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  • lfunc_lfunctions • Show schema
    {'Lhash': '309329382166766629269408741837,962593899823278450398825306740', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 180, 'a6': 0, 'a7': -700, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18211.591839476627, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '432.1', 'coefficient_field': '1.1.1.1', 'conductor': 186624, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, -180, 163765, -14062500, 6103515625], [1, 700, 584961, 576480100, 678223072849], [1, 10890, 68388367, 212215292190, 379749833583241], [1, 5480, 57188634, 343861873160, 3937376385699289], [1, -16416, 79007650, -6736119655968, 168377826559400929], [1, 16024, 1645526562, 14323400745736, 799006685782884121], [1, 24372, 2905606450, 82982405794284, 11592836324538749809], [1, 143280, 39622155718, 2471562277553520, 297558232675799463481], [1, -38708, 26496803553, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7e2-0', 'trace_hash': 25062474409149022, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24401785642753182930883691537', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.75935269517481539412687429908', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '1.84601531777269668974526213361', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 18211.591839476627, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 186624, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 180, 0, -700, 0, 0, 0, -10890, 0, -5480, 0, 0, 0, 16416, 0, -16024, 0, 0, 0, -24372, 0, -131365, 0, 0, 0, -143280, 0, 38708, 0, 0, 0, -126000, 0, 455620, 0, 0, 0, 731880, 0, 1088840, 0, 0, 0, -1561500, 0, -94961, 0, 0, 0, 2610468, 0, -1960200, 0, 0, 0, -1731960, 0, -620192, 0, 0, 0, -986400, 0, -346600, 0, 0, 0, 4242240, 0, -3145190, 0, 0, 0, 7623000, 0, -10110616, 0, 0, 0, -644202, 0, 2954880, 0, 0, 0, 6021000, 0, 3836000, 0, 0, 0, -2884320, 0, 4098670, 0, 0, 0], 'euler11': [1, 10890, 68388367, 212215292190, 379749833583241], 'euler13': [1, 5480, 57188634, 343861873160, 3937376385699289], 'euler17': [1, -16416, 79007650, -6736119655968, 168377826559400929], 'euler19': [1, 16024, 1645526562, 14323400745736, 799006685782884121], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 24372, 2905606450, 82982405794284, 11592836324538749809], 'euler29': [1, 143280, 39622155718, 2471562277553520, 297558232675799463481], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -38708, 26496803553, -1064958267008588, 756943935220796320321], 'euler37': [1, -455620, 173526750366, -43252861859337460, 9012061295995008299689], 'euler41': [1, -731880, 472932732862, -142536757968026280, 37929227194915558802161], 'euler43': [1, -1088840, 751093452114, -295966976517745880, 73885357344138503765449], 'euler47': [1, 1561500, 1424242194466, 791092002602974500, 256666986187667409334369], 'euler5': [1, -180, 163765, -14062500, 6103515625], 'euler53': [1, -2610468, 3933113324245, -3066545839788013716, 1379946262057143768386569], 'euler59': [1, 1731960, 4329510506038, 4310244825647115240, 6193386212891813387462761], 'euler61': [1, 620192, 6303036139818, 1949103964957536032, 9876832533361318095112441], 'euler67': [1, 346600, 12137122138146, 2100642642404951800, 36732225162896895721934329], 'euler7': [1, 700, 584961, 576480100, 678223072849], 'euler71': [1, -4242240, 14648438075182, -38583682540732635840, 82721210695570328927708881], 'euler73': [1, 3145190, 18855097518219, 34746167348278693430, 122045014039746588673695409], 'euler79': [1, 10110616, 57627345888222, 194163349458002963944, 368790120348678391253573281], 'euler83': [1, 644202, 52577539308895, 17481098319619692654, 736365263311636486061599129], 'euler89': [1, -6021000, 94843763242558, -266316867405980109000, 1956410986640441413344189841], 'euler97': [1, -4098670, 5732921354451, -331165504641907409710, 6528362774606076144776040769], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -180, 163765, -14062500, 6103515625], [1, 700, 584961, 576480100, 678223072849], [1, 10890, 68388367, 212215292190, 379749833583241], [1, 5480, 57188634, 343861873160, 3937376385699289], [1, -16416, 79007650, -6736119655968, 168377826559400929], [1, 16024, 1645526562, 14323400745736, 799006685782884121], [1, 24372, 2905606450, 82982405794284, 11592836324538749809], [1, 143280, 39622155718, 2471562277553520, 297558232675799463481], [1, -38708, 26496803553, -1064958267008588, 756943935220796320321], [1, -455620, 173526750366, -43252861859337460, 9012061295995008299689], [1, -731880, 472932732862, -142536757968026280, 37929227194915558802161], [1, -1088840, 751093452114, -295966976517745880, 73885357344138503765449], [1, 1561500, 1424242194466, 791092002602974500, 256666986187667409334369], [1, -2610468, 3933113324245, -3066545839788013716, 1379946262057143768386569], [1, 1731960, 4329510506038, 4310244825647115240, 6193386212891813387462761], [1, 620192, 6303036139818, 1949103964957536032, 9876832533361318095112441], [1, 346600, 12137122138146, 2100642642404951800, 36732225162896895721934329], [1, -4242240, 14648438075182, -38583682540732635840, 82721210695570328927708881], [1, 3145190, 18855097518219, 34746167348278693430, 122045014039746588673695409], [1, 10110616, 57627345888222, 194163349458002963944, 368790120348678391253573281], [1, 644202, 52577539308895, 17481098319619692654, 736365263311636486061599129], [1, -6021000, 94843763242558, -266316867405980109000, 1956410986640441413344189841], [1, -4098670, 5732921354451, -331165504641907409710, 6528362774606076144776040769]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/8/a/q'], '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': '4-432e2-1.1-c7e2-0-2', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [7, 7], 'order_of_vanishing': 0, 'prelabel': '4-432e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.616812428938527, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 25062474409149022, 'z1': {'__RealLiteral__': 0, 'data': '0.24401785642753182930883691537', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '309329382166766629269408741837,962593899823278450398825306740', 'Lhash_array': ['309329382166766629269408741837', '962593899823278450398825306740'], 'factors': ['2-432-1.1-c7-0-2', '2-432-1.1-c7-0-17'], 'label': '4-432e2-1.1-c7e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/8/a/q'}