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lfunc_lfunctions • Show schema
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{'Lhash': '3055158849120908425558050095373', 'a10': [31.249392567138155, -4.845148520416136], 'a2': [1.8368642399519266, -2.15079747163368], 'a3': [2.1213203435596424, 2.1213203435596424], 'a4': [-1.2518595279716613, -7.9014459260458505], 'a5': [8.477728114274537, 7.288904308635083], 'a6': [8.459107912020412, -0.6659529508859258], 'a7': [13.765192613014538, -13.765192613014538], 'a8': [-19.2939059203639, -11.821387157865479], 'a9': [0.0, 9.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5401146003444386, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.8368642399519266, 2.15079747163368]]], [3, [[1.0, 0], [-2.1213203435596424, -2.1213203435596424]]], [5, [[1.0, 0], [-8.477728114274537, -7.288904308635083]]]], 'bad_primes': [2, 3, 5], 'central_character': '60.7', 'coefficient_field': 'CDF', 'conductor': 60, 'conductor_radical': 30, 'conjugate': '2577175961233012441017912364394', 'degree': 2, 'euler_factors': 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'root_analytic_conductor': 1.8815192266741358, 'root_angle': 0.24982071371045972, 'root_number': '0.7075049430010967 + 0.7067083950463691*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.124910356855', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.41009537531150444807167933230', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.78090296596426730339108929374', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.83683364696114725788055734520', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5401146003444386, 'bad_primes': [2, 3, 5], 'central_character': '20.7', 'conductor': 60, 'conductor_radical': 30, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/60/4/j/b/7/11'], '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': '2-60-20.7-c3-0-13', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-60-20.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8815192266741358, 'root_angle': 0.12491035685522986, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.41009537531150444807167933230', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3055158849120908425558050095373', 'Lhash_array': ['3055158849120908425558050095373'], 'label': '2-60-20.7-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/60/4/j/b/7/11'}