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lfunc_lfunctions • Show schema
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{'Lhash': '3870062882498359078686717160325', 'a10': [-1.1697196057541233, -3.213778203902817], 'a2': [1.4228814386774968, -1.1939392904032853], 'a3': [-1.6207312029787864, -0.610925828305643], 'a4': [0.25180420403038245, -1.4280526044208164], 'a5': [0.6297483259238466, -1.7302193054151183], 'a6': [-3.0355166957402444, 1.0657796409141802], 'a7': [-1.6664857823707364, -2.8864380451572864], 'a8': [0.5107192168202437, 0.8845916319344476], 'a9': [2.2535392646181283, 1.9802931052812325], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6207312029787864, 0.610925828305643]]], [19, [[1.0, 0], [-4.3349778052903885, 0.45603445882929095]]]], 'bad_primes': [3, 19], 'central_character': '171.110', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '1669936072121352758969861850016', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.05294130874989378854565059826', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.76004211868876362348252760684', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.50617659430040670672422322660', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.110', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/x/a/110/16'], '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': '2-171-171.110-c1-0-15', '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': '2-171-171.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.3116688284736193, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.05294130874989378854565059826', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3870062882498359078686717160325', 'Lhash_array': ['3870062882498359078686717160325'], 'label': '2-171-171.110-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/x/a/110/16'}