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lfunc_lfunctions • Show schema
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{'Lhash': '313984656192427497179634866681', 'a10': [-3.392369445744969, 0.0], 'a2': [-2.031800368864313, 0.0], 'a3': [-1.0, 0.0], 'a4': [2.1282127389171577, 0.0], 'a5': [1.6696371837166042, 0.0], 'a6': [2.031800368864313, 0.0], 'a7': [-1.5246318889495134, 0.0], 'a8': [-0.26050269022498496, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.17172697437388, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]], [79, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 17, 79], 'central_character': '4029.1', 'coefficient_field': 'CDF', 'conductor': 4029, 'conductor_radical': 4029, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.031800368864313, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.6696371837166042, 0], [5.0, 0]], [[1.0, 0], [1.5246318889495134, 0], [7.0, 0]], [[1.0, 0], [3.97637598392542, 0], [11.0, 0]], [[1.0, 0], [5.529964133517177, 0], [13.0, 0]], [[1.0, 0], 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'2.25599040864860696933186118265923', '3.79567620708206109592874083511553', '4.96692409906376985753697001213521', '5.54667401812346088167047852181249', '6.46344357534835942241938735901681', '7.12647964950674870442615207679029', '7.79472509156870428946878670958346', '8.433285614591560330833594328168621'], 'prelabel': '2-4029-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6720126035097875, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24769022010946652530868098900', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01591522951575852108814220595', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.25599040864860696933186118266', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.17172697437388, 'bad_primes': [3, 17, 79], 'central_character': '1.1', 'conductor': 4029, 'conductor_radical': 4029, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4029/2/a/l/1/7'], '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': '2-4029-1.1-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': '2-4029-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6720126035097875, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.24769022010946652530868098900', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '313984656192427497179634866681', 'Lhash_array': ['313984656192427497179634866681'], 'label': '2-4029-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4029/2/a/l/1/7'}