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lfunc_lfunctions • Show schema
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{'Lhash': '591201628558575534724652166521,1666292976640104276040644618947', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -3304, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3441.2912350111283, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '144.1', 'coefficient_field': '1.1.1.1', 'conductor': 20736, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 50800, 0, 152587890625], [1, 3304, 14258706, 19046902504, 33232930569601], [1, 0, -239294114, 0, 45949729863572161], [1, -92608, 3775521858, -75543190610368, 665416609183179841], [1, 0, -1793808704, 0, 48661191875666868481], [1, -487328, 93339270978, -8276565809644448, 288441413567621167681], [1, 0, -136092106850, 0, 6132610415680998648961], [1, 0, -907364767184, 0, 250246473680347348787521], [1, 768328, 1853364053778, 655300065014968648, 727423121747185263828481], 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{'algebraic': True, 'analytic_conductor': 3441.2912350111283, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 20736, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -3304, 0, 0, 0, 0, 0, 92608, 0, 0, 0, 0, 0, 487328, 0, 0, 0, 0, 0, -50800, 0, 0, 0, 0, 0, -768328, 0, 0, 0, 0, 0, 993964, 0, 0, 0, 0, 0, -10668880, 0, 0, 0, 0, 0, -3342290, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4670740, 0, 0, 0, 0, 0, -61348912, 0, 0, 0, 0, 0, -23039456, 0, 0, 0, 0, 0, 5316488, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -305976832, 0, 0, 0, 0, 0, -103190336, 0, 0, 0], 'euler11': [1, 0, -239294114, 0, 45949729863572161], 'euler13': [1, -92608, 3775521858, -75543190610368, 665416609183179841], 'euler17': [1, 0, -1793808704, 0, 48661191875666868481], 'euler19': [1, -487328, 93339270978, -8276565809644448, 288441413567621167681], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -136092106850, 0, 6132610415680998648961], 'euler29': [1, 0, -907364767184, 0, 250246473680347348787521], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 768328, 1853364053778, 655300065014968648, 727423121747185263828481], 'euler37': [1, -993964, 7271950016166, -3491278127937132844, 12337511914217166362274241], 'euler41': [1, 0, -14953776865664, 0, 63759030914653054346432641], 'euler43': [1, 10668880, 51832650668802, 124700006177691756880, 136614025729312093462315201], 'euler47': [1, 0, -5979540196322, 0, 566977372488557307219621121], 'euler5': [1, 0, 50800, 0, 152587890625], 'euler53': [1, 0, -117184708681040, 0, 3876269050118516845397872321], 'euler59': [1, 0, -138802557649730, 0, 21559177407076402401757871041], 'euler61': [1, -4670740, 388868579031462, -895415015108920257940, 36751693856637464631913392961], 'euler67': [1, 61348912, 1753057606009218, 24911810216466743724592, 164890958756244164895763202881], 'euler7': [1, 3304, 14258706, 19046902504, 33232930569601], 'euler71': [1, 0, -1143138284216930, 0, 416997623116370028124580469121], 'euler73': [1, 23039456, 1745624316982146, 18580401802949635859936, 650377879817809571042122834561], 'euler79': [1, -5316488, 3041283880976658, -8065690782562512677768, 2301619141096101839813550846721], 'euler83': [1, 0, -1816636310871074, 0, 5072820298953863752478356399681], 'euler89': [1, 0, -6378488973234560, 0, 15496731425178936435099327730561], 'euler97': [1, 103190336, 18336928549702146, 808747405981446316248896, 61425365346268570446197767595521], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 50800, 0, 152587890625], [1, 3304, 14258706, 19046902504, 33232930569601], [1, 0, -239294114, 0, 45949729863572161], [1, -92608, 3775521858, -75543190610368, 665416609183179841], [1, 0, -1793808704, 0, 48661191875666868481], [1, -487328, 93339270978, -8276565809644448, 288441413567621167681], [1, 0, -136092106850, 0, 6132610415680998648961], [1, 0, -907364767184, 0, 250246473680347348787521], [1, 768328, 1853364053778, 655300065014968648, 727423121747185263828481], [1, -993964, 7271950016166, -3491278127937132844, 12337511914217166362274241], [1, 0, -14953776865664, 0, 63759030914653054346432641], [1, 10668880, 51832650668802, 124700006177691756880, 136614025729312093462315201], [1, 0, -5979540196322, 0, 566977372488557307219621121], [1, 0, -117184708681040, 0, 3876269050118516845397872321], [1, 0, -138802557649730, 0, 21559177407076402401757871041], [1, -4670740, 388868579031462, -895415015108920257940, 36751693856637464631913392961], [1, 61348912, 1753057606009218, 24911810216466743724592, 164890958756244164895763202881], [1, 0, -1143138284216930, 0, 416997623116370028124580469121], [1, 23039456, 1745624316982146, 18580401802949635859936, 650377879817809571042122834561], [1, -5316488, 3041283880976658, -8065690782562512677768, 2301619141096101839813550846721], [1, 0, -1816636310871074, 0, 5072820298953863752478356399681], [1, 0, -6378488973234560, 0, 15496731425178936435099327730561], [1, 103190336, 18336928549702146, 808747405981446316248896, 61425365346268570446197767595521]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/144/9/e/b'], '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': '4-12e4-1.1-c8e2-0-6', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8, 8], 'order_of_vanishing': 0, 'prelabel': '4-12e4-1.1-c8e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.659146156641897, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c8e2-0', 'trace_hash': 1024879283095870326, 'z1': {'__RealLiteral__': 0, 'data': '0.46637585187285428112383295937', 'prec': 103}}
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{'Lhash': '591201628558575534724652166521,1666292976640104276040644618947', 'Lhash_array': ['591201628558575534724652166521', '1666292976640104276040644618947'], 'label': '4-12e4-1.1-c8e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/9/e/b'}