1', 'normal_contained_in': ['27.a1', '27.b1', '27.c1'], 'normal_contains': ['243.b1'], 'normalizer': '1.a1', 'old_label': '81.c1', 'projective_image': '243.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '81.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112581
{'ambient': '729.395', 'aut_centralizer_order': 13122, 'aut_label': '81.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 118098, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['27.a1', '27.d1'], 'contains': ['243.a1', '243.c1', '243.d1'], 'core': '243.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3363, -1, 3445, -1], 'generators': [29229310, 29229283], 'label': '729.395.81.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '81.d1', 'projective_image': '243.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112582
{'ambient': '729.395', 'aut_centralizer_order': 162, 'aut_label': '81.e1', 'aut_quo_index': None, 'aut_stab_index': 243, 'aut_weyl_group': '12.4', 'aut_weyl_index': 39366, 'centralizer': '27.e1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['27.e1'], 'contains': ['243.a1', '243.e1'], 'core': '243.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [8888, -1, 9105, -1], 'generators': [29229310, 11888725], 'label': '729.395.81.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '81.e1', 'projective_image': '243.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112583
{'ambient': '729.395', 'aut_centralizer_order': 486, 'aut_label': '81.f1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '12.4', 'aut_weyl_index': 39366, 'centralizer': '27.e1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['27.e1', '27.g1', '27.i1'], 'contains': ['243.b1', '243.e1'], 'core': '243.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [8164, -1, 8363, -1], 'generators': [11888725, 533629], 'label': '729.395.81.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '81.f1', 'projective_image': '243.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.f1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112584
{'ambient': '729.395', 'aut_centralizer_order': 26244, 'aut_label': '81.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 78732, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.b1', '27.f1', '27.h1'], 'contains': ['243.b1'], 'core': '243.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5931, -1, 6076, -1], 'generators': [15062653], 'label': '729.395.81.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '81.g1', 'projective_image': '243.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112585
{'ambient': '729.395', 'aut_centralizer_order': 13122, 'aut_label': '81.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 78732, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.c1', '27.f1', '27.h1'], 'contains': ['243.b1'], 'core': '243.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6567, -1, 6727, -1], 'generators': [15062599], 'label': '729.395.81.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '81.h1', 'projective_image': '243.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112586
{'ambient': '729.395', 'aut_centralizer_order': 243, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1944.3709', 'aut_weyl_index': 243, 'centralizer': '3.b1', 'complements': ['243.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['9.a1', '9.c1', '9.e1', '9.g1'], 'core': '3.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3451, 7832, 3535, 7731], 'generators': [29229310, 24446350, 29411533], 'label': '729.395.3.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.a1', '9.c1'], 'normalizer': '1.a1', 'old_label': '3.b1', 'projective_image': '81.9', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112587
{'ambient': '729.395', 'aut_centralizer_order': 2916, 'aut_label': '81.i1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '6.2', 'aut_weyl_index': 78732, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['27.d1', '27.j1'], 'contains': ['243.d1'], 'core': '729.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1721, -1, 1763, -1], 'generators': [24446350], 'label': '729.395.81.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '81.i1', 'projective_image': '729.395', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112588
{'ambient': '729.395', 'aut_centralizer_order': 78732, 'aut_label': '243.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 236196, 'centralizer': '1.a1', 'complements': ['3.c1'], 'conjugacy_class_count': 3, 'contained_in': ['81.a1', '81.d1', '81.e1'], 'contains': ['729.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6911, 8861, 7080, 9365], 'generators': [29229310], 'label': '729.395.243.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '243.a1', 'normal_contained_in': ['81.a1'], 'normal_contains': ['729.a1'], 'normalizer': '1.a1', 'old_label': '243.a1', 'projective_image': '243.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '243.26', 'quotient_action_kernel_order': 243, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112589
{'ambient': '729.395', 'aut_centralizer_order': 236196, 'aut_label': '243.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 236196, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1', '81.c1', '81.f1', '81.g1', '81.h1'], 'contains': ['729.a1'], 'core': '243.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6098, 7500, 6248, 8022], 'generators': [533629], 'label': '729.395.243.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '243.b1', 'normal_contained_in': ['81.a1', '81.b1', '81.c1'], 'normal_contains': ['729.a1'], 'normalizer': '1.a1', 'old_label': '243.b1', 'projective_image': '243.53', 'quotient_action_image': '1.1', 'quotient_action_kernel': '243.53', 'quotient_action_kernel_order': 243, 'quotient_fusion': None, 'short_label': '243.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112590
{'ambient': '729.395', 'aut_centralizer_order': 39366, 'aut_label': '243.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 236196, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['81.b1', '81.d1'], 'contains': ['729.a1'], 'core': '729.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5251, -1, 5380, -1], 'generators': [14880349], 'label': '729.395.243.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '81.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '243.c1', 'projective_image': '729.395', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112591
{'ambient': '729.395', 'aut_centralizer_order': 78732, 'aut_label': '243.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 236196, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.c1', '81.d1', '81.i1'], 'contains': ['729.a1'], 'core': '729.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3724, -1, 3816, -1], 'generators': [29229283], 'label': '729.395.243.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '81.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '243.d1', 'projective_image': '729.395', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112592
{'ambient': '729.395', 'aut_centralizer_order': 972, 'aut_label': '243.e1', 'aut_quo_index': None, 'aut_stab_index': 243, 'aut_weyl_group': '2.1', 'aut_weyl_index': 236196, 'centralizer': '27.e1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['81.e1', '81.f1'], 'contains': ['729.a1'], 'core': '729.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [8164, -1, 8363, -1], 'generators': [11888725], 'label': '729.395.243.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '243.e1', 'projective_image': '729.395', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112593
{'ambient': '729.395', 'aut_centralizer_order': None, 'aut_label': '729.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['243.a1', '243.b1', '243.c1', '243.d1', '243.e1'], 'contains': [], 'core': '729.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6098, 8180, 6248, 8675], 'generators': [], 'label': '729.395.729.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '729.a1', 'normal_contained_in': ['243.a1', '243.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '729.a1', 'projective_image': '729.395', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 273112594
{'ambient': '729.395', 'aut_centralizer_order': 6, 'aut_label': '3.c1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '8748.ny', 'aut_weyl_index': 54, 'centralizer': '81.a1', 'complements': ['243.e1', '243.a1', '243.c1'], 'conjugacy_class_count': 9, 'contained_in': ['1.a1'], 'contains': ['9.b1', '9.c1'], 'core': '3.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [4731, 1048, 4846, 1034], 'generators': [31202896, 24446350], 'label': '729.395.3.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.b1', '9.c1'], 'normalizer': '1.a1', 'old_label': '3.c1', 'projective_image': '243.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.c1', 'subgroup_fusion': None, 'weyl_group': '81.9'}
id: 273112595
{'ambient': '729.395', 'aut_centralizer_order': 2187, 'aut_label': '9.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '216.170', 'aut_weyl_index': 2187, 'centralizer': '3.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.b1'], 'contains': ['27.a1', '27.b1', '27.c1', '27.f1', '27.h1'], 'core': '9.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4837, 5937, 4955, 6443], 'generators': [29229310, 29411533, 29229283], 'label': '729.395.9.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.a1', 'normal_contained_in': ['3.a1', '3.b1'], 'normal_contains': ['27.a1', '27.b1', '27.c1'], 'normalizer': '1.a1', 'old_label': '9.a1', 'projective_image': '81.9', 'quotient_action_image': '3.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112596
{'ambient': '729.395', 'aut_centralizer_order': 54, 'aut_label': '9.b1', 'aut_quo_index': 4, 'aut_stab_index': 9, 'aut_weyl_group': '972.447', 'aut_weyl_index': 486, 'centralizer': '81.a1', 'complements': ['81.e1'], 'conjugacy_class_count': 9, 'contained_in': ['3.a1', '3.c1'], 'contains': ['27.b1', '27.i1'], 'core': '9.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5975, 1893, 6121, 2450], 'generators': [11888725, 29411533], 'label': '729.395.9.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.b1', 'normal_contained_in': ['3.a1', '3.c1'], 'normal_contains': ['27.b1'], 'normalizer': '1.a1', 'old_label': '9.b1', 'projective_image': '243.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '81.9'}
id: 273112597
{'ambient': '729.395', 'aut_centralizer_order': 1458, 'aut_label': '9.c1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '108.43', 'aut_weyl_index': 4374, 'centralizer': '3.b1', 'complements': ['81.e1'], 'conjugacy_class_count': 3, 'contained_in': ['3.b1', '3.c1'], 'contains': ['27.b1', '27.j1'], 'core': '9.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [3053, 3584, 3128, 4120], 'generators': [24446350, 29411533], 'label': '729.395.9.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.c1', 'normal_contained_in': ['3.b1', '3.c1'], 'normal_contains': ['27.b1'], 'normalizer': '1.a1', 'old_label': '9.c1', 'projective_image': '243.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '9.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 273112598
{'ambient': '729.395', 'aut_centralizer_order': 27, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1944.3579', 'aut_weyl_index': 243, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.a1'], 'contains': ['27.a1', '27.e1', '27.g1', '27.i1'], 'core': '27.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8164, -1, 8363, -1], 'generators': [29229310, 11888725, 29229283], 'label': '729.395.9.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '9.d1', 'projective_image': '81.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
id: 273112599
{'ambient': '729.395', 'aut_centralizer_order': 243, 'aut_label': '9.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '648.603', 'aut_weyl_index': 729, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['27.a1', '27.d1', '27.j1'], 'core': '27.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1862, -1, 1908, -1], 'generators': [29229310, 24446350, 533629], 'label': '729.395.9.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '9.e1', 'projective_image': '81.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.