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lfunc_lfunctions • Show schema
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{'Lhash': '1674566789576462851342131462598', 'a10': [-4.583143386715411, 0.0], 'a2': [1.2998720915732085, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.31033254554909234, 0.0], 'a5': [-3.5258418243048264, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-3.0031367982125534, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.6926245622462, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '3969.1', 'coefficient_field': 'CDF', 'conductor': 3969, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2998720915732085, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.5258418243048264, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.1785346460077322, 0], [11.0, 0]], [[1.0, 0], [-3.2206050463529783, 0], [13.0, 0]], [[1.0, 0], [-4.903173480548535, 0], [17.0, 0]], [[1.0, 0], [-6.866368709789547, 0], [19.0, 0]], [[1.0, 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'6.58571544792468965189863105901724', '7.33133659017985148021995277846494', '8.168398249533081053234038607868097'], 'prelabel': '2-63e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.629620285796032, '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': '1.32100027347833208105545051225', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16092783012639919718146419418', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52453102780798530416122355370', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.6926245622462, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 3969, 'conductor_radical': 21, 'degree': 2, 'index': 101, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3969/2/a/bh/1/9'], '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': '2-63e2-1.1-c1-0-101', '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': '2-63e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.629620285796032, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32100027347833208105545051225', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1674566789576462851342131462598', 'Lhash_array': ['1674566789576462851342131462598'], 'label': '2-63e2-1.1-c1-0-101', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3969/2/a/bh/1/9'}