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  • lfunc_lfunctions • Show schema
    {'Lhash': '540648865324016660785020352076', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.6180339887498949, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.8541019662496847, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.618033988749895, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.05058653787412, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 29], 'central_character': '4640.1', 'coefficient_field': 'CDF', 'conductor': 4640, 'conductor_radical': 290, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.8541019662496847, 0], [7.0, 0]], [[1.0, 0], [3.23606797749979, 0], [11.0, 0]], [[1.0, 0], [5.0901699437494745, 0], [13.0, 0]], [[1.0, 0], [3.618033988749895, 0], [17.0, 0]], [[1.0, 0], [-2.76393202250021, 0], [19.0, 0]], 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'6.23394395621112211322025120020413', '6.94537000473268447033706961347939', '7.61899310432646710402783165389968', '8.257909003371320681937299431989125'], 'prelabel': '2-4640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.086919297795406, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42649675330621668308101257907', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.27875871819941325928168641245', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.92237715625787114604272229517', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 37.05058653787412, 'bad_primes': [2, 5, 29], 'central_character': '1.1', 'conductor': 4640, 'conductor_radical': 290, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4640/2/a/g/1/2'], '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': '2-4640-1.1-c1-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.086919297795406, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.42649675330621668308101257907', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '540648865324016660785020352076', 'Lhash_array': ['540648865324016660785020352076'], 'factors': ['2-4640-1.1-c1-0-9'], 'label': '2-4640-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4640/2/a/g/1/2'}