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  • lfunc_lfunctions • Show schema
    {'Lhash': '908788469117272681332763021019', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.5885917346584004, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.704349551916316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '3720.1', 'coefficient_field': 'CDF', 'conductor': 3720, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.5885917346584004, 0], [7.0, 0]], [[1.0, 0], [0.8613510434443109, 0], [11.0, 0]], [[1.0, 0], [-3.727240691214089, 0], [13.0, 0]], [[1.0, 0], [-5.016639594614275, 0], [17.0, 0]], [[1.0, 0], [2.3158324258724896, 0], [19.0, 0]], [[1.0, 0], 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'6.73451382336682115973757016280487', '7.87977747919328268660990348146834', '8.406924377448545225415057137830240'], 'prelabel': '2-3720-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.450169681020611, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71690769440226925882490940743', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.90471728286255752725907180518', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.10756776765516579937375718606', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 29.704349551916316, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 3720, 'conductor_radical': 930, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3720/2/a/t/1/2'], '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': '2-3720-1.1-c1-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3720-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.450169681020611, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71690769440226925882490940743', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '908788469117272681332763021019', 'Lhash_array': ['908788469117272681332763021019'], 'factors': ['2-3720-1.1-c1-0-9'], 'label': '2-3720-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3720/2/a/t/1/2'}