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lfunc_lfunctions • Show schema
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{'Lhash': '1319608980458832602291689308725', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [3.8897125515334254, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.46474497557813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': 'CDF', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.8897125515334254, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.2105622593925003, 0], [11.0, 0]], [[1.0, 0], [-5.397937169636999, 0], [13.0, 0]], [[1.0, 0], [-4.411076856060598, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.3979371696369993, 0], [23.0, 0]], [[1.0, 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'group': 'GL2', 'index': 76, 'label': '2-9576-1.1-c1-0-76', 'leading_term': '3.78907763559488137681005066239', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9576/2/a/co/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [3.7890776355948814, 3.7794904824843716, 3.750701984354416, 3.7026387495657413, 3.635203656814381, 3.5483117766177448, 3.44193709231874, 3.3161668456307516, 3.171259915842586, 3.007705488459166, 2.826278351234963, 2.6280874275895334, 2.4146145666507577, 2.1877411058642138, 1.9497602655838686, 1.7033739963332877, 1.451673460653321, 1.1981028834977707, 0.9464070443758079, 0.7005632096371125, 0.46469881310808736, 0.24299668455589823, 0.039590092303693016, -0.14154970008261025, -0.2967302742692197, -0.4226558754779906, -0.5165425318569924, 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'6.26239086546832364142451933834137', '6.81317202076819011414484188183949', '7.79999568231853951501627597291196'], 'prelabel': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04098793486253116509606413594', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.59944121109028231427853471114', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64806692057089703019525312092', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 76.46474497557813, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'index': 76, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/co/1/5'], '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': '2-9576-1.1-c1-0-76', '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': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04098793486253116509606413594', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1319608980458832602291689308725', 'Lhash_array': ['1319608980458832602291689308725'], 'label': '2-9576-1.1-c1-0-76', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/co/1/5'}