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lfunc_lfunctions • Show schema
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{'Lhash': '5757145841174539727200711068535', 'a10': [1.480726356971331, 2.6126186704099164], 'a2': [0.34759555517436724, -1.2972442723958495], 'a3': [-1.1895312574115031, -1.2589739423995274], 'a4': [0.17003077528201682, 0.09816731387959318], 'a5': [-1.593705101994479, 1.5684718830367241], 'a6': [-2.0466725136906234, 1.1054988640544798], 'a7': [1.9786949004557217, 0.5301897006446914], 'a8': [2.0857463618406333, -2.0857463618406333], 'a9': [-0.17003077528201682, 2.995177713501654], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3593268090957619, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.1895312574115031, 1.2589739423995274]]], [5, [[1.0, 0], [1.593705101994479, -1.5684718830367241]]]], 'bad_primes': [3, 5], 'central_character': '45.23', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '3088311671288941777566547627491', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'7.17681889691893007898273825841932', '8.437537083594077048053543962983843', '10.26066924461989647425472729829749', '11.39971997199377264959645947220339', '12.47597809362197005981148012919530', '14.34886667966410842395486522923957', '15.20691192613173736245995783313500', '16.02469853190150777759259864620238'], 'prelabel': '2-45-45.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5994387450738915, 'root_angle': 0.3912430968748001, 'root_number': '0.33506092103540447 + 0.9421964652846594*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.195621548437', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.54158727975833086853461579263', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.42372865323891128466115882957', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.17681889691893007898273825842', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3593268090957619, 'bad_primes': [3, 5], 'central_character': '45.23', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/2/l/a/23/4'], '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': '2-45-45.23-c1-0-3', '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': '2-45-45.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5994387450738915, 'root_angle': 0.19562154843740004, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.54158727975833086853461579263', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5757145841174539727200711068535', 'Lhash_array': ['5757145841174539727200711068535'], 'label': '2-45-45.23-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/2/l/a/23/4'}