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lfunc_lfunctions • Show schema
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{'Lhash': '2420027138899593292647817071627', 'a10': [-6.399054806439756, 0.0], 'a2': [-2.4728339089952556, 0.0], 'a3': [0.0, 0.0], 'a4': [4.1149075414767555, 0.0], 'a5': [2.5877414504720115, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [-5.229815082953512, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.533632860074733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '693.1', 'coefficient_field': 'CDF', 'conductor': 693, 'conductor_radical': 231, 'conjugate': '2420027138899593292647817071627', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.4728339089952556, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.5877414504720115, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [5.871888715435012, 0], [13.0, 0]], [[1.0, 0], [7.513962347916512, 0], [17.0, 0]], 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'6.67504972162371151591638790189894', '7.52134834263108139901158957655210', '8.610533503782056568724918333153322', '9.250753148388984556092838574681973', '9.960107807087348120975795329476759'], 'prelabel': '2-693-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.352367501066688, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90906479945174843608366595062', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52690372605223738358154073362', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55212610203629738141904396619', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.533632860074733, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 693, 'conductor_radical': 231, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/693/2/a/l/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': '2-693-1.1-c1-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-693-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.352367501066688, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90906479945174843608366595062', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2420027138899593292647817071627', 'Lhash_array': ['2420027138899593292647817071627'], 'label': '2-693-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/693/2/a/l/1/1'}