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lfunc_lfunctions • Show schema
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{'Lhash': '1684964907050904089878739943931', 'a10': [0.1078291146752006, 1.5076480221109079], 'a2': [-0.5406408174555976, 0.8412535328311812], 'a3': [0.0, 0.0], 'a4': [-0.41541501300188644, -0.9096319953545183], 'a5': [1.2100174041632301, -0.9058076827719271], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.9898214418809327, 0.14231483827328514], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5406408174555976, -0.8412535328311812]]], [3, [[1.0, 0], [0, 0]]], [89, [[1.0, 0], [-0.599277666511347, 0.8005412409243604]]]], 'bad_primes': [2, 3, 89], 'central_character': '3204.1259', 'coefficient_field': 'CDF', 'conductor': 3204, 'conductor_radical': 534, 'conjugate': '1523679911010762115676978714080', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5406408174555976, -0.8412535328311812]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'positive_zeros': ['1.32920294184181421757266985594695', '2.09735066693577889324310119945369', '3.21903473534475989799460423526439', '3.62800786538496993402275152681103', '4.96432584139771839398799298461523', '5.95415210220568173441165951055265', '6.48545907010600294446342421776740', '7.47004876101171996798102162479978', '8.229098141982529418391870053594529', '8.994311493206904932373030811725637'], 'prelabel': '2-3204-1068.191-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': -0.08800056386471615, 'root_number': '0.96202718806844228335309894781165 - 0.27295363968470173379431883282273*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.044000281932358075', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32920294184181421757266985595', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09735066693577889324310119945', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21903473534475989799460423526', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'bad_primes': [2, 3, 89], 'central_character': '1068.191', 'conductor': 3204, 'conductor_radical': 534, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3204/1/cd/b/1259/1'], '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': '2-3204-1068.191-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3204-1068.191-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': -0.044000281932358075, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32920294184181421757266985595', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1684964907050904089878739943931', 'Lhash_array': ['1684964907050904089878739943931'], 'label': '2-3204-1068.191-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3204/1/cd/b/1259/1'}