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lfunc_lfunctions • Show schema
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{'Lhash': '3048257756578692945661780480445', 'a10': [0.9880498549494023, 2.1635273953454495], 'a2': [2.2821199613227985, -0.6700908807078544], 'a3': [-0.6548607339452851, -0.7557495743542583], 'a4': [3.0765426637977806, -1.977173914616342], 'a5': [0.14231483827328514, 0.9898214418809327], 'a6': [-2.0008916506966643, -1.2858949834446733], 'a7': [0.8582178694208097, -1.879235002531335], 'a8': [2.581027218572416, -2.9786641964027667], 'a9': [-0.14231483827328514, 0.9898214418809327], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.754838869734175, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.6548607339452851, 0.7557495743542583]]], [5, [[1.0, 0], [-0.14231483827328514, -0.9898214418809327]]], [23, [[1.0, 0], [4.789143086800036, 0.25319655241615574]]]], 'bad_primes': [3, 5, 23], 'central_character': '345.331', 'coefficient_field': 'CDF', 'conductor': 345, 'conductor_radical': 345, 'conjugate': 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0.3423384973487299, 'root_number': '0.47530285132395 + 0.8798222545056036*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.171169248674', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.40465137320163837097363031890', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.96637240660417343601287399703', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.71828463047835028521500228366', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.754838869734175, 'bad_primes': [3, 5, 23], 'central_character': '23.9', 'conductor': 345, 'conductor_radical': 345, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/345/2/m/c/331/5'], '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': '2-345-23.9-c1-0-12', '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': '2-345-23.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6597707280628173, 'root_angle': 0.17116924867436495, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.40465137320163837097363031890', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3048257756578692945661780480445', 'Lhash_array': ['3048257756578692945661780480445'], 'label': '2-345-23.9-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/345/2/m/c/331/5'}