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lfunc_lfunctions • Show schema
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{'Lhash': '148358301475268128887365624492', 'a10': [-40.727338221436085, -1.2446030555722283e-60], 'a2': [-2.0, 2.0], 'a3': [0.0, 5.344465785358332], 'a4': [0.0, -8.0], 'a5': [10.181834555359021, 10.181834555359021], 'a6': [-10.688931570716663, -10.688931570716663], 'a7': [-94.0963560287377, 0.0], 'a8': [16.0, 16.0], 'a9': [52.43668546913415, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.649377268204482, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, -2.0]]], [37, [[1.0, 0], [913.6535162121158, -1019.5088289530586]]]], 'bad_primes': [2, 37], 'central_character': '74.43', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3581642099516009161161288236973', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, -2.0]], [[1.0, 0], [0, -5.344465785358332], [-81.0, 0]], [[1.0, 0], [-10.181834555359021, -10.181834555359021], [0, 625.0]], [[1.0, 0], [94.0963560287377, 0], [2401.0, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.379435867561', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11703406399883178732861041224', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06099650173271153187448753641', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84942072193650612333145556537', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.649377268204482, 'bad_primes': [2, 37], 'central_character': '37.6', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/5/d/a/43/5'], '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': '2-74-37.6-c4-0-1', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-74-37.6-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7657507603188836, 'root_angle': 0.3794358675609454, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.11703406399883178732861041224', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '148358301475268128887365624492', 'Lhash_array': ['148358301475268128887365624492'], 'label': '2-74-37.6-c4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/5/d/a/43/5'}