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{'Lhash': '747785981784059072879052817160,1491596443472465696590343686520,1924172272356268193796418904795,2013838074390974997245107317890,2433762874733618331885476056190,2810428428872206232860466156795,2864766295330761856307361996175,3019014819572880636944314831367,3136868028537753867872155307930,3290771947592003422095388850006', 'a10': 2, 'a2': -1, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.133799618206371e-08, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [89, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]], 'bad_primes': [2, 89], 'central_character': '356.1', 'coefficient_field': '1.1.1.1', 'conductor': 32696403157284220935602176, 'conductor_radical': 178, 'degree': 20, 'euler_factors': [[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], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 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'4.08951648027672363878557883061942', '4.12335814320254981136251413190285', '4.15136602897562091070779068693602', '4.25991714969369028345834757556517', '4.38629205516701804345563259197778', '4.47620867066593470015551072356435', '4.65902134290054762771054436555842', '4.70175834239538010451246861185146', '4.80256208970916065230455346038172', '4.94631698824415290759204860728439', '5.11861387101762678074135104534430', '5.23206406991899159833365310388913', '5.56972037490303040671959306364802', '5.61218577940975537705610903335393', '5.63695755926495030112047760693296', '5.64352350680799868596487939073993', '5.87632025525649559764098516766011', '5.93836739661991469740235716032503', '5.97216586259966517236947472575186', '5.97902097655187216165312634383455', '6.22362708773974093616529818072392', '6.40892424217859492136101671065992', '6.55221012970794193184197599773304', '6.64024356687401227999250305232844', '6.70460674422371654432434362854054', '6.98232302334960250281638281431392', '6.98602494061274444245408121921892', '7.00450323094848025843671418676882', '7.17738256660931123276803522498559', '7.28158006261966543826658860554703', '7.30327197122052875339081334337585', '7.31235184711894344765658258135039', '7.54134266018686160075915740395441', '7.68160458501905864163238195626415', '7.83824979641894509574092540404358', '7.85428528497170121043863387300304', '7.989199462992737651918684824165856', '8.019837377950061014002411897287570', '8.022913225831844171369269027384888', '8.073970434924753196930968871625532', '8.091869483319166135375866055568320', '8.361650293444840651816053092629270', '8.377689887753100524794826457856151', '8.777070412904505203136103249668595', '8.795078869248390990412117825177572', '8.910963019603515876907368781009038', '8.975641567851466309181354253149858', '9.048891956619564607631577559562077', '9.050505528827343914731871793282785', '9.055127950344283519409204048860349', '9.065625179417362439455250948704044', 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'11.45807563459095772761348561209649', '11.46784004115177743290110010522879', '11.71296446253980798931417776968442', '11.81368519061432727101835923543001', '12.00744411096826915239346197039732', '12.25744073981515099696611101802762'], 'prelabel': '20-356e10-1.1-c0e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4215058060066891, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e10-0', 'trace_hash': 153007530598173865, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58989912650175588470050742623', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17666212062213105491127690987', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.51790428057213699761760552862', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.133799618206371e-08, 'bad_primes': [2, 89], 'central_character': '1.1', 'conductor': 32696403157284220935602176, 'conductor_radical': 178, 'degree': 20, 'dirichlet_coefficients': [1, -1, 0, 0, -2, 0, 0, 0, -1, 2, 0, 0, -2, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 9, 0, 0, 0, 2, 0, 0, 0, -1, -1, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 4, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0], 'euler11': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler13': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler17': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler19': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler2': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler29': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler3': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler31': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler37': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler41': [1, -9, 36, -84, 126, -126, 84, -36, 9, -1, 0, -1, 9, -36, 84, -126, 126, -84, 36, -9, 1], 'euler43': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler47': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler5': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler53': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler59': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler61': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler67': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler7': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler71': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler73': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler79': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler83': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler89': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler97': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler_factors': [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, -9, 36, -84, 126, -126, 84, -36, 9, -1, 0, -1, 9, -36, 84, -126, 126, -84, 36, -9, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/356/1/l/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': '20-356e10-1.1-c0e10-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '20-356e10-1.1-c0e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4215058060066891, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e10-0', 'trace_hash': 153007530598173865, 'z1': {'__RealLiteral__': 0, 'data': '0.58989912650175588470050742623', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '747785981784059072879052817160,1491596443472465696590343686520,1924172272356268193796418904795,2013838074390974997245107317890,2433762874733618331885476056190,2810428428872206232860466156795,2864766295330761856307361996175,3019014819572880636944314831367,3136868028537753867872155307930,3290771947592003422095388850006', 'Lhash_array': ['747785981784059072879052817160', '1491596443472465696590343686520', '1924172272356268193796418904795', '2013838074390974997245107317890', '2433762874733618331885476056190', '2810428428872206232860466156795', '2864766295330761856307361996175', '3019014819572880636944314831367', '3136868028537753867872155307930', '3290771947592003422095388850006'], 'label': '20-356e10-1.1-c0e10-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/356/1/l/a'}