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lfunc_lfunctions • Show schema
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{'Lhash': '217434061980141058719221115417', 'a10': [348.90075343818745, 201.43794391800077], 'a2': [-7.797669705101607, -13.505960109876607], 'a3': [13.5, 7.794228634059948], 'a4': [-89.60730565971878, 155.20440613198713], 'a5': [-22.372116711350312, 12.916547605639828], 'a6': [0, -243.10728197777894], 'a7': [0, 0], 'a8': [1796.8109685412696, 0], 'a9': [121.5, 210.4441731196186], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.8179502921181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-13.5, -7.794228634059948]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.31', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'conjugate': '1631945782135006360051200971728', 'degree': 2, 'euler_factors': [[[1.0, 0], [7.797669705101607, 13.505960109876607], [-32.0, 55.42562584220407]], [[1.0, 0], [-13.5, -7.794228634059948]], [[1.0, 0], [22.372116711350312, 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['0.17152523095953566220513957392780', '1.67303280729078557028447042567013', '4.21656101287895391564004674142498', '5.62632220432911732903051011526063', '6.70047255968686075179198247010313', '7.57266026609390598637610843794004', '8.481394259109586747305552602145717', '9.267880734974254689295351583442227', '10.18162279373501749431710497119866', '11.63314655736396598827520185649194'], 'prelabel': '2-147-7.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.815320308643205, 'root_angle': -0.31316038027938725, 'root_number': '0.5538440336596778361168746798041453088456432212030186487 - 0.8326204335587601011836124599555761934816510565058770236*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15658019013969363', 'prec': 67}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17152523095953566220513957393', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.67303280729078557028447042567', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21656101287895391564004674142', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.8179502921181, 'bad_primes': [3, 7], 'central_character': '7.3', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/7/f/d/31/1'], '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': '2-147-7.3-c6-0-4', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-147-7.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.815320308643205, 'root_angle': -0.15658019013969363, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17152523095953566220513957393', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '217434061980141058719221115417', 'Lhash_array': ['217434061980141058719221115417'], 'label': '2-147-7.3-c6-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/7/f/d/31/1'}