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lfunc_lfunctions • Show schema
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{'Lhash': '990481844549959436644495204820', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-10.583005244258363, 0.0], 'a6': [0.0, 0.0], 'a7': [22.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.45157553074648, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-13.0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '1872.1', 'coefficient_field': 'CDF', 'conductor': 1872, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [10.583005244258363, 0], [125.0, 0]], [[1.0, 0], [-22.0, 0], [343.0, 0]], [[1.0, 0], [-5.291502622129181, 0], [1331.0, 0]], [[1.0, 0], [-13.0, 0]], [[1.0, 0], [-116.41305768684198, 0], [4913.0, 0]], [[1.0, 0], [-126.0, 0], [6859.0, 0]], [[1.0, 0], [31.74901573277509, 0], [12167.0, 0]], [[1.0, 0], 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'7.59398403599394666927823793812689', '7.998373767938106964748992131891262', '8.587312073348037404643404087013919'], 'prelabel': '2-1872-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78135240449665849959619226711', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.65302357910904430810153014684', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14702860015315655433302913679', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 110.45157553074648, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1872, 'conductor_radical': 78, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1872/4/a/ba/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': '2-1872-1.1-c3-0-29', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1872-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78135240449665849959619226711', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '990481844549959436644495204820', 'Lhash_array': ['990481844549959436644495204820'], 'label': '2-1872-1.1-c3-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1872/4/a/ba/1/1'}