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lfunc_lfunctions • Show schema
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{'Lhash': '999106061894541310773006953620', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.4142135623730951, 0.0], 'a4': [0.0, 0.0], 'a5': [1.5857864376269049, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.62621853429843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 13], 'central_character': '1456.1', 'coefficient_field': 'CDF', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, 0], [3.0, 0]], [[1.0, 0], [-1.5857864376269049, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.242640687119285, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [17.0, 0]], [[1.0, 0], [-7.242640687119285, 0], [19.0, 0]], [[1.0, 0], [-5.82842712474619, 0], [23.0, 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[[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-1456-1.1-c1-0-6', 'leading_term': '1.1513401207995613680015812946795', '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/1456/2/a/q/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.1513401207995613, 1.145887815144503, 1.1294282731560878, 1.1016623037886617, 1.0621195434245525, 1.0101986873638031, 0.9452197583397169, 0.8664850649262764, 0.7733453450623393, 0.6652677464739302, 0.541902650010574, 0.4031467749461778, 0.2492004246485063, 0.08061708296440603, -0.10165616046850502, -0.29624868334172, -0.5013480825430954, -0.7146946542704166, -0.9335895080981801, -1.1549170406251485, -1.3751822620836596, -1.5905631765007062, -1.7969780611225876, -1.9901670782101766, -2.1657871913029756, -2.319518862064122, 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'7.09127593849852051239291244859935', '7.73852980149127913833300826970621', '8.856272373091107965308915723805874', '9.703752402674943283876362732251473'], 'prelabel': '2-1456-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78815571239792810751339531517', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43422019764243956188977211336', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28047597967206939768183991727', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.62621853429843, 'bad_primes': [2, 7, 13], 'central_character': '1.1', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1456/2/a/q/1/1'], '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': '2-1456-1.1-c1-0-6', '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': '2-1456-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78815571239792810751339531517', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '999106061894541310773006953620', 'Lhash_array': ['999106061894541310773006953620'], 'factors': ['2-1456-1.1-c1-0-6'], 'label': '2-1456-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1456/2/a/q/1/1'}