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lfunc_lfunctions • Show schema
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{'Lhash': '73853857491082856996541778832', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.8989794855663562, 0], 'a6': [0, 0], 'a7': [0, 2.8284271247461903], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.77945290861241, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2304.1279', 'coefficient_field': 'CDF', 'conductor': 2304, 'conductor_radical': 6, 'conjugate': '1905058133146953727297337685028', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8989794855663562, 0], [25.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-49.0, 0]], [[1.0, 0], [0, -4.3855052687092515], [-121.0, 0]], [[1.0, 0], [-13.797958971132712, 0], [169.0, 0]], [[1.0, 0], [17.595917942265423, 0], [289.0, 0]], [[1.0, 0], [0, 4.3855052687092515], [-361.0, 0]], [[1.0, 0], [0, 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'2.40876382209212303335308704176736', '3.76822802458099101720611924561201', '4.08994213159793036001484222641401', '5.54434820360929871715459929417880', '5.92198900208118891268538536385722', '6.94541825447570038487187501165002', '7.66363993555265576021055112741115', '8.459254019482072786334807517818276'], 'prelabel': '2-48e2-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.923348591890452, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.05826042087447922638100226593', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.39920039701782216762236992909', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.40876382209212303335308704177', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.77945290861241, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/3/g/o/1279/4'], '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': '2-48e2-4.3-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-48e2-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.923348591890452, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.05826042087447922638100226593', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '73853857491082856996541778832', 'Lhash_array': ['73853857491082856996541778832'], 'label': '2-48e2-4.3-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/3/g/o/1279/4'}