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lfunc_lfunctions • Show schema
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{'Lhash': '760929615607052747163280098663', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-4.0195188608758325, -1.6649392263892238], 'a6': [0, 0], 'a7': [-2.722802631031678, 2.722802631031678], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.719', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '880218316858255477407955491100', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.0195188608758325, 1.6649392263892238], [3.5355339059327378, 3.5355339059327378]], [[1.0, 0], [2.722802631031678, -2.722802631031678], [0, -7.0]], [[1.0, 0], [2.4813856422350296, 1.0278235864916219], [7.7781745930520225, 7.7781745930520225]], [[1.0, 0], [0.14612441607106091, 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'7.76032107416215767335596364012856', '8.926445064205405320483900309166538', '10.04055005323878527070980067468387'], 'prelabel': '2-1152-96.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.03515284274041792, 'root_number': '0.99390814978835495456889533583244196355879274094300893547 - 0.1102115682870404084760165878625598691092176277356726295*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.01757642137020896', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60026762537725618264652867870', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87099440081096698504159961778', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59966900092014532122763960294', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '96.11', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/w/a/719/1'], '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': '2-1152-96.11-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1152-96.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.01757642137020896, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60026762537725618264652867870', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '760929615607052747163280098663', 'Lhash_array': ['760929615607052747163280098663'], 'label': '2-1152-96.11-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/w/a/719/1'}