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  • lfunc_lfunctions • Show schema
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  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 11027219.456951272, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 31640625, 'conductor_radical': 15, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8388608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1185907772, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -51909171652, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31381059609, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -1141246682444, 0, 488416496321038566679926, 0, -92900617679551232564007071185236524, 0, 6626407607736641103900260617069258125403649041], 'euler13': [1, 0, 0, 0, -4257044986106304824031937, 0, 0, 0, 10315908977942302627204470186314316211062255002161], 'euler17': [1, 0, 0, 0, 2349125753042296917948125378, 0, 0, 0, 1379597950901634641862681879083307429684165246101910721], 'euler19': [1, 0, 381268261954726, 0, 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1002018774744129923516369294161573737191759373151725198030728940263761], 'euler41': [1, 0, -2201316126864993764, 0, 1817172258898461494967559027409582886, 0, -666695099800812159587186372705774459149435651038520484, 0, 91725417180837143663326189086434787308803478524071148179882832902891361], 'euler43': [1, 0, 0, 0, -118073810193052561248643117267853977, 0, 0, 0, 745782254782301503355862595418917382807246689177519953982343989556806801], 'euler47': [1, 0, 0, 0, 12223142369449599606153404714110727618, 0, 0, 0, 37351302345958493037830232088788907611014369661290907772288660777346988481], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, 0, 0, 171830054119985215222536607621754820818, 0, 0, 0, 7381391874719262009044156620311078835772712945516819387010106565605821547281], 'euler59': [1, 0, 120623553778951370636, 0, 5456265647348840057787606461888641141686, 0, 109692358790871287125927865572860747352344874145641595988716, 0, 826967633734418240453603147406490983820063629653592282316619531810805486858961], 'euler61': [1, 51909171652, 1184516458544543508058, 15518344671801662344850490483904, 127660953462461287798059671741604692088595, 675263971514641864769359834003491935651041961412544, 2242835748785057533793107443282693559839918098674399238697418, 4276895647416356914222047213558359790711747448063965057018075230156212, 3585194656582687097035763534929220777070593006222509027099005738447779809872241], 'euler67': [1, 0, 0, 0, 13783606772788843052789633800351442677703, 0, 0, 0, 222480175701699090139272510552932572965903322627160280533457310251712459718974321], 'euler7': [1, 0, 0, 0, -3991163896037207977, 0, 0, 0, 15286700631942576193765185769276826401], 'euler71': [1, 0, -924489168486806261084, 0, 320505083493534920553921079520468839820646, 0, -49383913022455418905957262884130563272114461553723995401590044, 0, 2853430792922160849851180026124447862582908874197451107394128078286590649262440481], 'euler73': [1, 0, 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[[1, 0, 0, 0, 8388608, 0, 0, 0, 17592186044416], [1, 0, 0, 0, 31381059609, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -3991163896037207977, 0, 0, 0, 15286700631942576193765185769276826401], [1, 0, -1141246682444, 0, 488416496321038566679926, 0, -92900617679551232564007071185236524, 0, 6626407607736641103900260617069258125403649041], [1, 0, 0, 0, -4257044986106304824031937, 0, 0, 0, 10315908977942302627204470186314316211062255002161], [1, 0, 0, 0, 2349125753042296917948125378, 0, 0, 0, 1379597950901634641862681879083307429684165246101910721], [1, 0, 381268261954726, 0, 63481332729842573169221177691, 0, 5173802848796901560395017537026202467837686, 0, 184144368549628275143663229532787625188711914273876985521], [1, 0, 0, 0, 1815692869551992350813481122658, 0, 0, 0, 824185149135487077883465900577270766354751717380230010246241], [1, 0, 48802039062823316, 0, 893114631258499814636031387463446, 0, 7264302520376058289856097686172671267821417751156, 0, 22157048460222391505313258277903605213230926984354560377055172081], [1, 1185907772, 629025373969370818, 194635937156881389032274824, 38400131934182827226439164967278395, 4945402712460723361714100113529791153274744, 406092930363343936381044360757143955874996709912898, 19453010078979434353638288846365979752678412894284340720452, 416787349596085853594397793593920583748646209303727133530079150721], [1, 0, 0, 0, 2805478993138795299667106559840338, 0, 0, 0, 1002018774744129923516369294161573737191759373151725198030728940263761], [1, 0, -2201316126864993764, 0, 1817172258898461494967559027409582886, 0, -666695099800812159587186372705774459149435651038520484, 0, 91725417180837143663326189086434787308803478524071148179882832902891361], [1, 0, 0, 0, -118073810193052561248643117267853977, 0, 0, 0, 745782254782301503355862595418917382807246689177519953982343989556806801], [1, 0, 0, 0, 12223142369449599606153404714110727618, 0, 0, 0, 37351302345958493037830232088788907611014369661290907772288660777346988481], [1, 0, 0, 0, 171830054119985215222536607621754820818, 0, 0, 0, 7381391874719262009044156620311078835772712945516819387010106565605821547281], [1, 0, 120623553778951370636, 0, 5456265647348840057787606461888641141686, 0, 109692358790871287125927865572860747352344874145641595988716, 0, 826967633734418240453603147406490983820063629653592282316619531810805486858961], [1, 51909171652, 1184516458544543508058, 15518344671801662344850490483904, 127660953462461287798059671741604692088595, 675263971514641864769359834003491935651041961412544, 2242835748785057533793107443282693559839918098674399238697418, 4276895647416356914222047213558359790711747448063965057018075230156212, 3585194656582687097035763534929220777070593006222509027099005738447779809872241], [1, 0, 0, 0, 13783606772788843052789633800351442677703, 0, 0, 0, 222480175701699090139272510552932572965903322627160280533457310251712459718974321], [1, 0, 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59314420590258030980772760544661405787251822601630132400001155963107100089893048692641], [1, 0, 0, 0, 29927037916022144631822302889711238362292943, 0, 0, 0, 2617919618631058636393965401227693956107300157969550698791944746999930276251112354814081]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/12/e/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '8-75e4-1.1-c11e4-0-0', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [11, 11, 11, 11], 'order_of_vanishing': 0, 'prelabel': '8-75e4-1.1-c11e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.591161870357474, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c11e4-0', 'trace_hash': 1801256770842614670, 'z1': {'__RealLiteral__': 0, 'data': '0.05279509049021667045244243105065', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '66925728149026848333587356919,253280053545011942847025652455,2246484998499643547431572870666,2447727903150570457233675493685', 'Lhash_array': ['66925728149026848333587356919', '253280053545011942847025652455', '2246484998499643547431572870666', '2447727903150570457233675493685'], 'factors': ['2-75-15.8-c11-0-1', '2-75-15.2-c11-0-7', '2-75-15.2-c11-0-58', '2-75-15.8-c11-0-58'], 'label': '8-75e4-1.1-c11e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/12/e/a'}